Handbook of Spallation Research: Theory, Experiments and Applications

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Detlef Filges and Frank Goldenbaum Handbook of Spallation Research

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Detlef Filges and Frank Goldenbaum

Handbook of Spallation Research Theory, Experiments and Applications

The Authors Prof. Dr. Detlef Filges Institut f¨ur Kernphysik Forschungszentrum J¨ulich 52425 J¨ulich PD Dr. Frank Goldenbaum Institut f¨ur Kernphysik Forschungszentrum J¨ulich 52425 J¨ulich

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliograﬁe; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microﬁlm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not speciﬁcally marked as such, are not to be considered unprotected by law. Cover Typesetting Laserwords Private Limited, Chennai, India Printing and Binding Strauss GmbH, M¨orlenbach Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-40714-9

‘‘For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled.’’ Richard P. Feynman (1921–1988)

VII

Contents

Preface

XVII

Part I

Principles 1

1 1.1 1.2 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.5.1 1.3.5.2 1.3.5.3 1.3.5.4 1.3.5.5

The Spallation Process 3 Historic Remarks and Deﬁnitions 3 Spallation by Cosmic Ray-Induced Reactions 5 Physics of the Spallation Process 12 Introduction 12 The Fission Process 15 Spallation and Fission 17 The Logical Scheme of Spallation Reactions 21 Particle Interaction Mechanisms 23 The Elementary Forces and Particles 23 Feynman Diagrams 26 Resonance Decay, Pion Absorption, and Pion Charge-Exchange 27 Kinetic Energy, Total Energy, and Momentum 30 Cross Sections, Absorption Length, Collision Length, and Mean Free Path 31 Electromagnetic and Atomic Interactions 33 Energy Loss of Heavy Particles by Ionization and Excitation – the Bethe or Bethe–Bloch Formula 33 Coulomb Scattering 37 Bremsstrahlung 39 Energy Loss by Direct Pair Production and by Photonuclear Interaction 40 Total Energy Loss 40 High-Energy Hadronic Cascades and Nuclear Interactions 41 Qualitative Features of Hadron–Nucleus Collisions 41 Characteristics of Hadron Cascades in Thick Targets 42 Spatial Propagation of Hadron Cascades and Particle Production 43 Total Cross Sections in Nucleon–Nucleus Collisions 44

1.3.6 1.3.6.1 1.3.6.2 1.3.6.3 1.3.6.4 1.3.6.5 1.3.7 1.3.7.1 1.3.7.2 1.3.7.3 1.3.7.4

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

VIII

Contents

1.3.7.5 1.3.7.6 1.3.8

Total Reaction Cross Sections in Nucleus–Nucleus Reactions 49 Differential Cross Sections 54 Hadronic–Electromagnetic Cascade Coupling 57

2 2.1 2.2 2.2.1 2.2.2 2.2.2.1 2.2.2.2 2.2.2.3 2.2.2.4 2.2.3 2.2.3.1 2.2.3.2 2.2.4 2.2.5

The Intranuclear Cascade Models 63 Introduction 63 The BERTINI Approach 64 Features of the BERTINI Nuclear Model 64 The Nuclear Model 65 Nucleon Density Distribution Inside the Nucleus 65 Momentum Distribution of Nucleons Inside the Nucleus 68 Potential Energy Distribution Inside the Nucleus 70 Application of the Pauli Exclusion Principle 73 The Cross-Section Data 74 Nucleon–Nucleon Cross-Section Data 76 Pion Production and Pion Nucleon Reactions 77 Method of Computation 85 Assumptions, Limits, and Constraints on the Energy and Application Regime 87 The Cugnon INCL Approach 88 Features of the Model 90 Participants and Spectators 90 Nuclear Surface 91 Meson–Nucleon Cross Sections 92 Elastic Nucleon–Nucleon Cross Sections 93 Angular Distributions 94 Dynamic Pauli Blocking 97 Cutoff Criteria – Stopping Time of the Cascade 98 Light Clusters as Incident Particles 103 Surface Percolation Procedure for Emission of Light Charged Clusters 103 Assumptions, Limits, and Constraints on the Energy and Application Regime 109 The ISABEL Model 110 Features of the Model 110 The Nuclear Model 111 The Time-Like Basis Cascading of Particle–Nucleus Interactions 112 Nucleus–Nucleus Collisions 113 Assumptions, Limits, and Constraints on the Energy and Application Regime 114 The CEM (Cascade-Exciton Model) Approach 114 Features of the CEM Model 115 Assumptions, Limits, and Constraints on the Energy and Application Regime 117

2.3 2.3.1 2.3.1.1 2.3.1.2 2.3.1.3 2.3.1.4 2.3.1.5 2.3.1.6 2.3.1.7 2.3.1.8 2.3.1.9 2.3.2 2.4 2.4.1 2.4.1.1 2.4.1.2 2.4.1.3 2.4.2 2.5 2.5.1 2.5.2

Contents

2.6 2.6.1 2.6.2 2.6.3 2.7 2.7.1 2.7.1.1 2.7.1.2 2.7.1.3

Other Intranuclear-Cascade Models 119 The Dubna Models 119 The H¨anssgen–Ranft Model 122 The MICRES Model 123 Alternative Models 127 The Quantum-Molecular-Dynamic (QMD) Model 127 The Equation of Motion and the Reaction Treatment 128 The Cutoff Criteria – the Stopping Time of the QMD Process Selected Examples of QMD Simulations 132

3 3.1 3.2 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6 3.5 3.5.1 3.5.2 3.5.3 3.6 3.7 3.7.1 3.7.2 3.7.3 3.7.3.1 3.8 3.9 3.10

Evaporation and High-Energy Fission 135 Introduction 135 The Statistical Model in its Standard Form 136 The Evaporation Model EVAP of Dostrovsky–Dresner 139 The Level Density Parameter in the EVAP Model 140 The Inverse Cross Sections 142 The Generalized Evaporation Model (GEM) 143 Evaporation Model in GEM 144 The Decay Width in the GEM Model 145 Parameter of the Inverse Cross Sections and the Coulomb Barrier 146 The Level Density Parameter GCCI in the GEM Model 147 The High-Energy Fission Process in the GEM Model 148 Method of Computation 151 The GSI ABLA Model 154 Time-Dependent Fission Width 157 The Simultaneous Breakup Stage 158 Conclusion of ABLA 159 The GEMINI Model 159 High-Energy Fission Models 165 The Dynamics of the Fission Process 166 Basic Features of Fission Models 170 The RAL Model of Atchison 171 Postﬁssion Parameters of the RAL Model 173 Fermi Breakup for Light Nuclei 176 Photon Evaporation and Gamma Ray Production 178 Vaporization and Multifragmentation 181

4 4.1 4.2 4.3 4.3.1 4.3.2 4.4

The Particle Transport in Matter 185 Introduction 185 Hadronic and Electromagnetic Showers 185 The General Transport Equation 191 The Angular Flux, Fluence, Current, and Energy Spectra 195 Monte Carlo Estimation of Particle Fluxes and Reaction Rates 197 Range Straggling 200

130

IX

X

Contents

4.5 4.6

The Elastic Scattering of Protons and Neutrons 201 The Treatment of Pion Transport in Matter 205

5 5.1 5.2 5.2.1 5.2.2

Particle Transport Simulation Code Systems 207 Introduction 207 Particle Transport Code Systems and Event Generators 208 Particle Transport Systems and Event Generators 209 The Three-Dimensional Geometry Systems of Particle Transport Code Systems 210

6

Materials Damage by High-Energy Neutrons and Charged Particles 215 Introduction 215 Displacement of Lattice Atoms 216 Damage Energy and Displacements 220 Hydrogen and Helium Production 224 Cross Section Examples 227 Radiation Damage Effects of High-Intensity Proton Beams in the GeV Range 231

6.1 6.2 6.2.1 6.3 6.4 6.5

7 7.1 7.2 7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.2 7.4

Shielding Issues 233 Introduction 233 The Attenuation Length and the Moyer Model 234 Accelerator Shielding and the Generalized Moyer Model 235 The Moyer Model Parameters 238 Attenuation Lengths 241 Advanced Shielding Methods for Spallation Sources 242 Monte Carlo Discrete Ordinates Coupling 246 Monte Carlo Techniques and Deep Penetration 249 Sky- and Groundshine Phenomena 254

8 8.1 8.2 8.2.1 8.2.2 8.2.3 8.2.4 8.2.4.1 8.2.5 8.2.6 8.3 8.3.1 8.3.2 8.3.3 8.3.4

The Basic Parameters of Spallation Neutron Sources 257 Introduction 257 Parameter Regime for Spallation Neutron Sources 257 The Particle Type 257 The Kinetic Energy 259 The Target Material 262 The Neutron Production 263 Spatial Leakage Distribution of Neutrons and Target Shape The Target Heating 266 The Induced Radioactivity 267 The Spallation Neutron Source Facility 269 Continuous Spallation Neutron Sources 272 Short-Pulse Spallation Neutron Sources 272 Long-Pulse Spallation Neutron Sources 272 Scattering of Neutrons by Matter 273

264

Contents

Part II

Experiments 277

9 9.1 9.2 9.3 9.4

Why Spallation Physics Experiments? 279 Introduction 279 Application-Driven Motivation 279 Space Science and Astrophysics-Driven Motivation Nuclear Physics Driven Motivation 281

10

Proton-Nucleus-Induced Secondary Particle Production – The ‘‘Thin’’ Target Experiments 287 Introduction 287 Neutron, Pion, and Proton Double Differential Measurements and Experiments 288 The Double-Differential Neutron-Production Measurements at the LAMPF-WNR Facility 289 The Time-of-Flight Experiment at the LAMPF-WNR Facility 290 The Experimental Results of Double-Differential Neutron-Production Cross-Section Measurements 299 The Double-Differential Neutron-Production Measurements at the SATURNE Facility 303 The Experimental Apparatus at the SATURNE Accelerator 305 The Experimental Results of Double-Differential Neutron-Production Cross Section Measurements 310 The Double-Differential Neutron-Production Measurements at the KEK Facility 312 The Time-of-Flight Method with a Short Flight Path 312 The Experimental Results of Double-Differential Neutron-Production Cross Section Measurements 316 The Double Differential Pion Production Measurements 318 The Double Differential Pion Production Measurements at the Berkley Cyclotron with Incident Protons of 730 MeV 319 The Double Differential Pion Production Measurements at the Cyclotron of the Paul Scherer Institut (PSI) 325 The ‘‘Thin’’ Target Particle Production Measurements at the 2.5 GeV Proton Cooler Synchrotron COSY at J¨ulich 327 The COoler SYnchrotron COSY 331 The NESSI Experiment 333 Experimental Setup of NESSI 335 Experimental Results of NESSI 341 The PISA Experiment 355 Experimental Setup of PISA 356 Experimental Results of PISA 361 Data Library of H and He in Proton-Induced Reactions 369 Production of Residual Nuclides at Various Proton Energies 369

10.1 10.2 10.2.1 10.2.1.1 10.2.1.2 10.2.2 10.2.2.1 10.2.2.2 10.2.3 10.2.3.1 10.2.3.2 10.2.4 10.2.4.1 10.2.4.2 10.3

10.3.1 10.3.2 10.3.2.1 10.3.2.2 10.3.3 10.3.3.1 10.3.3.2 10.3.3.3 10.4

280

XI

XII

Contents

10.4.1 10.4.2 10.4.2.1

Excitation Functions and Production Cross Sections 370 Isotopic and Mass Distributions of Residual Nuclides 373 Inverse Kinematics Measurements at GSI 373

11

Proton-Matter-Induced Secondary Particle Production–The ‘‘Thick’’ Target Experiments 379 Introduction 379 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV 381 Experiments to Measure the Neutron Yield of ‘‘Thick’’ Targets 381 The Brookhaven Cosmotron Experiments 381 The Fertile-to-Fissile Conversion Experiments 382 The PSI Thick Target Lead/Bismuth Experiments 388 Neutron Multiplicities Measured with a 4π Detector at the COSY Accelerator at J¨ulich 390 Thick Target Results of the NESSI Experiment at the COSY Accelerator 394 A Summary of Neutron Yield Experimental Data 402 Neutron Leakage Spectra Distributions of Thick Targets 407 The LANL-WNR Thick Target Experiments 407 The KEK Time-of-Flight Thick Pb Target Experiments 408 The LANL SUNNYSIDE Experiments 409 Energy Deposition Experiments with Thick Mercury Targets 413 The Energy Deposition Thick Mercury Target Experiment at COSY J¨ulich 414 The Thick Mercury Target Experiment ASTE at the AGS Accelerator at BNL 419

11.1 11.2 11.2.1 11.2.1.1 11.2.1.2 11.2.1.3 11.2.2 11.2.2.1 11.2.2.2 11.2.3 11.2.3.1 11.2.3.2 11.2.4 11.2.5 11.2.5.1 11.2.5.2

12

Neutron Production by Proton, Antiproton, Deuteron, Pion, and Kaon Projectiles 425

13

Experiments to Study the Performance of Spallation Neutron Sources 431 Introduction 431 The Target–Moderator–Reﬂector Issue 431 Target–Moderator–Reﬂector Experiments with Complex Geometries and Realistic Material Compositions 437 The Early Experiments 437 Neutron Performance Studies at Reﬂected Target–Moderator Systems 438 Neutron Studies of a Reﬂected ‘‘T’’-Shape Moderator at LANL-WNR 438 The SNQ Target–Moderator–Reﬂector Experiments at the PSI Accelerator 439

13.1 13.2 13.3 13.3.1 13.3.2 13.3.2.1 13.3.2.2

Contents

13.3.3 13.3.3.1 13.3.3.2 13.3.3.3

14 14.1 14.1.1 14.1.2 14.1.2.1 14.1.2.2

15 15.1 15.2 15.3

Experiments of Short-Pulsed Target–Moderator–Reﬂector Systems 445 Target–Moderator–Reﬂector Experiments at the Hokkaido Electron Linear Accelerator 446 Target–Moderator–Reﬂector Experiments at the J¨ulich Proton Synchrotron COSY 454 Target–Moderator–Reﬂector Experiments at the Brookhaven Alternating Gradient Synchrotron AGS 466 Experiments on Radiation Damage in a Spallation Environment 471 Introduction 471 Irradiation Conditions and Studied Materials 472 Experimental Results 473 Microhardness and Three-Point Bending Tests 473 Tensile Strength, Scanning- and Transmission Electron Microscopy 475 Experiments to Shield High-Energy Neutrons of Spallation Sources 481 Shielding Experiments at the Los Alamos WNR Facility’s Spallation Target 482 Shielding Experiments at the ISIS Spallation Source 486 Shielding Experiments at the ASTE–AGS Target–Moderator–Reﬂector Assembly 491

Part III

Technology and Applications 495

16 16.1 16.2

Proton Drivers for Particle Production 497 An Introduction 497 Proton Drivers for Spallation Neutron Sources and Secondary Particle Production 498 Synchrotron-Based vs. Linear-Accelerator-Based Spallation Neutron Source 500 The Beam Loss Issue at High-Intensity Proton Accelerators 502

16.2.1 16.2.2 17 17.1 17.2 17.3 17.3.1 17.3.2 17.3.3

The Accelerator-Based Neutron Spallation Sources 505 Introduction 505 Research Reactors or Continuous/Pulsed Spallation Sources? 507 Spallation Neutron Sources 510 The LANL Spallation Neutron Source MLNSC and the Los Alamos Neutron Science Center LANSCE 510 The Rutherford and Appleton Laboratory Short-Pulsed Spallation Neutron Source ISIS 514 The PSI Continuous Spallation Neutron Source SINQ 519

XIII

XIV

Contents

17.3.4 17.3.5 17.3.6 17.3.7 17.3.8

18 18.1 18.2 18.2.1

The European Spallation Neutron Source Project ESS 524 The ORNL Spallation Neutron Source SNS 538 The Japanese Spallation Source and the Accelerator Complex J-PARC 548 Safety Aspects and Radiation Protection 554 Parameter Overview of the Existing, Commissioned and Planned Spallation Neutron Sources with a Beam Power Above 0.1 MW 558

18.2.2.3 18.2.2.4 18.2.3

Target Engineering 561 Introduction 561 Spallation Source Neutron-Generating Targets 562 Spallation Source Neutron-Generating Targets at Beam Power Levels of About Some 100 kW 562 Spallation Source Neutron-Generating Targets at Beam Power Levels in the MW Range 564 The SINQ Target Systems 565 The Mercury Targets for the Pulsed Spallation Neutron Sources ESS, SNS, and JSNS 569 Rotating High-Power Targets 579 Windowless Liquid Metal Targets 582 Materials for Accelerators and Targets of Spallation Sources 583

19 19.1 19.1.1 19.1.2 19.1.3 19.1.4 19.1.5 19.1.6 19.1.7 19.1.8

Research with Neutrons 585 Introduction 585 Solid-State Physics 587 Materials Science and Engineering 588 Chemical Structure, Kinetics, and Dynamics 588 Soft Condensed Matter 589 Biology and Biotechnology 589 Earth and Environmental Science 589 Fundamental Neutron Physics 590 Muons as Probes for Condensed Matter 590

20 20.1 20.2 20.2.1 20.2.2 20.3 20.3.1 20.4 20.4.1 20.5 20.6

Accelerator Transmutation of Nuclear Waste – ATW 593 Introduction 593 The Concepts of Transmutation 594 Balance Criteria for ADTT Systems 596 The Accelerator Issue of ATW/ADTT Systems 597 The Spent Reactor Fuel and Transmutation 600 An Example of a Transmutation Complex 602 Partitioning 605 EU Projects on Partitioning and Transmutation 606 Advances in Accelerator Breeding of Fissile Material 607 Accelerator Production of Tritium-APT 609

18.2.2 18.2.2.1 18.2.2.2

Contents

21 21.1 21.2 21.3 21.3.1 21.4 22 22.1 22.1.1 22.1.2 22.1.3 22.2 22.2.1 22.2.2 22.2.3 22.2.4 22.3 22.3.1 22.3.2 22.4 22.4.1 22.4.2 22.4.3 22.4.4 22.4.5 22.4.5.1 22.4.5.2 22.4.5.3 22.4.5.4 22.4.5.5

23 23.1 23.2 23.2.1 23.2.2

23.2.2.1

Accelerator Production of Electrical Energy – ‘‘Energy Amplifying’’ 613 Introduction 613 Principle of the ‘‘Energy-Ampliﬁer’’ 613 Feasibility of the ‘‘Energy Ampliﬁer’’ 615 An Energy Ampliﬁer Test Experiment 618 Advantages and Disadvantages of the EA Concept 619 Advanced Applications of Spallation Physics 623 Proton and Light Heavy Ion Cancer Therapy 623 History of Hadron Therapy 624 What is Radiation Therapy and How Does it Work? 626 Differences Between Protons, Heavy Ion, and X-ray Therapy 627 High-Energy Physics Calorimeter 631 The Physics of Particle Calorimetry 631 Electromagnetic Showers 633 Hadronic Showers 634 Combined Electromagnetic/Hadronic Calorimeters 635 Neutrino Factories and Neutrino Super/Beta Beams 638 Some Words on Research with Neutrinos 638 International Scoping Study of ν Factories and Superbeam Facilities 639 Ultracold Neutrons 642 History 642 Properties of UCNs 642 Reﬂecting Materials 644 UCN Production 645 Experiments with UCN 647 Measurement of the Neutron Lifetime 648 Measurement of the Neutron Electric Dipole Moment 648 Observation of the Gravitational Interactions of the Neutron 649 Measurement of the Neutron-Mirror Neutron Oscillation Time 650 Measurement of the a-Coefﬁcient of the Neutron Beta Decay Correlation 651 Space Missions and Radiation in Space 653 Introduction 653 Galactic Cosmic Ray (GCR) Induced Reactions in Moon and MARS Soil 654 GCR-Induced Neutron Flux Density in the Lunar Soil During Apollo Missions 654 The Mars Observer Orbiter Mission to Measure the Spallation-Induced Gamma Flux Return of GCR on the Martian Surface 657 The Aim of the Mars Observer Mission 657

XV

XVI

Contents

23.2.2.2 23.3 23.3.1 23.3.2 23.3.3

Application to the Martian Surface 659 The Space Experiment LDEF (Long Duration Exposure Facility) 663 The Aim of the LDEF Mission 663 The LDEF Orbiter System and Results on Induced Radioactivity of LDEF Materials 665 Hazard Radiations in Space 669

Appendix A Values of Fundamental Physical Constants and Relations 675 Appendix B Basic Deﬁnitions in Nuclear Technology Concerning the Fuel Cycle 679 Appendix C Material Properties of Structure and Target Materials 683 Appendix D Moderator and Reﬂector Materials Appendix E Shielding Materials 689 References 691 Index 757

687

XVII

Preface Spallation research is based on nuclear reaction mechanism called spallation as a source of an enormous radiation of many different particles such as neutrons, protons, pions, muons, electrons, photons, charged particles, and neutrinos. Originally the occurrence of spallation reactions was ﬁrst recognized in astrophysics. Most of the early systematic research on spallation processes was done at highenergy accelerators. Cosmic ray physicists refer usually to the spallation reactions as fragmentation. But for all practical applications, spallation reactions are inelastic nuclear reactions in which at least one of the two reaction partners is a complex nucleus. Spallation research has become popular, funding and industrial participation were increasing with the advent of different spallation research projects and with the study and construction of high-intensity neutron spallation sources all over the world. This was also a result of a continued progress in accelerator physics and research. Applications will provide new opportunities in particle physics, solid-state physics, and life- and material science. A recent renascence of interest for energetic proton-induced production of neutrons originates therefore largely from the inception of projects of intense spallation neutron sources in Europe, USA, Japan, and China. In particular, the new powerful spallation sources could provide a basis for various potentially important future applications as neutrino factories and accelerator-driven transmutation technologies. Such facilities may be used to achieve the incineration and transmutation of long-lived radioactive waste or in combination with ﬁssion to produce energy. The objective of this book is not only to gain insights into the complex spallation reaction mechanisms itself, but also to summarize and identify the essential applications. The purpose of this handbook is to provide a description of methods, problems, and issues in spallation research, which will be useful to those readers entering the ﬁeld and to those already engaged in spallation research, but more specializing in one area. The covered particle energy range in this book leads to a description of hadronic and electromagnetic phenomena over twelve orders of magnitude ranging from incident particle energies of several GeV down to the energy of subthermal meV neutrons of about 10−12 GeV, one of the important domains of spallation neutron sources for the investigation of the structural and dynamical properties of matter. Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

XVIII

Preface

The handbook has three main parts: Part 1 (Principles); Part 2 (Experiments); and Part 3 (Technology and Applications). Part 1, Principles, describes the theory of spallation reaction mechanisms in terms of the nuclear physics processes involved. For the ﬁrst stage of the reactions – the fast phase – the emphasis is put on the description of intranuclearcascade models. Alternative models are also explained. For the second stage – the slow phase – evaporation models including high-energy ﬁssion, subsequent deexcitation, and fragmentation are incorporated. The state-of-the-art used models and codes are addressed with their different features, parameters, and constraints. The propagation of particle showers induced by the internuclear-cascade-evaporation phenomena and the particle transport in thick target systems is explained. The important features of simulation code systems for particle transport in matter are considered. Theoretical issues on material and shielding problems in spallation research are presented. The basic design parameters for neutron spallation sources are reviewed. Part 2, Experiments, describes the proton-nucleus ‘‘thin’’ target experiments in terms of secondary particle production such as hadrons, pions, light and intermediate masses, and isotope production performed at various accelerators. A variety of proton-matter induced ‘‘thick’’ target experiments on neutron yield, neutron leakage and multiplicity distributions as well as heating and energy deposition measurements are illustrated. The neutron production is also discussed for primary incident particles other than protons. Target–moderator–reﬂector experiments to study the neutron ﬂux performance of spallation neutron sources, radiation damage investigations in a spallation environment, and high-energy neutron shielding experiments are characterized and speciﬁed. Many of the experiments have been associated with studies, investigations, and the design layout of spallation neutron sources until today. Part 3, Technology and Applications, describes the various issues associated with applications in spallation research. Proton drivers for secondary particle production, the features and parameters of high-intensity pulsed and continuous spallation neutron sources, e.g., LANSCE (USA), ISIS (UK), ESS (Europe), SNS (USA), J-PARC (Japan), and SINQ (Switzerland) as well as the concepts of neutron producing targets at beam power levels in the megawatt range are shown in detail. An overview about the research with neutrons is also given. The studies and projects on accelerator transmutation of radioactive waste from nuclear reactors, and the ideas of the ‘‘energy amplifying’’ using spallation reactions are considered. A broad spectrum of examples of advanced applications of spallation research as proton and light heavy ion therapy, high-energy physics calorimetry, neutrino factories, ultracold neutrons as well as the activation of space vehicles and hazard radiations in space are exempliﬁed. In the appendix, useful values of fundamental physical constants and relations, and material properties of target, structure, moderator, reﬂector, and shielding materials are summarized. The idea of this book is to give a detailed overview on spallation research. Most of the work and research in this ﬁeld is and was published in single articles

Preface

in journals and in reports of international or national institutions or presented at conferences during the last twenty years. A large amount of information was collected in national and international project reports of institutions working in spallation research, development, and applications in connection with construction and technical design of high-intensity spallation sources in the megawatt power range. Therefore, the authors of this book set a high value on describing the stateof-the-art of spallation research. This is also accomplished by a comprehensive bibliography. In general, we have tried to make the individual chapters independent of each other, even at the risk of repetition. Concerning the references, we have adopted the philosophy of quoting the original or the recent publications that we believe contained sufﬁcient details to be useful for the uninitiated reader. We have preferred this method because the referenced material usually illustrates the current knowledge. The reader is well advised to use the references in the cited literature if supplementary details are required. We would like to acknowledge for permission to reproduce various photographs and ﬁgures cited in the text to the following laboratories: Los Alamos National Laboratory, Los Alamos, USA, Paul Scherrer Institut, Villigen, Switzerland, Oak Ridge National Laboratory, Oak Ridge, USA, Rutherford and Appleton Laboratory, Didcot, United Kingdom, and the High Energy Accelerator Research Organization of the Japan Atomic Energy Agency, Tokai-mura, Japan. We also owe a great debt to Prof. Dr. Hans Ullmaier from the Forschungszentrum J¨ulich GmbH, Germany, for many suggestions and improvements during the preparation of the manuscript. Last but not least, we acknowledge the excellent co-operation with Dr. Christoph v. Friedeburg as well as Nina Stadthaus and Esther D¨orring of the publisher WILEY-VCH Weinheim, who contributed considerably to the success. J¨ulich, April 2009

Detlef Filges and Frank Goldenbaum

XIX

Part I Principles

3

1 The Spallation Process 1.1 Historic Remarks and Deﬁnitions

There is no generally accepted deﬁnition of the term ‘‘spallation reaction’’ although this type of nuclear reaction is observed in astrophysics, geophysics, radiotherapy, radiobiology, and at all applications together with accelerators. Cosmic ray physicists refer still to such reactions induced by cosmic rays as ‘‘fragmentation.’’ But for all practical purposes, spallation refers to nonelastic nuclear reactions that occur when energetic particles, for example, protons, neutrons, or pions interact with an atomic nucleus. So at least one of the two collision partners is a complex nucleus in which the available energy exceeds the interaction energy between nucleons in the nucleus. Thus, a nucleon–nucleus or pion–nucleus or nucleus–nucleus reaction, in which the incident energy exceeds some 10th of MeV per a.m.u. is referred to as spallation or spallation reaction. The term comes from the verb ‘‘to spall,’’ meaning to chip with a hammer [1]. There is no clear separation of spallation from the lower energy nuclear reactions. One type may merge into the other as the energy of the incident particle increases. (a) A deﬁnition found in Encyclopedia Britannica: ‘‘Spallation is a high-energy nuclear reaction in which a target nucleus struck by an incident (bombarding) particle of energy greater than about 50 million electron volts (50 MeV) ejects numerous lighter particles and becomes a product nucleus correspondingly lighter than the original nucleus. The light ejected particles may be neutrons, protons, or various composite particles equivalent.’’ (b) A deﬁnition for spallation to be speciﬁed in the context of accelerator driven systems or high-intensity neutron sources is ‘‘the disintegration of a nucleus by means of high energetic proton-induced reactions. Typically approximately 20 neutrons are created per incident GeV proton.’’ (c) A much shorter deﬁnition: ‘‘Spallation is a nonelastic nuclear interaction induced by a high-energy particle ≥50 MeV producing numerous secondary particles.’’ The following terminology is used here for clariﬁcation to describe the highenergy nuclear processes. The terms ‘‘inelastic,’’ ‘‘quasielastic,’’ ‘‘absorption,’’ and ‘‘nonelastic’’ describe usually reactions which are not pure elastic scattering from the nucleus as a whole. Absorption is in general used to describe all nonelastic Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

4

1 The Spallation Process

events when an optical analysis is made. The term inelastic is used in describing low-energy phenomena where scattered particles hold their identity but leave the nucleus in an excited state. The term ‘‘nonelastic’’ is used to describe all events which are not elastic scattering with the nucleus as a whole (see also page 44). Historically the idea of the basic reaction mechanism – the intranuclear cascade – was ﬁrst proposed by Serber [2]. He suggested that at energies of about 100 MeV, the deBroglie wavelength of the incident particle becomes comparable to, or shorter than, the average internucleon distance within the nucleus 10−13 cm. That is the collision time between the incident particle and a nucleon inside the nucleus becomes short compared to the time between nucleon collisions inside the nucleus. Goldberger [3] was the ﬁrst to perform calculations using Serbers’s model approach. (It was reported that two people working for 2 weeks were able to generate 100 Monte Carlo particle histories by hand calculations.) Metropolis et al. [4, 5] were the ﬁrst to report extensive calculations using computers and generated large amounts of data for incident particles <400 MeV below the pion threshold. Also Dostrovsky et al. [6, 7] studied by Monte Carlo simulation the systematics known as nuclear evaporation [8, 9] programmed ﬁrst for the Los Alamos MANIAC computer during the 1950s (see Section 2.2). Since then, numerous reﬁnements and extensions of the spallation models have been made in relation with experiments and nowadays with the development of spallation neutron sources. During the 1960s primarily three groups were active: Barashenkov et al. at Dubna [10], Chen et al. at BNL [11], and Bertini et al. at ORNL [12]. These groups had also studied numerical comparisons of results from the models as investigated by these three groups for low-energy protons at energies of 150 and 300 MeV [13]. Details of this early research will be discussed in Chapter 2. Still the most important physics uncertainty associated with the predicting the interaction of high-energy particles such as hadrons, leptons, and pions with matter lies in determining the description – multiplicities and energy and angular distributions – of particles produced in nonelastic nuclear collisions. Much of the research on spallation consists in experiments to measure cross sections. The early experiments were using cosmic rays as incident particles. But nowadays extensive experiments are done at high-energy accelerators also in connection with the development of high-intensity neutron spallation sources in the last 20 years. Very often the target in question is not a single nucleus. If it is not a ‘‘thin’’ target, where no secondary reactions are occurring, but a rather ‘‘thick’’ target further secondary reactions will arise and a so-called nuclear cascade will be produced within the ‘‘thick’’ target. Thick targets can be found in nature, e.g., meteoroids, the moon’s surface, the martian’s surface, the earth’s atmosphere, the earth itself, or the human body. The transport of cosmic rays through the earth’s atmosphere [14] is a good example of a nuclear cascade (see Section 1.2). Spallation will take place wherever a ﬂux of high-energy particles collides with some matter. There are two main types of high-energy particles in the universe: cosmic rays and particles from accelerators. The bombardment of matter with high-energy particles produces not only spallation but also a rather complex sequence of nuclear and atomic interactions, which will be discussed in detail in Section 1.3. In Figure 1.1,

1.2 Spallation by Cosmic Ray-Induced Reactions

Protons Nucleus

Pions

Primary particle Neutrons GeV Residuals Gammas Fig. 1.1 Generalized possible particle production of a particle–nucleus interaction in the GeV energy range.

a scheme of a more generalized possible particle production on a particle–nucleus interaction is depicted.

1.2 Spallation by Cosmic Ray-Induced Reactions

From experiments around 1912/1913, Hess found in free balloon ﬂights to an altitude of about 5300 m that there exists a radiation within the earth’s atmosphere of very great penetration power. Hess received the Nobel Prize for this discovery in 1936. It was concluded that these rays were of cosmic origin. They were referred to as ‘‘H¨ohenstrahlung,’’ which might be translated as ‘‘high altitude rays.’’ It is now common to speak of cosmic rays. The primary rays in outer space are relatively simple, but interaction with matter changes their nature as they pass through the atmosphere. Galactic cosmic rays or galactic cosmic radiation (GCR) consist of high-energy particles believed to propagate throughout all the space and to originate both within and outside our galaxy. The measured cosmic ray energy spectra of galactic protons, helium ions, carbon ions, and iron ions are shown in Figure 1.2. The primary cosmic ray ﬂux in the solar system at the earth’s orbit is a mixture of energetic protons, alpha particles, and a small mixture of heavier nuclei as shown in Figure 1.2. This ﬂux and its composition vary over the 11-year solar activity cycle. After passing the interplanetary medium and the geomagnetic ﬁeld, the primary cosmic rays propagate by means of a nucleonic cascade through the atmosphere. More details of the principal interactions by cosmic rays in the atmosphere and the produced energy spectra, the solar wind distribution, and trapped spectra by the geomagnetic ﬁeld may be seen in [15, 17–19]. Formulas (1.1) also show the general reaction mechanisms. Secondary cosmic rays include pions which decay in muons, neutrinos, and gamma rays, as well electrons and positrons by muon decay and gamma ray interaction with the earth’s atmosphere. The most abundant secondary cosmic rays reaching the earth’s surface are muons (see Figure 1.4), with an average intensity of about 100 per m2 . In Table 1.1 some basic properties of pions, kaons, and muons are summarized. More details are given in the ‘‘Review of Particle

5

1 The Spallation Process 10

1

Primary cosmic ray particle spectra [m2 sr s MeV/nucleon]−1

6

0.1

He

10−2

H C

10−3 Fe 10−4

10−5

10−6

10−7

10−8

10−9 10

102

103 104 105 Particle energy [MeV]

106

Fig. 1.2 Cosmic ray energy spectra measured at the orbit of the earth (1 AU = astronomical unit = mean distance between the Sun and the Earth) for hydrogen, helium, carbon, and iron (taken from Simpson [15, 16]). Some basic particle properties of pions, kaons, and muons.

Tab. 1.1

Particle

Charged pions Neutral pions Charged kaons Neutral kaon Charged muons

Symbol

Rest mass (MeV/c2 )

Mean lifetime (s)

π± π0 k± k0 µ±

139.6 134.0 493.7 497.7 105.7

2.60 × 10−8 0.84 × 10−16 1.24 × 10−8 Weak decay 2.20 × 10−6

107

1.2 Spallation by Cosmic Ray-Induced Reactions

Physics’’ of the Particle Data Group (PDG) [19] in Section 1.3.5.1 on page 23 in this book. p + air −→ p + n + π ± + π 0 + k± + k0 , n + air −→ p + n + π ± + π 0 + k± + k0 , π+

−→

µ+ + νµ ,

π−

−→

µ− + ν µ ,

−

µ

−→ e− + ν e + νµ ,

µ+ −→ e+ + νe + ν µ , µ± also inducing electromagnetic showers, π 0 −→ 2γ −→ electromagnetic showers, k+ −→ µ+ νµ , +

π π

or

0

π +π +π − π +π 0π 0 π 0 e+ νe π 0 µ+ νµ .

(1.1)

The branches of the cosmic ray atmospheric propagation process are shown in Figure 1.3. The kaon contribution is small. In the vicinity of the earth’s orbit, the composition of cosmic radiation is approximately 85% protons, 12% alpha particles, 1% nuclei of atomic numbers Z > 2, and 2% electrons and positrons [16]. At high energies above several GeV the spectra shown in Figure 1.2 could be well represented within interstellar space by a power-law energy dependence: φi ∝ 1.8(E/A)−γ [nucleons/(cm2 s sr GeV)],

(1.2)

with φi the differential ﬂux of element i at kinetic energy per nucleon (E/A) including rest mass energy and γ is in the range 2.5 to 2.7. The relative fractions of the primary and secondary incident nuclei are listed in Table 1.2. The spectra distributions at 1 AU of particles with A ≤ 4 are quite similar if the energies are taken per nucleon (E/A). They are characterized by a broad maximum of the differential spectrum between 100 and 1 GeV/A, and decrease by a power law for higher energies. Below ∼10 GeV/nucleon the spectra are effected by solar modulation or the solar magnetic ﬁeld [17]. Galactic radiation arriving within the heliosphere is isotropic. The spectra of nuclei extend to energies in excess of about 1020 eV. Figure 1.4 shows the vertical ﬂuxes and spectra of the major cosmic ray components in the atmosphere. Except for protons and electrons near the top of the atmosphere, all particles are produced in interactions of the primary cosmic rays with the air. Muons and neutrinos are products of the decay of charged mesons, while electrons and photons originate in decays of neutral mesons. Most of the measurements are made at ground level or near the top of the atmosphere.

7

8

1 The Spallation Process

Primary cosmic particles

Nuclear interactions with the Earth's atmosphere

p+ p−

k± k0

µ±

Hadronic cascade

µ+ nµ nµ µ− Muonic component and neutrinos

n

p p± k±

p±

k± k0

p0

µ±

g

e +e −

e +e −

e +g e −g

e +g e −g

Hadronic component nuclear fragments

Electromagnetic component

g

e +e −

Cherenkov and fluorescence radiation

Fig. 1.3 The development of the components of cosmic rays propagating in the earth’s atmosphere with kaon branches shown. Ratios of relative abundances of cosmic ray nuclei at 10.6 (GeV/nucleon) normalized to oxygen (≡1) with an oxygen ﬂux of 3.26 × 10−6 (cm−2 s−1 sr−1 (MeV/nucleon)−1 ) (see Ref. [20]). Tab. 1.2

Z

Element

Abundance ratio

1 2 3–5 6–8 9–10 11–12

Ha Hea Li–Be C–O F–Ne Na–Mg

540 26 0.40 2.20 0.30 0.22

a

Z

Element

13–14 15–16 17–18 19–20 21–25 26–28

Al–Si P–S Cl–Ar K–Ca Sc–Mn Fe–Ni

Abundance ratio 0.19 0.03 0.01 0.02 0.05 0.12

The hydrogen and helium abundances are from [21].

According to [26] the modulated differential GCR proton ﬂux can be described by the following formula:

(Ep , M) = Cp ·

Ep (Ep + 2mp c2 )(Ep + m + M)−2.65 −2 −2 cm s MeV−1 (1.3) (Ep + M)(Ep + 2mc2 + M)

1.2 Spallation by Cosmic Ray-Induced Reactions

Altitude [km] 15

104

10

5

3

2

1

0

Altitude flux spectra [m−2 s−1 sr−1]

103 nµ + n−µ µ+ + µ−

2

10

101

p+n

100

e+ + e− p+ + p −

10−1

10−2

0

200

400

600

800

1000

−2

Atmospheric depth [g cm ] Fig. 1.4 Vertical ﬂuxes and spectra of cosmic rays in the atmosphere with energy E > 1 GeV estimated from the nucleon ﬂux of formula 1.2 (see also [19]). The symbols show measurements of negative muons with energy E > 1 GeV [22–25].

with m = 780 · exp(−2.5 × 10−4 · Ep ), and the normalization factor Cp = 1.24 × 106 (cm−2 s−1 MeV−1 ), mp = 938.3(MeV c−2 ) the proton rest mass, c the velocity of light, Ep the proton energy in (MeV), and M (MeV) the modulation parameter of the sun. The solar modulation parameter M varies with the 11-year solar cycle. As shown in [26], small modulation parameters are typical for spectra during times of a quiet sun – 1965 M = 450 MeV and 1977 M = 300 MeV–, large modulation parameters for an active sun – 1969 M = 900 MeV. For the simulation of present-day irradiation processes, the arithmetic mean GCR spectrum from solar minimum (1965) with M = 450 MeV and solar maximum (1969) with M = 900 MeV may be adequate [27]. This spectrum is equivalent to a GCR spectrum with M = 675 MeV. An example for different values of M is shown in Figure 1.5 using formula (1.3) of [26]. The elemental composition of cosmic rays is an active area of research since the relative abundances provide tests of theories on the origin of the elements, or nucleosynthesis. Figure 1.6 shows the relative abundances of all elements at a typical energy of 2 GeV/nucleon. In radiation effect assessments, it is common to consider the cosmic ray ions in three groups:

9

1 The Spallation Process

M = 675

1.0 ×10−3 Proton flux distribution [cm−2 s−2 MeV−1]

10

1965 solar minimum at 1 AU

M = 450 1969 solar maximum at 1 AU 1.0 ×10−4

1.0 ×10−5 0.01

M = 900

0.1 1.0 Proton energy [MeV]

10.0

Fig. 1.5 Comparison of GCR cosmic ray spectra with different modulation parameters M = 450, 675, 900 MeV at 1 AU. (1 AU ≡ 1 astronomical unit = 1.49 × 1013 cm, the mean distance between the earth and the sun).

• H and He, • HZE ions (i.e., high charge number Z, and high-energy loss E, which includes ions having Z ≤ 30), • ultraheavy cosmic rays Z > 30. Since energy deposition by ionization is proportional to Z2 , the most important HZE ions in terms of the speciﬁc energy deposition density or speciﬁc dose density in materials are Fe (Z = 26) and to a lesser extent ions in the Z = 8–14 range. The idea of introducing spallation processes into astrophysics arose in 1970 [28], when it was realized that abundances of some elements in the cosmic rays are signiﬁcantly different than those observed in the solar system. For isotopes of Li, Be, B, F, Cl, K, Sc, Ti, V, Cr, Mn the cosmic ray abundances exceed the solar ones by at least one order of magnitude and in an extreme case of Li, Be, B – so-called LiBeB puzzle – it is even six orders of magnitude. This is seen in Figure 1.7, where the production of Li, Be, and B by high-energy spallation reactions between cosmic rays and the interstellar medium induced on C, N, and O is compared to the abundances of products of the solar system (see [15, 29–31]). The underestimation of the abundances of elements with atomic mass numbers from 20 to 25 by three to four orders of magnitude is also observed. The most possible formation of the LiBeB production is nowadays thought to be interactions of galactic comic rays with the interstellar medium, mainly carbon, nitrogen, and oxygen nuclei, where the most abundant high-energy cosmic ray particles are protons and α-particles. Other possible origins are primordial, stellar, or supernova neutrino spallation (see Refs. [32, 33]). Stable and radioactive nuclides are produced by the interaction of solar and galactic cosmic ray particles with terrestrial and extraterrestrial matter. In extraterrestrial materials, such as meteorites and lunar surface material samples, these product nuclides are called cosmogenic nuclides. A limited number of cosmogenic nuclides is observable in the earth’s atmosphere due to its relatively simple chemical composition. In extraterrestrial matter more than 30 cosmogenic nuclides have been

1.2 Spallation by Cosmic Ray-Induced Reactions

Relative cosmic ray flux (normalized to Si = 106)

1010 H

109

C

107

O Si

106

Fe

105 104 103 102 Zr

101

Ba

Pt

100

Pb

10−1

Individual elements

10−2

Fig. 1.6

Abundances relative to silicon = 106

Nuclear composition of galactic cosmic rays (~2 GeV/nucleon)

He

108

Even-Z elements

Element groups

10 20 30 40 50 60 70 80 90 100 Atomic charge number [Z]

Relative particle ﬂux of cosmic rays as a function of the nuclear charge Z.

He

109

O

C

107

Ne

Mg Si

N

Fe

S Ar Ca Ti

105

Cr

Ni

Na Al

103

B

F

P Cl

Mn

K

Co V

Li

101

Sc 70–280 MeV/nucleon cosmic rays (Simpson, 1983)

1

Be

0

5

Solar system elements (Lang, 1980)

10 15 20 25 Nuclear charge number [Z]

30

Fig. 1.7 Comparison of elemental abundances of 70–280 MeV/nucleon for cosmic rays (from Simpson [15]) and to the solar system abundances (from Cameron [29] and Lang [30]) normalized to (Si = 106 ).

observed. The production cross section of these nuclides with galactic cosmic or solar rays is an actual problem of modern cosmo-chemistry. To analyze the formation of the isotopic content of cosmic matter and its evolution under different radiation conditions, the knowledge of isotopic excitation functions is required. The observed

11

1 The Spallation Process 16O(p,x)7Be

14

Cross section [mb]

12

N(p,x)7Be

101

100

0.01

Exp. Mashnik et al. 1998

Exp. Mashnik et al. 1998

Bernas et al.1967

Bernas et al.1967

0.1

1

10 0.01

0.1

1

10

Proton energy [GeV]

Fig. 1.8 Comparison of cross sections used in astrophysical simulations (Mashnik et al. [41] and Bernas et al. [40]).

concentrations of cosmogenic nuclides in extraterrestrial matter could be used to determine the exposure history of the irradiated specimen or the history of the cosmic radiation itself (Michel et al. [34–36]). Theoretical and experimental investigations of cosmogenic nuclides in extraterrestrial matter yield information about spectral distribution, composition, and intensity of solar and galactic cosmic rays over time scales of up to 109 a. By no other means than by cosmic nuclides this information about the history of the solar system may be obtained. A large number of experiments were performed in the past to demonstrate the importance of excitation functions for the production of cosmogenic nuclides (see [37–39] and also Chapter 23 on page 653). In Figure 1.8, two examples of cross sections used in astrophysical simulations (solid lines) are compared with presently available data (open circles) [40, 41]. Meanwhile, many other reliable measurements were performed [38] and compared with simulations. But experiments are unable to provide all the necessary information. Some semiempirical systematics of nuclear the spallation reaction were evaluated in the 1960s called Rudstam systematics [42]. The Rudstam systematics were than further developed by Silberberg and Tsao [43–47], taking the validity of Serber’s model [2] into account. With the progress in spallation physics and the development of Monte Carlo particle reaction mechanisms and particle transport in matter during the recent years, the simulation of these reaction processes by using basic principles is possible nowadays. Experimental investigations, measurements, and validations, will be discussed and demonstrated in Part 2 on page 287.

1.3 Physics of the Spallation Process 1.3.1 Introduction

The production of secondary particles by bombarding the atomic nucleus by energetic particles was ﬁrst demonstrated by Rutherford in 1919 [48], who was using α-particles on 14 N causing the reaction 14 N +4 He −→ 17 O + p. In 1934 Curie and

1.3 Physics of the Spallation Process Tab. 1.3

Examples for some neutron-producing mechanisms.

Nuclear process

400 keV D on T absorbed in titanium 35 MeV D on liquid Li 100 MeV e− on 238 U 235 U(n,f) 1000 MeV protons on thick Hg target Laser-ion beam imploded pellet

Technical application

Neutronproduction yield

Energy deposition (MeV/n)

D, T solid target

4 × 10−5 (n/d)

10.000

Deuteron stripping Electron bremsstrahlung Thermal ﬁssion spallation

3 × 10−3 (n/d) 5 × 10−2 (n/e) 3 (n/ﬁssion) 30 (n/proton)

10.000 2000 190 55

(D, T) CTR fusion

1 (n/fusion)

3

Joliot [49] produced the ﬁrst artiﬁcial radioactivity using α-particles by the reaction 27 Al +4 He −→ 30 P + n. In 1932, the invention of the cyclotron by Lawrence and Livingston [50] and in 1939 the discovery of the nuclear ﬁssion by Hahn and Strassmann [51, 52] opened new possibilities for secondary particle production as high-intensity neutrons, radioactive isotopes, gammas, pions, and muons. In addition to ﬁssion, nuclear fusion of light elements produces secondary particles such as neutrons, produces energy, and radioactive species. The fusion of light nuclei (hydrogen isotopes) was ﬁrst observed by Oliphant in 1933 [53]. The cycle of nuclear fusion in stars and the subsequent reactions were worked out by von Weizs¨acker [54] and Bethe [55] in 1935/1939. Candidates for terrestrial reactions for neutron production are D + T −→ 4 He + n + 17.59 MeV and D + D −→ 3 He + n + 3.27 MeV or in the abbreviated form T(d, n)4 He and D(d, n)3 He, where the energy of the produced neutrons is 14.1 MeV and 2.45 MeV, respectively. It may be therefore very useful to compare several of the above-mentioned methods from the standpoint of possible mechanisms of neutron production. Features of several processes are shown in Table 1.3. Each of the processes, except the last one, has been used for the production of neutrons for certain purposes. Since power density limits must be considered, the energy deposition per neutron is a very important parameter. The usefulness of different reactions depends not only on the values of the given table, but also on other factors, such as the energy and angular distribution of the neutrons, the range of the charged particle production in charged particle reactions, the availability of suitable accelerators, and critical constraints in the case of ﬁssion reactors [56, 57]. In the case of the controlled thermonuclear reaction (CTR) the feasibility has still to be demonstrated. Together with one of the ﬁrst projects to design and build a high-intensity neutron spallation source ‘‘ING’’ (Intense Neutron Generator) [58] experiments on thick targets were done to measure neutron production yields [59] and to evaluate the energy- or heat depositions. In Figure 1.9 these results for cylindrical thick targets of uranium and lead are shown.

13

Energy deposition/ neutron [MeV]

1 The Spallation Process

80

Uranium

60 40

Lead

20 0

Neutrons per incident proton

14

40 30

Uranium

20 Lead

10 0.0

0.2

0.4

0.6

0.8

1.0

Incident proton energy [GeV] Fig. 1.9 ING measurements on neutron production yields and evaluated heat production for cylindrical targets of uranium and lead of diameter = 10 cm, and length = 60 cm.

At an incident proton energy of 1 GeV the ratio of the neutron yields and the ratio of the heat per neutron for the targets of lead and uranium (diameter = 10 cm, length = 60 cm) are • yielduranium /yieldlead = 36.9/20.8 = 1.77, • heaturanium /heatlead = 50.1/25.7 = 1.95. A part of the higher neutron yield for uranium comes from the ‘‘extra’’-neutronsproduced fast ﬁssion processes in uranium. The increase in heat production per neutron for the uranium target is due to fast ﬁssion. For a proton beam power of 1 MW at 1 GeV incident proton energy, the neutron source strength and the heat deposition for these targets are given in Table 1.4. For a neutron source strength of about 1017 neutrons per second and a proton beam power of 1 MW, a lead target would produce about 0.33 MW and a uranium target 1.2 MW. Carpenter [56] used the measurements of Figure 1.9 to determine a semiempirical relation for the neutron yield y(E) production for incident proton beam energies 0.2 GeV ≤ E ≤ 1.5 GeV as follows: y(E) = 0.1(A + 20)(EGeV − 0.12) for 9 ≤ A ≤238 U,

(1.4)

y(E) = 50(EGeV − 0.12) for

(1.5)

and 238

U,

where A is the atomic weight (g/mole) and EGeV is the incident proton energy in GeV. These semiempirical formulas (1.4) and (1.5) are only valid for targets of diameter 10 cm and length 60 cm. Other target geometries and material compositions will

1.3 Physics of the Spallation Process Estimated source strength and energy deposition of ‘‘ING’’ targets of Figure 1.9 on the facing page.

Tab. 1.4

Lead target

Uranium target

Source strengtha Number of neutrons

1.3 × 1017

2.3 × 1017

Energy deposition (MeV) (MW)

3.3 × 1018 0.33

1.2 × 1019 1.2

a

Calculated for an incident proton beam energy of 1 GeV and 1 MW beam power = 1 GeV mA, where 1 mA ≡ 6.24 × 1015 protons/s and 1 W ≡ 1 J/s, and 1 eV ≡ 1.6 × 10−19 J.

produce different neutron yields, which will arise from secondary processes such as production or absorption, of particle leakage and may be dependent on the full development of the so-called hadronic cascade inside the target. 1.3.2 The Fission Process

Because ﬁssion is a well-known process in physics and technology, it may be interesting to discuss some similarities and different basic features between spallation and ﬁssion. In the case of ﬁssion, slow neutrons of thermal energy (En ≈ 0.024 eV), interact with metastable 235 U. The excited nucleus decays in a cascade of ﬁssion products of smaller atomic weight. These fragments, or ﬁssion products, are about equal to half the original mass. This so-called binary splitting of an excited nucleus into two approximately equal parts is still considered as one of the most interesting phenomena of collective motion of nuclear matter and as an excellent example of the nuclear multiparticle problem. According to the ‘‘liquid drop model’’ [60], regarding the nucleus as an incompressible liquid, a surface tension is responsible for the inner forces on all surface nucleons, which in turn makes the nucleus unstable against deformation. The nucleus breaks apart when the Coulomb repulsion between the two halves of the deformed nucleus equals the restoring force of the nuclear surface tension. Neutrons will occasionally be freed during the scission process, but are mainly released by evaporation from the ﬁssion fragments. The fragments are neutron rich and have an excess of internal energy. Details may seen in Refs. [61] and [62]. On average about 2.5 neutrons are produced by the ﬁssion of one 235 U nucleus. The sum of the masses of these ﬁssion fragments is less than the original mass. This ‘‘missing’’ mass (about 0.1% of the original mass) is converted into energy according to Einstein’s equation E = mc2 . The so-called produced ﬁssion neutrons possess very elevated energies of about 2 MeV and are thus unsuitable for inducing further ﬁssion processes. With the help of moderators

15

16

1 The Spallation Process

Neutron Nucleus U-235

Neutron with thermal energy

Fission product

Neutrons

Proton

Slow neutron Fig. 1.10

Fission product

Neutron

Neutron

Fission

Chain reaction

Schematics of ﬁssion processes.

the fast neutrons are slowed down to meV energies. These slow neutrons sustain the chain reaction in a nuclear reactor. A chain reaction refers to a process in which neutrons released in ﬁssion produce an additional ﬁssion in at least one further nucleus. This nucleus in turn again produces neutrons, and the process repeats. If each neutron releases two more neutrons, then the number of ﬁssions doubles each generation. In that case, in 10 generations there are about 1024 ﬁssions and in 80 generations about 6 × 1023 ﬁssions, which is a mole of ﬁssions. In Figure 1.10, the schematic of the ﬁssion process is shown. One should refer to Sections 1.3.3, 3.4.5, 3.7, and 3.7.1 for more details of ﬁssion and spallation and ﬁssion. The spectrum of neutrons obtained in a reactor has a broad energy distribution, reaching from 0.001 eV to over 10 MeV. It is characterized by the spectrum (E). (E)dE is the ﬂux of neutrons between E and E + dE. Within this spectrum three different regions are distinguished: • E > 0.5 MeV – the region of fast neutrons. Here (E) (formula (1.6)) approximately follows the energy distribution of the neutrons produced in ﬁssion. The ﬁssion spectrum can be approximated by formula (1.7) (details may be seen also in Refs. [61, 63]) and is shown in Figure 1.11. • 0.2 eV < E < 0.5 MeV – the region of epithermal or resonance neutrons (formula (1.8)). In this energy range, the spectrum is mainly predominated by neutrons being slowed down by elastic collisions with the nuclei of the moderator substance. • E < 0.2 eV – the region of thermal neutrons. Thermal neutrons are nearly in thermodynamic equilibrium with the thermal motion of the moderator atoms. Their energy distribution can frequently be approximated by a Maxwell distribution (formula (1.9)). ∞ f =

(E)dE

(E > 0.5 MeV)

(1.6)

0.5 MeV

n(E) = 0.484 · e−E · sinh

√

2E

(MeV)

(1.7)

Neutron production n(E) [arbitrary units]

1.3 Physics of the Spallation Process

0.3

0.2

0.1

0.0 0.0

2.0

4.0 6.0 8.0 Energy of fission neutrons [MeV]

10.0

Fig. 1.11 The energy spectrum of neutrons produced in thermal neutron ﬁssion of 235 U using formula (1.7).

(E)dE =

epi dE E

(E)dE = th ·

(0.2 eV < E < 0.5 MeV)

E dE · e−E/kT · kT kT

(E < 0.2 eV).

(1.8) (1.9)

Here T is the absolute temperature and k is the Boltzmann constant, which is in fact a conversion factor between energy and temperature units. In terms of eV energy units it has a value of 8.617 × 10−5 (eV/K) with k = 1.38 × 10−23 (J/K) and 1 J 6.25 × 1018 (eV). The spectrum of ﬁssion neutrons could also be evaluated fairly well using the Maxwell distribution in the following form: n(E) =

2 · E 1/2 3/2

π 1/2 · ET

· e−E/ET .

(1.10)

Here ET is the kinetic energy and kT is corresponding to a certain ‘‘temperature’’ of the nucleons in the nucleus. Values for ET are 1.29 MeV for 235 U ﬁssion and 1.33 MeV for 239 Pu ﬁssion corresponding to temperatures of about 1.14 × 108 K and 1.18 × 108 K, respectively. The mean kinetic energy of the neutron distribution is E = (3/2) × ET here. The distribution of the energy released to the reaction products in nuclear ﬁssion is summarized in Table 1.5. 1.3.3 Spallation and Fission

In contrast to ﬁssion, the spallation process is not an exothermal process – energetic particles are necessary to enable the process. As mentioned in Section 1.1, spallation refers to nuclear nonelastic or inelastic reactions that occur when energetic

17

18

1 The Spallation Process Energy release of reaction products in nuclear ﬁssion. The ﬁssion reaction is therefore an exothermal process.

Tab. 1.5

Reaction product Fission fragments Neutrons Prompt γ s β-particles Decay γ s Neutrinos Sum

Released energy (MeV) 167 ± 5 5 6±1 8 ± 1.5 6±1 12 ± 2.5 204

subatomic particles – protons, deuterons, neutrons, pions, muons, etc. – interact with an atomic nucleus, which is usually referred to as ‘‘target’’ nucleus. In this context, energetic means kinetic energies of the primary incident particles on the target nucleus larger than several tens of MeV and more accurately, within the meaning of the validity of theoretical physical models, an incident energy of about 100–150 MeV. At these energies the deBroglie wavelength λ [64–66], e.g., of the proton, is only ≈ 10−13 cm (see Eq. (1.11)): λ = h/ 2 · mp · Ep (cm) = (h · c)/ 2 · mp · c2 · Ep ) (cm)

(1.11)

with mp = 938.2 (MeV/c2 ) the rest mass of the proton, Ep the energy of the proton in MeV, h = 6.626 × 10−34 (J s) = 4.136 × 10−21 (MeV s) the Planck constant, and h · c ≈ 1240 × 10−7 (eV cm). • For proton energies Ep = 100– 150 MeV, λ is about λ ≈ 2.8 × 10−13 –2.3 × 10−13 (cm), which is smaller as the size of the nucleus with about ≈ 10−12 (cm). • At an incident energy of Ep = 1000 MeV, λ is about λ ≈ 9.0 × 10−14 (cm). • For lower incident energies, e.g., Ep = 10 MeV, λ is ≈ 10−12 (cm), which is the size of the nucleus. In this case a nucleon does not interact with individual nucleons, but with the whole nucleus. At 100–150 MeV, the deBroglie wavelength λ is therefore short enough to allow the incident particle to interact with the individual nucleons inside the nucleus. As is discussed in more detail in Chapter 2, this is an important prerequisite for the application of particle nucleus collision models limiting their validity above some tens of MeV. Therefore, it is no longer correct that a spallation reaction is proceeding in the formation of a compound nucleus. The initial collision between the incident particle and the target nucleus leads to a series of direct reactions – the so-called intranuclear cascade – where individual nucleons or small groups of nucleons are ejected from the nucleus. Above a few GeV per incident nucleon fragmentation of the target nucleus may also occur. After the ‘‘intranuclear cascade’’ phase of

1.3 Physics of the Spallation Process

Target nucleus

Internuclear cascade

Intranuclear cascade

n

n

p

Incident particle

p a

≥ 150 MeV

n n d

High-energy fission n p n

n

g

Evaporation or de-excitation

n

Proton Neutron

Fig. 1.12

(n, xn), (n, f) Nuclear (n, g), (n, n p) reactions (n, n′a) etc.

The principal scheme of spallation.

the reaction the nucleus is left in an excited state. This is shown in principle in Figure 1.12. During the ﬁrst stage – cascade/pre-equilibrium stage – the incident particle undergoes a series of direct reactions with the nucleons–neutrons and protons – inside the target nucleus, where high-energy secondary particles such as protons, neutrons, and pions from 20 MeV up to the energy of the incident particle are created in an intranuclear cascade inside the nucleus. From the intranuclear cascade some of these high-energy hadrons escape as secondary particles. Also low-energy pre-equilibrium particles in the low MeV energy range are ejected from the nucleus leaving the nucleus in a highly excited state. In the second stage nuclear de-excitation or evaporation takes place, when the excited nucleus relaxes by emitting low-energy (<20 MeV) neutrons, protons, alpha particles, light heavy ions, residuals, etc., with the majority of the particles being neutrons. After evaporation the nucleus that remains may be radioactive and may emit gamma rays. The secondary high-energy particles produced during the intranuclear cascade phase move roughly in the same direction as that of the incident particle beam, due to the so-called Lorentz boost, e.g., the momentum transfer of the incident particle, and can collide with other nuclei in the target. The reactions that follow are a series of secondary spallation reactions (see Figure 1.12) that generate more secondary particles and low-energy neutrons. This so-called internuclear cascade or more general hadronic cascade is the accumulation of all reactions caused by primary and secondary particles in a target.

19

1 The Spallation Process

100

Cross section [mb]

20

High-energy fission products or intermediate mass fragments (IMFs)

Spallation products

10

1

40

60

80

100 120 140 160 Mass number [A]

180

200

Fig. 1.13 Experimentally measured spallation residual mass distributions from [68] of 1 A GeV 208 Pb + p reactions.

For some target materials, low-energy spallation neutrons (<20 MeV), e.g., preequilibrium/evaporation neutrons, may enhance the neutron production through low energy (n,nx) reactions. For very heavy nuclei, e.g., lead, tungsten, thorium, and natural or depleted uranium, the so-called high-energy ﬁssion can occur during the evaporation phase in competing with standard evaporation. Details are given in Chapter 3. Thorium and uranium are, in addition to undergoing high-energy ﬁssion, ﬁssionable by low-energy (1–20 MeV) neutrons. Fission and spallation differ in several ways [67]. One important difference is in the nuclear debris remained after the reaction is completed. In spallation, the nuclei that remain after evaporation are about 15 atomic mass units lighter, on average, than the original target nucleus, because very light particles such as protons and neutrons are emitted. In spallation, the nuclear debris – sometimes called spallation residuals – is distributed close to the original target material. A typical distribution measured for protons of 1 GeV on a 208 Pb target is illustrated in Figure 1.13. Note that high-energy ﬁssion produces symmetric ﬁssion products or intermediate mass fragments peaking in a range around an atomic mass A = 90. In ﬁssion, the nucleus divides into two fragments (Figure 1.10), typically producing a light fragment and a heavy fragment as ﬁssion products. For high-energy ﬁssion, the ﬁssion product distribution is more symmetric than the asymmetric ﬁssion products caused by low-energy neutrons. This is because at high energy – beyond some MeV – any shell effects are washed out. Another difference is in the number of neutrons released (Table 1.3). The overall number of neutrons released per ﬁssion event of about 2.5 to 3.0 is considerably less than that released per spallation event with about 25 to 30 using heavy target materials bombarded by 1 GeV energy protons. The amount of energy deposited per neutron produced in spallation and ﬁssion (Table 1.3) is also different. For ﬁssion, about 200 MeV of energy is deposited as

Neutron spectrum (integrals normalized to unity)

1.3 Physics of the Spallation Process

100 10−1 10−2

Spallation

10−3 Fission

10−4 10−5 10−6 10−4

10−3

10−2

10−1

100

101

102

103

Neutron energy [MeV] Fig. 1.14 Spallation neutron spectrum compared to a typical neutron spectrum from thermal neutron ﬁssion of 235 U. The spallation spectrum is measured at 90◦ from a ‘‘ﬁnite’’ 10 cm diameter by 30 cm long tungsten target bombarded by 800 MeV protons [67].

heat for each neutron produced; for spallation in Hg, the corresponding number is about 55 MeV. Although there is less heat generated with spallation, the beam power intensity of a proton beam of a high power spallation source can lead to cooling problems in target systems (cf. Part 3 on page 495). Spallation neutrons have higher energies than ﬁssion neutrons (cf. Figure 1.14). In a spallation source high-energy cascade neutrons approach the energy of the incident proton beam energy [67]. The high-energy tail of the spallation neutron spectrum compared to the ﬁssion spectrum is remarkable. High-energy neutrons are extremely penetrating. Therefore, well-designed shielding is needed to prevent high-energy neutrons from causing unwanted problems in radiation safety (cf. Chapter 7 on page 233). 1.3.4 The Logical Scheme of Spallation Reactions

The low-energy (<20 MeV) cascade, evaporation, and ﬁssion neutrons are isotropic in angle, whereas the high-energy (>20 MeV) neutrons from spallation have a strong angular dependence, where, in the very forward direction, these neutrons can have the same energy as the incident particle beam causing the spallation event. This is shown in Section 1.3.7.6. Also some of the features of the most important atomic interactions such as ionization, excitation effects and Coulomb scattering and hadron, pion, and muon decay will be discussed in Section 1.3.5 to complete the physics of spallation. In Figure 1.15, a logical scheme of performance of the spallation process is shown. In spallation a certain fraction of the incoming particle’s energy is transferred to the nucleus by nucleon–nucleon collisions, thus increasing the kinetic energy of the nucleons inside the nucleus, or, more precise heating up the nucleus. Three stages can be distinguished in a spallation reaction according to a certain time

21

22

1 The Spallation Process

Incident particle beam

Target surface

Atomic processes - Ionization - Coulomb scattering

Pre-evaporation

High-energy fission

Intranuclear cascade ~ 10−22 s

Internuclear cascade

Evaporation processes ~ 10−18 s

n, p, p-mesons high-energy particles

p-meson decay

p0 decay

p± decay

Photons

µ± -mesons, neutrinos

Nuclear reactions

n, p, d, t, a, g, residuals low-energy particles

Fig. 1.15 A logical scheme of the performance of spallation reactions showing the three stages on particle production.

scale, the intranuclear cascade phase, the pre-equilibrium phase, and the evaporation and high-energy ﬁssion phase. This is schematically shown in Figures 1.12 and 1.15. In the initial cascade, so-called intranuclear cascade, which takes place within about 10−22 s, the energy of the primary incident particle is transferred to the nucleons inside the target nucleus. During this process energetic particles may leave the nucleus and may induce another spallation reaction in a different nucleus – internuclear cascade. Internuclear cascade processes are generated in thick targets. This processes are called particle showers that means a cascade of secondary particles produced in interactions of high-energy particles in dense matter. As mentioned earlier, the intranuclear cascade is often called hadron cascade because during this phase charged pions, neutrons, and protons are produced. After the completion of the intranuclear cascade, the kinetic energy possessed by those nucleons which remain inside the nucleus is assumed to be equilibrated

1.3 Physics of the Spallation Process

among all of the nucleons. This residual excitation energy, as well as the mass and charge of the residual nucleus, can take a range of values because of the variety of different outcomes, e.g., neutrons, protons, pions, etc., possible for the reactions at high energies. Subsequent de-excitation is determined by the so-called evaporation, which occurs within a time frame of about 10−18 s or less. Thus, the second stage of a spallation reaction is the evaporation phase, which may compete with the so-called high-energy ﬁssion when using heavy target nuclei. Particles emitted during the evaporation phase are of low energies (1–10 MeV) and have isotropic angular distributions. Nucleon emission, especially of neutrons, in particular for targets with high atomic masses, is more probable than the emission of positively charged clusters such as deuterons, tritons, 3 He, or α or even heavier particles. After particle emission is no longer energetically possible, the nucleus can still be left with a small amount of excitation energy, which is assumed to be released by photon emission. 1.3.5 Particle Interaction Mechanisms

This section gives a brief review about the basic forces, the classiﬁcation of the fundamental particles, and some useful deﬁnitions concerning particle interaction with matter and transport in matter. When energetic particles with energies above several tens of MeV undergo nuclear interactions with matter they will produce either charged secondary particles, e.g., protons, tritons, deuterons, α-particles, light and heavy ions, π-mesons, electrons and positrons or uncharged neutrons, and photons. Electrons, positrons and photons can undergo further interactions with matter inducing an electromagnetic cascade. In principle, there are seven types of particles of concern to spallation reactions and their application: • protons and charged heavier particles of masses comparable to the mass of protons, tritons, deuterons, α-particles, etc., • neutrons at high energies – from some tens of MeV to several GeV, • electrons and positrons, • photons and γ -radiation, • π-mesons and their decay products, µ-mesons • also antiparticles such as the antiproton p or the positron e+ may be used to invoke spallation reactions, • neutrons at low energies – from meV to some tens of MeV. 1.3.5.1 The Elementary Forces and Particles The present knowledge of the physical phenomena suggests that there are four types of forces between physical bodies (Table 1.6). These forces are of decreasing strength, from the strong to the electromagnetic, the weak and the gravitational. The strong, the electromagnetic, and the weak forces determine the properties of the interactions on nucleon–nucleon or nucleon–nucleus collisions in the spallation process. The standard model in particle physics describes the known elementary particles and their interactions. According to the standard model there are six quarks and

23

24

1 The Spallation Process Tab. 1.6

Elementary particles and forces.

Force

Strong

Electromagnetic

Weak

Gravitational

Particles experiencing

Quarks, gluons

Electrically charged

Quarks, leptons

All

Particles mediating

Gluons

Photons

Bosons W + , W − , Z0

Graviton?

1

10−2

10−13

10−38

≤10−13

∞

≤10−16

∞

Approx. mass (GeV/cm2 )

0

0

80.4, 80.4, 91.2

0

Electric charge

0

0

+1, −1, 0

0

Spin

1

1

1, 1, 1

2

Strength at 10−13 cm compared to the strong force Range (cm)

each of them has three different colors. The neutron and the proton, and many other particles heavier than the proton and the neutron, the baryons, are made of three quarks and the mesons are made of a quark and an antiquark. The inner structure of such objects has been studied, for example, with high-energy electrons and it has been found that at higher bombarding energies – several GeV – additional quark–antiquark pairs are being ‘‘resolved” and a part of the energy and the momentum of these particles is not carried by the quarks, but by the massless gluons mediating the strong force. The simple picture of a proton or neutron composed only of three valence quarks has therefore to be extended to a more complex structure still not exactly understood. Other particles, such as the electron and the muon and the neutrinos are leptons and do not seem to have an internal structure. So the fundamental scheme of subatomic particles leads to the existence of 12 elementary particles. Their properties are given in Tables 1.7, 1.8, and 1.10. More details about the particle properties and the standard model are given in the references of the PDG [19] and in Refs. [69–71]. Quarks and leptons are the elementary particles which build up matter. The quarks are the ‘‘bricks’’ for all known mesons and baryons. More than 200 mesons and baryons are known. Gluons are the exchange particles for the so-called color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles. The gluon can be considered to be the fundamental exchange particle for the strong interaction between protons and neutrons in a nucleus. The short-range nucleon–nucleon interaction can be considered to be a residual color force extending outside the boundary of the proton or neutron. The strong interaction is involved by the exchange of pions, and indeed the theory of the Yukawa potential

1.3 Physics of the Spallation Process Properties of the leptons (the charge is given in terms of the elementary charge of the electron e = 1.602 × 10−19 (C)). Tab. 1.7

Particle name

Symbol

Approx. mass (GeV/c2 )

Electric charge

Mean life (s)

Spin ()

Electron neutrino Electron

e+

νe or e−

<1.0 × 10−8 0.000511

0 −1

Stable Stable

1/2 1/2

Muon neutrino muon

νµ µ+ or µ−

<0.0002 0.106

0 −1

Stable 2.197 × 10−6

1/2 1/2

Tau neutrino Tau

ντ τ + or τ −

<0.02 1.7771

0 −1

Stable 2.91 × 10−13

1/2 1/2

Tab. 1.8

Properties of the quarks.a

Particle name

Symbol

Approx. mass (GeV/c2 )

Electric charge

Spin ()

Up Down

u d

0.0015 − 0.003 0.003 − 0.007

+2/3 −1/3

1/2 1/2

Charm Strange

c s

1.25 0.095

+2/3 −1/3

1/2 1/2

Top Bottom

t b

174.2 4.2

+2/3 −1/3

1/2 1/2

a

The masses should not be taken too seriously, because the conﬁnement of the quarks implies that one can not isolate them to measure their masses directly. They are only determined by scattering experiments.

of Yukawa in 1935 [72] was helpful in developing our understanding of the strong force. Some features of the pions are summarized in Table 1.11. The quarks are fermions and possess the quantum numbers as given in Table 1.9. Baryons are massive particles which are made up of three quarks in the standard model (see Table 1.10). This class includes the proton and the neutron. There are others such as lambda, sigma, etc. Baryons are different from mesons in that mesons are composed of only two quarks. Baryons and mesons are included in the class known as hadrons, the particles which interact by the strong force (Table 1.6). This general classiﬁcation excludes leptons, which do not interact by the strong force. But the weak interaction acts on both hadrons and leptons. Hadrons as seen in Table 1.10 are composed of quarks, either as quark–antiquark pairs (mesons) or of three quarks (baryons).

25

26

1 The Spallation Process Tab. 1.9

Tab. 1.10

The quantum numbers of the quarks.

Type

Down

Up

Strange

Charm

Bottom

Symbol Spin Charge Isospin (T) T3 Strangeness Charm Bottom Topness Baryon number

d 1/2 −1/3 1/2 −1/2 0 0 0 0 1/3

u 1/2 2/3 1/2 1/2 0 0 0 0 1/3

s 1/2 −1/3 0 0 −1 0 0 0 1/3

c 1/2 2/3 0 0 0 1 0 0 1/3

b 1/2 −1/3 0 0 0 0 −1 0 1/3

Top t 1/2 2/3 0 0 0 0 0 1 1/3

Properties of the baryons.

Particle name

Symbol

Quark makeup

Approx. mass (MeV/c2 )

Electric charge

Spin()

Mean life (s)

Proton

p

uud

938.3

+1

1/2

Stable

Neutron

n

ddu

939.6

0

1/2

920

Lambda

0

uds

1115.6

0

1/2

2.6 × 10−10

pπ − , nπ 0

Sigma

+ − 0

uus dds uds

1189.4 1197.3 1192.5

+1, −1

1/2

0

1/2

0.8 × 10−10 1.5 × 10−10 6.0 × 10−20

pπ 0 , nπ + nπ −

0 γ

++ , 0 ±

uuu, udd uud, ddd

1232 1232

+2, 0 +1, −1

3/2 3/2

0.6 × 10−23 0.6 × 10−23

pπ + /nπ 0 , pπ − pπ 0 , nπ + /nπ −

Delta

Dominant decay modes ··· pe− ν e

1.3.5.2 Feynman Diagrams Feynman diagrams are the graphical way to represent the exchange of particle forces [73, 74]. Each point at which lines come together is called a vertex, and at each vertex one may examine the conservation laws which govern particle interactions. Each vertex must conserve charge, baryon, and lepton number. Particles are represented by lines with arrows to denote the direction of their travel, with antiparticles having their arrows reversed. Virtual particles are represented by wavy or broken lines and have no arrows. Figure 1.16 shows examples of Feynman diagrams for the three forces, the electromagnetic, the weak, and the strong interactions between quarks and between nucleons. Particle interactions can be represented by these diagrams with at least two vertices. They can be drawn for protons, neutrons, etc., even though they are composite objects and the interaction can be visualized as being between their constituent quarks.

1.3 Physics of the Spallation Process

e

Virtual photon

e

ne

p

e

W− e

e

n

Electromagnetic

Blue

Weak interaction

Green

p

n p

Green

Green-antiblue gluon

Blue

Between quarks

p

n

Between nucleons Strong interaction

Fig. 1.16 Examples of particle interactions, electromagnetic, weak, and strong interactions between quarks and between nucleons represented by Feynman diagrams.

1.3.5.3 Resonance Decay, Pion Absorption, and Pion Charge-Exchange Resonance decay Heisenberg suggested in 1932 that the proton and neutron could be treated as different substates of one particle, the nucleon. A nucleon is ascribed a quantum number, isospin I, with a value I = 1/2 with two substates I1 = +1/2 for the proton, and I2 = −1/2 for the neutron. The quark model explains in a simple way the conservation laws of the quantum numbers (see Table 1.9) in strong interaction between hadrons or between pions and hadrons. Baryons and mesons are composed of multiplets of members with different charges, but approximately of the same mass. Examples of these are the triplets of π + , π − , and π 0 , the doublet of nucleons and the quartet of ’s. This can be represented by attributing to the members of each multiplet the same isotopic spin or isospin T, which is related to the multiplicity M of the members of the multiplet by M = 2T + 1 and a different third component T3 . The number of members of hadron multiplets is limited to the maximum number of four so the isotopic spin of a hadron cannot exceed 3/2. It should be noted that to the highest charge member of each multiplet the highest value of T3 is attributed and to the lowest charge member the lowest. Thus in the -quartet made up of ++ , + , 0 , and − , the sequence of the isospin values of T3 is 3/2, 1/2, −1/2, and −3/2, respectively. More details could be see in Refs. [70, 75]. The early theoretical studies and investigations by Sternheimer–Lindenbaum [76] on secondary particle production in nucleon–nucleon or pion–nucleon interactions were concentrated on the question which spin and isospin contribute to the production process. The Sternheimer–Lindenbaum model assumes that one or more isobars [76] or nowadays called resonances are produced in such collisions. A number of intranuclear cascade models utilize the Sternheimer–Lindenbaum isobar model such as those of Bertini [12, 77] (see e.g., Section 2.2.3.1), Barashenkov

27

1 The Spallation Process Pion kinetic energy [GeV] 0.195

sp-p cross section [mb]

28

200

0.600 0.900

1.350

∆(1232) 3+/2

π+p

150

N(1688) 5+/2

100

N(1525) 3−/2

50

∆(1920) 7+/2

π− p 0 1.0

1.2

1.4

1.6

1.8

2.0

Mass of the pion proton system [GeV/c 2]

Fig. 1.17 Resonant structure of cross sections for the interaction of π + and π − with protons.

et al. [10, 78], and Harp [79]. Secondary particles produced in nucleon–nucleon and pion–nucleon collisions are observed as - or N-resonances (see Figure 1.17) in the cross sections of a given reaction. Complete tables of the baryon resonances, their masses, decay, spin, isospin, and quark makeup are given in the review of particle physics of the PDG reference Yao et al. [19]. Many of these particles have such a long lifetime on the subnuclear time scale (see Tables 1.7, 1.10, and 1.11) that it is possible to produce intense secondary beams such as pion and kaon beams of meson factories. In Figure 1.17, the lower pion mass resonances correspond to the doubly charged ++ and neutral 0 members of a quartet of particles (see Table 1.10) called the 33 - or the (3, 3)-resonance with a mass of 1232 MeV/c2 , a spin and parity of Jp = 3/2+ , and an isospin of I = 3/2. As Figure 1.17 indicates, more pion–nucleon resonances are observed, for example, there is an I = 1/2 resonance at 1525 MeV. The symbol refers here to resonances of I = 3/2 and N refers to I = 1/2. The positions of some other known states together with their spin-parity assignments are given. Higher mass resonances are also shown. Figure 1.18 shows the resonance decay of the (1232)++ mass in π + and proton as a Feynman diagram by using the quark makeup of the resonance. Pion absorption It should be mentioned that the absorption of pions by nuclei has long been of interest to nuclear physicist. The pion cannot be absorbed on a free nucleon and still conserve energy and momentum. Therefore, at least two nucleons must be involved in the absorption process. This yields even for nucleons inside a complex nucleus to make pion absorption on a nucleon in the nucleus obey energy and momentum conservation well above the Fermi momentum [80]. Several

1.3 Physics of the Spallation Process Tab. 1.11

Particle name pion pion kaon kaon kaon eta eta prime rho rho omega phi

Properties of some important mesons. Symbol

Anti particle

Makeup

Rest mass (MeV/c2 )

Mean life (s)

π+ π0 k+ k0s k0L η η ρ+ ρ0 ω0

π− Self k− k0s k0L Self Self ρ− Self Self

ud √ (uu + dd)/ 2 us 1a 1a 2b 2b ud uu, dd uu, dd

139.6 135.0 493.7 497.7 497.7 548.8 958 770 770 782

2.6 × 10−8 0.83 × 10−16 1.24 × 10−8 0.89 × 10−10 5.2 × 10−8 <10−18 5 × 10−19 0.4 × 10−23 0.4 × 10−23 0.8 × 10−22

ϕ

Self

ss

1020

20 × 10−23

Dominant decay modes µ+ νµ 2γ µ+ νµ , π + π 0 π + π − , 2π 0 π + e− ν e 2γ , 3γ π +π −η π +π 0 π +π − π +π −π 0 0

k+ k− , k0 k

a

The neutral kaons represent symmetric and antisymmetric mixtures of quark combinations down-antistrange and antidown-strange. √ b The neutral eta is a quark combination (uu + dd − 2ss)/ 6.

u d

p+

u ∆++

u

g

d

u

p u u

Fig. 1.18 Feynman diagram of the resonance decay of the (1232)++ mass in π + and proton (g stands for the gluon exchange particle as the color force between quarks; see Section 1.3.5.1).

experiments indicted that pion absorption in nuclei in the energy region of the -resonance often involved more than two nucleons, e.g., the BGO Ball experiment at LAMPF [81]. The prototype of the pion two-nucleon absorption process is the reaction π + + d → pp which is the dominant reaction on I = 0 pn-pairs and is sometimes referred to as the quasideuteron absorption. Contributions from the absorption, e.g., on I = 1 pp-pairs are much less important, especially near the peak of the -resonance. A recent review is given in Ref. [80] and the experimental work contains most of the data taken at meson factories reviewed in [82].

29

30

1 The Spallation Process

Pion charge exchange An important example of the conversation law in particle interactions is the isospin conservation arising in the strong interaction of nonidentical particles, which will generally consist of mixtures of different isospin states. An example is the pion–nucleon scattering process. The isospin for the pion is Iπ = 1 and for the nucleon IN = 1/2; therefore, they may couple to Itotal = 1/2 or 3/2. If the strong interactions depend only on I and not on T3 , then 3 × 2 pion–nucleon scattering processes can be described in terms of two isospin amplitudes (for details see Refs. [70, 75]). Six elastic scattering processes are possible. • Of the six elastic scattering interactions, processes

π + p −→ π + p,

π − n −→ π − n

(1.12)

have T3 = ±3/2, I = 3/2 and differ only in the sign of T3 . • the cross sections π − p −→ π − p,

π − p −→ π 0 n

(1.13)

π + n −→ π 0 p

(1.14)

• and the cross sections π + n −→ π + n,

have T3 = ±1/2, I = 1/2 or 3/2. The cross sections of Eqs. (1.12) and (1.13) are poor elastic ones, whereas the cross sections of Eqs. (1.14) are pion-exchange cross sections. 1.3.5.4 Kinetic Energy, Total Energy, and Momentum Kinetic energies of particles are measured in units of electron volts (eV), corresponding to the kinetic energy needed by a particle of electron charge crossing a potential difference of 1 V: 1 eV = 1.602 × 10−19 J. In particle and accelerator physics, usually the motion of energetic particles is subject to relativistic kinematics; therefore, some basic well-known properties are given below. For more details see the references in standard university textbooks such as [83, 84]. The rest energy, E0 , of a particle is deﬁned as

E0 = m0 · c2 ,

(1.15)

where m0 = particle rest mass, c = velocity of light ≡ 2.997 × 1010 cm s−1 . The total energy, E, is given by E = m · c2 = m0 · c2 (1 − β 2 )1/2 , where m is observed mass of the particle, and β = v/c.

(1.16)

1.3 Physics of the Spallation Process

The kinetic energy, Ekin , of the particle is then given by Ekin = E − E0 = (m − m0 ) · c2 .

(1.17)

From Eqs. (1.15) and (1.16) it follows that β = v/c = [1 − (E0 /E)2 ]1/2 .

(1.18)

The momentum, p, of the particle is then p = m · v = m · β · c = (1/c) · (E 2 − E02 )1/2 = (1/c) · [Ekin (Ekin + 2E0 )]1/2 . (1.19) From Eq. (1.19) one can see that at high kinetic energies (Ekin 2E0 ) the particle momentum p is approximately p ≈ Ekin /c ≈ E/c.

(1.20)

Equation (1.20) shows the correlation between energy and momentum frequently used by the units MeV/c or GeV/c for the particle momentum in spallation and particle research or in accelerator physics. 1.3.5.5 Cross Sections, Absorption Length, Collision Length, and Mean Free Path The cross section is an extremely important concept in describing the interaction of particles with matter. The angular and energy distribution of particles produced in nuclear reactions with matter is usually expressed by so-called partial or double differential cross sections. The probability of producing a particle of energy E in the energy range E + dE during an interaction of particles with matter in the solid angle region between and + d is denoted by

d2 σ/dE d.

(1.21)

The following basic deﬁnitions and some relations are taken from Bock and Vasilescu in [85]. The cross sections of two colliding particles is a measure of the probability that the two particles interacts. The cross section σ is a Lorentz invariant measure of the probability of interactions in a two-particle initial state. It has the dimension of an area (unit cm2 or barn ≡ 10−24 cm2 ), and is deﬁned such that the expected number of interactions in a small volume dr and a time interval dt is given as dN = F · σ · dr dt,

(1.22)

with F = ρ1 (r, t) · ρ2 (r, t) · u, and u = (|u1 − u2 |2 − |u1 × u2 |2 ). The parameters ρ1 and ρ2 are the number densities of the two particle species – number of particles per volume – and u1 and u2 are their velocities,

31

32

1 The Spallation Process

respectively. So ρ and u are the particle ﬂux and the relative direction, respectively. The cross section may be visualized as the area presented by the target particle or by a ‘‘thin’’ target, which must be hit by the point-like particle for an interaction to occur. The term interaction may be speciﬁed by the ﬁnal state of the reaction. As an example an elastic scattering reaction may serve. If a particle 1 is scattered into a solid angle d, the cross section may be denoted as dσ , and by the above deﬁnitions, the so-called differential cross section is given by dσ/d =

1 ·dN/d. F

(1.23)

The integration of these partial cross sections over an appropriate range of energy and in space gives the total cross section σtot often abbreviated as σT . The total cross section is σT = σelastic + σnonelastic . The cross section σnonelastic is often named as σinelastic . For the processes of nonelastic interactions of hadrons with matter the so-called mean free path for absorption is important. The mean free path is therefore determined by the nonelastic part of the hadronic cross section. The mean free path of a particle in matter is a measure of its probability of undergoing interactions of a given kind. It is related to the cross section corresponding to this special type of interaction. • mean free path or interaction length: λmeanfp = A/(NA · ρ · σnonelastic )

(1.24)

with • σ = cross section (b) or (cm2 ), • λmeanfp = mean free path or interaction length (cm), • A = atomic weight (g/mole), • NA = Avogadro number(6.022 × 1023 /mole), • ρ = target density (g/cm3 ). Tables often give λmeanfp · ρ in the dimension (g/cm2 ). The collision length λT often named as nuclear collision length and the probability density function (x) as the distance between successive collisions of a particle in matter are the functions of the total cross section σtot or σT and are given by the following expressions: • nuclear collision length: λT = A/(σT ·NA · ρ)

(1.25)

• probability density function: (x)dx = (1/λT )· exp(−x/λT )dx. Because σT > σnonelastic it always follows that λT < λnonelastic .

(1.26)

1.3 Physics of the Spallation Process Total and nonelastic cross sections for different media together with the nuclear collision length and the interaction length or mean free path (the values are based on Refs. [19, 86–91]).

Tab. 1.12

Medium

Z

A

Density (g/cm3 )

σT (b)

σ nonelastic (b)

H2 He Li Be C Al Fe Cu W Au Hg Pb U Concrete

1 2 3 4 6 13 26 29 74 79 80 82 92

1.0079 4.0026 6.941 9.0121 12.011 26.981 55.845 63.546 183.84 196.97 200.59 207.2 238.03

0.0838 0.1294 0.534 1.848 2.265 2.7 7.87 8.96 19.3 19.32 13.57 11.35 18.95 ∼2.5

0.0387 0.133 0.210 0.268 0.331 0.634 1.120 1.232 2.767 2.990 3.03 3.08 3.378 –

0.033 0.102 0.157 0.199 0.231 0.421 0.703 0.782 1.65 1.72 1.74 1.77 1.98 –

Nuclear collision length λT (cm)

Interaction length λmeanfp (cm)

516.7 385.82 102.24 30.19 26.58 26.15 10.52 9.55 5.72 5.9 8.1 10.23 6.17 26.9

606.21 503.09 137.45 40.69 38.10 39.4 16.76 15.05 9.64 9.9 14.11 17.07 10.50 39.96

In Table 1.12 on the following page some values of different media for σT , σnonelastic , the mean free path λmeanfp , and the nuclear collision length λT are given. The dependence of the cross sections on incident particle energy, incident particle species, and semiempirical expressions for cross section evaluation are given in Section 1.3.7.4. 1.3.6 Electromagnetic and Atomic Interactions

The most important atomic interactions of charged particles with matter are usually ionization and excitation effects, and, occasionally, Coulomb scattering. The physics of such atomic interactions for hadrons is well known. Neutral particles such as neutrons or photons interacting with matter ﬁrst produce charged particles, which then in turn produce ionization effects. Some of the basic features, which are important to understand energy deposition and the dissipation by energy losses of particles passing through matter will be given. 1.3.6.1 Energy Loss of Heavy Particles by Ionization and Excitation – the Bethe or Bethe–Bloch Formula Charged particles lose their kinetic energy passing through matter by excitation of bound electrons and ionization. Excitation processes such as e− + atom → atom∗ + e− → atom + γ produce low-energy photons. More important are direct

33

34

1 The Spallation Process

collision processes where ‘‘heavy’’ charged particles other than electrons or photons lose energy primarily by ionization and atomic excitation. This energy loss is important for hadrons because the mean free path and the nuclear collision length for the strong interactions are large (see Table 1.12). The mean energy loss of heavy charged particles, the so-called stopping power dE/dx is given by the Bethe formula [92, 93] often named as Bethe–Bloch formula [19, 94–97]: −

dE = 4π · NA · re2 · me · c2 · z2 · (Z/A)(1/β 2 ) dx 2me · c2 · γ 2 · β 2 − β 2 − δ/2 , × ln I

(1.27)

where the parameters are as follows: • NA – Avogadro number (6.02 × 1023 mol−1 ) • re – classical electron radius (2.82 × 10−13 cm) • me – electron rest mass (0.511 MeV/c2 ) • z – projectile charge in units of the elementary charge • Z – atomic number • A – atomic weight of the medium (g/mole) • γ – Lorentz factor (= E 2 ), where m0 is the rest mass (for example for a muon m0 ·c with mµ c2 = 106 MeV and energy E = 1.06 GeV the Lorentz factor is γ = 10) • β – projectile velocity in units of c(=v/c) • I – average ionization potential of a medium, which may be approximated by I = 16 · Z0.9 eV for Z > 1. I is also a function of the molecular binding of the atoms of the medium. I=15 eV for atomic hydrogen, 19.2 eV for molecular hydrogen, and 21.8 eV for liquid hydrogen. • δ – density correction, which takes into account shielding effects by the electrons of the medium on the transversal electrical ﬁeld of the incident relativistic charged particles. The density correction therefore reduces the energy loss of charged particles incident on high density media such as iron or lead. A useful abbreviation is the constant 4π · NA · re2 · me · c2 = 0.3071

MeV g/cm2

(1.28)

and an approximation by using the maximum kinetic energy Emax , which can be imparted to a free electron in a single collision leads to an abbreviated form of the Bethe–Bloch formula as given by Eq. (1.31): Emax = 2 · me · c2 · z2 · γ 2 · β 2 K = 2π · NA · re2 · me · c2 · z2 · (Z/A) · (1/β 2 ). Short Bethe–Bloch formula: Emax δ dE − = 2K · ln − β2 − . dx I 2

(1.29) (1.30)

(1.31)

1.3 Physics of the Spallation Process

10 8

-dE/dx [MeV/(g/cm2)]

6

H2 liquid

5 4 He gas 3

2

1 0.1

Sn Pb

1.0

0.1

0.1

0.1

1.0

Fe

10 100 b g = mincident-particle × c

Al

C

1000

10 000

1.0 10 100 Muon momentum [GeV/c]

1000

1.0 10 100 Pion momentum [GeV/c] 10 100 Proton momentum [GeV/c]

1000

1000

10 000

Fig. 1.19 The energy loss rate −dE/dx in liquid hydrogen, helium gas, carbon, aluminum, tin, and lead (after Yao et al. [19] and Barnett et al. [97]).

The energy loss − dE dx is usually given by the dimension 2

MeV g/cm2

. However, usually

the unit length dx is applied in (g/cm ), because the energy loss per distance ds in cm, the so-called mass thickness, with dx = ρ · ds and density ρ in (g/cm3 ), is weakly dependent of the material properties shown in the minimum of the stopping power functions of Figure 1.19. Equation (1.27) is only an approximation for the energy loss of charged particles in matter, but up to incident particle energies of several GeV predictions of the energy loss may have an accuracy of about several percent. The differences in stopping power for some materials such as H, He, C, Al, Fe, Sn, and Pb are given in Figure 1.19. The stopping power functions show very broad minima at around βγ = 3.0 for a Z from 6 to 100. In most practical cases relativistic particles – energies of several GeV – have energy loss values close to the minimum of their stopping power functions. They deﬁne the so-called minimum ionizing particles, or mips . The integration of Eq. (1.27) or (1.31) yields the total range R for a particle which loses energy through ionization. dE/dx depends only on β, whereas the range R

35

1 The Spallation Process

50000 20000

C Fe

10000 Range/mincident-particle [g cm−2 GeV−1]

36

Pb

5000 2000

H2 liquid

1000

He gas

500 200 100 50 20 10 5 2 1 0.1

2

5

1.0

2

5

10.0

2

5

100.0

2.0

5.0

10.0

b g = p/(c × mincident-particle) 0.02

0.05

0.1

0.2

0.5

1.0

Muon momentum [GeV/c ] 0.02

0.05

0.1

0.2

0.5

1.0

2.0

5.0

10.0

Pion momentum [GeV/c ] 0.1

0.2

0.5

1.0

2.0

5.0

10.0 20.0

50.0

Proton momentum [GeV/c] Fig. 1.20 Range of charged particles – protons, pions, and muons – in liquid hydrogen, helium gas, carbon, iron, and lead. As an example: a proton incident on lead with a momentum 1 GeV/c, a mass mincident−particle = 0.938 (MeV/c2 ), and βγ = 1.066. One may read R/mproton ≈ 195 g cm−2 GeV−1 , and this is a range R ≈ 195 g cm−2 or R ≈ 17.1 cm (after Yao et al. [19] and Barnett et al. [97]).

divided by the incident particle mass m is a function of the energy E divided by the incident particle mass mincident-particle or of p · c/mincident-particle with p = β · γ as the laboratory momentum of the incident particle in (GeV/c). The range R per incident particle mass m is a function of βγ = p · c/mincident-particle is given in Figure 1.20 for the materials liquid H, He gas, C, Fe, and Pb. Carpenter [56] gives a reasonably accurate semiempirical formula (1.32) for the range R of protons in spallation source target materials, which is helpful to estimate

1.3 Physics of the Spallation Process

200 Lead

180

Proton range [cm]

160 Aluminum

140

Mercury Iron

120

Uranium

100 80 60 Tungsten

40 20 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Proton energy [GeV] Fig. 1.21 Proton ranges in (cm) as a function of different incident proton energies on spallation target materials for Al, Fe, W, Hg, Pb, and U using Eq. (1.32).

the transversal dimensions of target systems. Neutrons are not uniformly produced in the target, and are spread out over a distance comparable with the range R of protons in the target material: R(Eproton ) = (1/ρ) · 233 · Z0.23 (Eproton − 0.032)1.4

(1.32)

for Z ≥ 10, 0.1 ≤ E ≤ 1 GeV, ρ = density in g/cm3 , and Ep = incident proton energy in GeV. R has the dimension (cm) in Eq. (1.32) or if multiplied by ρ the dimension (g/cm2 ). Calculations using Eq. (1.32) are shown in Figure 1.21 and Table 1.13 for the ranges of protons for different incident energies in spallation target materials. Other than for electrons, the range for charged hadrons is mainly dominated by energy loss due to ionization. Curves and tabulations of the range due to ionization exist for many different particles in different materials (see [97]). As mentioned earlier, Eq. (1.27) determines only the average energy loss of charged particles by ionization and excitation. Especially for thin targets – particularly for thin absorber layers – due to dx = ρ · ds, ﬂuctuations in the energy loss result in a distribution at the end of the range for the particles, which is called range straggling (cf. Section 4.4). This probability distribution is a Landau distribution [75], which describes the ﬂuctuations around the mean energy loss. The Landau distribution about the mean value is asymmetric, with a tail extending to values much greater than the average. 1.3.6.2 Coulomb Scattering A charged particle traversing a medium is deﬂected by many scatters, mostly at small angles. It will be scattered due to the interaction with the Coulomb potential

37

38

1 The Spallation Process Tab. 1.13 Numerical values of ranges for protons incident on different spallation target materials calculated by using Eq. (1.32) (the properties of the materials are given in Table 1.12).

Incident proton energy Ep (GeV)

0.4

0.6

0.8

1.0

1.5

Carbon range (cm)

38.2

70.2

107.1

148.1

265.3

399.9

Aluminum range (cm)

38.4

70.5

107.6

148.7

266.5

401.6

Iron range (cm)

15.6

28.6

43.7

60.4

108.2

163.1

Copper range (cm)

13.9

25.6

38.9

53.9

96.6

145.6

Tungsten range (cm)

8.0

14.7

22.5

31.0

55.6

83.8

Mercury range (cm)

11.6

21.3

32.5

44.9

80.5

121.4

Lead range (cm)

13.0

25.6

39.1

54.0

96.8

145.9

Uranium range (cm)

8.6

15.8

24.0

33.2

59.5

89.8

2.0

of the nuclei, and to a lesser degree, to the ﬁelds of the electrons of the atoms. As Eq. (1.27) indicates, dE/dx is inversely proportional to the target mass, so that in comparison with electrons, the energy lost in Coulomb collisions with nuclei is negligible. However, for hadronic incident particles and for large target masses, a transverse scattering is appreciable in the Coulomb ﬁeld of the nucleus. This is described by the Rutherford formula for the differential cross section at scattering angle given by Eq. (1.33). This results in many small-angle scatters and is called multiple Coulomb scattering: dσ () 1 = · d 4

Z · z · e2 β·c·p

2 ·

1 , sin4 (/2)

(1.33)

where p is the momentum in (MeV/c2 ), βc is the velocity, z is the charge of the incident particle, and Z is the charge of the nucleus, assumed to act as a point ` charge. The scattering distribution is described by Moliere’s theory [19, 98, 99] and approximates the projected scattering angle of multiple scattering by a Gaussian with a width of 2rms . The resultant distribution of the multiple scattering for small

1.3 Physics of the Spallation Process

deﬂections with a root-mean-square (rms) deﬂection in a layer x of a medium is given by rms =

13.6 MeV x ·z· 2 = · 1 + 0.038 · ln(x/X0 ) , β ·c·p X0

(1.34)

with the parameters deﬁned above, x the depth of the traversed medium, and x/X0 the thickness of the scattering medium in units of the radiation length. The value of rms may be determined by a ﬁt to a Moli`ere distribution [19, 99] for single charged particles with β = 1 for all Z, and is accurate to 11% or better for 10−3 < x/X0 < 100. The value of X0 is determined by the formula (1.35) with Z and A the charge and the atomic mass of the absorber or target medium, respectively, and α the ﬁne structure constant α = e2 /4 · π · ε0 · · c = 1/137.566 as given in Ref. [19]: X0 =

4 · α · NA ·

Z2

A g/cm2 . 2 −1/3 · re · ln(183 · Z )

(1.35)

Equation (1.34) is an approximation and is written for practical purposes using particles with z = 1 in the following form: rms =

13.6 MeV x · 2 = . β ·c·p X0

(1.36)

Coulomb scattering is important in practice because it limits the precision with which the direction of charged particles in particle beam interactions with thick targets in spallation applications can be determined. 1.3.6.3 Bremsstrahlung In addition to the ionization loss high-energy charged particles lose energy in interactions with the Coulomb ﬁeld of the nuclei of the medium. If charged particles are de-accelerated in the Coulomb ﬁeld, one part of the particle’s kinetic energy will be emitted as photons called bremsstrahlung. The energy loss due to bremsstrahlung is determined (see [96]):

−

Z2 2 dE = 4 · α · NA · ·z · dx A

1 e2 4πε0 mc2

2

· E · ln

183 Z1/3

,

(1.37)

where Z and A are atomic number and atomic mass of the medium, and z, m, and E are the atomic number, mass, and energy of the incident particle, respectively. The energy loss due to bremsstrahlung for electrons is determined as −

dE Z2 2 183 = 4 · α · NA · · re · E · ln dx A Z1/3

if E me · c2 /α · Z1/3 .

MeV g/cm2

(1.38)

39

40

1 The Spallation Process

Remarkable is the difference compared to the ionization loss of Eq. (1.27). The bremsstrahlung loss is proportional to the energy and inversely proportional to the squared mass of the incident particle, whereas the ionization loss beyond the minimum ionization is proportional to the logarithm of the energy. At the so-called critical energy Ec the average energy loss by bremsstrahlung and by ionization is the same: −

dE dE (Ec )|ionization = − (Ec )|bremsstrahlung . dx dx

(1.39)

The critical energy Ec could be evaluated using Eqs. (1.27) and (1.37). The critical energy Ec is approximately given for media with Z ≥ 13 [19, 85] as Ec =

(500) MeV Z

(1.40)

with Z the atomic number of the target material. The accuracy of approximate forms for Ec of Eq. (1.40) is limited by different media – gases, liquids, and solids –, which have substantial differences in ionization at the relevant energy because of density ﬂuctuation effects [19]. 1.3.6.4 Energy Loss by Direct Pair Production and by Photonuclear Interaction There exist two additional energy loss mechanisms if high-energy charged particles interact with matter. By traversing the Coulomb ﬁeld of the target nucleus highenergy particles may produce electron–positron pairs by virtual photons or the charged particles lose energy by virtual photon exchange undergoing nonelastic collisions. These energy losses are proportional to the incident particle energy. An instructive example is given for muons at 100 GeV incident on iron where the following approximation is valid:

−

dE MeV |pair production = 0.3 dx g/cm2

(1.41)

−

dE MeV |photonuclear = 0.04 dx g/cm2

(1.42)

Details are given in [89] and references therein. 1.3.6.5 Total Energy Loss The total energy loss of charged particles can be determined as the sum of the individual losses as ionization, bremsstrahlung, pair production, and photonuclear interactions:

−

dE dE dE |total = − |ionization − |bremsstrahlung dx dx dx dE dE |photonuclear . − |pair production − dx dx

(1.43)

1.3 Physics of the Spallation Process 1000

-dE/dx [MeV g−1 cm2]

U-total energy loss Fe-total energy loss

100

Fe-energy loss by ionization 10

H-total energy loss

1

Fe-energy loss by pair production

0.1 1

10

102

Fe-energy loss by bremsstrahlung Fe-energy loss by photo nuclear 103

104

105

Muon energy [GeV]

Fig. 1.22 Average energy loss of a muon in hydrogen, iron, and uranium as a function of energy. For iron the different contributions to dE/dx as ionization, bremsstrahlung, pair, and photonuclear production are also shown [19].

At sufﬁciently high energies radiative processes become more important for all charged particles. In Figure 1.22, this is shown for muons of energies from 1 GeV to about 105 GeV incident on hydrogen, iron, and uranium [19, 99]. Note that the energy scale in this ﬁgure is beyond the energy generally discussed in the framework of neutron spallation sources or currently discussed in acceleratordriven applications. 1.3.7 High-Energy Hadronic Cascades and Nuclear Interactions

Nonelastic collisions are important in predicting high-energy hadronic cascades, and it is the interaction mechanism, that is least understood and has the largest physics uncertainties. Some qualitative features of nonelastic hadron–nucleus collisions will be discussed. Elastic hadron–nucleus interactions are characterized by very small energy losses and small angular deﬂections. They can often be neglected in calculating the effects of hadronic cascades in thick targets. But there are several situations in narrow beam sources, accelerator shielding, high-energy physics calorimeters, heat deposition, etc., where elastic scattering effects may be important. The total cross sections, some useful semiempirical expressions, and double differential cross sections will be discussed in Sections 1.3.7.4 and 1.3.7.6. 1.3.7.1 Qualitative Features of Hadron–Nucleus Collisions Some qualitative features of hadron nucleus collisions which often allow signiﬁcant simpliﬁcations in predicting thick target cascades are as follows: • Above about a few 100 MeV, the total elastic and nonelastic cross sections are approximately constant; for an example see Figure 1.23.

41

1 The Spallation Process

Lead

1

Cross section [barn]

42

10−3

10−2

10−1

1

Iron

1

– snonelastic – selastic 10−1 10−3

10−2

10−1

1

Proton energy [GeV] Fig. 1.23 Example of elastic and nonelastic proton nucleus cross sections for Fe and Pb as a function of the incident proton energy of about E > 10−2 GeV calculated by GEANT4 [100].

• For high-energy particles produced in hadron–nucleus collisions, the perpendicular momentum is much smaller than the parallel momentum (i.e., the secondary particle direction is approximately ‘‘straight ahead” relative to the incident particle direction), and the perpendicular momentum component increases slowly with increasing incident particle momentum. • The multiplicity of high-energy particles created increases slowly with increasing kinetic energy E of the incident particle, roughly as ln(E). • The residual excitation energy, and hence, low-energy particle multiplicities, left after the high-energy particle production increases linearly with the energy of the incident particle. Examples of these general characteristics can be found in the literature [101–104] and will be shown and discussed in Part 2 on page 277. 1.3.7.2 Characteristics of Hadron Cascades in Thick Targets The main features of high-energy hadronic cascades generated in matter are demonstrated in Figure 1.24. The generation of a hadronic cascade in a thick target is characterized by an initial increase in particle ﬂux intensity with depth due to

Energy deposited per incident beam energy [(MeV/cm)/(MeV incident)]

1.3 Physics of the Spallation Process

10−1 Ep = 0.250 GeV protons Thick aluminum target 10−2

Ep = 10 GeV protons

10−3

Ee = 1 GeV electrons Ep = 1 GeV protons

10−4

0

40

80

120 160 200 240 280 320 360 400 Range depth [g/cm2]

Fig. 1.24 Energy deposition per unit incident beam energy produced in a semiinﬁnite aluminum target by proton and electron beams (after Armstrong [105]).

secondary particle production, followed by a gradual decline as the average energy of the cascade particles decreases, multiplicities decrease, and a greater fraction of individual particle energies is dissipated by ionization losses. Figure 1.24 shows the depth dependence of the energy deposition produced in a semiinﬁnite aluminum target by 0.250, 1, and 10 GeV proton beams, respectively, and for comparison, a 1 GeV electron beam. At 0.250 GeV the proton range of about 50 g/cm2 is less than the mean free path for nuclear collisions, so most of the protons stop without undergoing collisions, and the energy deposition curve exhibits a so-called Bragg peak. For the 1 and 10 GeV example, nuclear collisions occur before the stopping range is reached, and the deposition curves show the characteristics of well-developed hadronic cascades. 1.3.7.3 Spatial Propagation of Hadron Cascades and Particle Production For incident particle beam energies of about Enucleon ≤ 10 GeV, the most penetrating component in the cascade is usually nucleons-proton and neutron-above a few hundred MeV. High-energy neutrons are particularly important since the protons will be degraded by ionization losses and lower energy neutrons have smaller mean free paths. For depths greater than a few mean free paths, the effective cascade attenuation length approaches a relatively constant value, and e.g., the shape of the neutron spectrum varies weakly with depth. These phenomena are brieﬂy described in the following. • Pion production: For incident particle energies of about Enucleon ≥ 10 GeV, pion production becomes important. The charged pions do not have a major effect on the spatial propagation of the cascade because of their soft production spectrum. However, they may be an important contributor to energy deposition and an important muon source. Neutral pions are usually not a major component for

43

44

1 The Spallation Process

the spatial propagation of the cascade because the radiation length in matter for the electromagnetic cascade initiated by the high-energy photons from π 0 -decay is typically much less than the hadronic cascade attenuation length. However, neutral pions will become important contributors to energy deposition for pion energies Epion ≥ 10 GeV, and will provide the dominant deposition mechanism above 100 GeV in hadron cascades. • Muon production: For incident particle energies of about Enucleon ≥ 10 GeV, muon production becomes important, and, since muons are degraded only by ionization losses at about Emuon ≤ 100 GeV, they become the dominant cascade component at very large depths for energies of about Emuon ≥ 100 GeV. For energies above 10 GeV, muons may be abundant, particularly for cases where (a) the target material is of low density (e.g., air or other gaseous products) where pions predominately decay rather than interact, or (b) in dense materials (e.g., Fe, Pb, etc.) at large depths after the hadronic cascade has diminished. • Kaon production: The kaon production in nuclear collisions is typically about 1/10 of the pion production. Where muons are of interest in applications, the kaons may provide an important background source because they decay faster than pions. 1.3.7.4 Total Cross Sections in Nucleon–Nucleus Collisions As mentioned earlier, the interaction of high- and intermediate-energy protons in matter is of much interest. The fundamental observable is the total reaction cross section, which is deﬁned as the difference between the total cross section and the total elastic cross section:

σreaction = σtotal − σelastic ∼ σtotal-nonelastic .

(1.44)

Various semiempirical expressions and formulas have been derived for the total elastic and total-nonelastic cross sections, and for the mean free path for nonelastic collisions of protons incident on different target nuclei [90, 91, 106, 107]. The semiempirical expressions are usually derived by ﬁtting existing experimental data [87, 108, 109]: σtotal-elastic σtotal-nonelastic λmeanfp

≈ ≈ ∝

6 · A (mb) a · A2/3 (mb) A1/3 ,

(1.45)

where a ≈ 30 (mb) for A = 1, and a ≈ 50 (mb) for A > 1. For neutrons and pions, the nonelastic cross sections are smaller by about 10% and 20%, respectively. The mean free path λmeanfp for nonelastic interactions is not very dependent upon material it is varying only from ∼100 to ∼200 (g/cm2 ) from aluminum to lead or uranium. This is also shown in Table 1.12. The very simple semiempirical formulas for the total-nonelastic cross section of Eq. (1.45) were further reﬁned and tuned by ﬁtting experimental data (see Refs. [91, 107]).

1.3 Physics of the Spallation Process

Nonelastic cross section [mb]

1000 900 800

Iron

700 600 500

Aluminum

400 300

Carbon

200 200 400 600 800 1000 1200 1400 1600 1800 2000 Incident proton energy [MeV] Fig. 1.25 Calculated semiempirical total-nonelastic cross sections for C, Al, and Fe using formula (1.46).

The Letaw formula Letaw et al. [107] have published a formula for proton–nucleus nonelastic cross sections for incident proton energies E > 10 MeV as follows:

σ (E)nonelastic = σhigh-energy · 1 − 0.62 · exp(−E/200) · sin(10.9 · E −0.28) (mb),

with σhigh-energy = 45 · A0.7 · 1 + 0.016 · sin(5.3 − 2.63 · ln A) (mb), (1.46) where E is the energy of the incident proton in (MeV) and A is the atomic mass of the target nucleus. Two examples of calculations using the formula (1.46) are shown in Figures (1.25) and (1.26), respectively, for C, Al, Fe, W, Hg, Pb, and U. At energies below 2 GeV the total-nonelastic cross section is not independent of energy. In general, the cross section sharply increases to a maximum at about 20 MeV and then decreases to a minimum at 200 MeV. Letaw et al. [107] have evaluated the uncertainties in the energy-dependent formula (1.46) comparing the results with experimental data and discussed the reasons of further reﬁnements of the formula (1.46). The estimated maximum uncertainty for different energy ranges is listed in Table 1.14. The Wellish formula Wellisch and Axen [91] have also speciﬁed a general formula for the total-nonelastic cross section named here as total reaction cross section for the energy range of protons from 6.8 MeV to 10 GeV for all target materials with Z > 5. This evaluation is based mainly on Ref. [90]. This formula as given by Eq. (1.47) is used as a basis for the hadronic package GEANT4 [100]. For the most important isotopes in accelerator-driven technologies (ADT) such as iron, tungsten, and lead, Prael and Chadwick evaluated the total-nonelastic cross section for neutrons and protons up to incident energies of 2 GeV [110–112]. These cross-section evaluations are applied in the LAHET code [113] and validate also the

45

1 The Spallation Process 2600

2400 Nonelastic cross section [mb]

46

2200 Uranium 2000 Lead 1800

Mercury Tungsten

1600

1400 200

400

600

800 1000 1200 1400 Incident proton energy [MeV]

1600

1800

2000

Fig. 1.26 Calculated semiempirical total-nonelastic cross sections for W, Hg, Pb, and U using formula (1.46). Tab. 1.14

Errors in the energy-dependent formula (1.46).a

Energy range

Estimated maximum error (%)

E > 1 GeV 300 MeV < E ≤ 1 GeV 100 MeV < E ≤ 300 MeV 40 MeV < E ≤ 100 MeV 10 MeV < E ≤ 40 MeV a

2 5 10 20 ∼ a factor of 2

Mean errors are about 0.5 times the maximum errors

semiempirical formula of [91]. σtotal-nonelastic ∼ σreaction = fcorr · π · r02 · ln N · [1 + A1/3 − b0 (1 − A−1/3 ), (1.47) with N the number of neutrons in the target, A the atomic mass, and b0 and r0 deﬁned as published in [90]: b0

=

2.247 − 0.915 · (1 + A1/3 ),

r0

=

1.36 fm = 1.36 × 10−13 cm,

fcorr

=

1+0.15·exp(−Ekin ) . 1+0.0007·A

(1.48)

1.3 Physics of the Spallation Process

Uranium

Tungsten

1

1

10−3

10−2

10−1

1

10−3

10−2

Cross section [barn]

Lead

1

Mercury

1

10−3

10−1

1

10−2

10−1

1

10−3

10−2

10−1

1

Aluminum

Iron 1 1 − snonelastic

− snonelastic − selastic

10−1

− selastic 10−1 10−3

10−2

10−1

1

10−3

Proton energy [GeV]

10−2

10−1

1

Proton energy [GeV]

Fig. 1.27 Representative examples of total-elastic and totalnonelastic proton nucleus cross sections for Al, Fe, W, Hg, Pb, and U as a function of the incident proton energy in the MeV–GeV range calculated by GEANT4 [100].

In Figure 1.27 examples of total-elastic and total-nonelastic cross sections as determined by GEANT4 for Al, Fe, W, Hg, Pb, and U target materials of relevance for spallation reaction applications are depicted. A very useful source of evaluated experimental values as total cross sections, elastic cross sections, and nonelastic cross sections of interaction of neutrons and protons for many different target materials from deuterium to uranium nuclei is given in Refs. [87, 108, 109]. Only published data have been included. There are clearly gaps in energy and in target material in the data. Representative examples of the data are shown in Figures 1.28, 1.29, 1.30. The uncertainty of the measured data is mostly about 1σ = ±10% at incident proton energies E ≥ 200 MeV and is within the size of the plotted symbols. Measurements of the total reaction cross section in connection with the development of high power spallation sources were recently

47

1 The Spallation Process

Total cross section [mb]

104

103

- U - 238 - Pb - 207.8 - Fe - 55.9 - Al - 27 - C - 12

102 102

103 Incident proton energy [MeV]

104

Fig. 1.28 Examples of experimental values – uncertainty about 1σ = ±10% – of proton-induced total cross sections from [108, 109].

Total nonelastic cross section [mb]

48

103 9 ×102 8 ×102 7 ×102 6 ×102 5 ×102 4 ×102 3 ×102 2 ×102 Fe - 55.8 Al - 27 C - 12 102 100

101 103 102 Incident proton energy [MeV]

104

Fig. 1.29 Examples of experimental values – uncertainty about 1σ = ±10% – of proton-induced total-nonelastic cross sections of C, Al, and Fe from [108, 109].

reported in [114, 115]. These measurements give similar results as summarized in [87, 108, 109] (Table 1.15). As an example, the elastic scattering cross sections for protons are shown for the materials C, Al, Fe, and Pb in Figure 1.31 evaluated from Cloth et al. [88] (cf. elastic scattering of neutrons and protons in Chapter 4, Section 4.5).

1.3 Physics of the Spallation Process

Total nonelastic cross section [mb]

104

103

102

U - 238 Pb - 207.8 Ta - 180.9

101 100

101 103 102 Incident proton energy [MeV]

104

Fig. 1.30 Examples of experimental values – uncertainty about 1σ = ±10% – of proton-induced total-nonelastic cross sections of Ta, Pb, and U from [108, 109]. Tab. 1.15 Comparison of measured and theoretical evaluated nonelastic cross sections at an incident proton energy of E = 1.2 GeV.

References

Barashenkov [108] Enke et al. [114] Letourneau et al. [115] Letawa et al. [107] Wilsonb et al. [116] Cugnon model INCL 4.3 [117]

a b

Target element

Total reaction cross section/ Total nonelastic cross section (mb) ± 1σ (mb)

Pb U Pb U Pb U Pb U Pb Pb U

1713 ± 103 1975 ± 119 1780 ± 125 1730 ± 121 1650 ± 30 − 1850 ± 16 2090 ± 45 1693 ± 150 1801 ± 16 2013 ± 45

Semiempirical formula. Calculations by means of a high-energy heavy-ion model.

1.3.7.5 Total Reaction Cross Sections in Nucleus–Nucleus Reactions The transportation of light and heavy ions in matter is of much interest in science. The total reaction cross sections have been studied both experimentally and theoretically. Several empirical parameterizations as derived for nucleus–nucleus

49

1 The Spallation Process

104 Total nonelastic cross section [mb]

50

103

102

Pb - 208 Fe - 56 Al - 27 C - 12

101 101

103 102 104 Incident proton energy [MeV]

105

Fig. 1.31 Examples of proton-induced total elastic cross sections – uncertainty about 1σ = ±10% – for C, Al, Fe, and Pb evaluated in [88, 116] in the energy range from 0.1 to 22.5 GeV.

collisions (cf. Section 1.3.7.4) are given in the references by Sihver et al. [90], Kox et al. [118], and Tripathi et al. [119–121] and the citations therein. As given in Section 1.3.7.4, the total reaction cross section σ (N, N)R is deﬁned as σ (N, N)R = σtotal − σelastic

(1.49)

with σtotal the total cross section and σelastic the elastic cross section. The Sihver formula The formula of Sihver et al. [90] is in its simplest form similar to Eq. (1.46), the formula of Letaw et al. [107]:

2 1/3 1/3 −1/3 −1/3 , σ (N, N)R = π · r02 Aprojectile + Atarget − b0 Aprojectile + Atarget

(1.50)

where Aprojectile and Atarget are the atomic mass numbers of the projectile and the target nuclei, respectively, r0 = 1.36 fm and b0 is given by

−1/3 −1/3 b0 = 1.581 − 0.876 Aprojectile + Atarget . 1/3

(1.51) 1/3

The formula consists of a geometrical term (Aprojectile + Atarget ) and a transparency parameter b0 for the nucleons in the nucleus. It is assumed that the cross section is independent of incident energies ≥ 100 MeV/nucleon. The formula gives a good agreement with experimental data for most of the collision systems, which have been studied (see Ref. [90]). In the case of nucleon–nucleus interactions, formula (1.50) is almost identical for proton–nucleus (with Ztarget ≤ 26) if Aprojectile = 1 is a proton and the parameter b0

1.3 Physics of the Spallation Process −1/3

is expressed as a polynomial function of the ﬁrst order in (1 + Atarget ). The formula then becomes 1/3 −1/3 2 σ (p, N)R = π · r02 1 + Atarget − b0 [1 + Atarget ]

−1/3 (1.52) b0 = 2.247 − 0.915 1 + Atarget for incident proton energies Eproton ≥ 200 MeV and r0 = 1.36 fm. The Kox formula The Kox formula in Ref. [118] is based on the strong absorption model to describe low-energy nuclear reactions. The formula is based on the analysis of total reaction cross sections for heavy ion collisions in the intermediate-energy range of about 10–300 MeV/nucleon. The formula determines the total reaction cross section σ (N, N)R in terms of the interaction radius IR, the nucleus–nucleus interaction barrier BC , and the center-of-mass energy Ec.m. of the colliding system. In this framework it is considered that a reaction occurs whenever a substantial contact occurs between nuclear matter. The formula is given in its general form as

σ (N, N)R = π(IR)2 [1 − BC /Ec.m. ].

(1.53)

The parameter BC is the Coulomb barrier of the projectile–target system. It is given by

1/3 1/3 BC = Zprojectile · Ztarget · e2 / rC (Aprojectile + Atarget ) , (1.54) where rC = 1.3 fm, e is the electron charge, Zprojectile and Ztarget are the atomic numbers of the projectile and the target nuclei, and Aprojectile and Atarget are the atomic masses of the projectile and the target nuclei, respectively. The interaction radius IR is divided in the Kox formula into volume and surface terms, Rvol and Rsurf : IR = Rvol + Rsurf .

(1.55)

The terms Rvol and Rsurf correspond to energy-independent and energy-dependent components of the reactions, respectively. Collisions with smaller impact parameters are independent of energy and mass number and are characterized as a volume component of the interaction radius and therefore depends only on the volume of the projectile and the target nuclei. It is given by 1/3

1/3

Rvol = r0 (Aprojectile + Atarget ).

(1.56)

The second term of the interaction radius IR in Eq. (1.55) is a nuclear surface contribution and is parameterized by   1/3 1/3 Aprojectile · Atarget Rsurf = r0 a · 1/3 − c + D. (1.57) 1/3 Aprojectile + Atarget

51

52

1 The Spallation Process

The ﬁrst term in the brackets is the mass asymmetry term, which is related to the volume overlap of the projectile and the target. The second term c is an energydependent parameter, which takes into account the increasing surface transparency as the projectile energy increases. The parameter D is the neutron excess which is important in collisions with heavy or neutron-rich targets. It is given by D=

5(Atarget · Ztarget )Zprojectile . Aprojectile · Atarget

(1.58)

The parameters r0 = 1.1 fm and a = 1.85 are ﬁxed values where the parameter c is a function of the beam energy per nucleon which is a simple analytical function derived from Ref. [118] and used in GEANT4 [100] to 10 c = − 5 + 2.0 x

10 x 3 c = − 5 + 2.0 · 1.5 1.5 x = log(Ekin ),

for x ≥ 1.5, for x < 1.5, (1.59)

where Ekin is the kinetic projectile energy in units MeV/nucleon in the laboratory system. The Tripathi formula For nucleon–nucleon and nucleus–nucleus interactions Triphati et al. [119–121] have proposed alternative algorithms for calculating the interaction cross sections. The formula is a simple universal parameterization of the total reaction cross section for any system of colliding nuclei valid for the entire energy range from a few A MeV to a few A GeV. This approach treats the proton–nucleus collision as a special case of the nucleus–nucleus collision, where the projectile has charge and mass number 1. Parameters to treat the Coulomb interaction at lower energies and modiﬁcations of the reaction cross section at higher energies due to the Pauli blocking are also taken into account:

2 1/3 1/3 σ (N, N)R = πr02 · Aprojectile + Atarget + δE · 1 −

B Ec.m.

,

(1.60)

where r0 = 1.1 fm. In formula (1.60) the parameter B, the energy-dependent Coulomb barrier, and R are given by B = 1.44 ·

Zprojectile · Ztarget , R

R = rprojectile + rtarget +

1/3

1/3

1.2 · Aprojectile + Atarget 1/3

Ec.m.

(1.61)

,

(1.62)

where ri is the equivalent sphere radius and is related to the rrms,i radius by ri = 1.29 · rrms,i with i = projectile, target), and Ec.m. , the center of mass energy, is given in MeV.

1.3 Physics of the Spallation Process

There is an energy dependence of the reaction cross section at intermediate and higher energies mainly due to two effects, the transparency and the Pauli blocking [119]. This is represented by the energy-dependent term δE in formula (1.60) given as δE = 1.85 · S1 + 0.16 1/3

S1 = S2 =

S1 1/3

Ec.m.

− CE + 0.91 · S2

1/3

Aprojectile · Atarget 1/3

1/3

Aprojectile + Atarget (Atarget − 2Ztarget )Zprojectile , Aprojectile · Atarget

(1.63)

where S1 is the mass asymmetry term and is related to the volume overlap of the collision system and the term S2 in the formula is related to the isotope dependence of the reaction cross section. The term CE in formula (1.63) is related to the transparency and the Pauli blocking and is given by E E CE = DPauli · 1 − exp − − 0, 292 · exp − · cos 0.229 · E 0.453 . 40 792 (1.64) The parameter DPauli in formula (1.64) takes into account the density dependence of the colliding system, scaled with respect to the density of the (12 C +12 C) colliding system. DPauli = 1.75 · (ρAprojectile + ρAtarget )/(ρAC + ρAC ),

(1.65)

where the density of a nucleus using the hard sphere model [122] with a given nucleus of mass number Ai is given by ρAi = Ai /

3 π · ri3 , 4

(1.66)

where the radius of the nucleus ri is deﬁned above with the root-mean-square radius, (ri )rms , obtained directly from experimental data [123]. With the parameter DPauli simulates the modiﬁcations of the reaction cross section caused by the Pauli blocking which was introduced by Tripathi et al. [119] in the parameterization formula for the ﬁrst time. At lower energies where the overlap of interacting nuclei is small and Coulomb interaction modiﬁes the cross sections signiﬁcantly, the inﬂuence of the Pauli blocking is small. The modiﬁcation of the reaction cross section due to Pauli blocking plays an important role at energies above 100 Mev/nucleon in nucleus–nucleus collisions which lead to higher densities. For proton–nucleus collisions where the compression effect is low, a single constant value DPauli = 2.05 gives good results for all proton–nucleus collisions [119].

53

1 The Spallation Process 2500

1000 800 600 400 200 0 (a)

p+

27

p + 13 Al sabsorption [mb]

sabsorption [mb]

54

2000 1500 1000 500 0

1

10

100

1000

Proton energy [MeV]

208 82 Pb

1

(b)

10

100

1000

Proton energy [MeV]

Fig. 1.32 Absorption cross section for proton–aluminum collisions (a) and proton–lead collisions (b) as a function of the incident proton energy. The experimental data points are from de Vries et al. [123]. The solid lines are the results of calculations given in Ref. [120] (after Tripathi et al. [120]).

For alpha–nucleus and lithium–nucleus collisions, where there is also little compression, the following terms for the DPauli parameter are useful: DPauli (α) = 2.77 − (8.0 × 10−3 · Atarget ) + (1.8 × 10−5 · A2target ) − 0.8/[1 + exp[(250 − E)/75]] DPauli (lithium) = DPauli /3

(see Eq. (1.65)).

(1.67)

Figure 1.32 shows as an example the results of calculations for the reaction cross sections for protons on Al and Pb targets of Ref. [120]. The experimental data have been taken from the compilation of Ref. [123]. The Tripathi formalism gives a very good agreement with the experimental data also for other collision systems for the entire energy range1) . 1.3.7.6 Differential Cross Sections As mentioned earlier, the cross section is an extremely important concept in describing the interaction of particles with matter. By deﬁnition the angular differential cross section dσ/d is the derivative of σ to the solid angle and is proportional to the probability of a reaction of an incident particle with a nucleus by emitting a secondary particle into a cone d. The differential cross section has the dimension barns/steradian (b/sr). Note the condition (dσ/d)d = σ , which makes it clear why dσ/d is called the angular differential cross section. Another condition is to consider the incident particle to have a certain energy E and particles after interaction to have energy in an interval dE about E . This deﬁnes in a similar way as above an energy dependent differential cross section, dσ/dE , which is a measure of the probability that an incident particle with incident energy E will have as a result of the interaction an outgoing energy E . Both dσ/d and dσ/dE are distribution functions; the former is a distribution in the variable , the solid angle, whereas the latter is a distribution in E , the energy after scattering. Their dimensions are barns per steradian and barns per unit energy, respectively. 1) See comment in Section 2.5.1 on page 115.

1.3 Physics of the Spallation Process

Combining the two extensions above from the cross sections to differential cross sections, it follows a further extension to the so-called double differential cross section: d2 σ/d dE(b sr−1 MeV−1 ),

(1.68)

which is a quantity that has been extensively studied in particle scattering. This cross section contains the most fundamental information about the structure and dynamics of particle–nucleus or particle–matter interactions and collisions. Measurements of double differential production cross sections provide a very sensitive observable for the validity of the spallation physics models. In the past systematic studies and measurements were investigated as part of the development of intense spallation neutron sources, for a new generation of meson factories, and for the theoretical understanding of medium energy physics in the energy range up to several GeV [124–132]. For ADS (accelerator-driven systems) projects [133] in references on the interaction of protons and neutrons mainly for lead targets are summarized. The experiments are discussed in Part 2 on page 277. There is still interest in medium-energy particle reaction data as double differential secondary production cross sections of charged particles, neutrons, pions, radioactive isotopes, etc., mainly for incident particles above 100 MeV. Some examples of semiempirical systematics on neutron spectra measurements [129, 130] from high-energy proton bombardment by 318, 590, and 800 MeV protons on eight targets in the mass range A = 12 to 238 were considered by Pearlstein [134] to illustrate the general characteristics of the neutron emission spectra. In Figures 1.33 and 1.34, two examples of measurements of double differential neutron production cross sections at the Los Alamos WNR facility by Amian et al. [129, 130] (in angles 30◦ , 60◦ , 120◦ , and 150◦ ) by 800 MeV protons on targets of Fe and Pb are shown. More details of these experiments are given in Part 2. The cross-section curves are seen to be very much alike, showing a broad maximum at ∼2–3 MeV, followed by a rapid fall of about above ∼20 MeV. The two different main components in the spectra are attributed to evaporation neutrons dominating the range below ∼20 MeV, and the cascade neutrons governing the shape above ∼20 MeV. The double differential cross sections are increasing with increasing target mass over the entire energy range and for all neutron emission angles. It can be seen from these examples that the cross sections below about 20 MeV for all angles widely coincide, indicating an almost isotropic neutron emission. In contrast to the evaporation region, the neutron production cross sections in the cascade region are strongly angular dependent, and forward peaking is evident. While the cross sections around 20 MeV are still of about the same order for all angles, the cascade component tails off rapidly, increasing with increasing emission angle. The general features of the angular dependent cross sections – their anisotropy – are qualitatively very similar for most of the target masses. The total uncertainties of the experimental results presented here are determined by ±1σ = 10–15% and thus are of the order of the data point sizes. The aboveshown experimental results are based on the so-called time-of-ﬂight method (TOF), which will be described in more detail in Part 2 on page 289.

55

1 The Spallation Process

d2s /dΩdE cross section [b sr−1 MeV−1]

100 10−1 10−2 10−3 Fe Ep = 800 MeV - 30°

10−4

Fe Ep = 800 MeV - 60°

10−5

Fe Ep = 800 MeV - 120°

10−6

Fe Ep = 800 MeV - 150°

10−7 10−8 10−1

100

101 102 Neutron energy [MeV]

103

Fig. 1.33 Examples of proton (800 MeV) + Fe-induced experimental double differential neutron production cross sections at 30◦ , 60◦ , 120◦ , and 150◦ – measurements of Amian et al. [129, 130].

100 d2s / dΩdE cross section [b sr−1 MeV−1]

56

10−1 10−2 10−3 Pb Ep = 800 MeV - 30°

10−4

Pb Ep = 800 MeV - 60°

10−5

Pb Ep = 800 MeV - 120°

10−6

Pb Ep = 800 MeV - 150°

10−7 10−8 10−1

100

101 102 Neutron energy [MeV]

103

Fig. 1.34 Examples of proton (800 MeV) + Pb-induced experimental double differential neutron production cross sections at 30◦ , 60◦ , 120◦ , and 150◦ – measurements of Amian et al. [129, 130].

Although the neutron production channel in spallation collisions is the dominant one, other secondary particle production channels as the production of secondary protons, pions, or light charged, intermediate mass fragments (IMFs), and heavy residuals (cf. Figure 1.12 on page 19) are at least also important in model predictions and applications (cf. Part 2 on page 277 and Part 3 on page 495).

1.3 Physics of the Spallation Process

1.3.8 Hadronic–Electromagnetic Cascade Coupling

It should be noted that often both hadronic and electromagnetic cascades are important in the same problem whether the source is hadrons – protons or neutrons – or photons, electrons, and positrons. These processes are mainly a function of secondary particle production and their decay during the propagation of an intra- or internuclear-cascade in the target nucleus or in a so-called thick target, respectively. The ‘‘coupling’’ of hadronic and electromagnetic cascades may occur in the following way. The process may be initiated for example by either hadrons or leptons as incident particles on a target nucleus or a thick target: starting with hadrons, e.g., protons or neutrons: proton/neutron

+

nucleus/target −→

π 0 −→ 2 · γ

−→

π ± −→ µ± −→ e±

−→

k0 , k± −→ µ± , π ± , π 0 −→ e± , γ (1.69)

starting with leptons, e.g., electrons or positrons: electron

+

nucleus/target −→

γ , e± +

γ , e+ , e−

nucleus/target −→

hadron–meson cascade

(1.70)

The decay scheme and the particle properties have already been discussed in Section 1.2 in Eqs. (1.1) and in Table 1.1. A substantial fraction of the energy deposited in a hadron cascade is a direct result of electromagnetic cascades produced by the decay of neutral pions π 0 (mean life ∼ 10−16 s) into two photons, by low-energy photons produced during the intra- and internuclear evaporation process or by the decay of charged pions and muons. There is a large class of hadron cascade applications and issues which require the handling of electromagnetic cascades, their shower propagation, their energy deposition, and the production of hadrons and other secondary particles. The principal production processes during the development of electromagnetic showers (bremsstrahlung by production of electrons and positrons, pair production for photons) are well described by quantum electro dynamics (QED) theory. It should be mentioned that at higher incident hadron energies the hadron production rate, e.g., for protons and neutrons, deviates from the linear rule due to the increase of π 0 production and the subsequent 2γ decay into the electromagnetic channel the so-called electromagnetic drain of the hadron cascade. As mentioned above, the mean half-life of π 0 is with ∼10−16 s very short; therefore, this fast

57

1 The Spallation Process

decay does not allow π 0 to take part in the internuclear cascade whereas the π ± do. The π ± decay time of 26 × 10−9 s is sufﬁciently long to allow further hadronic interactions once the π ± are created. At higher incident energies above 10 GeV, other meson production channels will be opened which in addition deplete the cascade of energy. Applications where such showers are observed are e.g., high-intensity spallation sources, high-energy physics calorimeters, shielding of accelerators, or the impact of space radiation on space vehicles. Details are given in Part 3 on page 495. Besides the general way of spallation reactions induced by high-energy protons, hadron production, mainly neutrons, will also take place in target materials by electrons or bremsstrahlung photons. It should be noted that it is the photon interacting with the target material that releases the hadrons, rather than the direct interaction of the electrons. Several types of photonuclear interactions result in hadron production such as the so-called giant resonance production with photons of energy Eγ ≈ 10–30 MeV, photodisintegration with photons of energy Eγ ≈ 50–100 MeV, and photopion absorption with photons of Eγ about ≥ 140 MeV. Figure 1.35 shows for small incident photon energies the giant-resonance peaks for Cu and Pb and above the pion production threshold of about 200 MeV the photo–pion production cross section as the average of proton and neutron. Above 140 MeV, the cross section for photons on nuclei rises again, opening the channels for photopion production. The cross section is characterized by a number of resonance peaks below and above of about 1 GeV which are caused by nucleon isobar formation (see Section 1.3.5.3). Between these two energies, e.g., 10 and 101 Production cross section per nucleon [mb/nucleon]

58

Giant resonance s(g, n)

Pb Total neutrons

100

Cu Ta 10−1

s (g, p) (Z = 13 - 47) Pb

s QD(L = 5) Cu

10−2

101

103 102 Incident photon energy [MeV]

Fig. 1.35 A qualitative picture of the photoneutron production mechanism given as the cross section per target nucleon as a function of the incident photon energy (after Swanson [135]).

104

1.3 Physics of the Spallation Process

100 MeV, the behavior for medium Z-targets is shown as hachures [136], and a calculation for Ta [137] based on a intranuclear cascade model. Also shown for this energy region is the photoneutron cross section derived from a simple quasideuteron model, assuming N = Z = A/2, L = 5, where A, Z are for the target nucleus, and L is a dimensionless coefﬁcient (Eq. (1.71)). The quasideuteron effect above the giant resonance is the remaining dominant neutron production mechanism in which the photon interacts initially with a neutron–proton pair within the nucleus, rather than with the nucleus as a whole, hence the name quasideuteron. As Figure 1.35 shows, this cross section is an order of magnitude below the giant-resonance peak. The cross section is related to the deuteron photodisintegration cross section σD (E), qualitatively given by [138] σQD (E) L ·

NZ · σD (E), A

(1.71)

where N, A, and Z refer to the target nucleus, and L (between 3 and 13) is a dimensionless coefﬁcient as a measure of the probability that a neutron–proton pair is within a suitable interaction distance relative to the deuteron [139]. The overall effect is to add a tail of higher energy neutrons to the giant-resonance spectrum. Electrons and positrons lose their energy by ionization as charged particles do. However, because of their small mass, they have signiﬁcant losses also due to the production of radiation. For lead, the fractional energy loss due to bremsstrahlung exceeds that due to ionization for electron energies above 10 MeV, which is shown in Figure 1.36. Other signiﬁcant energy loss mechanisms are elastic scattering described by the Bhabha differential cross section for electrons and the Møller formula for positrons, and positron annihilation. The dominant energy losses for high-energy electrons are bremsstrahlung and pair production which lead to the production of electromagnetic radiation or electromagnetic showers by the motion of electrons and positrons through matter. The well-known physical processes are described in detail standard textbooks such as, e.g., in Ref. [140]. Electrons and positrons have similar electromagnetic interactions in matter. Figure 1.36 shows the fractional energy loss per radiation length in Pb as a function of electron or positron energy. Electron and positron scattering is considered as ionization when the energy loss per collision is below 2.55 MeV, and as Møller or Bhabha scattering when it is above. At low energies electrons and positrons lose energy essentially by ionization, although other processes (Møller and Bhabha scattering, electron annihilation) contribute as shown in Figure 1.36. The ionization losses decrease exponentially with energy, bremsstrahlung losses rise nearly linearly (the fractional loss is nearly independent of energy), and dominates above a few tens of MeV in most materials. The radiation length X0 , usually measured in (g/cm2 ), has been calculated by Tsai [141] and is provided by an approximation formula in Ref. [19]. X0 =

716.4 · A g cm−2 , √ Z · (Z + 1) · ln(287/ Z)

(1.72)

59

1 The Spallation Process

Positrons

0.20 Lead Z=82

Electrons

0.15

1.0 Bremsstrahlung

Ionization

0.10

[cm2 g−1]

−1

−1/E dE/dx [X0 ]

60

M ller (e−)

0.5

Bhabha (e+)

0.05

Positron annihilation

0

1

10 100 Particle energy [MeV]

1000

Fig. 1.36 Fractional energy loss per radiation length X0 in lead as a function of electron or positron energy (after Yao et al. [19]). Tab. 1.16 Calculated radiation lengths X0 of Be to U using Eq. (1.72).

Medium

Z

A

Radiation length (g cm−2 )

Be C Al Fe Cu Ta W Au Hg Pb U

4 6 13 26 29 73 74 79 80 82 92

9.01 12.01 26.98 55.85 63.55 180.95 183.84 196.97 200.59 207.2 238.03

65.19 42.70 24.01 13.84 12.86 6.83 6.76 6.42 6.39 6.31 6.00

where A and Z for the target material. In Table 1.16 calculated radiation lengths X0 are given for some materials using Eq. (1.72). It should be mentioned that the basic features of the energy loss already discussed for heavy particles in Section 1.3.6 are also valid for electrons and positrons, but the Bethe–Bloch formula (1.27) must be modiﬁed for several reasons: Electrons and positrons have a relatively small mass compared to heavy charged particles, at small incident energies the total energy loss is also determined by bremsstrahlung losses, and for electrons and positrons the collisions take place between identical particles, which lead to a indistinguishability. Also positron annihilation must be taken into

1.3 Physics of the Spallation Process

account (e+ + e− → γ + γ ). A modiﬁed Bethe–Bloch formula for (e+ + e− ) can for example be found in Ref. [140] As already discussed during the 1980s in Ref. [142], high power target systems of spallation sources or high-intensity proton accelerators are at the same time a source of charged pions and muons which decay into neutrinos ν and antineutrinos ν. Thus, such facilities can also provide a source for neutrino research in a so-called neutrino factory. There are currently two kinds of intense neutrino of factories discussed. 1 The neutrino production mechanism from pions and muons: The mesons π ± decay via the weak interaction with an average lifetime of about τ = 2.55 × 10−8 s in leptons:

π + −→ µ+ + νµ or π

+

π

−

−→ e+ + νe

branching ratio = 99.9877%

branching ratio = 1.2 × 10−4 %

and −→ µ− + ν µ

or π − −→ e− + ν e .

(1.73)

Muons µ± have an average lifetime of about τ = 2.2 × 10−6 s and decay via the following scheme: µ− −→ e− + ν e + νµ and µ+ −→ e+ + νe + ν µ

branching ratio ≈ 100% .

(1.74)

2 The decay of stored β-active emitters instead to produce neutrinos via the decay of pions and muons: The neutrino production with such emitters as 62 He and 18 10 Ne is as follows: 6 2 He

−→ 63 Li + e− + ν e , with a half-life and

18 10 Ne

+ −→ 18 9 F + e + νe , with a half-life

T1/2 = 0.8 s

T1/2 = 1.7 s .

(1.75)

The physics applications of the neutrino research are primarily neutrino oscillation physics and CP violation studies, but also measurements of cross sections of neutrino nucleus interactions. An example of a spallation neutron source for neutrino research is the KARMEN experiment at the Rutherford Laboratory (The KArlsruhe Rutherford Medium Energy Neutrino Experiment) [143]. Other projects on neutrino factories can be found in Refs. [144, 145] and references therein. Experiments at existing spallation sources and the production of different parent ions for neutrino beams will be discussed in Part 3 on pages 585 and 638.

61

63

2 The Intranuclear Cascade Models 2.1 Introduction

The most important physics uncertainty associated with predicting the interaction of high-energy hadrons with matter lies in determining the multiplicities, energy, and angular distributions of particles produced in nonelastic collisions. Theoretical models, e.g., the inter/intracascade-evaporation model, were developed over the past 30 years, with considerable success. The basic assumption of most methods employed in the models is that the interactions of high-energy particles with the nucleus can be represented by free particle–particle collisions inside the nucleus, an approach, as already mentioned on page 3, ﬁrst suggested by Serber [2]. The important justiﬁcation for this assumption is that the wavelength of the incident particle is of the order of the internucleon distance ∼10−13 cm. Details were given in the previous section and in Refs. [64–66]. Goldberger [3] was the ﬁrst to perform calculations using Serbers’s model approach. The physical process, approximately described by free particle collisions within the nucleus is called the cascade. The class of models are named as intranuclear-cascade (INC) models. The cascade process is usually followed by subsequent physical processes given in terms of evaporation, pre-equilibrium, ﬁssion or de-excitation processes in photons, etc., which will be described in Chapter 3 on page 135. To evaluate the physical observable in phase space the models are well suited to a statistical approach using Monte Carlo techniques and kinematics of high-energy particles [146–150]. There are several methods for generating nonelastic hadronic events in hadron nucleus interactions evaluating and calculating hadron cascades. • Sampling from exclusive cross sections – the exclusive approach: the hadron–nucleus interactions are treated as a series of nucleon–nucleon interactions. The most complete models in the energy from 0.1 GeV to about 5 GeV are the INC models. References of the different existing models are references of the BERTINI model are [3–7, 12, 76, 77, 103, 151–158], references of the DUBNA models are [10, 13, 78, 101, 159, 160], references of the ISABEL model are [11, 79, 161–167], references of the INCL model are [117, 168–172], references of the CEM model are [41, 173–175], and references concerning the H¨anssgen–Ranft model are [176–178]. The ﬁrst model sampling from exclusive cross sections was the model from Sternheimer [76], which was used by Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

64

2 The Intranuclear Cascade Models

Bertini [77, 153] for INC calculations. This early model of Bertini has been restricted so far to incoming and produced pions and nucleons only, and it is, besides the early investigations of Goldberger [3] and Metropolis et al. [4, 5], the precursor of all modern models. All the INCs models consider energy–momentum conservation and correlation in hadron cascades. • Sampling from single-particle inclusive cross sections – the inclusive approach: the hadron nucleus interactions are treated by means of some model representations, experimental data, and semiempirical single inclusive particle distributions. Such models work best at higher energies where the inclusive particle production cross sections are well understood. But they are unreliable at energies below a few GeV. A summary of the methodology of this approach is given by Ranft in [106, 179, 180] • Sampling from phase space: such models are often used for sampling well-deﬁned exclusive channels and simulating experiments using phase space kinematics. Monte Carlo methods are applied to calculate phase space distributions arising from particle interactions according to the Lorentz-invariant phase space [148, 181, 182]. • Other models are the QMD models (Quantum Molecular Dynamic) [183–186] and the BUU models (Boltzmann–Uehling–Uhlenbeck) [187–190]. The QMD and BUU models are mainly used in the ﬁeld of heavy ion collisions. A good overview about the applicability in nucleon interactions is given in Ref. [191] and references therein. The purposes of the following sections are (1) to give an overview of the main features of the existing INC models and codes, and (2) to discuss the differences of the models with their assumptions, their limits and constraints on energy and application regime. In Section 2.2, a very detailed description of the BERTINI model is given. Many ideas of this model were still the base of all the existing INC models. In Sections 2.3, 2.4, and 2.5 the state-of-the-art models, such as INCL, ISABEL, and CEM will be discussed and compared with the features used in the BERTINI model. Section 2.6 summarizes some special INC models mainly based on the previous ones and in the ﬁnal Section 2.7, a short review is given on alternative models for spallation reactions as quantum molecular models (QMD), a quantum extension of the classical molecular dynamics model widely used to analyze various aspects of heavy ion reactions.

2.2 The BERTINI Approach 2.2.1 Features of the BERTINI Nuclear Model

The basic assumptions and representations that have been used in the BERTINI model are summarized in the following. Most of the description may be found

2.2 The BERTINI Approach

in the references of Bertini et al. [12, 77, 154–156] and of Armstrong [105]. Further developments and reﬁnements of the BERTINI model [158], which are not included in the original model, will also be discussed. The description of the BERTINI model here is based on Refs. [12, 105, 154–156]. The BERTINI model has been used successfully in Monte Carlo simulations at intermediate energies. Standard implementations of the model can be found in code systems such as HETC and HERMES [88, 192], LAHET [193], MCNPX [194], CALOR [195], and TIERCE [196], and based on the original ideas of Bertini with advanced physics in FLUKA and GEANT4 [100, 197]. The limitations of the earlier models of Metropolis et al. [4, 5] are mainly in the nuclear models. These are: (a) the use of a uniform density nucleus with a sharp boundary, (b) no pion–nucleon potential was employed, and (c) the neglect of the refraction and reﬂection of cascade nucleons due to a spatial nonuniformity of the nuclear potential [11]. 2.2.2 The Nuclear Model

The target nucleus is modeled as a three-region approximation to the continuously changing density distribution of the matter within the nucleus. The Fermi gas model, one model to describe the behavior of nucleons in a nucleus, is used. A Fermi–Dirac gas obeys Fermi–Dirac statistics, and therefore obeys the Pauli exclusion principle. More details may be seen in Refs. [69, 70, 198]. The cascade process starts when an incident particle – proton, neutron, pion, etc. – hits a nucleon in the target nucleus and produces secondary particles. The life history of each particle is followed until it either escapes from the nucleus or its energy falls below an arbitrary cutoff energy, which, in general, is taken to be half of the Coulomb barrier of the surface of the nucleus. This energy is different for different particle species and can, e.g., be found in Ref. [88]. At this point the energy conversation of the cascade process is veriﬁed. Relativistic kinematics is applied throughout the BERTINI INC model. 2.2.2.1 Nucleon Density Distribution Inside the Nucleus The density distribution of the nucleons (protons and neutrons) is assumed to approximate a nonzero Fermi gas momentum distribution. In the model of BERTINI the nucleus consists of three concentric spheres – a central sphere and two surrounding spherical annuli, each with a uniform density of neutrons and protons. The proton density in each region is made to be proportional to the average value over the same nuclear region of a continuous nonzero Fermi charge distribution function obtained by the approximation of measurements of electron scattering data by Hofstadter [199]. The radial dependence of the charge density in a nucleus can be described by these measurements as

ρ(r) =

ρ0

0 1 + exp( ri −r α )

,

(2.1)

65

2 The Intranuclear Cascade Models

where ρ0 is a normalization constant, ri with i = 1, 2, 3 corresponds to the three zones of the nucleus, r0 = 1.07 · A1/3 × 10−13 cm, α is given by 0.545 × 10−13 cm, and A is the mass number of the nucleus. It is further assumed that neutrons are distributed in the same way as protons, therefore, ρ0 can be calculated by ρ0 =

4π A

·

∞

dr · r 2 · ρ(r).

(2.2)

0

As the model assumes a subdivision of the nucleus in three zones Vi , i = 1, 2, 3, the outer radii ri of the three zones of the nucleus are determined such that the distances are at 90%, 20%, and 10% of the central value of Hofstadter’s [199] continuous distribution. This means that the density decreases with increasing radius:    ρ(r1 ) = 0.90 · ρ0  . ri = ρ(r2 ) = 0.20 · ρ0   ρ(r3 ) = 0.10 · ρ0

(2.3)

In Eq. (2.3) the values for the standard nuclear conﬁguration are given. In cases where these values are all equal, the density distribution corresponds to a uniform density distribution as indicated by the dashed-dotted line in Figures 2.1 and 2.2. 1.0 0.9 Nuclear density r(r) [relative units]

66

0.8

Cu-65

r0

0.7 r1 0.6 0.5 0.4 r2 0.3 0.2 0.1 r3 0.0 0.0

2.0

4.0

6.0

8.0 10.0 12.0

Nuclear radius r [cm × 10−13 ]

Fig. 2.1 Comparison of various nucleon density distributions for nucleons inside the nucleus. Solid lines: the standard three zones’ nonuniform nucleon density conﬁguration; dashed-dotted lines: uniform nucleon density distribution; dashed line: experimental curve of Hofstadter [199].

2.2 The BERTINI Approach 1.0 0.9 Au -197 Nuclear density [relative units]

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

2.0

4.0

6.0

8.0 10.0 12.0

Nuclear radius [cm × 10−13]

Fig. 2.2 Nucleon density distributions within the nucleus when the nuclear radius is assumed to be medium. Solid lines: the three zones’ nonuniform nucleon density distribution; dashed-dotted lines: uniform nucleon density distribution; dashed line: experimental curve of Hofstadter [199].

With the deﬁnition of Eq. (2.3) the nucleon density ρi of the nucleons Ni in zone Vi is calculated by ρi =

4π · Vi

ri

dr · r 2 · ρ(r),

(2.4)

ri−1

with r0 = 0 and Vi the volume of zone Vi of the nucleus. Since proton and neutron densities are assumed to behave like Eq. (2.1) the fraction of the number of protons and neutrons in each of the three zones is the same as for the nucleus as a whole and is constant: pi

=

(ρi /A) · Z

ni

=

(ρi /A) · (A − Z)

or (ni /pi )Vi

=

((A − Z)/Z)nucleus .

(2.5)

Here pi and ni are the zone-dependent proton and neutron densities, A denotes the mass number of the nucleus, Z is the charge number, and A − Z = N is the number of neutrons. The examples of Figures 2.1 and 2.2 give comparisons of typical nucleon density distributions for nucleons inside the nucleus for 65 Cu and 197 Au showing the

67

68

2 The Intranuclear Cascade Models

functional dependence of the nuclear radii ri = r1,2,3 of the density ρi and the difference of Cu and Au. This functional dependence is also depicted in Figures 2.6 and 2.7 on page 72. 2.2.2.2 Momentum Distribution of Nucleons Inside the Nucleus The momentum distribution of the nucleons in the nucleus is assumed to be a mixture of degenerated Fermi gases of protons and neutrons. Considering the nucleus as a collection of free protons and neutrons enclosed in a sphere of radius R or volume V. The protons and neutrons are fermions and thus are two identical particles in different quantum states according to the exclusion principle. The number of states NST corresponding to a momentum smaller than the Fermi momentum PF for protons or for neutrons is given by Segre [198] as

NST =

2 4 · · π · V · PF3 , (2π)3 3

(2.6)

which may be obtained by dividing the phase space into cells of volume (2π)3 and assigning two particles to a cell, to take into account the statistical weight of states of particles of spin = 12 . At a complete degeneracy of the Fermi gas, the Fermi momenta for protons PFp and neutrons PFn for the ground state are given as PFp = (3π 2 )1/3 · · (Z/V)1/3 PFn = (3π 2 )1/3 · · ((A − Z)/V)1/3 .

(2.7)

By the approximation Z = N = A/2 the Fermi momentum is given in a common form [198] as PF = ·

3π 2 · A 2·V

1/3 ,

(2.8)

with V = (4/3) · R3 and R = r0 A1/3 , V being the volume of the nucleus. In the BERTINI model the momentum distribution in each of the three zones Vi , i = 1, 2, 3, of the nucleus follows a Fermi distribution with zero temperature:

PFi (ri )

f (p) dp = Np

or Nn ,

(2.9)

0

where Np and Nn are the number of protons and neutrons, respectively. The above integral is the total number of protons or neutrons in one of the three zones of the nucleus and PFi (ri ) is the radius-dependent momentum of a nucleon corresponding to the radius-dependent Fermi energy (see Eq. (2.11)). In this picture the Fermi momentum PFi (ri ) is given for different zones of the nucleus by PFi (ri ) = ·

3π 2 · ρ(ri ) 2

1/3 .

(2.10)

2.2 The BERTINI Approach

As the target nucleus is a mixture of degenerated Fermi gases of protons and neutrons, the Fermi energy EF is represented by Eq. (2.11) and can be calculated by a local radius-dependent density approximation as EFi (ri ) =

2/3 2 · 3π 2 · ρp,n (ri ) , 2 · mN

(2.11)

where the subscripts p, n stand for the proton and neutron densities, respectively, and i stands for the three zones i = 1, 2, 3, mN is the nucleon mass, = h/2π is the Planck constant (1.054 × 10−34 J s), and ρp,n (ri ) is the density of protons and neutrons deﬁned by Eqs. (2.1), (2.4) and (2.5), respectively. The momentum PFi (ri ) corresponds to the Fermi energy as follows: EFi (ri ) = (PFi (ri ))2 /2 · mN .

(2.12)

In general, the Fermi gas model considers all nucleons to move as elements of a fermion gas within the nuclear volume V given as V 43 · π · r03 · A. Since the Fermi energy is dependent upon the nucleon density and, therefore, different for each type of nucleon in each zone Vi , the composite momentum distribution for the entire nucleus is not a zero-temperature Fermi distribution. As an example, the composite Fermi distribution and a Maxwell–Boltzmann distribution with a kT value of 15 MeV are shown in Figure 2.3. (× 10−14) 12.0

Fraction per unit momentum

10.0

8.0

6.0 Atomic mass A =120

4.0

2.0

0.0 0.0

0.5

1.0

1.5

2.0

2.5 (× 10−14)

Momentum [g cm s−1]

Fig. 2.3 Fermi momentum distribution of nucleons inside the nucleus. Solid lines: distribution from the three zero-temperature Fermi energy distributions; dashed line: Maxwell–Boltzmann distribution with the kT value of 15 MeV (after Bertini [153]).

69

70

2 The Intranuclear Cascade Models

As mentioned earlier and may be seen from Eqs. (2.10), (2.11), and (2.12), the value of the Fermi energy depends rather sensitively on the value of the nuclear radius ri and the assumed density. This requires the use of a radius- and density-dependent nuclear model. 2.2.2.3 Potential Energy Distribution Inside the Nucleus The potential for a nucleon may be written as

V(A, Z, ri ) = EFi (ri ) + B(A, Z) + VC (A, Z),

(2.13)

where EFi (ri ) is the radius-dependent Fermi energy, B(A, Z) is the binding energy of a nucleon, and VC (A, Z) is the Coulomb potential1) . Using expressions (2.11) and (2.12) this results for the proton or neutron potential in zone Vi to the following equation: Vi (A, Z) = EFi (ri ) + B(A, Z) = ()2 · ((3π 2 · ρp,n (ri ))2/3 )/(2mN ) + B(A, Z) = (PFi (ri ))2 /(2mN ) + B(A, Z),

(2.14)

with i = 1, 2, 3. In order to get an idea of the maximum potential well depth Emax in MeV, a simple expression for the Fermi momentum PF is derived using Eqs. (2.7) and (2.8). The proton and neutron momentum may be written as PFproton = /r0 · (9π · Z/4A)1/3 PFneutron = /r0 · (9π · N/4A)1/3 ,

(2.15)

where Z and N are the numbers of protons and neutrons, respectively, and the nuclear volume V is given as V (4/3)π · r03 · A. Based on Eq. (2.15) a simple estimate of the Fermi momenta can be given by considering self-conjugate nuclei [200] with N = Z = A/2, resulting in the following expression: PFproton PFneutron /r0 ·

9π 8

1/3 .

(2.16)

Using the expression · c = 197 (MeV fm) (with = 1.054 × 10−34 (J s) = 6.582 × 10−22 (MeV s), c = 2.9979 × 1010 (cm/s), 1f m = 10−13 (cm)) yields PFproton = PFneutron

297 r0

MeV/c.

1) The Coulomb barrier or potential VC = EC is the energy in the c.m. system, which is needed to overcome the Coulomb repulsion

(2.17) and is given by EC = (Z1 Z2 e2 )/RC , where RC is the Coulomb radius.

2.2 The BERTINI Approach Proton potential

Fermi surface

Binding energy 8 MeV

Fermi sea Nuclear potential depth Fermi energy Emax ~ 42 MeV

EF, proton

Fermi energy ECoulomb EF, neutron ~ 34 MeV

Fig. 2.4 Example of the potential well for protons and neutrons in a nucleus, showing the Fermi energy level of the proton and the neutron, the nucleon binding energy B of the last nucleon, and the maximum potential depth Emax .

The corresponding kinetic Fermi energy F(Emax ) by using a value of r0 = 1.07 fm or 1.07 × 10−13 cm is then estimated as F(Emax ) = (PFproton )2 /(2 · mproton ) = (PFneutron )2 /(2 · mneutron ) 34 MeV. (2.18) This Fermi energy corresponds to the kinetic energy of the highest occupied orbit, e.g., smallest binding energy. By giving a binding energy B = 8 MeV the result of Eq. (2.18) yields a good estimate of the nuclear well depth with Emax = F(Emax ) + B 42 MeV. Figure 2.4 is an example of the potential well for protons and neutrons in a nucleus. The Fermi energy EF of the neutron is here 34 MeV. This is the maximum kinetic energy of a neutron bound in the nucleus. If the binding energy of the most loosely bound nucleon is 8 MeV, the maximum potential energy Emax must then be 42 MeV. Note also the difference between proton and neutron wells due to the Coulomb well. The binding energy of the most loosely bound nucleon is taken to be 8 MeV in the BERTINI model and is assumed to be the same for all the three zones and for all the nuclei. The potential energy in each of the zones of the nucleus is determined by the sum of the zero-temperature Fermi energy of the nucleons in each zone plus the binding energy of the most loosely bound nucleon. The pion potential in each zone is taken to be the same as the potential of the nucleon with which it interacts. This is in contrast to a more reﬁned approach in the INCL-Cugnon [170] INC model as will be described later in Section 2.3 on page 88. Potential values and distributions for a typical case (Cu-65) are illustrated in Figure 2.5. As can be

71

2 The Intranuclear Cascade Models

0.0

Nucleon potential [MeV]

Binding energy 8 MeV

−10.0 Protons Neutrons 65Cu

−20.0 −30.0 −40.0 −50.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Nuclear radius [cm × 10−13] Fig. 2.5 Nucleon potential as a function of the nuclear radius for a typical nucleus Cu-65. The ﬁxed binding energy is 8 MeV of the most loosely bound nucleon (after Bertini [153]).

10 9 Nuclear radii [cm × 10−13]

72

Radius r3

8

Radius r2

7 6

Radius r1

5 4 3 2 1 0 0

20 40 60 80 100 120 140 160 180 200 220 240 Atomic mass number A

Fig. 2.6 The radial boundaries deﬁning the three zones V1,2,3 of the nucleus as a function of the atomic mass number A.

seen, the potentials are constant in the zones limited by the radii given in Eq. (2.3). The effects of the reﬂection and refraction of the nucleons at the zone boundaries are not considered in the model. Figures 2.6, 2.7, and 2.8 show as a function of the atomic mass number A the radial boundaries deﬁning the three zones V1,2,3 of the nucleus, the nucleon density in each of the three zones V1,2,3 of the nucleus, and the Fermi energy per nucleon in each of the three zones V1,2,3 .

Nuclear densities per atomic mass A [cm−3]

2.2 The BERTINI Approach

108

107 Radius r1 106 Radius r2 105 Radius r3 104 0

20 40 60 80 100 120 140 160 180 200 220 240 Atomic mass number A

Fig. 2.7 The nucleon density in each of the three zones V1,2,3 of the nucleus as a function of the atomic mass number A.

Fermi energies [MeV]

102

101 Radius r1 Radius r2

100

Radius r3 10−1 0

20 40 60 80 100 120 140 160 180 200 220 240 Atomic mass number A

Fig. 2.8 The Fermi energy per nucleon in each of the three zones V1,2,3 as a function of the atomic mass number.

2.2.2.4 Application of the Pauli Exclusion Principle The only quantum mechanical effect included in the INC model is the Pauli exclusion principle, which is taken into account by introducing the Pauli blocking factor. The Pauli blocking factor accounts for the fact that the nucleons are fermions and therefore obey the Pauli principle. It should be mentioned that in the model only nucleons (protons and neutrons) observe the Pauli exclusion principle, since the densities of other fermionic particles are small. Since collisions are considered inside nuclear matter, the Pauli exclusion principle forbids interaction where

73

74

2 The Intranuclear Cascade Models

the collision products would be in occupied states. For a completely degenerate Fermi gas, the levels are ﬁlled starting from the lowest level. Therefore, collisions are forbidden in which either very large or very small amount of energy is transferred. The minimum energy allowed for the low-energy product of a collision corresponds to the lowest unﬁlled level of the system, which is the Fermi energy in the appropriate zone Vi of the nucleus. Since the time scale of INC reactions is rather small (≤10−22 s), it can be supposed that the nucleus will stay in the ground state. Therefore the Fermi momentum PF is well deﬁned by PF = · (3π · ρ(r))1/3 ,

(2.19)

where ρ(r) is the nucleon density as deﬁned in Eq. (2.1). However, because the nucleus is subdivided into three zones Vi , i = 1, 2, 3, Eq. (2.19) is written as PFi = · (3π · ρi )1/3

(2.20)

with ρi from Eq. (2.4). As a consequence the Pauli factor f is given by − → f = (x) · (| P | − PFi ).

(2.21)

(x) is the Heavyside step function, written as (x) =

1 for x > 0 . 0 for x < 0

(2.22)

Thus, the ﬁnal state particle will be blocked in the case when the absolute value − → of its momentum P is smaller than the Fermi momentum in zone Vi where it is located. In the Monte Carlo calculations the exclusion principle is taken into account by neglecting any collision where the energy of any collision product falls below the Fermi energy. So in practice, the Pauli exclusion principle is taken into account by accepting only secondary nucleons which have an energy EN larger than the Fermi energy EF , EN > EF . 2.2.3 The Cross-Section Data

The greatest advantage of the BERTINI model is that the basic ingredients required are only the free particle cross-section data for nucleon–nucleon elastic and nonelastic, pion–nucleon elastic scattering, charge exchange, and pion production cross sections, which is relatively well known from experimental data [19]. In the BERTINI model, single and double-pion production in pion–nucleon collisions are taken into account. This restricts the upper energy limit of the original BERTINI model [12] to about 3 GeV since at higher energies higher order pion production, other meson production channels or higher baryon resonances become important.

2.2 The BERTINI Approach Tab. 2.1

Cross sections required for the BERTINI INC model.

Cross section

Reaction

n–p p–p π + –p π − –p π − –p π 0 –p π − –p p–p n–p π + –p π − –p

Differential Differential Differential Differential Differential charge exchange Differential Charge exchange Single-pion production Single-pion production Single-pion production Single pion production

Cross section n–p p–p π − −p π 0 –p π 0 –n π + –p π 0 –p p–p n–p π 0 –p π 0 –n

Reaction Elastic Elastic Elastic Elastic elastic Absorption Absorption Double-pion production Double-pion production Single-pion production Single pion production

Twenty-two cross-section sets are only needed with ∼3 × 104 values. In Table 2.1 the used nucleon–nucleon and pion–nucleon cross sections for the BERTINI model are summarized. Making the assumption to use for example particle–nucleus cross sections for the INC model instead of nucleon–nucleon cross sections one would like to know for nonelastic collisions the differential cross sections, for example, d2 σnonelastic − → (Ej , j , hi , Ei , Ak ), dE d

(2.23)

− → in energy E and direction of secondary particles of type j produced when a hadron hi of type i and energy Ei interacts with a target nucleus of mass Ak . This information is presently not known accurately over the wide range of parameters of interest in spallation research and would need about 107 input values for the INC model. This is still the major physics uncertainty in predicting hadronic cascades. Basic approaches are therefore to estimate d2 σ/dE d by using available hadron–hadron data or extending the models to hadron–nucleus collisions by theoretical models in conjunction with accelerator and cosmic ray data to evaluate the semiempirical formula [106, 179]. The energy range to treat nuclear collisions of the BERTINI model is for neutron and proton reactions up to 3.5 GeV and for pion reactions up to 2.5 GeV. The methods used in treating nuclear collisions depend upon • whether the collision is elastic or nonelastic, • whether the struck nucleus is hydrogen, and • whether the energy of the particle is above or below an energy cut Ecut about 3.5 GeV for nucleons or 2.5 GeV for pions, respectively. Hence the upper boundary momenta are 4.34 GeV/c for nucleons and 2.64 GeV/c for pions. The treatment of nuclear collisions of the BERTINI model is given in Table 2.2. In a later extension of the BERTINI model [12], it should be mentioned here, that

75

76

2 The Intranuclear Cascade Models BERTINI model treatment of nuclear collisions in the original version based on Ref. [12] and the extended version on Refs. [202, 205].

Tab. 2.2

A = 1a E < Ecut same n–p, p–p, π –p cross sections as used in INCc

A > 1b E > Ecut Ranft–Borak distributions [201, 202, 206]

E < Ecut INCc model

E > Ecut INCc model with extrapolation model [202, 205]

Elastic collisions A = 1a E < Ecut same p cross sections as used in INCc

A > 1b E > Ecut parametric ﬁts to experimental data [201, 202]

E < Ecut for p and n

E > Ecut INCc model with extrapolation model [202, 205]

= 1 denotes collisions with hydrogen nuclei. > 1 denotes all nonhydrogen target nuclei. Intranuclear-cascade model original version Ref. [12].

aA

bA c

at nucleon energies >3.5 GeV and pion energies >2.5 GeV particle production data for nonelastic collisions are obtained in the BERTINI model from a very approximate model investigated by Gabriel et al. [201, 202]. Basically, this extension of the BERTINI model [12] employs particle production data from the INC model at energies ∼3 GeV and uses energy- and angle-scaling relations to estimate particle production data for higher energy nucleon–nucleus and pion–nucleus collisions. Examples for the validity of the extrapolation model are given in Refs. [158, 203, 204]. In the following the differently used particle–particle cross section data used by the BERTINI model are graphically shown. A short overview of the pion production model – the Sternheimer–Lindenbaum isobar model [76, 152] – is also presented. The BERTINI model is restricted to incoming and produced nucleons and pions only. A discussion about the production of secondary particles in nonelastic collisions via resonance decay was already given in Section 1.3.5.3 on page 27. The BERTINI model data will be also discussed in context with available evaluated data, which are provided by the Particle Data Group given in Ref. [19]. A graphical representation of these data is shown in Figures 2.11, 2.12, 2.14, and 2.15. 2.2.3.1 Nucleon–Nucleon Cross-Section Data The differential cross sections for p–p scattering (dσ/d)pp used in the BERTINI model are assumed to be isotropic in the center-of-mass system for protons up to

2.2 The BERTINI Approach

0.500 GeV. For energies from 0.44 to 4.4 GeV semiempirical ﬁts used an expression of the form (dσ/d)pp = A + B · µ3 ,

(2.24)

where µ represents the cosine of the scattering angle in the center-of-mass system. The angular distribution is assumed to be symmetric about µ = 0. The differential cross sections for np-scattering (dσ/d)np used in the BERTINI model are treated for forward and backward scattering separately. The semiempirical ﬁts used an expression of the form given below for different energy ranges. For the energy range: • for 0 ≤ Eneutron ≤ 0.3 GeV and 0 ≤ µ ≤ 1 (dσ/d)np = AF + BF · µ3 (dσ/d)np = AB + BB · µ4 .

(2.25)

For the energy range: • for 0.3 GeV ≤ Eneutron ≤ 0.74 GeV and −1 ≤ µ ≤ 0 (dσ/d)np = AF + BF · µ3 (dσ/d)np = AB + BB · µ6 .

(2.26)

And for the energy ranges: • for 0.66 GeV ≤ Eneutron ≤ 3.52 GeV and cross section tabulated for µ intervals, forward scattering µ ≥ 0 • for 0.66 GeV ≤ Eneutron ≤ 3.52 GeV and cross sections tabulated for µ intervals, backward scattering µ ≤ 0 where the index F stands for forward scattering and the index B for backward scattering. The different coefﬁcients A, AB , AF , B, BB , and BF are tabulated in Refs. [77, 88]. The total proton–proton and total neutron–proton scattering cross section that are used in the BERTINI model [12] are shown in Figures 2.9 and 2.10. For comparison proton–proton (pp) and neutron–proton (np) scattering cross-section data evaluated by the Particle Data Group [19] as a function of the laboratory momentum plab in GeV/c are shown in Figures 2.11 and 2.12. The agreement with the original BERTINI data shown in Figures 2.9 and 2.10 is fairly well concerning the energy range up to 3.5 GeV. 2.2.3.2 Pion Production and Pion Nucleon Reactions Single- and double-pion production in nucleon–nucleon collisions For single-pion production the nonelastic reaction channel with the lowest threshold opens around 290 MeV in nucleon–nucleon collisions (pp or np), and arrive a maximum at about 700 MeV. Double-pion production starts at a threshold at about 800 MeV by

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2 The Intranuclear Cascade Models

Cross sections [mb]

100 80 60 pp - total 40 pp-elastic

20 0 0.0

0.4

0.8

1.2

2.0

1.6

2.4

2.8

3.2

3.6

Proton energy [GeV]

Fig. 2.9 Total proton–proton σpp -total and -elastic cross sections as a function of the incident proton energy used in the original BERTINI INC model (after Bertini [12]). 100 Cross sections [mb]

78

80 60 snp -total 40 20 0 0.0

snp -elastic 0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

Neutron energy [GeV]

Fig. 2.10 Total neutron–proton σnp -total and -elastic cross sections as a function of the incident neutron energy used in the original BERTINI INC model (after Bertini [12]).

nucleon–nucleon collisions. The nonelastic reaction channels are dominated by the existence of several resonances. Details are already discussed on page 27. The most prominent one is the (1232) resonance (see Figure 1.17 on page 28), which has a mass of m = 1232 MeV/c2 and width of about = 110–120 MeV/c2 . The resonance decays via the strong force corresponding to a decay time τ 5 × 10−24 s. As already mentioned, this resonance is usually named 33 or (3,3)-resonance. For nucleon–nucleon or pion–nucleon collisions that lead to pion production, the isobar model of Sternheimer–Lindenbaum [76, 152] is used to determine the ﬁnal states. The model assumes that pions are produced through the decay of isobars N ∗ or of -resonances of the excited nucleon system, which is formed when a nucleon is excited in a collision. All reactions proceed through an intermediate state containing at least one resonance. There are two main classes of reactions, those which form a resonant intermediate state (possible in π –nucleon reactions) and those which contain two particles in the intermediate state. The former exhibits bumps in the cross sections corresponding to the energy of the formed resonances (cf. Figure 1.17 on page 28 and Figure 2.13).

2.2 The BERTINI Approach

Cross section [mb]

103

pp-total pp-elastic

102

101

100 10−1

100

101

102

103

104

Laboratory beam momentum Plab [GeV/c] Fig. 2.11 Proton–proton σpp -total and -elastic cross sections as a function of the laboratory proton momentum plab MeV/c evaluated by the Particle Data Group (pdg) from Ref. [19].

105

Cross section [mb]

104

np-total np-elastic pn-total

103

102

101

100 10−3

10−2 10−1 100 101 102 Laboratory beam momentum Plab [GeV/c ]

103

Fig. 2.12 Neutron–proton σnp -proton–neutron σpn -total, and neutron–proton σnp -elastic cross sections as a function of the laboratory proton momentum plab MeV/c evaluated by the Particle Data Group (pdg) from Ref. [19].

The models of Sternheimer–Lindenbaum [76, 152] used in the BERTINI intranuclear-cascade allows single and double-pion production in p–p and n–p nuclear collisions and single-pion production in pion–nucleon collisions.

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2 The Intranuclear Cascade Models

225

Cross sections [mb]

80

175 stotal (p+ + p)

125

stotal (p− + p)

75 25 0 0.0

0.4

0.8 1.2 1.6 Pion energy [GeV]

2.0

2.4 2.5

Fig. 2.13 Pion π + + proton and π − + proton total cross sections as a function of the incident pion energy used in the original BERTINI INC model (after Bertini [12]).

The reaction formalism for single- and double-pion production in nucleon– nucleon collisions is given by Eqs. (2.27) and (2.28). • single-pion production close to the threshhold of 290 MeV: ˆ 1 + (1232) −→ N ˆ1 +N ˆ2 +π N1 + N2 −→ N ˆ2 +π with (1232) −→ N

(2.27)

• double-pion production: ˆ 1 + π1 + N ˆ 2 + π2 N1 + N2 −→ 1 (1232) + 2 (1232) −→ N ˆ ˆ with 1 (1232) −→ N1 + π1 , 2 (1232) −→ N2 + π2 .

(2.28)

Single-pion production in pion–nucleon collisions All nonelastic pion–nucleon reactions are assumed to be single π-meson production events. The formalism for pion production in pion–nucleon nonelastic collisions is also based on the Sternheimer–Lindenbaum model [76, 152]. The pion is produced also via the formation and the subsequent decay of the (1232) or 33 which limits the model to produce one pion in pion–nucleon collisions. The reaction formalism for singlepion production in pion–nucleon collisions is given by Eqs. (2.29). Figure 2.13 shows the total pion–proton reaction cross sections of π − p and π + p collisions used by the BERTINI model (see also Figures 2.14–2.17). The resonance structure as indicated in Figure 1.17 on page 28 is clearly seen.

ˆ2 π + N1 −→ (1232) −→ π + N

(2.29)

To determine the ﬁnal-state momentum distributions, the angular distributions of the isobars or resonances and the decay of the pions must be speciﬁed. These

2.2 The BERTINI Approach

Cross section [mb]

103

p+ p-total p+ p-elastic

102

101

100 10−1

100

101

102

103

Laboratory beam momentum Plab [GeV/c] Fig. 2.14 Pion π + + proton total- and elastic cross sections as a function of the laboratory momentum plab MeV/c evaluated by the Particle Data Group (PDG) from Ref. [19].

102

Cross section [mb]

p− p-total p− p-elastic

101

100 10−1

100

101

102

103

Laboratory beam momentum Plab [GeV/c ] π −+

Fig. 2.15 Pion proton total- and elastic cross sections as a function of the laboratory momentum plab MeV/c evaluated by the Particle Data Group (pdg) from Ref. [19].

distributions are calculated phenomenologically through comparisons with experimental data [156]. These distributions are given for nucleon–nucleon single- and double-pion production in Table 2.3 and for pion–nucleon single-pion production in Table 2.4.

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2 The Intranuclear Cascade Models

25

Cross section [mb]

20

15

10

5

np-s p np-d p

pp-s p, pp-d p,

0 250

1000

2000

3000

4000

Incident proton / neutron energy [MeV] Fig. 2.16 Single (pp), (np)-s π and double-pion (pp), (np)d π pion production cross sections for nucleon–nucleon collisions as a function of the incident proton and neutron energy used in the original BERTINI INC model (Ref. [12]). 35 30 Cross section [mb]

82

25 20 p+ p-single production

15

p0 p-single production

10

p− p-single production p0 p-single production

5 0 100

500

1000 1500 2000 Incident pion energy [MeV]

2500

3000

Fig. 2.17 Single-pion (π + p), (π − p), (π 0 p), and (π 0 n) production cross sections for pion–nucleon collisions as a function of the incident pion energy used in the original BERTINI INC model (Ref. [12]). The (π − p) and (π 0 p) cross section are assumed to be the same.

Pion–nucleon absorption, charge-exchange, and scattering Pion absorption is considered to occur on a two-nucleon cluster [12, 77, 105, 156]. The type of cluster pp, pn, or nn for absorption is determined from the number of each type of particle pairs within the nucleus. Pair types which would violate charge conservation are not considered in the calculation of the absorption probabilities. This means, e.g.,

2.2 The BERTINI Approach Angular distribution in the center-of-mass system for nucleon–nucleon single- and double π -production reactions.

Tab. 2.3

Laboratory kinetic energy range (GeV)

E< 0.5 0.5 ≤ E 1.0 ≤ E 1.3 ≤ E 2.5 ≤ E

< 1.0 < 1.3 < 2.5 < 3.5

All energies

Percentage of angular distribution Isotropic

Forward

Single-pion production 100 75 50 25 0 Double-pion production 0

Backward

0 12.5 25 37.5 50

0 12.5 25 37.5 50

50

50

Angular distribution in the center-of mass-system for pion–nucleon single π -production reactions.

Tab. 2.4

Laboratory kinetic energy range (GeV)

All energies E < 0.5 E ≥ 0.5

Percentage of angular distribution Isotropic π + p and π − n 75 π − p and π + n 80 80 π 0 p and π 0 n assumed to the same as π − p

Forward

0 12.5 20 0

Backward

25 12.5 0 37.5

that π + absorption can take place with np pair and nn-pair clusters only. When π + absorption occurrs, the probability of the pair type being a np-pair is given by the ratio of the number of np-pairs to the sum of np and nn pairs in the nucleus. A short overview about the physics of pion absorption is given on page 27. It should be mentioned here that at the time 1963–1972 when the Bertini model was designed the knowledge in pion physics concerning the -resonance decay was poor, although Brueckner et al. [207] and Gell-Mann and Watson [208] proposed a model that the cross section for pion absorption is related to a deuteron absorption cross section. The cross sections for π − p charge exchange are given in [12, 77]. The cross section for elastic π 0 p scattering is calculated from the relation σelastic (π 0 p) = 1/2[σelastic (π + p) + σelastic (π − p) − σexchange (π − p)].

(2.30)

The π 0 n cross section is set equal to the π 0 p cross section concerning the conservation of the isotopic spin.

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2 The Intranuclear Cascade Models

50

Cross section [mb]

40 p+ p-absorption

30

p0 p-absorption

20

10

0 0

50

100 150 200 250 300 Incident pion energy [MeV]

350

400

Fig. 2.18 Pion–nucleon (π + p) and (π 0 p) absorption cross sections as a function of the incident pion energy used in the original BERTINI INC model [12].

50

40 Cross section [mb]

84

30 p− p- charge exchange 20

10

0 10

500

1000 1500 2000 Incident pion energy [MeV]

2500

3000

Fig. 2.19 Pion–proton (π − p) charge-exchange cross section as a function of the incident pion energy used in the original BERTINI INC model (Ref. [12]).

In Figures 2.18 and 2.19 the pion absorption π + p, π 0 p and the pion chargeexchange π − p cross section data, and in Figures 2.20, 2.21, and 2.22 the proton–proton pp, neutron–proton np, and the pion–nucleon π + p, π − p, π 0− p, π 0 n elastic scattering cross sections used by the BERTINI model are graphically shown.

2.2 The BERTINI Approach

2× 103

Cross section [mb]

103 np - elastic cross section pp - elastic cross section

102

101 100

101

102

103

4× 103

Energy [MeV] Fig. 2.20 Proton–proton (pp) and neutron–proton (np) elastic scattering cross section as a function of the incident proton and neutron energy used in the original BERTINI INC model [12].

Cross section [mb]

102

101

100 p0p/p0n - elastic cross section p−p-elastic cross section

10−1 5

101

102 Energy [MeV]

103

4× 103

Fig. 2.21 Pion–nucleon (π − p), (π 0− p), and (π 0 n) elastic scattering cross section as a function of the incident pion energy used in the original BERTINI INC model [12]. The (π 0 p) and (π 0 N) cross section are assumed to be the same.

2.2.4 Method of Computation

The method of computation used in the BERTINI INC model is the Monte Carlo technique essentially in an analog fashion that is nonelastic interactions of hadrons with nuclei are simulated. At the beginning the incident particle interacts with a

85

2 The Intranuclear Cascade Models

2.5×102 102 Cross section [mb]

86

101 p+ p-elastic cross section

100 5

101

102 Energy [MeV]

103

4×103

Fig. 2.22 Pion–nucleon (π + p) elastic scattering cross section as a function of the incident pion energy used in the original BERTINI INC model [12].

single nucleon inside the nucleus, much as the nucleons were in free space. The collision is not exactly analogous in free space because the Pauli principle will exclude those encounters with a certain momentum transfer (see page 73). Also, at high energies the incident particle can traverse the nucleus without experiencing an interaction, resulting in a nuclear transparency. The locations of the collisions, the momentum of the struck nucleon, scattering angles, etc. can be determined by using a statistical sampling technique together with the free particle (pp, pn, πp, etc.) cross-section data. The basic steps of the Monte Carlo simulation are straightforward, and given below: 1 The spatial point – the impact parameter – where the incident particle enters the nucleus is determined by selecting uniformly over a circular area representing the projected area of the nucleus. This is shown in Figure 2.23. 2 A path length is selected for the distance the incident particle tracks before undergoing a collision, using the total particle–particle cross sections and the radial-zone-dependent nucleon densities (cf. pages 65 and 74). The internuclear distance to a collision point, the type of collision, and the momentum of the struck particle are ‘‘sampled’’ by a rejection technique well known in Monte Carlo particle transport through matter (see Refs. [149, 150]). For example, by sampling from e− T ·z , where T = Np · σp + Nn · σn is the total interaction cross section determining how far the particle travels before interacting. From the ratio i / T , the probability that the ith interaction occurs, where N j=1 j = T. 3 If the particle escapes the nucleus without having a collision, this particle contributes to the ‘‘nuclear transparency.’’ Otherwise, the momentum of the

2.2 The BERTINI Approach

x Nucleus

Incident particle z z

Projected circular area of spherical nucleus

ri

y

Fig. 2.23 The entry of an incident particle into a nucleus by select uniformly over a projected area.

struck nucleon, the type of reaction, and the energy and direction of the reaction products are determined. 4 If the collision is allowed according to the exclusion principle, and if the kinetic energy of the product is above a predeﬁned cutoff energy, then the simulation chooses again point (2) and the resulting product particles are transported further. 5 After the completion of the intranuclear-cascade for an incident particle, the mass and charge, A∗ and Z∗ , of the residual nucleus are determined from a particle balance, and the residual excitation energy, E ∗ , is determined from an energy balance. The general outcome of the INC model of the BERTINI model is then the double differential particle spectra of cascade particles in energy E and − → laboratory angle , dσp,n,π /dE d and a residual nucleus Nresidual (A∗ , Z∗ , E ∗ ).

2.2.5 Assumptions, Limits, and Constraints on the Energy and Application Regime

The BERTINI INC model describes the target nucleus as a three-zone approximation of the continuously changing density distribution of nuclear matter within the nucleus. The cascade begins when the incident particle strikes a nucleon in the target nucleus and produces secondary particles. The secondaries may in turn interact with other nucleons in the nucleus or be absorbed. The cascade ends when all particles, which are kinematically able to do so, escape the nucleus. At that point conservation is checked. Relativistic kinematics is applied throughout the model. • The BERTINI model is essentially parameter free and provides results with absolute normalization. • The model requires mainly only fundamental particle–particle cross-section data, which are relatively well known. • The model has been shown to be in reasonably good agreement with a wide range of experimental data (see Part 2 on page 277).

87

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2 The Intranuclear Cascade Models

• The model has rather general applicability. (a) All target nuclei with A ≥ 1 are allowed. But it should be noted that the approximation of subdividing the nucleus into several zones is only valid for heavier nuclei. For light nuclei more realistic models, e.g., the shell model should be used, as shown and studied in Ref. [209]. If the target material is hydrogen A = 1, a direct particle–particle interaction is performed, and no nuclear model is required. (b) Different incident particles (protons, neutrons, and charged pions, with recent extensions to light heavy ions [88]) are possible. (c) The model covers a wide energy range of about 0.1–3.0 GeV. The valid energy range is not well deﬁned. The lower energy limit is ∼100–150 MeV. The original BERTINI model [12] is limited to energies below ∼3 GeV because only single- and double-pion production is included. (d) Extensions are made to the BERTINI model [12] version. Extensions to tens or even hundredsof GeV have been made by using approximate scaling relations by Gabriel et al. [202]. Also Barashenkov et al. [10] and Bertini et al. [158] have made modiﬁcations to the basic model [12] (e.g., to incorporate nuclear depletion, which takes into account the time dependence of the changing nucleon density in the path of the development of the cascade inside the nucleus and to divide the nucleus into a maximum of 50 spherical zones compared to the three-zone model of the nucleus used in the basic model.) • The model is capable of providing very detailed results on an event-by-event basis. (a) type, energy, and direction of each emitted particle; (b) type, excitation and recoil energy of the residual nuclei; (c) the photo source from π 0 decay and nuclear de-excitation; (d) the low-energy En ≤ 15 MeV neutron production, which is important in many applications. • The BERTINI model is only valid for incident protons, neutrons, and pions and valid for particles treated in the model such as protons, neutrons, pions, nuclear isotopes (residuals), and photons. The necessary condition for the low-energy limit of the model is λdeBroglie /v << τc << t, where λdeBroglie is the deBroglie wavelength, v is the average velocity between collisions, τc is the decay time of the particle, and t is the time interval between collisions. At energies below 150–200 MeV, this condition is no longer strictly valid, and a pre-equilibrium or evaporation model should be invoked (see Chapter 3 on page 135).

2.3 The Cugnon INCL Approach

Even though the BERTINI approach [77] as has been discussed in Section 2.2 is still implemented and widely used as a standard in a variety of transport models and codes (e.g., CALOR, GEANT4, FLUKA, HERMES, LAHET, MCNPX, TIERCE,

2.3 The Cugnon INCL Approach

cf. Chapter 5 on page 207), it is certainly in part superseded by the latest physics insights and nuclear data ﬁndings and improvements. A more recent and still actively developed and benchmarked alternative to the BERTINI INC model is the approach originally realized by Cugnon et al. [168–170, 172, 210–212]. Since the ` model and the code was originally developed at the University of Liege, Belgium, the acronym is INC-Li`ege or abbreviated INCL followed by its release number. Some of the basic fundamental assumptions of the INCL approach resembles to a large extend the semiclassical microscopic description of a collision between a particle and a nucleus as outlined in detail in Section 2.2 for the BERTINI model. As for any INC model, the basic physical assumptions apply also for the INCL model: 1 The motion of particles involved in the cascade obeys the laws of classical mechanics. 2 The collision of a pair of particles takes place in a domain of ‘‘macroscopically small’’ dimensions. The duration of such a process is small compared to the time between subsequent collisions. Therefore, any collision can be considered as instantaneous and as a point interaction. 3 Reaction cross sections can be computed if not available. 4 Relativistic kinematics is used. 5 The only quantum-mechanical effect included in the INCL is the Pauli exclusion principle, which is taken into account by introducing the Pauli blocking factors. However, compared to the BERTINI model the INCL model uses the so-called dynamic Pauli blocking (see Section 2.3.1.6). 6 Compared to the quantum molecular dynamic (QMD), and the Boltzmann Uehling Uhlenbeck (BUU) model, the INCL model is particularly attractive since it is superior as far as computing time is concerned.

The INCL model was ﬁrst developed for heavy-ion collisions and quite successful to study the physical aspects of these collisions in the GeV range [210]. Later the model was used for antiproton–nucleus interactions [212]. Finally, the INC Li`ege model for nucleon–nucleus interactions was designed as described in Refs. [168, 169]. Minor improvements of the earlier model are discussed in Refs. [170, 211], which basically introduced a better parameterization of baryon–baryon collisions. These improvements will be presented in the following subsections. A major upgrade referred to the INCL4 version of the INC model for a comprehensive description of spallation reaction data has been released in 2002 [172] as will be ` INC model [117] a discussed in Sec. 2.3.1.9. Based on the same INCL4 Liege surface percolation procedure has been developed. This procedure is proposed to describe the emission of light charged clusters during the cascade stage in nucleon-nucleus reactions. In the family of INC codes the newest version of the INCL model appears to be the most sophisticated and elaborated model and code including latest hadron and meson reaction data, and reaction mechanisms and therefore manifests apparently superior to, e.g., the BERTINI approach.

89

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2 The Intranuclear Cascade Models

2.3.1 Features of the Model

The idea of the model is to provide a tool for physicists to check various models and options compared with observables obtained in the one interaction limit, and/or to make a good choice before using the proposed physics models in complex geometries treated by transport codes as will be discussed in Chapter 5. The physics case in INCL is deﬁned by • the incident particle–proton, neutron, deuteron, triton, 3 He, 4 He, π + , π − or π 0 and its kinetic energy; • a target nucleus at rest (all inputs and outputs are expressed in the ‘‘target at rest’’ system); • number of incident particles sent in a rather large ‘‘geometrical’’ cross section. Compared to other currently used INC models, such as the BERTINI [77], and ` the ISABEL [162, 164, 167] models, and to the previous versions of the INCL Liege code, the INCL4 release incorporates new features: (i) it can accommodate a diffuse nuclear surface, i.e., includes a realistic target density distribution; (ii) the treatment of the Pauli blocking is improved, removing nonphysical features linked with the statistical blocking factors and being consistent with the progressive depletion of the Fermi sphere; (iii) collisions between moving spectator nucleons are explicitly suppressed; (iv) the rest angular momentum is included in the output of the model; (v) the history of all particles is followed as a function of time, and a self-consistent determination of the stopping time, i.e. the time at which the INC calculation is terminated and may be coupled to pre-equilibrium or evaporation models, is introduced. Some of the latest developments and in particular the features which are handled differently in the INCL compared to the BERTINI or other INC model approaches are discussed in the following subsections. The programming language of INCL is Fortran 77 and for compiling the code, the CERN libraries ‘‘cernlib packlib kernlib pawlib’’ are prerequisite for ﬁlling histograms or creating NTUPLE formatted outputs to be ﬁnally treated and visualized by PAW [213]. For each projectile–target interaction, all produced particles are recorded by the particle type, their energy, their momentum, and their θ , φ direction in phase space as well as more global variables as impact parameter b or intermediate quantities such as thermal excitation energy E ∗ , intrinsic spin, momentum of the rest nucleus at the end of the intranuclear cascade or nature of the eventual ﬁssion nucleus. Global numbers are also given for normalization to an absolute cross section for any choice of particles or correlation between them. 2.3.1.1 Participants and Spectators The term participants is deﬁned as particles having collided with at least one other particle of the nucleus, the incident particles being the only participants at the beginning. The other particles are called spectators. All particles are moving but, contrary to the previous versions of the model, collisions are forbidden between spectators. Propagation of spectators provides a natural evolution of the early

2.3 The Cugnon INCL Approach

perturbations of the spatial density. This procedure is more satisfactory than the corresponding one in other INC models with a continuous density distribution, which implies some ad hoc ﬁlling of the holes punched inside the nucleus by the participants [162]. In addition, forbidding collisions between spectators eliminates the ‘‘spontaneous boiling’’ of the Fermi sea: in the absence of this prescription, nucleons close to the Fermi surface can gain energy through collisions between themselves at the expense of others, and escape from the target even if the latter is left alone. In the previous versions of the INCL Lie`ge model, this erroneous evaporation could lead to an increase of a few percent of the neutron emission in the cascade. 2.3.1.2 Nuclear Surface In INCL4 [172] a diffuse nuclear surface corresponding to a Woods–Saxon density distribution (for details see Ref. [200], pages 249–252) up to a maximum distance Rmax , ﬁxed to R0 + 8a has been introduced:

ρ(r) =

ρ0 r−R0 1+exp a

for r < Rmax

0

for r > Rmax .

(2.31)

The values of R0 and a are taken from electron scattering measurements and parameterized, for Al to U, as R0 = (2.745 × 10−4 A + 1.063)A1/3 (fm), a = 0.510 + 1.63 × 10−4 A (fm). For the quantity ρ0 the distribution is normalized to the atomic mass number A of the target nucleus. The momentum distribution is kept as a uniform Fermi sphere with the Fermi momentum pF . Particles with momentum between p and p + dp are those that can move up to a maximum radial distance between R(p) and R(p + dp). Consequently, the numbers of nucleons corresponding to the shaded areas in Figure 2.24 should be the same. This deﬁnes the function R(p). Nucleons with a large momentum in the central part of the nucleus are expected to travel farther out than those with a small momentum. These r –p correlations make it impossible to generate the r and p distributions independently. As illustrated in Figure 2.24, these distributions should remain constant when the r–p correlations ρ(r) n(p)

r R(p) R(p+dp)

pF p

p +dp

Fig. 2.24 Correlation between the spatial and momentum distributions implied by the phase space distribution equation (2.31). See the text for details (ﬁgure taken from Boudard et al. [172]).

91

2 The Intranuclear Cascade Models

target is left alone, supposing nucleons evolve freely in an average nuclear potential. These two requirements can be fulﬁlled by placing nucleons of momentum p in a square well of the potential depth V0 with a momentum-dependent well radius R(p) suitably chosen: nucleons with momentum between p and p + dp will be characterized by a constant uniform probability within a sphere of radius R(p), once they are initially generated with this property. They contribute to the density proﬁle by the layer shown by the shaded area on the left-hand side of Figure 2.24. This implies that the number of nucleons with momentum between p and p + dp is the same as the number of nucleons populating this layer. In Ref. [172] the details are shown of the procedure outlined above. Note that the method is at variance with the one used in many transport models [183], where nucleons are placed in a potential with a Woods–Saxon or similar shape. In INCL4, this choice is discarded because it removes the possibility of propagating particles in a single step between collisions or reﬂections, a very appealing feature of the INCL4 Li`ege model, since their momentum is going to change in between. 2.3.1.3 Meson–Nucleon Cross Sections In particular, inelastic cross sections generally used in the INC models have been comprehensively discussed in Section 2.2. As already stated and discussed in detail for the BERTINI model in Section 2.2, also in the INCL model the meson production (e.g., Nπ → Nππ) in meson–hadron interactions will proceed through an intermediate resonance as in baryon–baryon collisions. The three-body ﬁnal state is modeled by two subsequent two-body decays (e.g., Nπ → R → 1232 π → Nππ). Representatively in Figures 2.25 and 2.26 the total cross sections for the π + p and π − p reactions as used in the INCL model are displayed. These are obtained by summing up all partial cross sections. The resonant character of the pion–nucleon 250 Experimental data stot (p +p+ ) INCL

200

s [mb]

92

150 100 50 0

0.5

1.0

1.5

2.0

2.5

plab [GeV/c ] Fig. 2.25 Total π + p cross section as a function of the laboratory momentum plab . The ◦ represent experimental data from [214].

3.0

2.3 The Cugnon INCL Approach

80 Experimental data s (p +π−) INCL

s [mb]

60

40

20

0

0.5

1.0

1.5

2.0

2.5

3.0

plab [GeV/c] Fig. 2.26 Total π − p cross section as a function of the laboratory momentum plab . The ◦ represent experimental data from [214].

interaction is clearly seen. The ﬁrst peak in Figure 2.25 corresponds to the reaction p + π + → ++ 1232 whereas in Figure 2.26 the peak at about 0.25 GeV/c is caused by the reaction p+π − → 01232 . While Figure 2.25 is totally determined by ++ resonances, N ∗ resonances contribute to the total cross section shown in Figure 2.26. Very good agreement with experimental data [214] up to plab ≈ 2.0 GeV/c is found in both ﬁgures. At higher momenta the experimental cross sections are larger than the INCL ones. 2.3.1.4 Elastic Nucleon–Nucleon Cross Sections Contrary to the situation in the case of inelastic scattering, the energy dependence of elastic nucleon–nucleon cross sections is well known. As described in Ref. [215] for INCL model, the following parameterizations are used. All cross sections are given as a function of the laboratory momentum of the nucleons plab in (GeV/c). Proton–proton elastic scattering It should be mentioned that for elastic nucleonresonance scattering (N + R → N + R) the parameterization of the elastic proton–proton cross section is used, since no experimental data exist for the N + R → N + R case:

el σpp = 34 el σpp el σpp el σpp

p

lab

−2.104

for 0.1 ≤ plab < 0.4 0.4

4 = 23.5 + 1000 plab − 0.7 for 0.4 ≤ plab < 0.8

1250 2 − 4 plab − 1.3 = for 0.8 ≤ plab < 2.0 plab + 50 77 for 2.0 ≤ plab . = plab + 1.5

(2.32)

93

2 The Intranuclear Cascade Models

50.0 Experimental data sel(p +p) INCL

40.0

s [mb]

94

30.0 20.0 10.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

plab [GeV/c ] Fig. 2.27 The elastic cross section for the proton–proton initial state obtained with the parameterization of Cugnon (see Eq. (2.32)). The symbol represents data from [214].

Neutron–proton elastic scattering The cross sections shown here have been directly extracted from the INCL2.0 model code, since they differ slightly from the parameterization given in [215]: el σnp = 6.35 exp(−3.2481 ln plab − 0.377(ln plab )2 ) for plab < 0.45 el = 33.0 + 196.0 |plab − 0.95|5 for 0.45 ≤ plab < 0.80 σnp

31 el σnp = √ for 0.80 ≤ plab < 2.0 plab 77 el for 2.0 ≤ plab . = σnp plab + 1.5

(2.33)

The elastic cross section for the proton–proton initial state is plotted in Figure 2.27. In the range up to a laboratory momentum of plab = 2.0 GeV/c good agreement with data from [214] is obtained. However above 2 GeV/c the cross section is overestimated. In Figure 2.28 the total cross section, together with the elastic and total inelastic cross section for proton–proton interactions is plotted as a function of laboratory momentum plab . For momenta below 1 GeV/c the agreement between the parameterization and the experimental data is good. Nevertheless, the onset of the rise at low energies is slightly shifted. Moreover, due to the overestimation of the elastic cross section above plab = 2 GeV/c the total cross section is also overestimated by about 5 mb. 2.3.1.5 Angular Distributions The cross sections described in the previous sections do not contain any information about the direction of outgoing particles. Usually transport codes use analytic expressions to determine these differential cross sections. In the following the parameterization implemented in the INCL model will be discussed.

2.3 The Cugnon INCL Approach 100.0 stot sel sinel Exp. data

90.0 80.0

s [mb]

70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0

1.0

2.0

3.0 4.0 plab [GeV/c]

5.0

6.0

7.0

Fig. 2.28 The total proton–proton cross section (solid line) as used in INCL – calculated as the sum of the elastic (dotted) and the total inelastic cross section (dashed line). The symbols are experimental data from [214].

The inelastic baryon–baryon case As already stated, experimental data are quite scarce so that ﬁts to the experimental data – especially for heavier resonances – cannot be evaluated with a good accuracy. Therefore, one conﬁnes to reactions where the 1232 -resonance is involved and assumes that the angular dependence is the same for each isospin channel as well as for N ∗ production. Furthermore, one can assume the same energy dependence of angular distributions for double-resonance-production reactions. The parameterization implemented in INCL for reactions of the type N + N → N + R, R + R is published in Ref. [216] and is of the form

dσ ∼ exp (Bin · t), d

(2.34)

where t is a Mandelstam variable [217], with the deﬁnitions in Eq. (2.37). t = −2p2cms (1 − cos θ ),

(2.35)

with pcms the center-of-mass momentum; Bin is given by Bin =

−1 5.287 1 + exp{(1.3 − plab )/0.05} 4.65 + 0.706(plab − 1.4)

for plab < 1.4 GeV/c for plab > 1.4 GeV/c, (2.36)

where plab is the laboratory momentum. For resonance absorption reactions an isotropic angular distribution is assumed. The Mandelstam variables [217] are Lorentz invariant variables describing the kinematics of particle reactions via a relation of relativistic momentum-energy

95

96

2 The Intranuclear Cascade Models

four vectors. The two-body elastic scattering amplitudes is given in terms of the dispersion relations as functions of two complex variables s and t. Nowadays, Mandelstam variables are also widely used to describe the kinematics of multibody ﬁnal states seen as two incident and two outgoing systems [85]. By deﬁning the incident particles 1 and 2, the outgoing systems 3 and 4, and using four-momentum conversation, it follows that p1 + p2 − p3 − p4 = 0

and (p1 )2 = mi2 .

The Mandelstam variables can be written as follows: s = (p1 + p2 )2 = (p1 + p2 )2 t = (p1 + p3 )2 = (p2 + p4 )2

(2.37)

u = (p1 + p4 ) = (p2 + p3 ) 2

2

from which it follows s + t + u = constant = m12 + m22 + m32 + m42 . Elastic baryon–baryon collisions Cugnon et al. [215] proposed a simple form for the differential elastic proton–proton cross section, which – with regard to isospin symmetry – is also valid for neutron–neutron scattering. It is similar to Eq. (2.34)

dσ ∼ exp (Bpp · t), d

(2.38)

with Bpp given as a function of the center-of-momentum energy or equivalently of the laboratory momentum plab , Bpp =

(5.5p8lab )/(7.7 + p8lab ) for plab ≤ 2 GeV/c . 5.334 + 0.67 plab − 2 for plab > 2 GeV/c

(2.39)

For elastic neutron–proton scattering the situation is more complicated, since the charge exchange reaction has to be considered as well. In the INCL model the parameterization for the differential behavior in neutron–proton elastic reactions suggested by Cugnon et al. [170] is used. Later on, it was slightly modiﬁed by Cugnon et al. in Ref. [216]: el dσnp

d

el = σnp Const eBnp t + aeBnp u + ceαc u ,

(2.40)

where the term within the brackets give the angular distribution in terms of the Mandelstam variables t and u (see Eq. (2.37)). u = −2p2cms (1 + cos θ ),

(2.41)

2.3 The Cugnon INCL Approach

with pcms denoting the center-of-mass momentum. The third term in (2.40) accounts for the charge exchange interaction. The parameter Const in Eq. (2.40) el is ﬁxed by normalization, as the angular integration should yield σnp . The energy, the momentum dependence of the slope parameter Bnp and of the coefﬁcients a, c, and αc are, respectively, given by  −1  (7.16 − 1.63plab )(1.0 + exp(0.45 − plab /0.05)) , plab < 0.8 GeV/c Bnp = 9.87 − 4.88plab , plab < 1.1 GeV/c  3.68 + 0.76plab , plab ≥ 1.1 GeV/c, (2.42) a=

0.8 plab

2 ,

(2.43)

6.23 exp(−1.78plab ) for plab ≤ 1.7 GeV/c 0.3 for plab > 1.7 GeV/c αc = 100. c=

(2.44) (2.45)

In these relations plab should be given in GeV/c. Bnp and αc are provided in units of (GeV/c)2 . Moreover, it should be noted that the parameterization for Bnp for plab < 0.8 GeV/c is directly taken from the INCL2.0 code [169, 170, 215, 216, 218]. For resonance-nucleon elastic scattering experimental data are not available. Hence the same differential scattering behavior as in the case of proton–proton elastic scattering as deﬁned in Eq. (2.39) is used in the model presented here. 2.3.1.6 Dynamic Pauli Blocking − → In Section 2.2.2.4, Eq. (2.21), the Pauli blocking factor f = (x) · (| P | − PFi ) was formally introduced into the collision integral. As discussed in Section 2.2.2.4 on page 72, the term accounts for the fact that the nucleons are Fermions and therefore obey the Pauli principle. Note that in the INC models only nucleons, i.e., neutrons and protons, observe the Pauli exclusion principle, since the density of other fermionic particles (-particles, baryonic resonances) is small. That is why one can safely neglect this effect for resonance states. Nevertheless, Pauli blocking is enforced to nucleons resulting from resonance () decays. Generally the strict Pauli blocking as discussed on page 73 is realized in INC programs. One shortcoming of the strict Pauli blocking is that the depletion of the Fermi sphere due to prior reactions is neglected. Furthermore, collision processes also introduce a temporary depletion of the spacial density. However, as the strict Pauli blocking is implemented in many heavy-ion collision models and in the INCL Li`ege [170] code, the Pauli blocking should operate in phase space. If two particles i and j suffer → → a collision at a position − r i(j) leading to a ﬁnal state with the momenta − p i(j) , the phase space occupation probabilities are calculated by counting nearby nucleons in a small phase space volume:

fdyni(j) =

1 1

→ → → → Rr − |− r i−− r k | Rp − |− p i−− p k| , 2 Vr Vp k =i

(2.46)

97

98

2 The Intranuclear Cascade Models

where Vr and Vp are spherical volumes in the coordinate or momentum space of the nucleus, respectively. The factor 1/2 is introduced because spins are ignored. The sum in Eq. (2.46) is limited to particles k with the same isospin component as particle i (or j). The collision between participant i and j is allowed or forbidden following the comparison of a random number with the product (1 − fi )(1 − fj ). In the INCL2 model as published in Ref. [170] the radii in coordinate and momentum space were set to Rr = 2 fm and Rp = 200 MeV/c. The parameters Rr and Rp should not be taken too small; otherwise fi is going to be always vanishingly small, nor too large, otherwise the details of the phase-space occupation can be missed. There is no a priori criterion for the appropriate choice of these parameters. In practice Rr and Rp are taken just large enough for results to be roughly insensitive to moderate modiﬁcations of their values (see Ref. [170]). In Ref. [172] for the INCL4 model slightly different values of Rr = 3.18 fm and Rp = 200 MeV/c have been chosen, which correspond to a measuring volume of ≈2.3 natural units of phase space. 2.3.1.7 Cutoff Criteria – Stopping Time of the Cascade A special attention is drawn in the INCL model to the stopping time tstop , i.e., the time at which the cascade is stopped to give way to pre-equilibrium and evaporation. The time evolution of various quantities, like the excitation energy E ∗ , the mass number of the residual nucleus Ares , and the number of ejectiles and participants, is discussed in [169, 170, 216] and shown in Figure 2.29. The panels of Figure 2.29 refer, in a clockwise order, starting from the upper left, to the excitation energy E ∗ , the average kinetic energy of the ejectiles T, the asymmetry ζzz of the participant momentum distribution, and the time derivative of the excitation energy dE ∗ /dE. The asymmetry ζzz is a quantity measuring the anisotropy of the momentum content of the participant baryons inside the target volume. In the early time of the collision, ζzz is different from zero because of the motion of the incident particle. It then decreases and tends to zero signaling that the system reaches a high degree of randomization. The results shown in Figure 2.29 correspond to collisions of 1 GeV protons with Pb nuclei with an impact parameter of b = 4 fm. As presented in Figure 2.29, the time evolution of the average value of many physical quantities show, when the cascade is run for a long time, a phase of rapid variations, followed by a phase of much slower variations. In addition, the time of separation between the two phases is roughly the same for most of these physical quantities. These results enable us to deﬁne the stopping time more or less precisely as the common separation time of the phases of variation of the physical quantities. As discussed in Refs. [169, 172], the excitation energy E ∗ raises rapidly when the incident particle penetrates the target nucleus, reaches a maximum excitation energy after some fm/c and then decreases rather steeply. However, as shown in Figure 2.29, the slope ﬂattens with increasing times similar to an evaporation process. It is also manifested from Figure 2.29 that the change of slope in the curve of E ∗ is correlated with the change in the curve representing the average kinetic energy of the emitted particles: the latter quantity is rather large in the ﬁrst phase,

2.3 The Cugnon INCL Approach

2000

1000 900 800 700 600 500

Average kinetic energy of ejectiles

< T > [MeV]

E* [MeV]

Excitation energy E*

400 300

102

200 10 100 90 80 70

0

50 100 Time [fm/c]

0

150

dE*/dt

100 Time [fm/c]

150

Momentum asymmetry of partcipants

25

102

50

10

xzz [%]

dE*/dt [MeV (fm/c)−1]

20

15

10 1 5

0 0

50

100 Time [fm/c]

150

0

Fig. 2.29 Time variation of the average value of a few physical quantities, within our INC model. The arrows indicate the chosen stopping time. (Figure taken from Boudard et al. [172].)

50

100 Time [fm/c]

150

99

2 The Intranuclear Cascade Models

but reaches in the second phase a small and smoothly decreasing value, typical of the evaporative cooling of an equilibrated system. Thus, it is the idea to stop the cascade at this particular time and proceed with an evaporation calculation. This cutoff is not only introduced to save computational time, but it seems to be necessary as the evaporation process is known to depend sensitively on the level density, which is presumably different from the single particle model value, to which INC models correspond. In summary, the collision process of a hadron–nucleus reaction can be divided into two parts. The ﬁrst one corresponds to a rapid variation of physical quantities and the second one is characterized by slow variations, in which the nucleus is fairly well equilibrated. Unfortunately, this transition is not very sharp. Hence there will be some uncertainty of about 2–5 fm/c in the cutoff time. The INCL model adopts a parameterization of the stopping time tstop presented in [172]. It is given by tstop = fstop t0

A 208

0.16 (fm/c),

(2.47)

where fstop = 1, t0 = 70 fm/c and A is the atomic mass of the target nucleus. In Figure 2.30 the dependence of the stopping time tstop on the mass number of the target nucleus A according to Eq. (2.47) is shown. The INC process will end in the case when the elapsed time exceeds tstop . Moreover, the calculation is also terminated if no particle that was participating in the reaction is able to escape from the nucleus. The time as given by Eq. (2.47) [172] for the INCL4 version is substantially larger than the values adopted in the standard older versions (as described in Refs. [216, 219]), although the criteria are basically the same. This is merely due to the fact that, because of the presence of a diffuse surface, the incident particle is initially situated farther away from the target than

70

Time tstop [fm/c]

100

60 50 40 30 20

0

50

100 150 Atomic mass A

200

Fig. 2.30 Stopping time tstop used in INCL as a function of the mass number A of the target nucleus.

250

2.3 The Cugnon INCL Approach

p (1200 MeV) + Pb

102 0° 10

10° (10−1) 1 25° (10−2)

10−1

40° (10−3)

d2s/ dΩ dE [mb/sr MeV]

10−2

55° (10−4)

10−3

70° (10−5)

10−4

85° (10−6)

10−5

100° (10−7)

10−6 10−7

115° (10−8)

10−8

130° (10−9)

10−9

145° (10−10)

10−10

160° (10−11)

10−11 10−12 1

10 102 Neutron energy [MeV]

103

Fig. 2.31 Comparison of simulated neutron double differential cross section with measurements for proton-induced reactions on a 2-cm-thick Pb target at 1200 MeV and detection angles from 0◦ to 160◦ . The predictions are given by the histograms, and data are as circles from Ref. [220]. The spectra have been multiplied by decreasing powers of 10, except for 0◦ (after Boudard et al. [172]).

in the previous INCL versions. The stopping time is now largely independent of the impact parameter and of the incident energy, for the same reason. The most important observable for applications to spallation reactions in spallation neutron sources or in general in all accelerator-driven systems (ADS) is the neutron production cross section. As examples in Figures 2.31 and 2.32, predictions of double differential neutron production cross sections in proton-induced reactions on Pb and Th targets for 1200 MeV along with measurements at the

101

2 The Intranuclear Cascade Models

103 p (1200 MeV) + Th

102 0° 10

10° (10−1) 1 25° (10−2)

10−1

40° (10−3)

10−2 d2s/dΩ dE [mb/sr MeV]

102

55° (10−4)

10−3

70° (10−5)

10−4

85° (10−6)

10−5

100° (10−7)

10−6 10−7

115° (10−8)

10−8

130° (10−9)

10−9

145° (10−10)

10−10

160° (10−11)

10−11 10−12 10−13

Fig. 2.32

1

10 102 Neutron energy [MeV]

103

Same as Figure 2.31 for a 2-cm-thick Th target (after Boudard et al. [172]).

SATURNE accelerator [220] are given. The targets used in Ref. [220] had a ﬁnite thickness of 2 cm. The data are plotted versus the logarithm of the neutron energy. The comparison with experimental data requires the coupling of the INCL with an evaporation model. The predictions in Figures 2.31 and 2.32 have been done by coupling the INCL4 model with the GSI evaporation model ABLA-KHSv3p [221, 222] also known as the Schmidt model (cf. Section page 154). The overall agreement is rather good although the cross section values are extending over several decades. It is easily seen that the INCL model plus the ABLA model reproduce the neutron production cross sections in the whole phase space satisfactorily. Another feature may be seen in Figures 2.31 and 2.32 is the correctly reproduced cross section of the quasielastic peak at 0◦ . More examples at lower incident proton energies and other target materials are shown in Ref. [172].

2.3 The Cugnon INCL Approach Parameters of the Gaussian forms used to describe radial distance and momentum distributions in light incident clusters.

Tab. 2.5

Incident particle d t 3 He 4 He

r 2 (fm) 1.91 1.8 1.8 1.63

p2 (MeV/c) 77 110 110 153

2.3.1.8 Light Clusters as Incident Particles Besides proton, neutron, π + , π − , or π 0 as types of incident particles, the INCL model has been extended to incident clusters of nucleons (deuteron, triton, 3 He, 4 He) [172]. It is sufﬁcient to generate the initial distribution of nucleons inside the incoming cluster, as the history of all particles is followed in time. For their initial state due to the small size of these clusters, it is not appropriate to use a distribution of the form (2.31). In INCL a Gaussian shape for the spacial distribution is used with a width which is determined by the charge r.m.s. radius. Except for the deuteron, the same is done for the momentum distribution, with widths taken from the literature [223–226] (see Table 2.5). For the deuteron as the loosely bound system, a more careful microscopic treatment is required. Here the modulus squared of the wavefunction in momentum space, as calculated with the Paris potential [172, 227], has been used. There is no nuclear mean ﬁeld introduced inside the incoming ion. This approximation is reasonable in view of their weak binding (except for 4 He). To correct for the latter in the energy balance, the incident kinetic energy is decreased by an amount equal to the binding energy in order to have the correct total incident energy. 2.3.1.9 Surface Percolation Procedure for Emission of Light Charged Clusters To describe the emission of light charged clusters during the cascade stage in nucleon–nucleus reactions, a surface percolation procedure has recently been developed for the INCL4 Li`ege INC model [117]. As has been discussed in Sections 1.3.3 and 1.3.4 on page 21, the reaction process can be divided into two stages. The ﬁrst one is dominated by fast particle emission and in the second one, the residuum of the target releases its remaining excitation energy by evaporation of slow particles (and/or by ﬁssion for heavy targets). Not only nucleons, but also light charged clusters (d, t,3 He,4 He) are emitted in two stages, as suggested by the observation of their spectra (see Figures 2.33, 2.34, and spectra shown in Part 2 on page 277). As an example for light charged particle production, double differential energy spectra of 1,2,3 H and 3,4 He ejectiles following 1.2 GeV p-induced reactions on the Ta target as measured by NESSI collaboration at the COSY-J¨ulich accelerator [228] are shown for different angles in respect to the incident proton in Figure 2.33.

103

2 The Intranuclear Cascade Models 30° 10

75° 1

150° 1

H

1

H

H

1 −1

10

10−2 10

2H

2H

2H

3H

3H

3H

1 10−1 d2s/(dE·dΘ) (mb/(MeV sr))

104

10−2 1 10−1 10−2 10−3 10

4

4

He

4

He

He

1 10−1 10−2 1

3He

3He

3He

10−1 10−2 10−3 0

25

50

75

0

25

50

75

0

25

50

75

Ekin (MeV)

Fig. 2.33 Energy spectra of 1,2,3 H and 3,4 He for 1.2 GeV p+Ta. dots: experimental data, shaded histogram: calculated evaporation spectra, dashed histogram: pre-equilibrium protons as calculated by INCL2.0 [228].

The experimental data shown clearly feature the two components, an evaporation component dominant for all angles and at low kinetic energies and a high-energy component all the more pronounced the smaller the angle of the ejectile in respect to the incident proton is. In Figure 2.33 for theoretical description the INCL2.0 [170] INC code is coupled to the evaporation code GEMINI [229] (cf. Section 3.6) on page 159. Only for protons (upper panels) both components can be well described. Due to the lack of composite particle emission in the early phase of the reaction in the INCL2.0 model, the high-energy tails of the spectra for d,t,3,4 He are not described by the calculations. The shape of the calculated evaporation component (shaded gray histogram in Figure 2.33) however is well reﬂected also for composite particles.

2.3 The Cugnon INCL Approach

The description of cluster ejectiles in the ﬁrst phase of a nuclear reaction, i.e. the high-energy tails of the spectra in Figure 2.33, is a quite important aspect of INCL4, a feature missing in the previous versions of INCL and other codes designed for transport calculations with GeV hadron beams. The deﬁciency to accommodate emission of light clusters in the evaporation stage only is not a serious problem as far as global particle multiplicities are concerned. The analysis of experimental data has shown that in proton-induced reactions on heavy targets in the GeV range, the ratio of the number of nucleons appearing in the form of clusters emitted during the cascade stage to the total number of emitted nucleons, whatever their origin, lies between 5 and 10%. However, the lack of cascade light cluster emission appears more serious in view of technological applications. Indeed light clusters correspond to gaseous elements (H, He), which are liable to create voids or other damages in materials. Therefore, it is of utmost interest for the designers of (solid) spallation sources to have at their disposal a good model for the production of these elements. Another motivation for the incorporation of light cluster emission in the cascade stage is that for spallation reactions in the energy range under consideration, it is very hard to couple nucleon degrees of freedom and cluster degrees of freedom on a microscopic basis, i.e., to handle the formation of clusters from nucleons (and their possible destruction) via a microscopic and dynamical model involving the explicit effects of nuclear forces. Emission of light charged clusters prior to the eventual evaporation is generally described on a phenomenological basis, either by the standard coalescence model [230, 231] (in momentum space) or by percolation models applied at the end of the cascade stage [232]. In the approach realized in the current INCL4, the cluster emission relies on the microscopic phase space occupancy at the nuclear surface. They are emitted according to the following procedure: (1) When a nucleon hits the surface and satisﬁes successfully the test for emission, i.e., has sufﬁcient energy and escapes reﬂection (after the usual test of comparing a random number with the calculated transmission probability through the appropriate barrier including Coulomb potential for the protons), it is tested to see whether it belongs to a possible cluster. Such a cluster is deﬁned as a set of nucleons which are sufﬁciently close to each other in phase space. Actually, the candidate cluster is constructed, starting from the considered nucleon, by ﬁnding a second, then a third, etc., nucleon fulﬁlling the following condition: ri,[i−1] pi,[i−1] ≤ h0 ,

(2.48)

where ri,[i−1] and pi,[i−1] are the Jacobian coordinates of the ith nucleon, i.e., the relative spatial and momentum coordinates of this nucleon with respect to the subgroup constituted of the ﬁrst [i − 1] nucleons. The following light clusters are considered: d, t,3 He,4 He. (2) Fast nucleons are checked for emission at R(pF ), in the outer fringes of the nucleus, where the density is very small and where they have little chance of being in a cluster. Particles are checked for emission so far away, since they may undergo collisions before reaching this place. To correct for this, the candidate is moved for

105

106

2 The Intranuclear Cascade Models

emission along its trajectory until it is at a distance D outside the sphere of radius R0 , before building the possible clusters. (3) A hierarchy between clusters is established for testing their possible emission. It is evident, from the way clusters are constructed, that if the candidate nucleon belongs to a given cluster, e.g., an α-particle, it also belongs to a lighter cluster. Clusters are checked for emission in the following priority list: 4 He > (3 He or t)> d. In other words, the largest candidate cluster is ﬁrst tested for emission. The total energy of the cluster, including the potential energy, and corrected by the binding energy of the cluster, should be positive in such a way that a composite with positive kinetic energy can be emitted. Furthermore, it is checked whether the cluster can tunnel through the appropriate Coulomb barrier, comparing a random number with the relevant transmission probability. If these conditions are met, the cluster is emitted in the direction of its c.m. momentum. Energy conservation is fulﬁlled in this process. If the test for emission fails, then the next cluster candidate in the priority list is checked for emission on the same criteria, and so on. If the test for emission fails for all clusters, the original candidate nucleon is emitted (-resonances are not considered in the cluster formation). Summarized, this simple model appears as a kind of ‘‘surface-coalescence’’ model, compatible with two rather well-established features: the small probability of having pre-existing clusters inside nuclei, at least in medium-heavy and heavy ones, and the necessary dynamical generation of correlated clusters of nucleons near the surface before emission. Clusters can be emitted at any time during the cascade stage. This is to be in contrast with the composite emission in preequilibrium models, in which a cluster can be emitted from an uncorrelated target with a suitable probability. The cluster production model implemented in INCL4 utilizes the microscopic phase space distribution, as generated dynamically by the INC. It however contains some limited amount of phenomenology, since explicit coupling of individual nucleon and composite degrees of freedom is avoided and replaced by a geometrical construction, involving the introduction of two parameters h0 and D. In Ref. [117] which describes the surface-coalescence model implemented in INCL4 in detail, the values have been ﬁxed to h0 = 387 MeV fm/c (=pF × 1.4) and D = 1.75 fm. The value of h0 roughly corresponds to selecting a unit volume of phase space. The value of D is such that the cluster is formed in a region of relatively low density on the average. In Figure 2.34 the INCL4 surface coalescence model coupled with the GEM evaporation model (see Section 3.4.1 on page 144 has been confronted with experimental data of the NESSI collaboration for p, d, t,3,4 He ejectiles [233] emitted in the 2.5 GeV p + Au reaction at different angles (30◦ , 75◦ , 105◦ , 150◦ ) in respect to the incident proton beam. The experimental data range to energies as large as 200 MeV, allowing a meaningful test of cascade emission. The comparison with model calculations of INCL4 coupled to GEM shows an overall agreement being satisfactory. The evaporation contributions are well described for deuterons d and tritons t. However, the 3 He evaporation spectrum at larger angles seems to be underestimated. The 4 He evaporation peak is well reproduced by GEM. Also the production of alpha-particles in the cascade stage is underestimated. The comparison of

2.3 The Cugnon INCL Approach

10

: q = 30°

1 10

10

p

1

: q = 75°

−1

n

q = 30° q = 75°

−1

10 : q = 105°

10−2

: q = 150°

10−3

q = 105°

10−2

q = 150°

10−3

10−4

10−4 0

50

100

150

200

0

50

100

150 3

d2s/dΩdE [mb/sr Mev]

d

He

1

10−1

10−1

10−2

10−2

10−3

10−3

10−4

10−4

10−5

10−5

0

50

100

150

200 t

1

10−6

0

50

100

150

10

200 4

He

1

10−1

10−1

10−2

10−2

10−3

10−3

10−4

10−4

10−5

200

0

50

100

10−5 150 200 0 Particle energy [MeV]

Fig. 2.34 Double differential cross sections for proton, neutron, and light charged cluster d, t,3,4 He-production in the 2.5 GeV p + Au reaction (symbols: experimental data [233], histograms: full lines INCL4+GEM model including the coalescence option, dotted lines: without coalescence). Different symbols

50

100

150

200

correspond to different emission angles as indicated. In each panel, the cross sections are given in absolute values for the smallest angle. They are multiplied by 10−1 , 10−2 etc., for the other angles, in increasing order. Note the different vertical scales (after Boudard et al. [117]).

107

2 The Intranuclear Cascade Models 102 Residue mass production cross section s(A) [mb]

108

Pb (1 GeV/A) + proton 10

1

10−1

0

25

50

75 100 125 150 Atomic mass number A

175

200

Fig. 2.35 Comparison of INCL4-ABLA model results for residue mass production in the proton+208 Pb system of 1 GeV energy with experimental results of Enquist et al. [68] with and without cluster production in the INCL4 model (histograms: full lines INCL4+GEM model including the coalescence option, dotted lines: without coalescence, dots: experimental results) (after Boudard et al. [117]).

calculations and experimental data in Figure 2.34 clearly indicates that the cascade production of protons and cluster particles is not negligible. As expected, clusters in the cascade stage are formed at the expense of neutron and proton production. This is particularly noticeable for protons (cf. Figure 2.34, upper-left panel) at small angles in the energy range spanning from 40 to 100 MeV, whose yield is clearly underestimated when the coalescence option is chosen in the INCL4 model. Figure 2.35 of Boudard et al. [117] shows a comparison of INCL4-ABLA model results for residue mass production in the proton+208 Pb system of 1 GeV energy with experimental results of Enquist et al. [68] with and without cluster production in the INCL4 model. There is only a small difference in the residues production. The lack of residue production in the low mass region suffers from the used ABLA model [221, 222] which is not able to evaporate light particles already mentioned in [172] (cf. Section 3.5). A comprehensive discussion and comparison of the results with and without cluster formation in the cascade stage is left for Ref. [117]. Also comparisons of INCL4 coupled to the ABLA evaporation code [221, 222] as an alternative statistical evaporation code are performed. On summarizing the following observations are made: including the coalescence concept, as expected, about 20% less free nucleons are emitted in the cascade stage. However, this is overcompensated by the emission of nucleons bound within the emitted clusters. In the cascade stage, the total multiplicity of the emitted nucleons, free or bound, is increased by 10% for neutrons and 15% for protons. With the cluster scenario activated in the code, the emission of nucleons is facilitated for three reasons:

2.3 The Cugnon INCL Approach

1 removing a bound system costs less energy than removing all of its nucleons independently; 2 tunneling through the potential + Coulomb barrier favors the emission of clustered nucleons: for instance, the tunneling probability is smaller for an α-particle than for a proton, but the test is applied only once for the latter. The probability of the uncorrelated emission of two protons and two neutrons is equal to the square of the proton emission probability multiplied by the square of the neutron emission probability; 3 inherent to the scenario itself, probably the emission of a group of nucleons is favored, which otherwise would have somehow diverging trajectories. The excitation energy E ∗ at the end of the intranuclear cascade is not really changed when the cluster emission is added. Consequently, the evaporation multiplicities are not really changed either. In sum, the total yield of emitted neutrons (either free or bound) is increased by ≈4% and that of emitted protons by ≈7%. The production of light charged clusters in the cascade stage of spallation reactions opens the possibility of having a uniﬁed INC + evaporation model handling cluster emission on the same footing as nucleon emission, ﬁlling a long-standing gap. Nonevaporative light cluster emission has often been handled by introducing a so-called pre-equilibrium stage between the cascade and the evaporation stages. In this stage, based ordinarily on exciton models, emission of clusters is usually treated on a phenomenological basis, just by attaching cluster emission probabilities, generally ﬁtted to experiment, to exciton conﬁgurations. The method presented here has thus the double advantage of being more microscopically founded and of allowing the emission of composites at any time. It remains the extension of the coalescence model implemented in INCL4 to the production of heavier composites (6,7 Li, 8 Be, 9,10 B, C,. . .) and the extension of the model to low incident energies (less than ≈100 MeV). 2.3.2 Assumptions, Limits, and Constraints on the Energy and Application Regime

The INCL model in its newest form (cf. Ref. [117, 172, 234]) is a well-validated INC model applicable in the energy range from 0.2 to 2.0 GeV for the incident energy per nucleon. As for any INC model the basic physical assumptions apply also for the INCL model as has been outlined in detail in this chapter. As already mentioned, the basic fundamental assumptions of the INCL approach resemble to a large extent the semiclassical microscopic description of a collision between a particle and a nucleus as outlined in detail in Section 2.2 for the BERTINI model. In the INCL model latest physics insights and nuclear data ﬁndings and improvements have been incorporated and some new features as described in Section 2.3 have been considered (diffuse nuclear surface, treatment of the Pauli blocking improved, progressive depletion of the Fermi sphere, collisions between moving spectator nucleons explicitly suppressed, rest angular momentum included, history of all

109

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particles followed as a function of time, self-consistent determination of the stopping time). As incident particles not only proton, neutron, and π + , π − or π 0 are considered, but the INCL model has been extended to light incident clusters of nucleons (deuteron, triton, 3 He, 4 He). The applicable incident particle energy regime in INCL is essentially subject of the same constraints and restrictions as the ones for Bertini, i.e., approximately 100–3000 MeV. In contrast to the BERTINI model, for INCL also versions for antiproton–nucleus interactions [212] had been developed. Unfortunately in latest releases the antiproton–nucleus description has been abandoned, such that the interested user would have to return to older releases. As for the description of high-energy composite ejectiles, a major step has been achieved in 2004 [117]. A surface percolation procedure of the nucleus has been developed which is proposed to describe the emission of light charged clusters during the cascade stage in nucleon–nucleus reactions. Clearly as mentioned earlier, in the family of INC codes the newest version of the INCL model appears to be the most sophisticated and elaborated code including latest hadron and meson reaction data, and reaction mechanisms. It therefore manifests apparently superior to, e.g., the BERTINI approach. The model is tested successfully against a large database (cf. Ref. [234] and references therein).

2.4 The ISABEL Model

The ISABEL INC model was developed by Yariv and Fraenkel [162, 164] during the years 1978–1981 and is implemented as an event generator in the particle transport code LAHET [193] and the system MCNPX [194]. The ISABEL model is an INC model based on the Monte Carlo method for hadron–nucleus and nucleus–nucleus interaction in the energy range from about 0.1 to 1.5 GeV/particle. The model allows in the original version as incident particles hadrons, pions, kaons, and antinucleons. The model is based on the VEGAS model of Chen et al. [11, 235] and on the ISOBAR model of Harp et al. [79, 161]. The model was further developed and extended to take into account heavy-ion reactions [162, 164, 167, 236], including additional options for the nuclear potential density distributions [163], subthreshold π 0 production [166], and a revised Sternheimer–Lindenbaum isobar model for pion production [167, 237, 238]. 2.4.1 Features of the Model

The nucleon–nucleon cross sections used in ISABEL are free nucleon–nucleon cross sections via the parameterization used in the VEGAS model [11, 235]. The differential cross sections for the intranuclear nucleon–nucleon collisions are obtained by interpolation of tabulated values, which give normalized differential cross

2.4 The ISABEL Model

sections for elastic scattering, together with the corresponding total cross sections for neutron–proton collisions, for proton–proton collisions, and neutron–neutron collisions [11]. The pion production and pion absorption are included in the ISABEL model via the 33 -resonance formation as a pion–nucleon isobar in nucleon–nucleon scattering as given by Harp [79]. This is very similar to the realization of the BERTINI and INCL models (cf. Sections 2.2 and 2.3). A physics model for antiproton–nucleus interactions to describe antinucleon annihilation is also employed in the ISABEL model (cf. Ref. [165]). 2.4.1.1 The Nuclear Model • The nuclear charge distribution: the original VEGAS model [11] uses nuclear charge distributions as measured by Hofstadter [199, 239] according to a Fermi distribution given by

ρ(r) = ρ0 /[1 + exp(r − c)/a],

(2.49)

where the ‘‘sharp radius’’ is c = 1.07 · A1/3 fm and the so-called skin thickness is a = 0.55 fm. These parameters are identical to the BERTINI model (cf. Section 2.2). The ISABEL model includes some additional options for the nuclear charge density distributions named as the Yukawa-folding distributions [163], which takes into account a reduction of the nuclear potential energy in such cases where the ﬁnite range of the nuclear force and the diffuse nuclear surface become important. A step function distribution is used to approximate the nuclear charge distribution. The target nucleus is divided into several concentric zones, e.g., 8 to 16 zones, each of constant density, respectively. The ratio of the proton to the neutron density is assumed to be Z/(A − Z) in all concentric zones of the nucleus (cf. Sections 2.2 and 2.3). The relative densities in the 8–16 constant density zones are ﬁtted to a folded Yukawa sharp-cutoff density distribution [163] with a sharp cutoff radius cISABEL = 1.18 · A1/3 fm different to the VEGAS model. • The momentum distribution: as assumed by the BERTINI and the INCL model, the momentum distribution of the nucleons inside the nucleus is a degenerate Fermi gas distribution with the Fermi energy given as EFi = (2 /2m) · (3π 2 · ρi )2/3 ,

(2.50)

where the subscript i stands for either protons or neutrons, m is the nucleon mass, and ρi is the density of protons and neutrons. • Antiproton–nucleus interactions: for antinucleons of kinetic energy EN GeV, the following parametrizations are used (cf. Ref. [165]):

NN σtotal = exp[4.5485 · exp(−0.060 · ln EN ) (mb), NN σelastic

= exp[4.6052 − 1.0365 · exp(0.380 · ln EN ) (mb),

(2.51) (2.52)

111

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2 The Intranuclear Cascade Models

σ

pp−→nn

charge-exchange

= 4.40/ EN

dσ/dt = exp(b · t),

(mb), and

b = 12.94 + 39.03 · exp(−2.075 · Plab ),

(2.53) (2.54) (2.55)

where t is the four-momentum transfer in (GeV/c2 ) and Plab is the laboratory antiproton momentum in (GeV/c). These parametrizations are valid in an energy range 0.1 GeV < Ep < 3.0 GeV. The Coulomb interactions between the target nucleus and the incident or emitted charged particle is explicitly considered [167]. The refraction of the particles just outside the nuclear boundary is determined by taking into account the Coulomb potential there. 2.4.1.2 The Time-Like Basis Cascading of Particle–Nucleus Interactions An important difference to other INC models compared to the ISABEL model lies in the sequence in which the history of particles taking part in the intranuclear cascade is followed. Previous models, i.e., of Metropolis et al. [4, 5] or of BERTINI [12, 77] follow one particle at a time from its ﬁrst interaction with another cascade particle or its entrance into the nucleus until either its energy falls below a certain cutoff energy or it escapes from the nucleus. In the ISABEL model the development of the intranuclear is followed on a time-like basis [167, 238]. The method to follow an intranuclear cascade on a time-like basis was originally described and used in the VEGAS model by Chen et al. A short description of the main steps of the method is given below. More details are given in Ref. [11]. • At the beginning of the intranuclear cascade the total nonelastic cross sections σtotal-proton and σtotal-neutron of the incident particle with a stationary proton and neutron in the laboratory system, respectively, are determined and an approximate mean free path λ of the incident particle is then determined as

λ = (A/ρmax )/ Z · σtotal-proton + (A − Z) · σtotal-neutron ,

(2.56)

where ρmax is the total nuclear density in the center of the nucleus. Equation (2.56) gives a sufﬁcient good estimate of the mean free path for the selection of a time interval, if there are no resonances in σtotal-proton and σtotal-neutron . The ﬁrst time interval τ is then given by τ = λ/nβ,

(2.57)

where β is the velocity of the incident particle. The nucleon distribution is assumed to be that of a degenerated Fermi gas. A good estimate of n is n =20–30 as calculated in Ref. [11]. • An impact parameter is randomly chosen. The momentum from the interaction of the incident particle with a proton or neutron of the Fermi zone of the nucleus is determined.

2.4 The ISABEL Model

• The path length is determined according to Eq. (2.57) as λ/n = β · τ . If no interaction takes place, the particle is transported by the path length λ/n = β · τ , a new value of τ is calculated for the next time interval, and a new candidate for the interaction is chosen and the process is repeated until the particle makes an interaction or escapes from the nucleus. • If an interaction takes place in a given time interval, the position of the interaction is determined, the particle is transported to this point, and the energy of the outgoing particle is calculated. Outgoing particles are checked for the Pauli principle violation. • At the end of each time interval a new candidate for an interaction partner is chosen and a new time interval τi is for each particle determined: τi = λi /nβi .

(2.58)

The smallest τi is the one that is chosen for the next time interval τ = min[τi ].

(2.59)

• The Fermi sea is now depleted and the cascade starts again. The whole cascade process stops when all the cascade particles leave the target volume or fall below a certain energy cutoff, which sets the limit between the cascade stage of the intranuclear cascade and the pre-equilibrium and theevaporation stages (cf. Section 1.3.4). The cutoff energy for neutrons must be at least its separation energy EF + EB and the cutoff energy for protons must be the separation energy plus the Coulomb barrier EF + EB + EC , where EF , EB , and EC are the Fermi, the binding, and the Coulomb barrier energies, respectively. The advantage of the time-like basis procedure is the possibility in changing the global properties of the cascade as the cascade proceeds. As the cascade develops the density of the participating Fermi sea is depleted. In the ISABEL model a prescription for this density rearrangement named as slow density rearrangement is foreseen [167]. After each collision a hole of radius rmin is punched in the density distribution of the conﬁguration space of the nuclear system around the actual position of the nucleon–nucleus interaction. No more interactions are allowed in this hole. The best rearrangement prescription was found to be isospin-dependent holes with a radius of rmin,I = 1.1 fm for nucleon–nucleus and nucleus–nucleus collisions. The depletion of the Fermi sea affects the Pauli blocking. Two possibilities of Pauli blocking procedures similar to the INCL model (see Section 2.3.1.6 on page 97) full Pauli blocking and partial Pauli blocking can optionally be chosen in the ISABEL model. 2.4.1.3 Nucleus–Nucleus Collisions The extension of the ISABEL model for nucleus–nucleus collisions uses several assumptions [162, 164]. In the nucleus–nucleus collision one has two Fermi seas interacting with each other.

113

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2 The Intranuclear Cascade Models

• To calculate the interaction between nucleons of the projectile Fermi sea and the nucleons of the target Fermi sea the projectile Fermi sea is assumed to be a gas of discrete particles whose position in space and momenta can be randomly chosen from the appropriate distribution. • For calculating the interaction between the discrete cascade particles and the Fermi sea of the projectile or the target, the latter two distributions are considered continuous. • The above procedure treats the collision in the same manner as in nucleon–nucleus INC calculations. It ensures the equal treatment of projectile and target, i.e., the Lorentz invariance of the calculation. Following the interactions processes on a time-like basis has also in nucleus–nucleus collisions the advantage to include interactions between cascade particles –cascade–cascade interactions (Ref. [164]) – which is neglected in previous versions of the ISABEL model (cf. Ref. [11, 162]). In addition, the ISABEL model considers the reﬂection and refraction of cascade particles at the zone boundaries of the nucleus. 2.4.2 Assumptions, Limits, and Constraints on the Energy and Application Regime

The important features of the ISABEL model are to follow the intranuclear cascade on a time-like basis and to accommodate nucleus–nucleus interactions. Many other features are similar to the models of VEGAS or BERTINI (cf. Ref. [11, 12, 155, 235]) and especially of the INCL model (cf. Ref. [117, 170–172, 240]). The ISABEL model is only applicable up to incident particle energies of 1.5 GeV per nucleon. Antinucleon–nucleus interactions to calculate the very strong attraction between antiprotons and nuclei have also been employed in the model [165].

2.5 The CEM (Cascade-Exciton Model) Approach

The CEM model (cascade-exciton model) was originally developed at the JINR, Dubna, by Gudima, Mashnik and Toneev [173] during the 1980s and further improved by Mashnik and co-workers [41, 174, 175, 241–249] during the last few years. The CEM model considers the spallation reactions as proceeding through three stages [173]: (i) cascade, (ii) pre-equilibrium, (iii) equilibrium. The last stage considers the compound nucleus evaporation and ﬁssion. All these three components contribute to a reaction of a high-energy particle interacting with matter, which has already been discussed in Section 1.3.4. In this respect the CEM model is different to pure cascade models, e.g., the models of BERTINI, INCL or ISABEL. The improved versions of the CEM model are named as CEM03 and LAQGSM03 (Los Alamos quark gluon string model) [175, 247, 249, 250]. The improved versions of the CEM model are also able to treat nucleus–nucleus reactions [249, 251].

2.5 The CEM (Cascade-Exciton Model) Approach

The cascade stage of the interaction is based on the standard version of the DUBNA model [10] (see also Section 2.6.1) with further improvements concerning the energy momentum conservation, a better approximation of the total reaction cross sections and using real binding energies for nucleons during the cascade stage [175]. The Los Alamos quark gluon string model LAQGSM is a further development of a model of Amelin et al. (Ref. [252] and references therein) and describes particle- and nucleus-induced reactions up to about 1 TeV/nucleon. The excited residual nucleus remained after the emission of cascade particles determines inside the CEM model the starting point for the second stage, the pre-equilibrium stage of the reaction. The subsequent relaxation of the nuclear excitation is then treated by an extended modiﬁed exciton model MEM [253] of the pre-equilibrium decay, which also includes a description of the equilibrium evaporation third stage of the reaction. The up to date version of the CEM03 model [175] includes in addition the evaporation model GEM [254, 255] to describe ﬁssion and light fragment production and the sequential binary-decay model GEMINI of Charity [229, 256, 257] (see details in Sections 3.4 and 3.6). 2.5.1 Features of the CEM Model

The three components of the CEMmodel, cascade, pre-equilibrium, and equilibrium, determine the inclusive cross sections of the spallation reactions in the following way [173]: σ (p )dp = σnonelas [Ncascacade (p ) + Npre−eq (p ) + Neq (p )],

(2.60)

where p is the linear momentum of a single particle state speciﬁed by its position vector r . The values N represent the total number of particle interactions considered by the cascade, pre-equilibrium, and equilibrium process, respectively. The nonelastic cross section σnonelas is not taken from experimental data, but is calculated within the cascade part of the CEM model by using the geometrical cross section of the target nucleus σgeom σnonelas = σgeom · Nnonelas /(Nnonelas + Nelas ),

(2.61)

where Nnonelas and Nelas are the total nonelastic and elastic simulated events. The value of the geometrical cross section is given as σgeom = π · R2 with R the radius of the last zone of the target nucleus. This approach provides a good agreement with available data at incident particle energies above about 100 GeV, but this is not valid at lower incident particle energies. For all incident protons and neutrons in the latest CEM model [244] the NASA systematics by Tripathi et al. [119–121] is used (cf. Section 1.3.7.5). As shown in Figure 2.36, these systematics describe much better the total reaction cross sections for neutron and proton-induced reactions at incident energies below about 100 MeV and correspondingly any other partial cross sections.

115

2 The Intranuclear Cascade Models

1200 n + 27Al

snonelastic [mb]

1000 800 600 400 200 0 10

800 snonelastic [mb]

116

Barashenkov '93 CEM2k CEM97 HMS-ALICE

100 1000 Incident neutron energy

p + 27Al

600 400 Barashenkov '93 CEM2k CEM97 HMS-ALICE

200 0 10

100 1000 Incident protron energy

Fig. 2.36 Total nonelastic reaction cross sections for neutron- and proton-induced reactions on Al calculated by CEM2k and CEM97 compared with experimental data compiled by Barashenkov [108] and calculations from the ALICE model of Blann [258, 259] (after Mashnik and Sierk [244]).

The INC DUBNA model version (see Ref. [10] and Section 2.6.1) inside the CEM model includes assumptions, which are similar to the BERTINI and INCL models. The target nucleus is divided into seven concentric spherical zones different to the BERTINI model which uses only three zones. • The CEM model uses a different approach to decide when a particle is leaving the cascade. For this purpose an effective local optical absorptive potential Wopt.mod. (r) is deﬁned from the local interaction cross section of the particle, including a Pauli blocking procedure. In models such as BERTINI, ISABEL or INCL, fast particles are followed down to some minimal energy, the cutoff energy Ecut (or in INCL to a certain cutoff time). This energy is usually about 7–10 MeV above the nuclear potential, below which particles are considered to be absorbed. The optical potential Wopt.mod. (r) calculated in the cascade model of CEM is related to its experimental value Wopt.exp. (r), which is obtained from analysis of data on particle-nucleus elastic scattering [173]. The difference of these potentials is given by a parameter P: P = |(Wopt.mod. (r) − Wopt.exp. (r))/Wopt.exp. (r)|.

(2.62)

2.5 The CEM (Cascade-Exciton Model) Approach

When P increases above an empirically chosen value, the particle leaves the cascade, and is then considered to be an exciton. In the CEM model a ﬁxed value P = 0.3 is used. With the value it was found that the cascade stage in CEM is generally shorter compared to other cascade models. • Recently published better systematics for pp, np, and nn interactions by Boudard and Cugnon et al. of the INCL model [172] and of Duarte et al. of the BRIC code [260, 261] are implemented in the CEM model and used instead of the 30-year-old data of the DUBNA INC model [10]. • When the cascade stage of the reaction is completed the CEM and LAQGSM models also use a coalescence model (cf. Section 2.3.1.9 and Refs. [250, 262]). The high-energy d, t, 3 He, and 4 He ejectiles are created by ﬁnal state interactions among cascade particles [250]. The subsequent relaxation of the nuclear excitation is treated in terms of an improved version of the modiﬁed exciton model of pre-equilibrium decay followed by the equilibrium evaporation-ﬁssion stage of the reaction using the models GEM and GEMINI (see Sections 3.4 and 3.6). If residuals after the INC cascade have atomic mass numbers with A ≤ 12, a Fermi break-up model is used [263, 264] (see Section 3.8) to determine their further disintegration instead of using the pre-equilibrium and evaporation models. The Fermi break-up model is much faster and the results are very similar to the more detailed models [249].

Figure 2.37 shows the benchmark examples of calculated neutron production spectra from the interaction of protons with a thin 208 Pb target at incident energies of 0.8 and 1.5 GeV compared with experimental data from Ishibashi et al. [265]. The CEM model describes well neutron spectra for proton–nucleus collisions. Similar results are obtained for other incident energies and for other target nuclei and even for nucleus–nucleus collisions (see Refs. [175, 249, 257]).

2.5.2 Assumptions, Limits, and Constraints on the Energy and Application Regime

As mentioned before, the cascade exciton model (CEM) is not a pure cascade model compared to the BERTINI, INCL, or ISABEL models. Many different physics simulation models are merged in CEM: the Dubna cascade model, the BRIC model, an EXCITON model, the evaporation models GEM and GEMINI, the RAL ﬁssion model, a quark gluon string model, a Fermi-breakup model, a Coalescence model, and a model to describe high-energy photonuclear reactions. The CEM model is very well validated although with its monolithic structure it may be difﬁcult to validate the signiﬁcance of different physics implications. The CEM model covers an energy regime from eV to several TeV. The advantage of the model is lying in the prediction of residual nuclei, ﬁssion fragments, low- and high-energy light particle such as d, t, 3 He and 4 He, and product yields and recoil properties from high-energy photonuclear reactions.

117

2 The Intranuclear Cascade Models

108 0.8 GeV protons on Pb

107 106 105 Double-differential neutron-production cross section d2s / dE/dΩ [mb/MeV/sr]

118

104 103 102 101

15 deg × 105 30 deg × 104 60 deg × 103 90 deg × 102 120 deg × 10 150 deg × 1 CEM2K CEM97

100 10−1 10−2 10−3

1

10

100

1000

108 1.5 GeV protons on Pb

107 106 105 104 103 102 101

15 deg × 105 30 deg × 104 60 deg × 103 90 deg × 102 120 deg × 10 150 deg × 1 CEM2K CEM97

100 10−1 10−2 10−3

1

10 100 Neutron energy Elab [MeV]

Fig. 2.37 Comparison of the measured double differential neutron production cross sections of Ishibashi et al. [265] from incident protons of 0.8 and 1.5 GeV energy with CEM2k and CEM97 calculations (after Mashnik et al. [175]).

1000

2.6 Other Intranuclear-Cascade Models

2.6 Other Intranuclear-Cascade Models

The previous sections on pages 64, 88,110, and 114 were devoted to such INC models which in general are currently utilized and implemented in the most important and commonly used Monte Carlo simulation systems for particle transport and interaction with matter (see also the introduction of Chapter 2 on page 63). For completion in the following section, a description and an overview of similar models are given mainly based on the previous ones. These modiﬁcations were sometimes undertaken for the purpose of special applications such as, e.g., cosmic ray studies, experimental background investigations, shielding of high-energy particles, and detector development and simulation in medium- and high-energy physics. 2.6.1 The Dubna Models

The INC models, in this section called the Dubna models, were independently developed in Dubna, Russia, during the 1960s and further in the 1970s. The ﬁrst advanced Dubna INC model developed by Barashenkov [266], similar to the BERTINI model [13] was then further developed by Gudima of the JINR, Dubna, during the years 1968–1969 [267]. First publications only in Russian are internal reports of the Joint Institute for Nuclear Research (JINR), Dubna (see Refs. [10, 78, 101, 266, 268]). The Dubna model was further developed by young people from Barashenkov’s school and also implemented as the INC model in many particle transport codes and models developed in Dubna, e.g., in the SHIELD system of Sobolevsky et al. [269, 270], and in the CEM model of Mashnik [32, 41, 174] which was discussed in Section 2.5. An INC model to describe heavy-ion collisions to study the behavior of hot and dense matter was also developed by Toneev and Gudima [262] during the 1970s based on the DUBNA INC model. Furthermore, INC models considering the trailing effect in intranuclear cascades, i.e., depletion of the nuclear density due to the knocking out of intranuclear nucleons by the cascade particle shower, were studied to determine explicitly the time coordinate during the development of the intranuclear cascade discussed in Ref. [271]. It should be noted here that the time coordinate was ﬁrst introduced into INC model calculations originally published by Chen et al. [11], where the cascade particle positions and their interaction points inside the nucleus were ﬁxed for a series of discrete time moments separated by a time interval t so small that the results of the calculations are practically independent of a further decrease of the time interval t. The whole process could be considered as continuously changing in time. It was found that the value of t should be smaller than the time which is necessary for a cascade particle to cover about 1/20–1/30 of its mean free path. That means the calculation time needed for cascade calculations would be exceptionally long.

119

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2 The Intranuclear Cascade Models

The approach given in Ref. [271] considers the time coordinates values only at interaction points. Intermediate times ti are included implicitly by the means of the integral t =

2

dS/V(S),

(2.63)

1

which determines the interval between two successive collisions of a cascade particle with intranuclear nucleons. V(S) is the particle velocity changing along a trajectory S as a function of the intranuclear potential variations. If an intranuclear collision is permitted by the Pauli principle, then for each of the created particles an interaction point is sampled and the corresponding moment of time ti = t + ti is calculated. Here t is the time of the particle’s creation and t is determined by Eq. (2.63), where the integral is replaced by the sum

2

dS/V(S) =

1

Sj /V j .

(2.64)

j

In Eq. (2.64) the Sj = Sj+1 − Sj are projections of the internucleon distances on the direction of the cascade particle momentum (Figure 2.38) and V j = 1/2(Vj + Vj+1 ) is the average velocity of this cascade particle in the interval Sj . The summation is performed over all nucleons inside a cylinder with the radius Rint = r + λ, where r 1.3 fm is the radius for the strong interaction and λ is the deBroglie wavelength deﬁned by Eq. (1.11). A similar method of time tracing the intranuclear cascade has been used by Bertini et al. [158], which is not included in the standard BERTINI model [12, 77]. Some of the common features of different Dubna models are as follows: • The matter density is described by a Fermi distribution with parameters taken from electron–nucleus scattering experiments [199, 239]. The nuclear outer radius is assumed to be 1.3 · A1/3 × 10−13 (cm), where A is the mass number of the target nucleus. The radial step distribution – the number of zones – of the nucleus is assumed as a three-step distribution similar to the Bertini model already introduced in Figure 2.6 on page 71. t + ∆ tn

t Rint

S1

S2

S3

Sn

Fig. 2.38 Movement of a cascade particle within a nucleus between successive collisions with intranuclear nucleons at the planes S1 and S2 . The particle is able to interact with any nucleon inside a cylinder with radius Rint .

2.6 Other Intranuclear-Cascade Models

A newer version of the Dubna model called CASCADE uses a seven-step distribution of the nuclear density [160]. The model takes the Pauli exclusion principle into account. • The hadron interactions are sampled by means of tables of phenomenological parameters [10]. Energy–momentum conservation and the decrease of the internuclear density due to a knock-out of nucleons during the intranuclear cascade which results in a depletion of the nuclear density [271] are determined and the time dependence of the intranuclear cascade is considered. The sampling of the nucleon coordinates inside the nucleus is carried out by the method of random rejection according to the Wood–Saxon nuclear density distribution ρ(r) with parameters from electron scattering experiments. • The interaction of the incident particle with the nucleus is approximated as a series of successive quasifree collisions of nucleons or pions with the nucleus similar to that in the BERTINI model. The model uses elementary nucleon–nucleon and pion–nucleon cross sections given in Ref. [108] simulating angular and momentum distributions of secondary particles by polynomial expressions with energy-dependent coefﬁcients [10]. Pion production and pion absorption processes are treated comparably to the Bertini model. Intercomparison of the Dubna, BERTINI, and VEGAS models A comparison of the Dubna model of JINR, Dubna, Russia, with the Bertini model of ORNL, USA [12, 155], and the VEGAS model of BNL, USA, of Chen et al. [11, 235] was made. Results are given in Ref. [13]. The three models were used to study the interactions of protons with incident energies of 150 and 300 MeV on thin 27 Al and 181 Ta targets. Compared were: (1) energy distributions of emitted protons at angles of 30◦ ± 5◦ and at 80◦ ± 5◦ , (2) excitation energy distributions for various residual nuclei produced in the INC process, and (3) mass yields produced. All of the models represent the nuclear radial density distribution by a series of radial zones inside the nucleus which approximates a Fermi distribution consistent with Hofstadter’s data on the radial variation of the nuclear charge distribution. The number of radial zones is different. The Bertini and the Dubna models use three zones whereas the VEGAS-Chen model uses eight. In all models the radial density distribution determines concentric zones, each having a constant density. The proton and neutron density, and the proton and neutron momentum distributions were determined as described by the BERTINI model on page 64. In the BERTINI and Dubna models the potential acting on the cascade particles in a certain zone is the sum of the proton or neutron Fermi energy in this zone and the average binding energy of a nucleon in the nucleus. The kinetic energy in both models of the cascade nucleon is increased or decreased as it travels from a potential region to another, but the direction of the nucleon is unchanged. Thus in these models refraction or reﬂection of cascade nucleons at potential boundaries is neglected.

121

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2 The Intranuclear Cascade Models

In the VEGAS-Chen model the potential is energy dependent and of the form V = Vzone · (1 − E/Emax ),

(2.65)

with E < Emax , V = 0 for E ≥ Emax , E is the kinetic energy of the nucleon and Emax is taken to be 100 MeV. The zone-dependent potential Vzone is given as Vzone = −(EF-zone + B)/[(1 − (EF-zone /Emax )],

(2.66)

where EF-zone is the Fermi energy in the particular zone for the same type of particle as the cascade nucleon and B is the average binding energy of a nucleon in the nucleus. The three different INC simulations compared in Ref. [13] give remarkably similar results in the particle spectra. Large discrepancies are observed in the excitation energy distributions of the cascade residual products. 2.6.2 The H¨ anssgen–Ranft Model

H¨anssgen and Ranft have chosen another approach to model the intranuclear cascade. A description of the model is given in Refs. [176–178] and some technical details of the program organization can be found in Refs. [272–274]. According to their ansatz, the nuclear cascade below 5 GeV kinetic energy can be split into two processes, namely the emission of cascade nucleons (simulated by the NUCRIN model [273]) and ‘‘one inelastic’’ hadron–nucleon collision of the projectile with ‘‘one’’ of the target nucleons at a reduced energy (simulated by the HADRIN model [274]). The authors justify the assumption of only one inelastic collision at a reduced energy with the experimental fact that the number of π − produced in inelastic hadron–nucleus collisions is less than the corresponding number for hadron–nucleon collisions. The average energy available for the emission of cascade nucleons and for the excitation of the residual nucleus is parameterized as a function of the atomic mass number A of the target nucleus and the kinetic energy E0 of the incident particle or projectile. For every event, the cascade energy Ecascade and excitation energy Eex are sampled from Gaussian distributions at around average values. The remaining energy is used to simulate an inelastic hadron–nucleon collision. The inclusive distribution of the cascade nucleons is assumed to factorize according to d2 Ni /dE d = fi (A, E0 , E) · g(A, E, ).

(2.67)

The index i denotes proton or neutron, E is the kinetic energy, and is the emission angle of the cascade nucleon. After sampling E from the distribution fi , the emission angle is sampled from the normalized function g. This procedure is repeated until the cascade energy is less than the binding energy of the nucleons in the target nucleus. Then, the remaining cascade energy as well as the kinetic

2.6 Other Intranuclear-Cascade Models

energy of all particles falling below some cut-off value is added to the excitation energy of the residual nucleus. For the modeling of inelastic hadron–nucleon collisions the most important assumption is that all inelastic channels are produced by quasi two-body reactions which produce one or two resonances in the intermediate state according to one of the following equations: h1 + h2 −→ h3 + h∗4 h1 + h2 −→ h∗3 + h∗4 h1 + h2 −→ h∗3 .

(2.68)

Here, h1 and h2 denote the incident particle or projectile and the target nucleon, respectively. The parameters h∗3 and h∗4 denote the produced resonances in the intermediate state. The production cross sections of all resonances contributing more than 2% to the total inelastic cross section are taken into account. The scattering angles of the intermediate state resonances are determined from the four-momentum transfer t, which are sampled from the distribution dσ/dt = N · exp[B(M) · t],

(2.69)

where t is the four-momentum transfer t = (p1 − p3 )2 , N is a normalization constant, and B(M) a mass-dependent slope parameter. After the type and scattering angle of the outgoing resonances are determined, a decay algorithm (DECAY) determines their subsequent decay [272]. Up to three decay particles are considered and the decay channels are sampled from tabulated branching ratios. After the decay which is assumed to be isotropic in the rest system of the decaying particle, the products are Lorentz transformed into the laboratory system. This procedure is repeated until all particles are stable. It should be noted that the cascade particles have no kinematical correlation to each other, since the cascade is not followed in detail but sampled from inclusive distributions. In contrast, in the microscopic models, the BERTINI model [12], the VEGAS -Chen model [11, 235], the ISABEL model [164, 167], and the INC-Li`ege model [117, 170, 172, 212] energy and momentum conservation is satisﬁed at each reaction vertex in the nucleus. This also allows for a simple implementation of total momentum conservation, which does not hold for the NUCRIN model [273]. 2.6.3 The MICRES Model

The MICRES model [275–277] was developed to overcome the limitations of INC models in considering all resonances in elementary collisions contributing more than 2% to the total cross section up to kinetic energies of 5 GeV. In addition, angular distributions based on phase shift analysis are used for elastic nucleon–nucleon as well as elastic and charge exchange pion–nucleon scattering.

123

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2 The Intranuclear Cascade Models

Also kaons and antinucleons can be treated as incident particles. A similar model was also designed with a revised pion production model and described in Ref. [278]. For the NUCRIN model of H¨anssgen and Ranft, see Section 2.6.2, the way of emitting cascade nucleons is unsatisfactory, since it leads to the loss of the kinematical correlations which is important when treating problems like estimation of backgrounds in exclusive experiments. As shown below, it even cannot account for particle production spectra to the same level of accuracy as more microscopic models. On the other hand, for certain applications the BERTINI or INCL Li`ege models are limited to relatively low energies due to the fact that only the formation of the 33 -resonance is included. This must not be a limitation for more inclusive problems, e.g., to calculate the energy deposition in a thick absorber or for calorimeter simulations, but may again lead to discrepancies when using the model for background simulations in exclusive experiments. Here, the correct multiplicity in each event is essential. Applying trigger conditions may suppress those ﬁnal states which make up the major part of the total cross section but do not affect other channels which contribute relatively little to the total cross section. The argument that the latter can be neglected does not hold anymore. This is especially true for light nuclei where larger multiplicities stem only from one- or two-step processes and the emission of additional cascade nucleons is not important. To overcome those shortcomings the positive features of NUCRIN/HADRIN and the BERTINI model are combined, i.e., the inclusion of all resonances contributing more than 2% to the total cross section in hadron–nucleon collisions and the microscopic description of the intranuclear cascade is considered. The precision of the resonance model used inside the HADRIN model is shown in Figure 2.39 where measured and calculated total cross sections for various channels are given for pion as incident particles. For kaon projectiles the accuracy is the same as seen in Ref. [176]. In most cases the data are reproduced within the experimental error. The basic idea for the improvement is to use the more sophisticated HADRIN model for the elementary hadron–nucleon collisions inside the nucleus and to keep the microscopic description of the cascade and the nuclear model of the BERTINI model basically unchanged. The ansatz in the MICRES model is very similar to that given in Ref. [178]. Another advantage of this procedure is the extension of the BERTINI model to all other particles which are accepted by HADRIN, namely antinucleons and kaons. For this aim a model of Cloth et al. [279] was used as a starting version and all necessary modiﬁcations were performed to include the HADRIN description for hadron–nucleon collisions. In addition, it was found that the parameterization of the differential cross section equation (2.69) as used in HADRIN is not sufﬁcient for reproducing the elastic nucleon–nucleon collisions inside the nucleus, i.e., the intranuclear cascade, to the same accuracy as in the original INC code. Therefore, normalized angular distributions have been calculated from nucleon–nucleon phase shifts as given by Arndt et al. [280, 281]. For the elastic and the charge exchange scattering of pions the phase shifts of the Helsinki group are used [282]. By assuming the principle of isospin invariance, the following relations hold:

2.6 Other Intranuclear-Cascade Models

2

p++p exclusive channels total inelastic pp+p0 np+p+ pp+p+p− pp+p+p−p0

Cross section [µb]

104

4

2

103

0.6 0.7 0.8 0.9 1.0

2.0

3.0

4.0

Particle momentum plab [GeV/c ]

Fig. 2.39 Comparison of experimental and calculated exclusive total reaction cross section as given by H¨anssgen and Ranft [176].

dσ d (pp

→ pp) =

dσ d (nn

→ nn)

dσ + d (π p

→ π + p) =

dσ − d (π n

→ π − n)

dσ − d (π p

→ π − p) =

dσ + d (π n

→ π + n → π + n)

dσ 0 d (π p

→ π 0 p) =

dσ 0 d (π n

→ π 0 n)

dσ + d (π n

→ π 0 p) =

dσ − d (π p

→ π 0 n)

=

dσ 0 d (π p

→ π + n)

=

dσ 0 d (π n

→ π − p).

(2.70)

The angular distributions for elastic and charge exchange scattering of charged pions and for elastic scattering of nucleons on proton have been incorporated into MICRES by tables in the energy range from 0.05 to 3 GeV/c laboratory momentum of the projectile in bins of 50 MeV/c. A linear interpolation is used in between, and for higher momenta the distribution at 3 GeV/c is used. For all other channels the simple parameterization of Eq. (2.69) is done. Since in the energy range under consideration, pions and nucleons are by far the most important shower particles, there should be no need for a similar precise description of other particles. Also for

125

2 The Intranuclear Cascade Models

200

stot [mbarn]

175 150 p+ p

125

p− p

100 75

pp

np

50 25 0

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

Particle momentum plab [GeV/c ] Fig. 2.40 Total cross sections for nucleon–nucleon and pion–nucleon scattering as used in theMICRES model.

30 Total cross sections stotal [mb]

126

pp→pp (elastic) MICRES

25 20 pp→pnp +

15 10

pp→ppp0

5 0

0.5

1

1.5

pp→ppp+p− 2 2.5

3

Energy [GeV] Fig. 2.41 Calculated pp-scattering cross sections with the MICRES model compared with experimental data [214].

the total cross section of pions and nucleons tables were calculated from the phase shifts mentioned above. Here an energy binning of E = 20 MeV/c from 0 to 4 GeV/c is used. Also in this case, for higher momenta the cross section at 4 GeV/c is used. This is justiﬁed because there is only a very small momentum dependence of σtot in the GeV energy range (see Figure 2.40). Calculations of pp-scattering cross section [283] with the MICRES model were compared with experimental data of Ref. [214]. Figure 2.41 shows the values of the absolute cross sections of the most important exit channels of the pp-scattering from [214] at energies of 793, 1500, and 2589 MeV. The cross sections are normalized to the total cross section. The elastic scattering cross section and the pnπ + are in good agreement with the experimental results, whereas the cross section ppπ 0 is lower by a factor 3 at lower energies and the cross section ppπ + π − is a factor 2 higher at higher energies. The main goal for the development of the MICRES model was to provide an event generator to support experimentalists in detector design and data analysis of experiments in the medium energy range up to 5 GeV/c. The MICRES model was therefore implemented into the GEANT detector simulation package [100, 284].

2.7 Alternative Models

The EDDA collaboration [285] has performed a great number of simulations to test the validity of the MICRES model, has simulated the EDDA experiment during its design and has estimated the detector performance especially the contributions concerning the background [277, 283]. The essential steps in simulating inelastic hadron–nucleus collision by the MICRES model are described in more detail in Ref. [277].

2.7 Alternative Models

In addition to the INC models, the presently most commonly used alternative models are microscopic models which follow the time evolution of the onebody phase space distribution and models which are based on n-body molecular dynamics. The microscopic models for the one-body Wigner phase space have different names although they solve the same equation. The models differ in their technical realization, i.e., in the numerical algorithms or the computer programs. The models are named as Boltzmann–Uehling–Uhlenbeck (BUU) as cited in [187–189, 286] and as Vlasov–Uehling–Uhlenbeck (VUU) as cited in [190, 286, 287]. The approach beyond the one-body description is the quantum molecular dynamics (QMD) model as cited in [183, 184, 191, 288–291] which is an n-body theory simulating ion reactions at intermediate energies on an event-by-event basis. The QMD model has the advantage to take into account ﬂuctuations and correlations that means calculating many-body processes by treating the formation of complex fragments. The QMD model is also capable of analyzing on an event-by-event basis ion reactions similar to the methods which are used for the simulation of INC methods [191]. Although the QMD approach was developed for heavy ion collisions, it is interesting to use the QMD approach for spallation reactions on nucleon–nucleus, meson–nucleus, or lightion-nucleus-induced reactions [184–186, 292]. Since QMD and BUU calculations for proton–nucleus reactions generally are CPU consuming models in particular for nuclei with a large number of nucleons, they still do not ﬁnd routine applications in spallation relevant issues so far albeit the physics implemented is most realistic. A detailed description of the quantum molecular dynamics approach shall not be contents of this book. Therefore, we restrict ourselves to giving some important references and a short overview about QMDs in the next sections. 2.7.1 The Quantum-Molecular-Dynamic (QMD) Model

The QMD theory includes, in a self-consistent way, many important aspects of the nucleon-induced reaction mechanisms of particle interactions at the intermediate energy range [185], i.e., (1) a realistic momentum distribution of the nucleons inside nuclei, (2) entrance and exit channel refraction, (3) Coulomb deﬂection, (4) multistep processes, (5) multiple pre-equilibrium emission processes

127

128

2 The Intranuclear Cascade Models

(MPEs), (6) variation of the mean-ﬁeld potential due to particle hole excitation and particle emission, (7) transition between unbound and bound states, and (8) energy-dependent, anisotropic N–N elastic and nonelastic scattering including the Pauli blocking effect. All these features make the QMD model a useful tool to determine the systematics of nucleon-induced processes ﬁrst investigated by Peilert et al. [291]. Niita et al. [184] analyzed (N, xN ) reactions by QMD models plus a statistical decay model, Chiba et al. [185] determined nucleon-induced preequilibrium reactions in terms of quantum molecular dynamics, and Polanski et al. [292] studied QMD models to describe ﬁssion and fragment production applying proton–nucleus interactions. Although the QMD method is widely used to study nuclear fragmentation [189], the details of the prescription may differ from author to author. 2.7.1.1 The Equation of Motion and the Reaction Treatment In the following the prescription of a simple QMD standard model, useful for spallation interactions, derived by Niita et al. [184], is given. The model takes into account relativistic kinematics and the relativistic correction for the effective interaction. In addition, the and N ∗ (1440) resonances of the nucleon are treated, and pions with their isospin degrees of freedom in the equation of motion are taken into account. A statistical decay model SDM is incorporated to compare various measured double differential cross sections calculated with the QMD model for proton-induced reactions with incident energies from 0.1 GeV up to 3.0 GeV. In the QMD approach all nucleons are spread out in the phase space with a Gaussian wavefunction of width L [183–185, 191]:

i (r − Ri )2 + r · Pi , φi (r) = 1/(2πL)3/4 · exp − 4L

(2.71)

where Ri and Pi are the centers of the position and the momentum of the ith nucleon, respectively. The total wavefunction is assumed to be a direct product of these wavefunctions. Thus the one-body distribution function is determined by a Wigner transform of the wavefunction, f (r, p) =

fi (r, p),

(2.72)

i

2L(p − Pi )2 (r − Ri )2 − . fi (r, p) = 8 · exp − 4L 2

(2.73)

The time evolution of Ri and Pi is described by Newtonian equations and the stochastic two-body collision term. The Newtonian equations are derived on the basis of the time-dependent variational principles [183] as R˙ i = ∂H/∂Pi ,

P˙ i = −∂H/∂Ri ,

(2.74)

2.7 Alternative Models

where the Hamiltonian H consists of the single-particle energy including the mass term and the energy of the two-body interaction. Further the Skyrme-type effective N–NMinteraction2) plus the Coulomb, and the symmetry energy terms are taken into account. By using the Gaussian function of the nucleons (cf. Eq. (2.73)), it follows (see Ref. [184]) that H=

B 1 A 1 · ·

ρi +

ρi τ 2 ρ0 1 + τ ρ0τ i i i √ 1 e2 · erf |Ri − Rj |/ 4L + ci · cj · 2 |Ri − Rj | Ei +

i,j( =i)

Cs · (1 − 2|ci − cj |) · ρij , + 2ρ0

(2.75)

i,j( =i)

with Ei = mi2 + P2i , and erf as the error function. In Eq. (2.75) the parameter ci has the value 1 for protons and the value 0 for neutrons. The quantity ρi deﬁnes an overlap of the density with other nucleons and is deﬁned as

ρi ≡

ρij ≡

j =i

drρi (r)ρj (r)

j =i

=

(4πL)−3/2 exp[−(Ri − Rj )2 /4L],

(2.76)

j =i

with ρi (r) ≡

dp · fi (r, p) (2π)3

= (2πL)−3/2 · exp[−(r − Ri )2 /2L].

(2.77)

Niita et al. [184] have used the following parameters in Eqs. (2.76) and (2.77) for their QMD simulations to validate spallation reactions in the energy range from 0.1 GeV up to 3.0 GeV. (a) The symmetry energy parameter Cs is chosen to be 25 MeV. (b) The remaining four parameters, the saturation density ρo , and the Skyrme parameters A, B, and τ are ρ0 = 0.168 fm−3 , A = −219.4 MeV, B = 165.3 MeV, and τ = 4/3, respectively. (c) These values give a binding energy/nucleon 16 MeV for inﬁnite nuclear matter at the saturation density ρ0 and a compressibility 237.3 MeV for nuclear matter limit. (d) The only arbitrary parameter in QMD, the width parameter L, is ﬁxed as L = 2.0 fm2 . In the QMD approach of Niita et al. [184] to calculate nuclear cascades, nucleon–nucleon collisions are considered when the impact parameter of two √ nucleons is smaller than a value of σ/π , where σ denotes the energy-dependent 2) The Skyrme-type interaction for nuclear structure calculations is based of the mean effective internucleon potential in the shell

model description of nuclei derived by T.H.R. Skyrme 1958 (for details see Refs. [293, 294]).

129

2 The Intranuclear Cascade Models

N–N cross section for elastic or nonelastic N–N collisions. A parametrization of the N–N cross sections is used [184] similar to the INCL model of Cugnon et al. [210] to take into account the in-medium effects which reduce the absolute magnitude and the forward peaking of the N–N cross sections. The Pauli blocking of the ﬁnal phase space is checked after each collision. In order to treat spallation reactions of particles with higher incident energies in the QMD model, the nucleons N, deltas (1232), N ∗ (1440)’s, and pions with their isospin degrees of freedom are included. In the following, a list is given of all channels included in the collision term: (1) (2) (3) (4) (5) (6) (7) (8)

Bi + Bj −→ Bi + Bj , N + N −→ N + , N + −→ N + N, N + N −→ N + N∗ , N + N∗ −→ N + N, N + π −→ , N + π −→ N∗ , + π −→ N∗ ,

(2.78)

where B denotes a baryon and a N a nucleon. 2.7.1.2 The Cutoff Criteria – the Stopping Time of the QMD Process At the end of the fast stage of a QMD simulation the result yields many fragments, which are normally in highly excited states. Although the QMD models allow us to continue the simulation by applying then the decay process of the fragments, it might be in general only applicable if one can continue the calculation for a long enough time. Therefore, it is practically more useful to stop the fast stage of the 104 208Pb

ds/ dE [mb/MeV]

130

(p,xn) Ep = 1500 MeV tsw = 50 fm/c tsw = 100 fm/c tsw = 150 fm/c

103

102

101

0

20

40

60

80

100

Neutron energy [MeV] Fig. 2.42 The total neutron energy spectrum calculated by a QMD + SDM model with different switching times tsw as parameter (after Niita et al. [184]).

2.7 Alternative Models 104 Pb (p,xn) Ep = 1500 MeV

d2s/dΩdE [mb/sr/MeV]

208

103

Ishibashi et al. QMD +SDM from QMD from SDM

102 101 100 10−1 10−2 100

101 102 Neutron energy [MeV]

103

Fig. 2.43 Double differential neutron energy spectrum at 30◦ laboratory angle for the reaction p+208 Pb at Eproton = 1500 MeV. The solid line is the result of the QMD + SDM model simulation with a switching time tsw = 100 fm/c. The experimental data are taken from Ref. [296] (after Niita et al. [184]).

103 102

208

Pb (p,xn) Ep = 1500 MeV

103

15°

d2s / dΩdE (mb/sr MeV)

d2s / dΩdE (mb/sr MeV)

10 30° (×10−2)

10−1 10

−2

−4

60° (×10 )

10−3 10−4

90° (×10−6)

10−5 10−6 10

−7

QMD + SDM Ishibashi et al.

QMD + SDM Ishibashi et al.

1

15°

100 10−1

30° (× 10−2)

10−2 10−3 10−4 10

60° (×10−4)

−5

10−6

90° (×10−6)

10−7

10−8 10−9 100

Pb (p,xn) Ep = 1500 MeV

102

101 100

208

10−8 101

102

103

10−9 0

500

En (MeV)

1000

1500

En (MeV)

Fig. 2.44 Double differential neutron energy spectrum at different laboratory angles for the reaction p+208 Pb at an incident beam energy Eproton = 1500 MeV. The x-axis En is plotted in a logarithmic scale on the left-hand side, and in a linear scale on the right-hand side. The experimental data are taken from Ref. [296] (after Niita et al. [184]).

QMD at a certain time and switch to a statistical decay SDM model (cf. Chapter 3). There two reasons for such a coupling: (i) the time scales of the dynamical and statistical processes are quite different, e.g., for the fast stage about 10−23 s to 10−22 s and 10−21 s to 10−15 s, respectively. (ii) A more fundamental reason is that the

131

2 The Intranuclear Cascade Models

Fermi statistics which describe the decay process of the fragments may not be treated correctly by QMD simulations [184, 295]. In QMD cascade spallation reaction simulations one may identify fragments together with their excitation energies at about 100–150 fm/c. The dependence of different switching times tsw when the QMD simulations are stopped and switched to a SDM model is depicted in Figure 2.42, where the total neutron energy spectrum determined by the model QMD + SDM is shown as a function of the neutron energy. It was concluded that the results are not sensitive to the switching tsw as long as it is chosen after the time when thermal equilibrium is achieved. A switching time of about 100 fm/c seemed to be sufﬁcient. 2.7.1.3 Selected Examples of QMD Simulations Figure 2.43 shows a typical double differential neutron spectrum at 30◦ laboratory angle for the reaction protons +208 Pb at an incident proton energy Ep = 1500 MeV. The ﬁgure shows the spectra obtained by the QMD + SDM model, by the QMD model only, and the SDM model with a switching time of tsw = 100 fm/c. Simulations have been shown that the sum of the two components of the spectrum (QMD and SDM) will be almost unchanged if an adequately long time is chosen for the switching time tsw (cf. Figure 2.42). Figures 2.44 and 2.45 show a comparison of double differential neutron energy spectra determined by the QMD + SDM simulations with experimental data of 208

103

Pb (p,xn)

Ep = 3000 MeV

208

Pb (p,xn) Ep = 3000 MeV

103

15°

102

102

101

QMD + SDM Ishibashi et al.

101 30° (×10−2)

100

d2s / dΩdE (mb/sr MeV)

d2s / dΩdE (mb/sr MeV)

132

10−1 10−2

60° (×10−4)

10−3 10−4

90° (×10−6)

10−5 10−6

10−1

10−3 10−4 60° (×10−4)

10−5 10−6

QMD + SDM

10−7

10−8

Ishibashi et al.

10−8

100

30° (×10−2)

10−2

10−7

10−9

15°

100

101

102 En (MeV)

103

90° (×10−6)

10−9 0

Fig. 2.45 Same as Figure 2.44 for the reaction p+208 Pb at an incident beam energy Eproton = 3000 MeV. The experimental data are taken from Ref. [296] (after Niita et al. [184]).

1000 2000 En (MeV)

3000

2.7 Alternative Models

Ishibashi et al. [296] for a Pb target with incident proton energies of 1.5 and 3.0 GeV at different laboratory angles. Such data, from 1 MeV up to the incident beam energy, play an important role in the ﬁelds of application of accelerators, such as spallation sources, accelerator transmutation systems, and shielding of cosmic rays in space activities. For an efﬁcient comparison the same results are shown in the two ﬁgures with the x-axis in a logarithmic and a linear scale, respectively. The present QMD model plus a SDM model of Niita et al. [184] is applied on (N,xN’] reactions for a broad range of incident proton energies from 100 MeV to 3000 MeV on different target masses. The model reproduces the double differential neutron production spectra quite well without changing the used parameter set given above. Although there are many parameters in the model which are not extensively studied, the neutron spectra do not depend very much on them [184].

133

135

3 Evaporation and High-Energy Fission 3.1 Introduction

As mentioned in Chapter 2, in practice for modeling pN or NN reactions intranuclear cascade or equivalent models are applied in order to describe the ﬁrst stage of a nuclear collision. These INC calculations are stopped once it can be assumed that equilibrium has been achieved (cf. Section on page 98). After equilibration is reached, generally an evaporation model is appended to account for the full nuclear reaction process. This chapter is devoted to models which are needed to continue the de-excitation process after the fast stage of the spallation process (cf. Section 1.3.4, page 21) and describes the modeling of the de-excitation and the associated particle emission of the highly excited nucleus remaining after the intranuclear cascade or the fast stage of the spallation reaction. Most of the models apply the statistical theory of evaporation from the excited compound nucleus, which was originally developed by Weisskopf [8]. All the models are based on similar essential assumptions; however, the individual models differ in their particular algorithms or their implementations. Dostrovsky et al. [7, 297, 298] have described a Monte Carlo model based on this theory which is known as the Dresner EVAP model [299]. The original EVAP model [299] has been further revised by Guthrie [300, 301], by Cloth et al. [88] taking into account, (i) the atomic mass tables of Ref. [302], (ii) the level density parameters with shell corrections by Baba [303], and (iii) by Prael [193]. Prael added to the version of EVAP in LAHET [193, 304] a level density parameter using the energy-dependent formulation of Ignatyuk [305–307]. The latest version of the EVAP model is described in Section 3.3. A generalized evaporation model GEM was recently developed by Furihata et al. [255, 308] and described in Section 3.4. In Sections 3.5 and 3.6 two important evaporation models, the abrasion-abla model ABLA by Schmidt et al. [221, 222] and a binary sequential decay model GEMINI by Charity [229, 256] are discussed. High-energy ﬁssion becomes an important nuclear mechanism for nucleon collisions in the spallation energy regime mainly with high atomic mass targets. In this case there is competition between ﬁssion and evaporation at each step of the nuclear de-excitation process [309, 310]. Evaporation models such as the EVAP or the GEM models are linked with ﬁssion models developed, e.g., by Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

136

3 Evaporation and High-Energy Fission

Atchison [311–313] and by Alsmiller et al. [314], see Section 3.7. Other evaporation models included their own ﬁssion model algorithms (cf. Sections 3.5 and 3.6 on pages 154, 159). In addition, the subsequent de-excitation of the residual nucleus left after the fast stage of the spallation reaction may optionally employ a multistage multistep pre-equilibrium exciton model ﬁrst proposed by Grifﬁn [315, 316]. If residuals after the fast stage of the spallation cascade have atomic mass numbers with A ≤ 17, a Fermi breakup model may be used [263, 264] (see Section 3.8) to determine their further disintegration instead of using the pre-equilibrium and evaporation models. The Fermi breakup model is much faster and the results are very similar compared to the more detailed models [249]. At the very end of the deexcitation process when the excitation energy falls below some speciﬁed cutoff, usually at about 7 MeV, further deexcitation is assumed to occur by evaporation or emission of photons with discrete energies. There exist libraries with a large number of isotopes with experimentally measured excited level energies, spins, parities, and relative transition probabilities [317]. Models for the evaporation of photons, e.g., the Los Alamos PHT model [304] and the FZ-J¨ulich NDM model [88] are discussed brieﬂy in Section 3.9. Section 3.10 about vaporization and multifragmentation completes this chapter. The interested reader is also referred to the book of Cole [318] which provides in greater detail the theoretical considerations of the statistical models for nuclear decay as elements of equilibrium statistical mechanics, single- and multistep evaporation, sequential binary decay and multifragmentation, statistical models for multifragmentation, e.g., the Copenhagen liquid drop model, the Metropolis algorithm, percolation, caloric curves and vaporization.

3.2 The Statistical Model in its Standard Form

The basic principles of the nuclear reactions are ﬁrst postulated by Bohr [309, 319] and the theory of the emission of particles from excited compound nuclei is originally due to Weisskopf [8, 320]. An excellent overview is given by LeCoutier [9]. The theory of Weisskopf is based on the following assumptions: • The formation and decay of the compound nucleus are independent. • The total energy and the angular momentum are conserved. • All possible decay channels are occupied with identical probability. • In the case of barriers existing for particular decay channels, the probability for that occupational state is reduced by a transmission coefﬁcient. • The intrinsic degrees of freedom of the compound nucleus are equilibrated and a quasistationary situation of collective degrees of freedom at the saddle point is assumed. In any statistical evaporation model generally an excited compound nucleus decays via ﬁssion or by the emission of light particles. For the particle emission the

3.2 The Statistical Model in its Standard Form

partial decay width ν (E ∗ , J) can be expressed as a function of angular-momentumdependent level densities ρ of the initial and ﬁnal state and the transmission coefﬁcients Tl , J +s

ν (E ∗ , J) =

f ∞ 1 · 2πρ(E ∗ , J)

J+S

l=0 S=|Jf −s| |J−S|

·

E ∗ −E

r (Jf

)−Bν

0

ρ(E ∗ − Bν − Eν , Jf )Tl (Eν ) dEν .

(3.1)

The coupling of the angular momenta of the mother nucleus J and the residual Jf is performed via the angular momentum l of the emitted particle ν with Spin s and energy Eν . E ∗ represents the thermal excitation energy of the parent nucleus. Er (Jf ) is the rotational energy of the residual nucleus, Bν is the particle binding energy and S = Jf + s. The transmission coefﬁcients1) are based on the ﬁt of optical potentials of elastic scattering data, which partly are quite uncertain [321]. In contrast to the channel for particle decay, the ﬁssion decay widths do not depend on particle level densities or other statistical properties of residuals (here the fragments in inﬁnite distance), but following the hypothesis of Bohr–Wheeler on the properties of the compound nucleus at which the level density exhibits a minimum between equilibrium location and separated fragments [8, 320]. This point is generally named saddle point conﬁguration; the angular-dependent potential energy (ﬁssion barrier Bf (J)) has its maximum for this conﬁguration. Fission is handled analog to the particle decay [309, 322], fBW (E ∗ , J) =

1 2πρ(E ∗ , J)

E ∗ −Bf (J)

ρ(E ∗ − Bf (J) − Ek ) dEk .

(3.2)

0

The transmission coefﬁcient is equal to 1, in the case of the total energy exceeding the ﬁssion barrier; else it is set to 0. The ﬁssion barrier Bf (J) can be calculated employing the ‘‘Rotating Finite Range Model2) .’’ Very similar to the calculation of intrinsic or thermal excitation energy determining the density of the quantum mechanical states, k represents the kinetic energy at the saddle point and not the asymptotic relative kinetic energy. For hot nuclei with E ∗ Bf + k , Eq. (3.2) can be simpliﬁed as fBW =

Bf T exp − . 2π T

(3.3)

In this equation, fBW only depends on temperature and ﬁssion barrier. 1) In the statistical model GEMINI the transmission coefﬁcients are taken from the ‘‘incoming wave boundary condition’’ model [229].

2) GEMINI [229] uses the conditional barriers for symmetric ﬁssion as calculated by Sierk [229, 323].

137

138

3 Evaporation and High-Energy Fission

Hot nuclei de-excite via many successive decay steps until after particle emission, γ -emission, or possibly ﬁssion only a heavy residual or cold ﬁssion fragments remain in a ground state. Generally statistical codes used nowadays follow the decay of an individual compound nucleus of a given ensemble by Monte Carlo methods, until the residual does not emit particles anymore, or as a competing process of particle emission, ﬁssion is favored. The precision of any observable predicted in a statistical model depends on the abundance of its appearance and the number of simulated cascades. The modiﬁcations necessary in the statistical model for taking into account nuclear dissipation and therefore a delay of the ﬁssion process are taken into account, e.g., in the ABLA and GEMINI models in Sections 3.5 and 3.6. Besides the transmission coefﬁcients, the partial emission widths (cf. Eq. (3.1)) are mainly determined by the nuclear level densities. For a given thermal excitation energy E ∗ and considering a nucleus as a Fermi gas of A independent particles, the level density ρ(E ∗ ) given by the number of possibilities E ∗ can be distributed on the different single particle states, e.g., [324] ρ(E ∗ ) =

1√ π a(q)−1/4 (E ∗ )−5/4 exp 2 a(q)E ∗ . 12

(3.4)

As the thermal excitation energy E ∗ of a nucleus increases, excited level stages get closer together in energy. At large E ∗ , the density of excited levels is 1/D with D being the average distance between the levels with the form 1/D ∝ exp(2 · (a · E ∗ )2 ), where a affects the decay width of particles emitted during the evaporation process and called the level density. For the level density parameter a(q) in the literature simple relations such as a = A/x (x = 7 to 14 MeV) are found as well as phenomenological approaches which take the inﬂuence of the surface structure and shape of the nuclei into account. Different parameterizations exist [305, 306, 325, 326], partly even considering a dependence on the temperature of the decaying system [327]. The level density parameter is deﬁned by [324] a(q) =

π2 g(q) 6

with

g=

3A 2 · EF

(3.5)

with g(q) being the nucleus shape-dependent single particle level density at the Fermi energy EF and representing the sum of proton- and neutron-level densities. For the validity range of the statistical model, the following shall apply: EF · A−1 E ∗ EF · A1/3 .

(3.6)

The lower limit is given by the condition that E ∗ should be large compared to the energy g −1 of the ﬁrst excited level of the Fermi gas. With increasing E ∗ , the level density increases or the number of degrees of freedom of single particle states and

3.3 The Evaporation Model EVAP of Dostrovsky–Dresner

therefore the entropy S = ln ρ. In this context the nuclear temperature T can be introduced, T −1 =

∂S ∂E

= V

1 ∂ρ . ρ ∂E

(3.7)

Using the level density ρ(E) given in Eq. (3.4) the temperature can be expressed as a 1/2 5 T −1 = − E −1 + , 4 E

(3.8)

with E EF A−1 and Eq. (3.5) a E −1 and therefore with the Fermi gas expression E = a · T 2.

(3.9)

The following sections are committed to the description of speciﬁc models generally employed for modeling the statistical evaporation and high-energy ﬁssion processes.

3.3 The Evaporation Model EVAP of Dostrovsky–Dresner

In the following a short outline of the EVAP model is given with the basic assumptions which have been considered in the model. More speciﬁc details about the GEM model can be found in Section 3.4. Although the GEM model is based on the classical Weisskopf–Ewing formalism, the GEM model is a signiﬁcant step in solving light fragment production from medium-energy proton-induced spallation reactions. As mentioned in Section 3.1, the basic theory of evaporation was developed by Weisskopf [8] and Weisskopf–Ewing [320]. The EVAP model originally developed by Dostrovsky et al. [7] has been continuously reﬁned. The different EVAP model versions are summarized in Table 3.1. The revised versions of the EVAP model are implemented, e.g., in the ORNL CALOR [195], the LANL- LAHET, and the MCNPX [113, 193, 194, 304, 328] code systems. The probability Pi (E) that a nucleus excited to the energy U will emit a particle of type i having kinetic energy E is given by Weisskopf as Pi (E) ∝ (2Si + 1) · mi · σinvi (E) · ω(E ∗ ) with i = emitted particle type (n, p, d, t, 3 He, 4 He), E = kinetic energy, Si = spin of the emitted particle, mi = emitted particle mass,

(3.10)

139

140

3 Evaporation and High-Energy Fission Tab. 3.1

The different versions of the EVAP evaporation model.

Model

Comments

Nuclear mass data

EVAP - original model Dostrovsky et al., [7, 297, 298] and Dresner [299]

- 19 types of emitted particles from any compound nucleus: (n,p, d, t,3 He,4 He,6 He,6,7,8,9 Li,7,9,10 Be) and (6,7,8 Li,7,10 Be) with excited statesa

- Tables by Wapstra [329, 330] and Huizenga [331] - semiempirical formula of Cameron [332, 333]

EVAP-NEW - EVAP-2/EVAP-3 Guthrie [300, 301] - and updates by Cloth et al. [88], Prael et al. [113, 193, 304]

- 6 types of evaporated particles: (n,p,d,t,3 He,4 He)b - breakup of 8 Be into two 4 He particles excited recoil nucleus (A, Z ∗ ) - kinetic energy, Erecoil , of recoil nuclei - modiﬁed level density parameter: Ignatyuk [305, 306], Gilbert–Cameron–Cook [336, 337] and Baba formalism [303]

- shell plus pairing energy corrections for Z or N < 13 by Peele, Aebersold [334] - tables by Wapstra, Bos [302] Audi, Wapstra [335]

a The evaporated particles (6,7,8 Li,7,10 Be) have excited states lying at 3.56, 0.477, 0.430, 0.970, and 3.370 MeV above the ground state. b Only six types of evaporated particles are considered instead of Dresner’s original 19.

σinvi = the ‘‘inverse’’ cross section (see Eqs. (3.15) and (3.16)), e.g., the compound nucleus formation cross section corresponding to bombarding the residual nucleus with particles of type i and energy E, E ∗ = excitation energy of the residuals (A∗ ,Z∗ ), with E ∗ = U − Q − E, Q = binding energy, U = energy of the excited nucleus, ω(E ∗ ) = density of energy levels of the excited residual nucleus.

3.3.1 The Level Density Parameter in the EVAP Model

The density of states in a nucleus of A = N + Z nucleons at excitation energy E ∗ can be approximately represented in terms of the ‘‘level density parameter’’ a and is evaluated using the level density formula given below. This is the mass and isospin-dependent model which is used in the EVAP model of Dostrovsky et al. [7] and Dresner[299]: ω(E ∗ ) = exp 2 · a · (E ∗ − δ) ,

(3.11)

where δ = pairing energy, with δ = 0 for odd–odd nuclei and δ ≥ 0 for other nuclei. The parameter a = level density is computed as

3.3 The Evaporation Model EVAP of Dostrovsky–Dresner

a = A/B0 ·

1 + Y · 2 A2

(3.12)

with = A − 2Z the neutron excess. The parameters B0 ≈ 8-20 MeV−1 and Y ≈ 1.5 to 1.8 are a kind of ‘‘universal’’ constants. The quantity in parenthesis in Eq. (3.12) differs little from unity, so a realistic approximation of the parameter assumes a linear mass dependence, a∼

A MeV−1 . B0

(3.13)

This relation is used in the EVAP version of Dresner [299]. A commonly used value is a = A/8 MeV−1 . In the latest version of the EVAP model (cf. Table 3.1) two other parameterizations [193] for the level density parameter a are used. This is the energy-dependent formulation for a of Ignatyuk et al. [305, 306] with the provision lim a(E ∗ ) = a0 ,

(3.14)

E ∗ →0

Level density parameter a [MeV−1]

where E ∗ is the excitation energy and a0 is the Gilbert–Cameron–Cook (GCC) level density parameter [336]. The low- and high-excitation limits are given in Figure 3.1. A different approach for the mass-dependent level density parameter a is that of Cloth et al. [88]. It takes into account shell effects by using compiled level densities from neutron resonance measurements for about 200 isotopes of Baba [303] (see Figure 3.2). From experiments on nuclear level spacing it is observed that the level density is strongly inﬂuenced by the nuclear shell structure, with densities for 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0

50

100 150 Atomic mass number A

200

Fig. 3.1 Level density parameters as a function of the atomic mass number A. The points are Gilbert–Cameron–Cook values for atomic masses near the line of stability. The line is the Ignatyuk high-excitation limit. ¨ The circles are the Julich mass-dependent model (after Prael [193]).

250

141

3 Evaporation and High-Energy Fission

Level density parameter a [MeV−1]

142

35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0

50

100 150 Atomic mass number A

Fig. 3.2 Level density parameters as a function of the atomic mass number A. The thick line gives typical values for the original EVAP mass- and isospin-dependent model for masses near the line of stability ¨ of Dresner [299]. The circles are the Julich

200

250

mass-dependent model. For comparison the dotted line gives the A/8-dependence, the solid line gives the A/10-dependence, and the dashed line gives the A/14-dependence (after Prael [193]).

magic or nearly magic nuclei several orders of magnitude lower, Figure 3.2, than for mid-shell nuclei [303]. This is important on neutron production from spallation targets applying, e.g., lead or lead–bismuth materials [338]. These extensions in EVAP for the level density parameter are adopted into the LAHET code by Prael et al. [304]. Nowadays these new parameterizations are named the Gilbert–Cameron–Cook– Ignatyuk (GCCI) level density parameter (cf. Section 3.4 on page 143 about the physics in the GEM evaporation model). 3.3.2 The Inverse Cross Sections

The inverse cross section σinvi (Eq. (3.10)) in EVAP are those recommended by Dostrovsky et al. The cross section is taken to be the geometric cross section modiﬁed by an empirical expression to take into account the energy dependence, and a Coulomb barrier correction for charged particle emission. For neutrons the inverse cross section is given as σinvi -neutron (E) = α · (1 + β/E) · π R2 α = 0.76 + 1.93 · A1/3 α · β = 1.66 · A−2/3 − 0.05 R = 1.7 · A1/3 fm.

For charged particle emission the inverse cross section is given as

for E ≥ ki Vi πR2 · (1 + ci )(1 − kiE·Vi ) σinvi -charge (E) = 0 for E < ki Vi ,

(3.15)

(3.16)

3.4 The Generalized Evaporation Model (GEM) Parameters used in the EVAP model to compute inverse charged particle cross sections as a function of the charge Z of the mother nucleus (Dostrovsky et al. [7] and Cloth et al. [339]).

Tab. 3.2

Z

kproton

cproton

k4

10 20 30 40 50 60 > 70

0.36 0.51 0.60 0.66 0.68 0.69 0.69

0.08 0.00 −0.06 −0.10 −0.10 −0.10 −0.10

0.77 0.81 0.85 0.89 0.93 0.97 1.00

He

where Vi is the Coulomb barrier determined from the classical electrostatic expression (Eq. (3.17) and Section 2.2.2.3) and the factor ki is inserted to take into account approximately barrier penetration effects3) . The numerical values of ci and ki are those given by Dostrovsky et al. [7]. Values for protons and 3 He are given in Table 3.2, whereas values for the deuterons, tritons, and 3 He are determined from Eqs. (3.18): Vi =

Zi · Z · e2 , R + Ri

(3.17)

where e is the electron charge, Ri is zero for protons and 1.2 fm for all other particle types, Z is the parent nucleus, and Zi is the emitted particle: kdeuteron = kproton + 0.06, ktriton = kproton + 0.12, k3 He = k4 He − 0.06,

cproton 2 cproton ctriton = 3 c3 He = c4 He = 0

cdeuteron =

(3.18)

3.4 The Generalized Evaporation Model (GEM)

The generalized evaporation model (GEM) of Furihata [254, 255, 308] is based on the classical Weisskopf–Ewing approach [8, 320] as the EVAP model, which is restricted to the emission of particles up to 4 He only (cf. Section 3.3). It is obvious 3) The empirical expected Coulomb radius RC is larger than the sum of the radii of the mass distributions for R1 , R2 , e.g.,

Rc = R1 + R2 + (3.0 ± 0.5) (fm), and Ri = 1/3 1.12Ai − 0.93A1/3 (fm).

143

144

3 Evaporation and High-Energy Fission

however [340] that light nuclei heavier than 4 He particles can be emitted from excited nuclei via the evaporation process. In the GEM, 66 nuclides up to Mg are included as ejectiles. The ﬁssion model used in GEM is based on Atchison’s model [311, 312] as implemented in LAHET [110–113, 193], often referred to in the literature as the Rutherford Appleton Laboratory4) (RAL) model. The ﬁssion model of Atchison is discussed in Section 3.7. For GEM here only the differences and re-evaluated parameters compared to the standard Atchison approach are reviewed.

3.4.1 Evaporation Model in GEM

According to the Weisskopf approach [8], the probability Pj of evaporation of the particle j in its ground state with Aj and Zj from a parent compound nucleus i with Ai and Zi and with a total kinetic energy E in the center-of-mass system between energy E and energy E + dE is deﬁned as Pj (E)dE = gj σinv (E)

ρd (E ∗ − Q − E) EdE, ρi (E ∗ )

(3.19)

where E ∗ is the excitation energy of the parent nucleus i, d denotes a daughter nucleus produced after the emission of ejectile j, and ρi , ρd are the level densities (MeV−1 ) for the parent and daughter nucleus, respectively. Q denotes the Q-value of the reaction for emission of particle j. For the determination the Audi-Wapstra mass table [335] has been used. The statistical and normalization factor gj is deﬁned as gj = (2Sj + 1)mj /π 2 2 ,

(3.20)

where Sj and mj are the spin and the mass of the emitted particle j, respectively. The cross section σinv for the inverse reaction is evaluated from σinv (E) = σg · P(E)

(3.21)

where σg is the geometrical cross section. The evaluation and the parameters are given in Section 3.4.3. The 66 nuclides heavier than helium GEM are considered as ejectiles are not only in their ground state, but also in their excited states. Including the excited states in the particles emitted via the evaporation process enhances signiﬁcantly the yield of heavy particle emission [341]. The ejectiles listed in Table 3.3 are characterized by the following criteria: (i) isotopes with Zj ≤ 12, (ii) isotopes naturally existing or near the stability line, (iii) isotopes with half-life longer than 1 ms. For the barrier 4) Name originated from the Rutherford Appleton Laboratory, UK, where the code was developed.

3.4 The Generalized Evaporation Model (GEM) Tab. 3.3

The ejectiles taken into consideration in the GEM model.

Zj

Ejectiles

0 1 2 3 4 5 6 7 8 9 10 11 12

n p 3 He 6 Li 7 Be 8B 10 C 12 N 14 O 17 F 18 Ne 21 Na 22 Mg

d

t

4 He

6 He

7 Li

8 Li

9 Li

9 Be

10 Be

11 Be

10 B

11 B

12 B

13 B

11 C

12 C

13 C

14 C

15 C

13 N

14 N

15 N

16 N

17 N

15 O

16 O

17 O

18 O

19 O

20 O

18 F

19 F

20 F

21 F

19 Ne

20 Ne

21 Ne

22 Ne

23 Ne

24 Ne

22 Na

23 Na

24 Na

25 Na

23 Mg

24 Mg

25 Mg

26 Mg

27 Mg

28 Mg

8 He 12 Be 16 C

penetration probability P the form of Ref. [7] is used. The parameters for light particles (n, p, d, t, 3 He, and 4 He) are taken from Dostrovsky et al. [7] whereas those for IMFs (intermediate mass fragments) were adopted from the work of Matsuse et al. [342] (cf. Section 3.4.3). 3.4.2 The Decay Width in the GEM Model

The total decay width j is calculated by integrating Eq. (3.19) using Eq. (3.21) with respect to the total kinetic energy E from the Coulomb barrier V up to the maximum possible value (E ∗ − Q) (Q = binding energy) and is expressed as j =

gj σg ρi (E ∗ )

E ∗ −Q

E · P(E) · ρd · (E ∗ − Q − E)dE.

(3.22)

V

According to the Fermi gas model expression the total level density ρ(E ∗ ) = ρi (E ∗ ) of a nucleus summed over all the possible states with the angular momentum is given by the expression of Ref. [336]: π exp (2 a(E ∗ − δ) 12 a1/4 (E ∗ − δ)5/4 π 1 exp(E ∗ − Eo )/T = 12 T

ρ(E ∗ ) =

for E ∗ ≥ Ex∗ for E ∗ ≤ Ex∗ .

(3.23)

The parameters in Eq. (3.23) are as follows: • a (MeV−1 ) is the level density parameter usually given in its simplest form as a = A/B0 (MeV−1 ), e.g., a = A/8 (cf. Section 3.3.1).

145

146

3 Evaporation and High-Energy Fission

• δ (MeV) is the pairing energy of the residual of the daughter nucleus. The pairing energy δ is expressed as a sum of separate contributions from neutrons and protons. • Cook et al. [337] calculated Ex∗ for which the level density changes as Ex∗ = Ux + δ where Ux = 2.5 + 150/Ad . Ad is the produced daughter nucleus and U is the energy of the excited nucleus. • T is again the nuclear temperature given by 1/T =

a/Ux − 1.5/Ux .

(3.24)

• To obtain a smooth continuity between the two formulas, the E0 parameter is determined as follows: E0 = Ex∗ − T · log T − 0.25 log a − 1.25 log Ux + 2 aUx .

(3.25)

3.4.3 Parameter of the Inverse Cross Sections and the Coulomb Barrier

The formulas to determine the inverse cross sections and the Coulomb barrier are in principle similar to the ones used in the EVAP model (cf. Section 3.3.2, Eqs. (3.15)–(3.18), and Table 3.2)5) . Because the prescription is slightly different in the GEM model for completion the used ansatz in GEM will be considered below. The cross sections for the inverse reaction σinvi and the Coulomb barrier V are given by

σinvi (E) =

π · R2b · cn (1 + b/E) for neutrons π · R2b · cj (1 + V/E) for charged particles

V = kj ·

Zj · Zd · e2 , Rc

(3.26)

where the indices i and j stand for the incident particle and the emitted particle, respectively, and d is the index for the daughter nucleus. Rb is the radius of the geometric cross section σg = πR2b (fm2 ), kj is deﬁned as in Eq. (3.16), Rc is the Coulomb radius, and e is the electron charge. The GEM model uses two different parameter sets, one is named the ‘‘simple’’ parameter set, and the other is named the ‘‘precise’’ parameter set. • The simple parameter set: using the formulas of Eq. (3.26) the parameters are −1/3 1/3 + Ad ) (fm). So only r0 is needed as cn = cj = kj = 1 and Rb = Rc = r0 · (Aj the parameter for determining the inverse cross section. 5) See the publication of Dostrovsky et al. added as a note in Ref. [7] on page 699.

3.4 The Generalized Evaporation Model (GEM) Parameters used in the GEM model to compute inverse charged particle cross sections (Dostrovsky et al. [7] and (cf. Table 3.2)).

Tab. 3.4

Zd

k

k4 He

≤ 20 30 40 ≥ 50

0.51 0.60 0.66 0.68

0.81 0.85 0.89 0.93

c 0.0 −0.06 −0.10 −0.10

• The ‘‘precise’’ parameter set to estimate the inverse cross section is a combination of the approach of Dostrovsky et al. [7] and that of Matuse et al. [342]. (1) For n, p, d, t, 3 He, and 4 He Dostrovsky’s approach gives the following parameters for Eq. (3.26): −1/3

cn = 0.76 + 1.93Ad −2/3

b = (1.66Ad

−1/3

− 0.05)/(0.76 + 1.93Ad

)

(b = 0 for Ad ≥ 192) cp = 1 + c,

cd = 1 + c/2,

ct = 1 + c/3,

c3 He = c4 He = 0 kp = k, kd = k + 0.06, kt = k + 0.12, k3 He = k4 He − 0.06

(3.27)

where c, k, and k4 He are given in Table 3.4. (2) For protons and neutrons the nuclear distance is given with a radius 1/3 Rb = 1.5 · Ad , and for d, t, 3 He, and 4 He with a radius 1/3 1/3 Rb = 1.5(Ad + Aj ). (3) The nuclear distance for the Coulomb barrier given as Rc = Rd + Rj is for: neutrons and protons −→ Rd = 1.7 · A1/3 (Rj = 0) (fm) d, t, 3 He, and 4 He −→ Rj = 1.2 (fm). (4) IMFs emission parameters were adopted from the work of Matsuse et al. [342], where the critical distance was evaluated from fusion reactions of heavy ion systems. cj = k = 1, Rb = R0 (Aj ) + R0 (Ad ) + 2.85 (fm) Rc = R0 (Aj ) + R0 (Ad ) + 3.75 (fm), where R0 (A) = 1.12 · A1/3 − 0.86 · A−1/3

3.4.4 The Level Density Parameter GCCI in the GEM Model

In the calculation with the precise parameter set of the GEM model, the Gilbert–Cameron–Cook–Ignatyuk (GCCI) level density parameter [113, 193] is

147

148

3 Evaporation and High-Energy Fission

used, in which pairing corrections and the energy dependence of the level density parameter are taken into account, instead of the simple expression a = Ad /8 (see also the comments about the level density in the EVAP model, Section 3.3.1). The GCCI level density parameter is also employed in the LAHET code [113, 193]. For the calculation of the total decay widths, expressions (3.23) is used. The simple form ρ ∝ exp(2 a(E ∗ − δ)) as used in Dostrovsky’s evaporation model [7] is a good approximation for high excitation energies; however, it is not applicable for residual nuclei with small mass and at low excitation energy. In the GEM model, the GCCI level density parameter a (MeV−1 ) is given for produced residuals for charge numbers Zd ≤ 98 and numbers of neutrons Nd ≤ 150 – practically without limitation a = a1 ·

1 − exp(−u) 1 − exp(−u) + a2 1 − u u

(3.28)

where u = 0.05(E ∗ − δ), and

Zd < 9 or Nd < 9 Ad /8 Ad · (a3 + 0.00917 · S) for all others

a2 = Ad · 0.1375 − 8.36 × 10−5 · Ad . a1 =

(3.29)

For deformed nuclei with 54 ≤ Zd ≤ 98, 86 ≤ Nd ≤ 122, or 130 ≤ Nd ≤ 150, the constants are given by a3 = 0.12 and a3 = 0.142 for all other nuclei. The shell correction S is the sum of the contributions from protons and neutrons, and is given as S = S(Zd ) + S(Nd ).

(3.30)

The shell correction parameters are tabulated in detail in Ref. [255]. 3.4.5 The High-Energy Fission Process in the GEM Model

The initial version of the GEM model only simulates spallation and does not calculate the process of ﬁssion, nor does it provide ﬁssion fragments and a further possible evaporation of particles from them. To be able to describe nuclide production in the ﬁssion region, the model has to be extended by incorporating a model for high-energy ﬁssion. In order to account for ﬁssion the GEM model is improved with Atchison’s ﬁssion or RAL model [311, 312] as implemented in LAHET [110, 111, 193]. There are two choices of parameters for the ﬁssion model in the improved version GEM2: one is the original parameter set by Atchison [311, 312], and the other one is a parameter set evaluated by Furihata [255, 308, 343]. The Atchison ﬁssion model is designed only to describe ﬁssion of nuclei with Z ≥ 70. It assumes that ﬁssion competes only with neutron emission,

3.4 The Generalized Evaporation Model (GEM)

i.e. from the width j of n,p,d,t,3 He, and 4 He; the RAL code calculates the probability of evaporation of any particle. When a charged particle is selected for evaporation, no ﬁssion competition is taken into account. When a neutron is selected for evaporation, the model does not actually simulate its evaporation; instead it considers that ﬁssion may compete and chooses either ﬁssion or evaporation of a neutron according to the ﬁssion probability Pf . The parameters for the ﬁssion used in the GEM model and their difference to the original ﬁssion of Atchison are discussed. More details about high-energy ﬁssion models and about the RAL ﬁssion model of Atchison are given in Sections 3.7 and 3.7.3. (1) Mass distribution: (a) Mass distribution σm-GEM in the GEM model of Furihata: The mass of a ﬁssion fragment produced by symmetric ﬁssion has a Gaussian distribution with mean Ai /2 with the index i as the fragment type and width σm . Furihata [308] assumed for the GEM model that σm based on experimental data from Refs. [344, 345] is given as σm-GEM = C1 · (Zi2 /Ai )2 + C2 · (Zi2 /Ai ) + C3 · (E ∗ − Bf ) + C4 , (3.31) with the coefﬁcients C1 = 0.122, C2 = −7.77, C3 = 3.32 × 10−2 , C4 = 134.0. The ﬁssion barrier Bf is given by Myers and Swiatecki [346]. σm-GEM is assumed to be constant for E ∗ − Bf > 450 (MeV). Figure 3.3 shows the Z2 /A dependence of the width σm-GEM of the ﬁssion fragment mass distribution.

Mass distribution width sm [MeV]

30.0 25.8 21.7 17.5 13.3 9.2 5.0 20

25

30

35

40

Z2 / A Fig. 3.3 The dependence of the dispersion of the ﬁssion fragment mass distribution on Z 2 /A where σm-GEM is determined by setting (E − Bf ) = 0 (cf. Eq. (3.31)) (after Furihata et al. [255]).

45

149

150

3 Evaporation and High-Energy Fission

(b) Mass distribution σm-RAL in the RAL model of Atchison: The σm-RAL in the original RAL model of Atchison is given as  3.97 + 0.425(E ∗ − Bf ) − 0.00212(E ∗ − Bf )2    for (E ∗ − Bf ) < 100 MeV σm-RAL =  25.27   for (E ∗ −Bf ) ≥ 100 MeV (2) Charge distribution: (a) Charge σZ-GEM in the GEM model of Furihata: The charge distribution of a ﬁssion fragment is assumed to be also a Gauss distribution of mean Zf and width σZ-GEM · Zf and is given as Zf =

Zi + Z1 + Z2 2

with Zx =

65.5 · Ax 2/3

131 + Ax

for x = 1, 2

(3.32)

The evaluation of formula (3.32) gives a value for σZ-GEM = 0.75, which gives better results for the RAL model. (b) Charge σZ-RAL in the original RAL model of Atchison: The original RAL model uses a value of σZ-RAL = 2.0. (3) Kinetic energy distribution: (a) The kinetic energy distribution with the parameters f and σf in the GEM model of Furihata: The kinetic energy of ﬁssion fragments is determined by a Gaussian distribution with mean Ef and width σEf . The reﬁnement of Furihata for the improved GEM model looks as follows:

Ef =

1/3

1/3

for Zi2 /Ai ≤ 900 0.131Zi2 /Ai 1/3 1/3 2 0.104Zi /Ai + 24.3 for 900 < Zi2 /Ai ≤ 1800 (3.33)

and

σE f =

1/3 C1 Zi2 /Ai − 1000 + C2 C2

1/3

> 1000

1/3 Zi2 /Ai

≤ 1000

for Zi2 /Ai for

(3.34) where C1 = 5.7 × 10−4 and C2 = 86.5. For details refer to [255]. (b) The kinetic energy distribution parameters Ef and σEf in the RAL model of Atchison: The original parameters in the Atchison model are given by 1/3

Ef = 0.133 · Zi2 /Ai

− 11.4

and σEf = 0.084 · Ef

(3.35)

3.4 The Generalized Evaporation Model (GEM)

Incident protons of 1 GeV on 208Pb

Cross section [mb]

102

Exp. data / GSI ISABEL / GEM ISABEL / PREQ / EVAP4

101

100

10−1 30

50

70

90 110 130 150 170 190 210 Atomic mass number [A]

Fig. 3.4 Comparison of the experimental mass distribution [68, 347] of nuclides produced in the reaction p(1 GeV) + Pb with different calculations (ISABEL + GEM and ISABEL + Preq + EVAP4).

Figure 3.4 confronts the experimental mass distribution of the inverse kinematics reaction p(1 GeV)+Pb measured at GSI [68, 347] with results found by merging ISABEL + GEM and ISABEL + Preq + EVAP4 [299]), respectively. The solid line shows the results of ISABEL merged to GEM as described in subsection 3.4.1 on page 144, while the dashed line is the ISABEL + Preq + EVAP4 [299] calculation. The combination of ISABEL+GEM reproduces the mass distributions of ﬁssion fragments with 50% accuracy, whereas ISABEL + Preq + EVAP4 does not reproduce the width and the heights of the distributions. The use of Furihata’s σm in the ﬁssion model improves the predictions [308]. As concerns the mass distributions of the spallation products shown in Figure 3.4, ISABEL + GEM and ISABEL + Preq + EVAP4 produce almost identical cross sections and for both models the isotopes predicted in the spallation region (not too far from the target) agree well with the experimental data [347]. It should be mentioned that the original RAL ﬁssion model has modiﬁed recently and improved by Atchison [313, 348]. The modiﬁcations of [313] however have not yet been taken into account in the improved GEM model. 3.4.6 Method of Computation

In the Monte Carlo simulation, ejectile j is selected according to the probability distribution calculated as pj = j / j j . The total kinetic energy E of the emitted particle j and the daughter nucleus (residual) is chosen according to the probability distribution given by Eq. (3.19). The angular distribution of the motion is randomly selected to be isotropic in the center-of-mass system. The excitation energy of the daughter nucleus (residuum) Ed is calculated as Ed = E ∗ − Q − E.

151

3 Evaporation and High-Energy Fission

The contribution of the emission of IMFs in a long living excited state is taken into account together with those which decay to the ground state. The condition for the lifetime of excited nuclei considered in GEM is as follows: T1/2 / ln 2 > / j∗ . The value of the decay width of the resonance emission j∗ is deﬁned as the emission width of the decaying ejectile and is calculated in the same way as for the ground state, i.e., by Eq. (3.22). Rather than treating a resonance as an independent particle, the decay width of the ground state is simply enhanced in the following way. The total emission width j of an ejectile is summed over its ground state j0 and all its excited states jn , i.e., j = j0 + n jn . The Q-value for the resonance emission is expressed as Q ∗ = Q + Ej∗ , with Ej∗ being the excitation energy of the resonance. The spin state of the ground state Sj is replaced by the spin state of the resonance S∗j for the calculation of gj in Eq. (3.19). The ground state masses mj are also used for the excited states, since the difference between the masses is negligible. The total kinetic energy distribution of the excited particle emission is assumed to be identical to that of the ground state particle emission. The values for S∗j , Ej∗ , and T1/2 have been taken from the Evaluated Nuclear Structure Data Files (ENSDF) database by the National Nuclear Data Center [317]. The original focus when developing GEM was put to the proper description of 7 Be nuclei produced by proton-induced reactions in the energy range 10 MeV to 3 GeV, because 7 Be is the most intensively measured light fragment produced from various targets, and many experimental data are available for comparison. The excitation functions of 7 Be produced by protons impinging onto the 27 Al target are shown in Figure 3.5 in comparison with different INC/GEM predictions. The open square symbols are experimental data taken from Ref. [340], and the dashed and solid lines are BERTINI and ISABEL [162, 164, 167] INC calculations coupled 102

Cross section [mb]

152

101

100

Exp. data INC/GEM ISABEL/GEM

10−1

10−2 101

103 102 Incident proton energy [MeV]

Fig. 3.5 The excitation function of the production cross section of 7 Be as a function of the proton incident energy on the 27 Al target.

3.4 The Generalized Evaporation Model (GEM)

to GEM, respectively. For ISABEL the code implemented in LAHET has been applied for incident energies below 1 GeV. The combination of ISABEL/GEM underestimates the cross sections by a factor of 2 for incident proton energies above 300 MeV. ISABEL/GEM produced less 7 Be than INC-Bertini/GEM does, because the average excitation energy calculated by the ISABEL model is lower than that predicted by the BERTINI model in the medium- to high-incident energy region. For detailed comparison to experimental data and model parameters confer Ref. [254]. Merging the improved GEM by Furihata [254, 255, 308] with the INCL or ISABEL model allows us to describe reasonably well ﬁssion and fragmentation/spallation reactions. This overall good agreement lends credibility to the approach; however, there are some drawbacks to be mentioned [175]: (1) Evaporation of up to 66 particles in GEM becomes extremely time consuming, in particular, when calculating reactions with heavy targets at high incident energies. (2) The current improved version of GEM2 suffers some lack of self-consistency, e.g., – using different not physically related parameterizations for inverse cross sections and Coulomb barriers for different particles and fragments; – using different level density parameters for the same compound nuclei when calculating evaporation and ﬁssion probability from the widths of neutron evaporation and ﬁssion; – different and purely phenomenological treatments of ﬁssion for pre-actinide and actinide nuclei; – not taking into account at all the angular momentum of compound and ﬁssioning nuclei; – rough estimations for the ﬁssion barriers and level density parameters, etc.

This means that an approach like the improved GEM [255] has the potential, in principle, to be used to describe ﬁssion and evaporation of particles and fragments heavier that 4 He after the INC, but it should be considerably improved, striving ﬁrst to progressively incorporate better physics, and then adjusting the selected data. An example for isotopic distributions of light fragments for He and heavier than He produced from 480 MeV protons on a Ag target is shown in Figure 3.6. The calculated results by Bertini-INC/GEM simulations are compared with experimental data of Ref. [349]. The simulations of He, Li, and Be production rates agree with the experimental data within an accuracy of about 50%, whereas Bertini-INC/GEM underestimate the cross sections for heavier fragment masses. All input parameters are given as standard parameters in the model. GEM is written in Fortran 77 and freely available, i.e., in the LAHET/LCS [113, 193] or MCNPX model packages. For further details of GEM interested readers are directed to Refs. [175, 254, 255, 308].

153

154

3 Evaporation and High-Energy Fission

103 Production cross section [mb]

He

Li

Be

B

C

N

O

F

Ne

102 101 100 10−1 10−2 10−3 10−4 4

66

8

8 10 8 10 12 10 12 14 12 14 16 Atomic mass number A

16 18 20 18 2018 20 22

Fig. 3.6 Isotope distributions of nuclei produced from 480 MeV protons incident on a nat Ag target, (open squares with dashed lines denote the Bertini-INC/GEM calculations, black circles with the solid lines denote experimental data from Ref. [349], the numbers given at the abscissa are the atomic mass numbers of the isotopes from He to Ne, only the even numbers are printed) (after Furihata et al. [255]).

3.5 The GSI ABLA Model

At GSI, the abrasion–ablation code system ABRABLA [221, 222] was developed and extended to describe also spallation reactions. For this purpose the BURST model [68, 350] developed at GSI was recently inserted in the ABRABLA code [351]. The ABLA code is part of the model ABRABLA describing the evaporation/ﬁssion competition in the decay of excited nuclei. Lately ABLA was improved by including a time-dependent ﬁssion decay width [352], emission of composite light-charged particles and intermediate mass fragments [350] as well as the simultaneous breakup. The particular strength of the ABLA code is the consideration of the dynamical nature of ﬁssion in the ﬁssion model taken into account. In the following some general but detailed features of the ABLA code are described although they resemble basically the assumptions of other evaporation/ﬁssion codes –though with some differences. ABLA is a dynamical code that describes de-excitation of the compound nucleus through the evaporation of light particles and ﬁssion. The probability that a compound nucleus with charge Z, neutron number N, and excitation energy E ∗ decays via channel ν is given by ν (Z, N, E ∗ ) , Pν (E) = ∗ i i (Z, N, E ) (3.36)

3.5 The GSI ABLA Model

where i denotes all the possible decay channels (speciﬁcally, neutron emission, proton emission, alpha emission, ﬁssion). The particle evaporation is considered in the framework of the Weisskopf formalism. The particle decay widths can be written as [8] 1 4mνR2 2 T · ρd · (E − Sν − Bν ), 2πρc (E) 2

ν (E) =

(3.37)

where mν denotes the particle mass, Sν is the particle separation energy, Bν is the effective Coulomb barrier that takes into account the tunneling through the barrier, R is the radius of the nucleus, T is the temperature of the residual nucleus after particle emission, and ρc and ρd are the level densities of the compound nucleus and the daughter nucleus, respectively. The density of excited states, ρ, is calculated with the well-known Fermi gas formula [353]: √ ρ(E) =

π exp(S) , 12 a1/4 E 5/4 eff

(3.38)

with the entropy S: S=2·

aEcorr = 2 ·

a(Eeff + δUk(Eeff ) + δP · h(Eeff ))

(3.39)

and the asymptotic level density parameter a as given in [305]: a = 0.073 · A + 0.095 · BS · A2/3 ,

(3.40)

where A is the mass of a nucleus, and BS is the ratio of the surface of the deformed nucleus to that of a spherical nucleus. δU is the shell correction, which for the ground state is calculated as the difference between the experimental ground-state mass and the corresponding macroscopic value from the ﬁnite-range liquid-drop model [323]. As pointed out already, at the saddle point, shell corrections are assumed to be negligible. The function k(Eeff ) describes the damping of the shell effects with excitation energy, and is calculated according to Ref. [305] as k(Eeff ) = 1 − exp(−γ Eeff ), with the parameter γ determined by γ = a/(0.4 · A4/3 ). The effective pairing energy shift δP is calculated as 1 δP = − 2 · g + 2, 4

(3.41)

√ with an average pairing gap = 12/ A, and the single-particle level density at the Fermi energy g = 6 · a/π 2 . h(Eeff ) parameterizes the superﬂuid phase transition [354] at the critical energy Ecrit = 10 MeV:

h(Eeff ) =

1− 1− 1

Eeff Ecrit

2

for Eeff < Ecrit for Eeff > Ecrit .

(3.42)

155

156

3 Evaporation and High-Energy Fission

The effective energy Eeff is shifted with respect to the excitation energy E ∗ to accommodate for different energies of even–even, odd-mass, and odd–odd nuclei: Eeff = E ∗ for odd–odd Eeff = E ∗ − for odd mass Eeff = E ∗ − 2 for even–even

(3.43)

As was shown in Ref. [222], collective excitations can contribute considerably to the nuclear level density. In deformed nuclei, the most important contribution to the collective enhancement of the level density originates from rotational bands, while in spherical nuclei the collective enhancement is caused by vibrational excitations. In ABLA, the contribution of collective excitation to the level density is described in the following way: for nuclei with a quadrupole deformation |β2 | > 0.15, the rotational enhancement factor Krot (Ecorr ) is calculated in terms of the spin-cutoff parameter σ⊥ : (σ⊥2 − 1)f (Ecorr ) + 1 for σ⊥2 > 1 (3.44) Krot (Ecorr ) = 1 for σ⊥2 < 1, with σ⊥2 =

JT , 2

Ecorr − Ec −1 f (Ecorr ) = 1 + exp , dc

(3.45)

where Ecorr is deﬁned in Eq. (3.39), J⊥ = 2/5m0 AR2 (1 + β2 /3) is the rigid-body moment of inertia perpendicular to the symmetry axis, and m0 is the mass unit. The ground-state quadrupole deformation β2 is taken from the ﬁnite-range liquid-drop model including microscopic corrections [355], while the saddle point deformation is taken from the liquid-drop model as given in Ref. [356]. The damping of the collective modes with increasing excitation energy is described by a Fermi function f (E) with parameters Ec = 40 MeV and dc = 10 MeV. The vibrational enhancement for spherical nuclei is generally smaller than the rotational enhancement for deformed nuclei. For nuclei with a quadrupole deformation |β2 | < 0.15, the 2 vibrational enhancement factor is calculated as Kvib (Ecorr ) = 50βeff Krot (Ecorr ), where βeff is a dynamical deformation parameter: βeff = 0.022 + 0.003N + 0.005Z. N and Z are the absolute values of the number of neutrons and protons, respectively, above or below the nearest shell closure. More details about collective enhancement can be found in Ref. [222]. Finally, the total level density is calculated as the product of the intrinsic level density given by Eq. (3.38) and Kvib (Ecorr ) and Krot (Ecorr ). To deﬁne the ﬁssion-decay width, apart from the level densities, the necessary ingredients are also the dissipation effect that will be described in the next subsection and ﬁssion barriers. The angular-momentum-dependent ﬁssion barriers are taken from the ﬁnite-range liquid-drop model predictions of Sierk [323]. In order to describe the ﬁssion fragments’ mass and charge distributions, as well as their kinetic energies, the ABLA code is coupled to the semiempirical ﬁssion model described below.

3.5 The GSI ABLA Model

157

3.5.1 Time-Dependent Fission Width

The modeling of the ﬁssion decay width at high excitation energies requires the treatment of the evolution of the ﬁssion degree of freedom as a diffusion process, determined by the interaction of the ﬁssion collective degree of freedom with the heat bath formed by the individual nucleons [357]. Such a process can be described by the Fokker–Planck equation (FPE) [358], where the variable is the time- and dissipation-dependent probability distribution W(x, p; t, β) as a function of the deformation in the ﬁssion direction x and its canonically conjugate momentum p. β is the reduced dissipation coefﬁcient. The solution of the FPE leads to a time-dependent ﬁssion width f (t) . The results for the case of 238 U at a temperature of 3 MeV for different values of reduced dissipation coefﬁcient β are shown in Figure 3.7 with solid lines. However, these numerical calculations are too time consuming to be used in nuclear-reaction codes. Therefore, in most of the model calculations one of the following approximations for the time-dependent ﬁssion width f (t) is used: a step function that sets in at time τf :

f (t) =

0 fk

for t < τf for t ≥ τf .

(3.46)

An exponential in-growth function: f (t) = fk (1 − exp (−t/τ )),

(3.47)

where τ = τf /2.3, with τf being the transient time deﬁned as a time in which τf (t) reaches 90% of its asymptotic value given by the Kramers ﬁssion width τfk [357]. These approximations strongly deviate from the numerical solution and thus severely inﬂuence the results [352, 359]. Therefore, a new highly realistic description of the ﬁssion width based on the analytical solution of

l f(t) [1021 s−1]

0.04 0.03 0.02 b=2.0 × 1021 s−1

0.01 0.00

0 (a)

1

2

3

4

5

6

b =1.0 × 1021 s−1 7 0 (b)

1

2

3

4

5

Time t [10−21 s]

Fig. 3.7 Fission rate λf (t) = f (t) / as a function of time for three different values of the reduced dissipation coefﬁcient β for 238 U at T = 3 MeV. The solid line is the numerical solution of the FPE while the dashed line is calculated using an analytical solution as described in Ref. [359].

6

b = 0.5 × 1021 s−1 7 0 (c)

1

2

3

4

5

6

7

158

3 Evaporation and High-Energy Fission

the FPE when the nuclear potential is approximated by a parabola was developed [359]. The new analytical solution is based on the following assumptions: 1. the shape of the probability distribution at the barrier deformation as a function of the velocity v is constant and only its height varies with time; 2. for Wn (x = xb ; t, β) the solution of the FPE obtained using a parabolic nuclear potential can be used 3. zero deformation and zero velocity are considered as initial conditions. In addition, the zero-point motion was taken into account by shifting the time scale by the time needed to establish the initial shape of the probability distribution. A detailed description can be found in Ref. [359]. As one can see in Figure 3.7, this analytical approximation reproduces the exact solution for the critical damping (β = 2 × 1021 s−1 ) rather well. A similar agreement is reached in the overdamped regime (β > 2 × 1021 s−1 ). The approximation also gives a rather good description of the slightly underdamped motion (β = 1 × 1021 s−1 ). Even in the under-damped case (β = 0.5 × 1021 s−1), the oscillations are reproduced very well, although the absolute magnitude of the ﬁssion width is somewhat underestimated. In the previous investigations, it was shown that the total suppression of the ﬁssion width for small time values and the gradual increase are the most critical features of a realistic in-growth function. Both features, missing in the previously used descriptions, are well reproduced by the analytical approximation [352, 359]. The actual version of the ABLA code explicitly treats the relaxation process in deformation space and the resulting time-dependent ﬁssion-decay width, using the described approximate solution of the FPE. 3.5.2 The Simultaneous Breakup Stage

As for example the analysis [360] of the isotopic distributions of heavy projectile fragments from the reactions of a 238 U beam in a lead target and a titanium target gave evidence that the initial temperature of the last stage of the reaction, the evaporation cascade, is limited to a universal upper value of approximately 5 MeV. This is consistent with results on the caloric curve from multifragmentation experiments [361]. The interpretation of this effect relies on the onset of the simultaneous breakup process for systems whose temperature after the ﬁrst stage of the reaction (e.g., the intranuclear cascade) is larger than 5 MeV. In ABLA, the simultaneous breakup stage is modeled in the following way: if the temperature after the ﬁrst stage of reaction exceeds the value of 5 MeV, the additional energy is used for the formation of clusters and the simultaneous emission of these clusters and several nucleons. The number of protons and neutrons emitted is assumed to conserve the N-over-Z ratio of the projectile (or target) spectator, and an amount of about 20 MeV per nucleon emitted is released. The breakup stage is assumed to be very fast, and thus the ﬁssion collective degree of freedom is

3.6 The GEMINI Model

not excited. The major fragment left over from the projectile (or target) spectator undergoes the sequential decay. A more elaborate description of the breakup process on the basis of the statistical multifragmentation model (SMM) is given in ref. [362]. In the case of spallation reactions, the breakup stage plays an important role for light targets, while for heavy targets only a small fraction of prefragments in the upper tail of the excitation-energy distribution are formed with temperatures exceeding 5 MeV. As a consequence, the production of intermediate-mass fragments through the simultaneous breakup is more enhanced for light targets (e.g., iron). This could explain the failure of a standard evaporation model to describe the cross section for the production of intermediate-mass fragments (e.g., 7 Be, 14 C). 3.5.3 Conclusion of ABLA

The coupling of an intranuclear cascade code (e.g., INCL) to the ABLA model has shown to give a satisfying agreement with the isotopic distributions of spallation residues in the region of ﬁssion and heavy evaporation products. For the deexcitation stage of the reaction, the ABLA model has proved to give a much better reproduction of isotopic distributions and ﬁssion yields than other well-known models. The INCL4–ABLA combination has been compared to a large set of available experimental data obtained during the HINDAS project but also to earlier experimental results. An overall good agreement has been found for a broad range of different observable and bombarding energies. Most recently the evaporation part of ABLA was extended to the emission of not only neutrons, protons, tritons, deuterons, 3 He, and alphas but also intermediate mass fragments, i.e., light nuclei with Z > 2 [350]. ABLA has been implemented to high-energy transport codes widely used for the spallation neutron source and ADS design such as LAHET3, MCNPX, HERMES, MC4 and just recently to GEANT4 (cf. Table 5.2 on page 211 and is now available to the community.)

3.6 The GEMINI Model

GEMINI is a statistical model code capable of describing the decay of compound nuclei and complex fragment cross sections by sequential binary decays. All possible binary divisions from light-particle emission to symmetric division are considered. The model employs a Monte Carlo technique to follow the decay chains of individual compound nuclei through sequential binary decays until the resulting products are unable to undergo further decay. The decay width for the evaporation of fragments with Z ≤ 2 is calculated using the Hauser–Feshbach formalism [363]. Similar to previously described evaporation models (cf. Eq. (3.1)), for the emission of a light particle (Z1 , A1 ) of spin J1 from

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3 Evaporation and High-Energy Fission

a system (Z0 , A0 ) of excitation energy E ∗ and spin J0 , leaving the residual system (Z2 , A2 ) with spin J2 , the decay width is given by J2 (Z1 , A1 , Z2 , A2 ) =

2J1 + 1 · 2πρ0

J0 +J2

E ∗ −B−Erot (J2 )

Tl ()ρ2 (U2 , J2 )d,

0

l=|J0 −J2 |

(3.48) where l and are the orbital angular momentum and kinetic energy of the emitted particle, respectively, ρ2 (U2 , J2 ) is the level density of the residual system with thermal excitation energy U2 = E ∗ − B − Erot (J2 ) − , B is the binding energy, Erot (J2 ) is the rotation plus deformation energy of the residual system, and ρ0 is the level density of the initial system. The transmission coefﬁcients Tl () were calculated with the sharp cutoff approximation for a classical system of absorptive radius R, and are given by

Tl () =

0

for > ECoul +

1

for ≤ ECoul +

2l(l+1) 2µR2 2l(l+1) 2µR2 ,

(3.49)

where µ is the reduced mass. The Coulomb barriers ECoul were calculated using the empirical expressions of Vaz and Alexander [364] and the absorptive radius was taken as

1/3 1.16A2 + 2.6 fm for proton and neutron emission R= (3.50) 1/3 1.16A2 + 3.7 fm for alpha particle emission. In calculating the binding energy for heavy systems (A > 12), the masses of the initial and residual systems were obtained from the Yukawa-plus-exponential model of Krappe, Nix, and Sierk [163] without the shell and pairing correction terms. The parameters for this model were taken from the more recent ﬁt to experimental masses of M¨oller and Nix [365]. These separation energies are expected to be more appropriate at high excitation energies where shell and pairing effects are predicted to wash out. For very light systems (A ≤ 12), binding energies were calculated from the experimental masses. The rotation plus deformation energy Erot of a nucleus was taken from the RFRM calculations of Sierk [323]. For binary divisions corresponding to the emission of heavier fragments, the decay width was calculated using the transition state formalism of Moretto [366]: (Z1 , A1 , Z2 , A2 ) =

1 · 2πρ0

E ∗ −Esad (J0 )

ρsad (Usad , J0 )d,

(3.51)

0

where Usad and ρsad are the thermal energy and level density of the conditional saddle point conﬁguration, respectively, Usad = E ∗ − Esad (J0 ) − . Esad (J0 ) is the deformation plus rotation energy of the saddle point conﬁguration and now is the kinetic energy of the translational degree of freedom. The deformation plus rotation energy was calculated with the RFRM using a two-spheroid

3.6 The GEMINI Model

parameterization for the shape of the conditional saddle point conﬁguration. This parameterization results in conditional barriers which are within 2 MeV of saddle point energies calculated with more realistic shape parameterizations [367] for A0 = 110 [323]. Better agreement is obtained for lighter nuclei. To correct for this difference to ﬁrst order, the two-spheroid saddle point energies were scaled by a constant factor for all mass asymmetries and angular momentum. The scaling factor was chosen so that for symmetric division, the scaled saddle point energy was equal to the value calculated with the more realistic shape parameterization by Sierk [323, 367]. For Z ≤ 6, these RFRM saddle point energies (E RFRM (J0 )) were modiﬁed by RFRM (J0 ) − MY+e (Z1 , A1 ) + Mexp (Z1 , A1 ), Esad (J0 ) = Esad

(3.52)

where MY+e is the mass predicted by the Yukawa-plus-exponential model without shell and pairing corrections and Mexp is the experimental mass. This modiﬁcation is an attempt to introduce shell effects into the saddle point energies for very asymmetric divisions, where one expects them to become more important. For all level densities, the Fermi gas (cf. also Sections 2.2.2.1 and 2.2.2.2 on pages 2.2.2.1 and 2.2.2.2) expression [324, 368] ρ(U, J) = (2J + 1)

2 2J

√ a exp(2 aU) 12 U2

2/3 √

(3.53)

was used, where J is the moment-of-inertia of the residual nucleus or saddle point conﬁguration. The level density parameter was taken as a = A/8.5 MeV−1 for both the residual nucleus and in saddle point conﬁgurations. The integrations in Eqs. (3.48) and (3.51) were performed by ﬁrst expanding the integrand around the lower limit, giving the approximate expression for the decay width for Z1 ≤ 2 as (Z1 , A1 , Z2 , A2 ) =

∞ 2J1 + 1 · 2πρ0

J0 +J2

t2 ρ2 (U2 , J2 ),

(3.54)

J2 =0 l=|J0 −J2 |

where now U2 = E ∗ − B − Erot (J2 ) − ECoul −

2l(l + 1) 2µR2

and the nuclear temperature is approximately t2 = For Z1 > 2 (Z1 , A1 , Z2 , A2 ) =

1 tsad ρsad (Usad , J0 ), 2πρ0

(3.55) √ U2 /a.

(3.56)

where now Usad = E ∗ − Esad (J0 ) and the temperature of the saddle point conﬁgura√ tion is approximately tsad = Usad /a . The secondary products formed in the binary

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3 Evaporation and High-Energy Fission

decay of the initial system, (Z1 , A1 ) and (Z2 , A2 ), were allowed to undergo sequential binary decay. The spin of the residual system was chosen in a Monte Carlo fashion from the calculated partial decay widths J2 (Z1 , A1 , Z2 , A2 ). Its excitation energy was calculated as E2∗ = U2 − 2t2 + Erot (J2 ).

(3.57)

For Z1 > 2, the spin of the fragments was calculated in the sticking limit, i.e., for fragment 1: J1 = (J1 /J )J0 , where J1 is the moment of inertia of the fragment and J is the total moment of inertia of the system. Its excitation energy was derived assuming equal temperatures for the two fragments, as E1∗ =

A1 [Usad − tsad ] + Erot (J1 ). A0

(3.58)

This is strictly valid only when the saddle and scission point conﬁgurations are degenerate and this is approximately true for the systems and reactions under consideration in, e.g., Ref. [229]. However, Eq. (3.58) is not applicable for heavier systems. As for the level density parameter a (cf. also Sections 3.2, 3.3.1, and 3.4.4), several model options can be chosen in the GEMINI model: • a = A0 /const • Toke, Swiatecki level density parameters [325]1) • Ignatyuk et al. [305]1) • Gottschalk and Ledergerber [369]1) • Ormand et al. [327]2) • Lestone [370]3) • Fineman et al. [371]3) . It is up to the user to select the most appropriate one for his or her respective system. The model also contains options for enabling or disabling ﬁssion and intermediate-mass (IMF) emission. Either a formalism is used which is identical to the one used in the models PACE and CASCADE (Bohr–Wheeler formalism) or all asymmetric divisions may be considered (Moretto’s formalism). Sequential decay from the IMFs and ﬁssion fragments is considered. In a simpliﬁed way the ﬁssion dynamics is taken into account by introducing optionally the Kramers factor [60, 309, 357, 372–377] depending on the viscosity at the saddle point. The Kramers factor scales down the ﬁssion decay width at the saddle point by a constant (cf. also detailed description in Section 3.7). Charity [229] has 1) Mass asymmetry dependent. 2) The temperature dependence of the level density parameter is used, however, surface area dependence was neglected.

3) Temperature dependent.

3.6 The GEMINI Model

extended this formalism by an additional degree of freedom – the mass asymmetry. The mass asymmetry is deﬁned by m1 − m2 , η = m1 + m2

(3.59)

with m1 and m2 being the two primary fragments of a binary decay process. The value of η ranges from 0 for symmetric ﬁssion to 1 for the emission of light particles. Following this deﬁnition, and assuming a Gaussian distribution for the mass asymmetry dependence, the delay time τ (η) is expressed as 1 −η 2 , τ (η) = τ (0) exp 2 ση

(3.60)

with τ (0) being the maximum possible delay time for the symmetric splitting of the system. For a chosen width of the distribution of ση = 0.25, the delay time τ (η) for the emission of light particles is signiﬁcantly smaller than typical times of statistical emission (/ evap ). Complex fragment decays can be very improbable events. Thus in analog Monte Carlo simulation one may have to run a large number events to achieve reasonable statistics for intermediate mass fragments. To solve this problem and reduce CPU time, to some extent, weighting has been introduced in the GEMINI model by modifying the simulation of the event histories in a nonanalog manner. There exist various variance reduction methods used in nonanalog Monte Carlo which are described, e.g., by Lewis and Miller, Jr., in Ref. [378]. The GEMINI model considers the following Monte Carlo procedure in nonanalog fashion. • At the beginning of the nonanalog procedure a parameter Iweight = 1 is set to include weighting. • At the start of an event, Kweight is set to 1. While Kweight = 1, the decay widths for complex fragment emission are increased relative to their calculated values. If in the decay chain, a complex fragment is emitted, then Kweight is set to 0 and the complex fragment decay widths are not weighted for the remainder of the decay chain. • To take into account the increased yield of complex fragments, each event now has a weight. If a complex fragment is emitted the weight is decreased, whereas if no complex fragment is emitted, the weight is increased. • The weight of an event is given as Prob(statistical model) , Prob(simulation)

(3.61)

where Prob(statistical model) is the probability of that event, as calculated by the statistical model, and Prob(simulation) is the probability of GEMINI simulating that event.

163

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3 Evaporation and High-Energy Fission

• If GEMINI simulates events according to the statistical model probabilities (i.e., Iweight = 0), then the weight of each event is always 1, as is expected. • If Iweight = 1, GEMINI selects the existing channels in the following manner: – The complex fragment decay widths are multiplied by a constant (FACT), so that at the ﬁrst chance the complex fragment emission probability is at least a value given by a given parameter FACT0 (set to FACT0 = 0.1, which may be changed in GEMINI). – The same value of FACT is used for the second, third, etc. chance complex fragment emission. If the ﬁrst chance complex fragment decay probability is already greater than FACT0, then the parameter FACT is set to 1. – Also after a complex fragment decay, FACT is set to 1 in simulating the decay of the primary fragments. • Now the probability of GEMINI selecting a light particle decay channels is channel , total−light + FACT ∗ IMF−total

(3.62)

where channel is the decay width of the exit channel, total−light is the total decay width for light particle emission and IMF−total is the total decay width for complex fragment emission. • Now the probability of choosing any complex fragment exit channel is FACT ∗ IMF−total . total−light + FACT ∗ IMF−total

(3.63)

The actual channel is chosen so that all charge splits are equally likely. The mass split is then chosen according to the statistical model decay widths. In the GEMINI model caution must be given for input angular momenta larger than where the ﬁssion barrier vanishes. For instance, the subroutine of Sierk to give rotating ground state energies often gives rotation energies which decrease with angular momentum in this range. Sierk never intended his subroutines to be run at these angular momenta. Similar caution must be given concerning the extrapolation of asymmetric barriers. GEMINI principally considers the compound nuclei decay only up to 194 Hg. In this case the ﬁssility of the nucleus is larger than the one of 194 Hg, the asymmetry dependence of the ﬁssion barriers of 194 Hg is assumed, and barriers are scaled such that the symmetric barriers for the respective nucleus are correct. This procedure is valid only for nuclei not much heavier than 194 Hg. Furthermore, as for any statistical model, the excitation energies E ∗ shall be considerably smaller than the binding energy of the nucleus. This is one of the fundamental assumptions of statistical models, because before and after the emission of any fragment a statistical equilibrium is required. This prerequisite is fulﬁlled only, if enough time is left for the nucleus to achieve equilibrium again after the emission of a fragment.

3.7 High-Energy Fission Models

To the best of our knowledge, for GEMINI there exists no published manual or handbook and mostly users of the code have to refer to the original article of Charity et al. [229]. Actually this publication presents a variety of observables, e.g., charge distributions, excitation energy of the compound nuclei, compound-nucleus spin distributions, etc., as calculated with GEMINI and confronts experimental data and complex fragments with 3 < Z ≤ 35 for Nb + Be, C, and Al reactions. As a general tendency cross sections calculated with the GEMINI model code reproduce both the shape and magnitude of the experimental charge distributions rather well as has also been shown in Refs. [114, 228, 379]. Probably the most comprehensive and helpful description of the physics and parameters of GEMINI is found in the well-commented source code of the model and notes therein. The computer code of the GEMINI model by Charity [229] is written in standard Fortran 95 language except that for a number of OPEN statements where the author uses the DEC/Compaq option ‘‘shared.’’ This can be removed and will not affect the program; it does however allow you to sort the data while they are being generated, without it you risk killing GEMINI if you sort an event ﬁle which is being written to. Most recent versions of GEMINI are available from http://wunmr.wustl.edu/rc/.

3.7 High-Energy Fission Models

Without ﬁssion, spallation collisions can be treated as a two-step process: (i) an intranuclear cascade, described by a series of independent particle collisions inside the nucleus, and (ii) subsequent de-excitation by a series of particle emissions, which are described by evaporation models. For heavy nuclei, there is competition between evaporation and ﬁssion at each step of the de-excitation sequence. The probability of ﬁssion at some step during de-excitation in high-energy (E ≥ 100 MeV) collisions is proportional to Z2 /A of the target nucleus. For example, the ratio of the ﬁssion cross section to the total cross section for 1 GeV protons on lead and uranium targets is σﬁssion /σtotal ≈ 0.05 for lead and is σﬁssion /σtotal ≈ 0.8 for uranium (see for example Ref. [380]). As illustrated in Figure 3.8, the high-energy ﬁssion in spallation reactions may be considered as a four-step process. The information which must be determined by ﬁssion models is the probability of ﬁssion Pf = Pf (E ∗ , A, Z) of the residual nucleus (A, Z) with the excitation energy E ∗ , which is left after the intranuclear cascade, at each step and the parameters of the ﬁssion fragments after ﬁssion, which are then used as input for a postﬁssion evaporation calculation for each fragment [338], respectively. The four steps shown in Figure 3.8 consider mainly the following reaction mechanisms: (1) production of high-energy particles and an excited residual nucleus, (2) emission of low-energy neutrons, protons, tritons, 3 He, and 4 He particles, (3) ﬁssion-evaporation competition at each stage of the de-excitation, (4) deexcitation of ﬁssion products by particle emission. After step 4, a ﬁfth step may follow by de-excitation to the ground state of the residual nucleus by a gamma-ray

165

166

3 Evaporation and High-Energy Fission Protons

1. Intranuclear cascade

2. Prefission evaporation

3. Fission

4. Postfission evaporation

Fig. 3.8

The principle of the high-energy ﬁssion model considered as a four-step process.

cascade. The dynamics of the ﬁssion process as a collective motion of nuclear matter is shortly described in Section 3.7.1. A short overview about the ﬁssion process was already given in Section 1.3.2 on page 15 and in Section 1.3.3 on page 17. 3.7.1 The Dynamics of the Fission Process

The binary splitting of an excited nucleus into two approximately equal parts is still considered as one of the most interesting phenomena of collective motion of nuclear matter and as an excellent example of the nuclear multiparticle problem [62]. A simple model regarding the nucleus as an incompressible liquid is drawn by the liquid drop model (LDM) [60]. Analog to a liquid drop, a surface tension is responsible for the inner forces acting on all surface nucleons. As demonstrated in Figure 3.9(a), ﬁssion is understood as a consequence of the deformation when repelling electrostatic Coulomb forces on the protons overbalance the short-range attractive nuclear forces. A ground-state-deformed nucleus is situated in the minimum of the potential energy which increases with increasing deformation toward the so-called saddle point deformation. Beyond the saddle point the potential energy declines due to the decreasing Coulomb repulsion until the scission point is reached. Then the nucleus is constricted in such a way that fragmentation into two parts is likely. The ﬁssion barrier Bf represents the difference of the potential energy at the ground-state and the saddle point deformation. As shown in Figure 3.9(b), there is a maximum of Bf at A 70 and a substantial decline for light and heavy nuclei. Also with increasing E ∗ the ﬁssion barrier declines, because due to the expansion of the nucleus at high excitations the surface energy

3.7 High-Energy Fission Models

Potential [MeV]

tF

t

Bf

tss

E* = 0

50

50 MeV

40

0

100 MeV

−200

Saddle

−30

Ggw

30 Scission

Deformation

200 MeV

20 10 0

0

50 100 150 200 250 Atomic mass number

(a)

Potential deformation

(b)

Fission barrier

Fig. 3.9 (a) Potential energy as a function of deformation. The transition time from equilibrium (Ggw) to the saddle point τ and the one from saddle to scission τss are indicated (the ﬁgure adapted from [381]). (b) Fission barrier Bf as a function of the atomic number A and E∗ along the β-stability line (the ﬁgure adapted from [382]). Bf is given in units of MeV.

decreases faster than the Coulomb energy. The barrier is also a function of the angular momentum of the nucleus, because additional rotational energies disperse the nucleus. These phenomena are considered in the ‘‘rotating LDM’’ [383] which describes the ﬁssility by [384] χ=

Z2/A Ec0 = 2 · Es0 50.883(1 − 1.7826 · I2 )

with

I = (N − Z)/A,

(3.64)

where Ec0 and Es0 being the Coulomb and surface energy of the nucleus in the ground state, and Z, N, and A the atomic, neutron, and mass numbers, respectively. Asymmetric mass splitting at low E ∗ cannot be explained by the LDM. Shell effects have to be taken into account, which however disappear for excitations larger than a few 10 MeV [385–388]. At high E ∗ , ﬁssion is in competition to the successive neutron emission of the excited nucleus. The competition between ﬁssion and particle emission as well as the characteristics of ﬁssion products can be described by statistical models. Under the assumption of thermal equilibrium the probability for ﬁssion or neutron emission can be described according to Eq. (3.65) by the ratio of decay widths n and f [389]: 4A2/3 af (E ∗ − Bn ) n = 1/2 f C0 an [2af (E ∗ − Bf )1/2 − 1] 1/2 ∗ 1/2 × exp 2a1/2 − 2af (E ∗ − Bf )1/2 , n (E − Bn )

(3.65)

167

168

3 Evaporation and High-Energy Fission

where Bf , E ∗ , and Bn represent the height of the ﬁssion barrier, the excitation energy and the binding energy of the neutron, respectively. The constant C0 is C0 = 2/2mn r0 2 (mn = neutron mass) and af and an are the level density parameter at the saddle point and the ground-state deformation after the emission of a neutron. For small angular momenta and nuclei with ﬁssion barriers smaller than their neutron binding energy (Bf < Bn in Eq. (3.65), the ﬁssion takes place early, since n / f increases after the emission of each emitted neutron. For high angular momenta n / f decreases with increasing E ∗ and consequently the nucleus ﬁssions at a later stage. A phenomenological approach for ﬁssion product yield calculations at intermediate incident particle energy has been proposed by Konobeyev et al. [388]. This approach is based on the Fong statistical model and empirical expressions. A good agreement with experimental data was demonstrated. For a comprehensive description of the dynamics of the ﬁssion process the concept of dissipation and the viscosity of nuclear matter refer to review articles [60, 309, 357, 372–375, 377]. Dissipative processes are accompanied by statistical ﬂuctuations which exchange energy between intrinsic and collective degrees of freedom. Latterly collective transport models are discussed which consider these statistical ﬂuctuations [390–393]. Besides the saddle to scission time τss these models require a transient time6) τ . The transient time is a function of dissipation or friction and can be parameterized by the so-called Kramers factor [376]. The total time scale τF of the dynamical ﬁssion process is described by the sum of the transient time and the saddle to scission time τF = τ + τss (Figure 3.9(a)). Actually the time shall not be subdivided into pre- and postsaddle, because in reality the saddle point could be passed through several times. In collective transport models the dynamical process of the system from the ground state to the scission is continuously traced. While the characteristic time scales for processes described by intrinsic degrees of freedom are of the order of 10−23 s [394], the ones for collective motions are two orders of magnitude larger. Therefore, a theory is proposed decoupling the Hamiltonian for the total energy of the system into a collective and an intrinsic part. The transport equations are controlled by one or several transport coefﬁcients, such as, e.g., the reduced dissipation coefﬁcient β, which reﬂects the coupling strength between the collective and intrinsic degrees of freedom. These coefﬁcients can be used for deﬁning the time scale of the process. The total energy of the system in the collective transport model is given by the temperature-dependent function H(q, p, T) [324, 395]: H(q, p, T) = Ekin (q, p) + F(q, T).

(3.66)

Ekin (q, p) and F(q, T) are the kinetic and free energy of the system, respectively, and q ≡ q1 , q2 , . . . , qN denote the N generalized collective coordinates representing 6) The transient time is the time the system needs for passing the saddle point conﬁguration.

3.7 High-Energy Fission Models

the form of the system. pi = Mij (q) q˙ j are the collective generalized momenta. The dynamics of the system and the equations of motion, which contain the effects of dissipation, can be deduced from the Hamiltonian equations [396]: ∂H ∂Ekin = ∂pi ∂pi ∂Ekin ∂F ∂H ∂F p˙ i = + Qi + δXi = + + + δXi . ∂qi S ∂qi T ∂qi ∂ q˙ i q˙ i =

(3.67) (3.68)

The dissipative force Q is expressed by the ‘‘Rayleigh dissipation function’’ F and a ﬂuctuation term δXi . The conservative force ∂H ∂qi S can be described either by the free energy F or by the entropy S according to the thermodynamical relation

∂S ∂H ∂F = = T . ∂qi S ∂qi T ∂qi E

(3.69)

The collective kinetic energy Ekin (q, p) is given by Ekin (q, p) = 1/2Mij (q)˙qi q˙ j [60, 396]. The Rayleigh dissipation function F = 1/2ηij (q)˙qi q˙ j [60, 396] includes a shapedependent dissipation tensor ηij (q), which describes the conversion from collective to single particle energy. For the term representing the ﬂuctuations no history, e.g., no temporal correlations exist (Markovian assumption). Employing the collective energy Ekin and the dissipation function F in Eqs. (3.67) and (3.68) the multidimensional Langevin equation is obtained, which represents in most general form the collective transport model. Due the ﬂuctuation term δX the Langevin equation is a stochastic equation with stochastic variables p and q. The temporal evolution of the function F(q, p, T) in the phase space of collective coordinates and their conjugated momenta is presented by the generalized Fokker–Planck equation [358]. The stochastic description of the Langevin equation is equivalent to the Fokker–Planck equation provided that the Markovian assumption is accepted. Previous investigations which try to describe the ﬁssion process using transport equations are based on the Fokker–Planck equation with one collective degree of freedom [390–392]. These studies certainly resulted in some insight into the dynamics of the ﬁssion process, but with the addition of latest precise measurements of the ﬁssion lifetime as a function of E ∗ using blocking effects in a single crystal, important consequences for the dynamical description of the collective process have been illustrated. This work essentially carried out at GANIL, France, by Goldenbaum [397–399] and Morjean et al. [400] will not be part of the present book. As another approach, besides the application of these transport models, the statistical model can be modiﬁed in such a way that pre- and postsaddle time scales are evaluated by the measurement of pre- and post scission particle multiplicities and the magnitude of dissipation is estimated. Measurements of prescission neutron multiplicities [401–403], light charged particles [404, 405] and giant γ resonances [406] allowed for accessing the relative time scales of ﬁssion and particle emission. A signiﬁcant relaxation time of collective degrees of freedom pointing to a large dissipation has been demonstrated. The total time scale of

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3 Evaporation and High-Energy Fission

ﬁssion has been limited to τF ≤ 50 × 10−21 s [401]. Lestone [407] conﬁnes applying his measurements τF to τF ≤ 30 × 10−21 s. 3.7.2 Basic Features of Fission Models

There are several high-energy ﬁssion models developed for use in spallation reaction calculations and in thick-target nucleon meson transport codes (i) the RAL Atchison model of the Rutherford Appelton Laboratory, UK [311–313], (ii) the ORNL model at the Oak Ridge National Laboratory, USA, developed by Alsmiller et al. [314, 408], (iii) the BNL model at the Brookhaven National Laboratory, USA, by Takahashi [409], the JAERI model at the Japan Atomic Energy Research Institute, Japan, by Nakahara [410, 411], and the Barashenkov model at Dubna by Barashenkov [412]. In addition to the more stand-alone ﬁssion models there are ﬁssion models included into evaporation models as in the ABLA model of Schmidt et al. [221, 222] or in the GEMINI model of Charity et al. [229, 256] (cf. Sections 3.5 and 3.6 on pages 154 and 159). The fundamental basis of all these models is the statistical model of ﬁssion developed by Fong [310, 413]. Basically, the assumption is that the ﬁssion process is ‘‘slow,’’ i.e., the nucleus exists in an equilibrium state at any time, so the probability of a particular ﬁssion mode, the state of the ﬁssion fragments, is proportional to the density of the quantum states at the time of splitting. From the theory of Fong the ﬁssion mode probability is expressed as a function of 12 variables: • N(A1 , A2 , Z1 , Z2 , E1∗ E2∗ j1 , j2 ) C, D, K, E, where the subscripts denote the two ﬁssion fragments; • A, Z, E ∗ , and j denote the mass number, charge number, excitation energy, and angular momentum, respectively; • the remaining parameters are energy variables, C = Coulomb energy, D = deformation energy, K = translational energy, E = total kinetic energy. The high-energy ﬁssion models developed differ in the approximations made in arriving at a practical application and implementation. It is not the purpose here to evaluate the various approximations. Therefore as an example only the features of the RAL model of Atchison are discussed in more detail. A comparison of the RAL model with the ORNL model of calculated ﬁssion cross sections, neutron production, and residual mass distributions with experimental data is given in Ref. [380]. Indeed, many of the approximations of the above ﬁssion models are interdependent, making a judgment of the practical importance of particular assumptions difﬁcult. A simple characterization of the differences is given for different models such as follows: • RAL model: empirical formulas used as far as possible, • ORNL model: heavy reliance on empirically derived constants, ﬁssion is neglected for subactinides Z < 91, • BNL model: close simulation of Fong’s statistical model formulas with minimum reliance on experimental data,

3.7 High-Energy Fission Models Tab. 3.5

B0 values used in standard versions of ﬁssion models.

Fission model

RAL

ORNL

BNL

Parameter B0

14

10

8

JAERI 8

• JAERI model: similar to the RAL approach, but it is different in detail.

As discussed in the context of the level density in Sections 3.3.1 an 3.4.4 on pages 140, 147 and given by Eq. (3.13), the level density a is in the simplest form depending on the value of the parameter B0 . The different ﬁssion models are used in the standard versions values of B0 as shown in Table 3.5. It should be noted that the value of B0 has an important inﬂuence on neutron production as shown in Refs. [338, 380]. 3.7.3 The RAL Model of Atchison

The RAL ﬁssion model is based on several general assumptions. • Fission competes at all stages of the nuclear de-excitation with ﬁssion probabilities that vary with the nuclear state. • Postﬁssion parameters depend only on the state of the nucleus at the time of ﬁssion and not on the previous sequence of events leading to the state of the nucleus at the time of ﬁssion. • Only binary ﬁssion will occur. This means that ﬁssion is locked off for ﬁssion fragments themselves. Although ternary ﬁssion and high-order ﬁssion have been observed, e.g., Ref. [414], they occur with probabilities for which most spallation research applications are insigniﬁcant. • The mass split is always complete. The two ﬁssion fragments will conserve baryons and charge number. Thus, ‘‘ﬁssion’’ neutrons will be produced from either evaporation prior to ﬁssion or de-excitation of the ﬁssion fragments. • Fission for nuclei with Z < 70 is not considered. The ﬁssion probability Pf is given by the ratio of evap = n and f for the widths for evaporation and ﬁssion at some point in the de-excitation cycle: Pf =

f 1 = . f + n 1 + n / f

(3.70)

Because ﬁssion is only considered for heavy nuclei for which evaporation is dominated by neutron emission, the evaporation width is adequately represented

171

172

3 Evaporation and High-Energy Fission

by the width for neutron emission n . The treatment of the ﬁssion probability Pf is differently considered for elements above and below Z = 89. In the subactinide region, Z < 89, results of experiments show that the ﬁssion probability Pf is strongly dependent on the excitation energy E ∗ (e.g., [412]). The RAL model [311, 312] uses the Weisskopf–Ewing statistical model [320] with an energy-independent pre-exponential factor for the level density and Dostrovsky’s [7] inverse cross-section. Separate ﬁts are made for neutron emission and ﬁssion to allow separate level density parameters. The expressions for the neutron emission or neutron width n for nuclei with 70 ≤ Zj ≤ 88 are: 1/3

2/3

n = 0.352(1.68J0 + 1.93Ai J1 + Ai (0.76J1 − 0.05J0 )),

(3.71)

where J0 and J1 are functions of the level density parameter an and Sn with Sn = 2 an (E ∗ − Q − δ) = 2 an (E ∗ − B ) and (Sn − 1) · exp(Sn ) + 1 2an (2S2n − 6Sn + 6) · exp(Sn ) + S2n − 6 J1 = 8a2n J0 =

(3.72) (3.73)

with E ∗ the excitation energy and B the separation energy minus pairing energy. The expression for the ﬁssion width f for nuclei with 70 ≤ Zj ≤ 88 are: f =

((Sf − 1) · exp(Sf ) + 1) , af

(3.74)

where Sf = 2 af (E ∗ − Q − δ) = 2 af (E ∗ − Bf ) and the level density parameter in the ﬁssion mode af is ﬁtted by Atchison to describe the measured f / n as af = an (1.08926 + 0.01098(Zi2 /Ai − 31.08551)2 )

(3.75)

with E ∗ the excitation energy and Bf the ﬁssion barrier. The ﬁssion barriers Bf in [MeV] are estimated as 2 Zi2 Zi2 + 0.218 . Bf = Q + 321.2 − 16.7 Ai Ai

(3.76)

The RAL model uses a ﬁxed value for the level density parameter an , namely, (an = (Ai − 1)/8 (MeV)−1 ). Note that neither the angular momentum nor the excitation energy of the nucleus is taken into account in estimating Bf . The above expressions are used for Z ≤ 88.

3.7 High-Energy Fission Models

The ﬁt parameters for the ﬁssion barrier Bf and the level density ratio, af /an , are based on data for Z < 85, so the model ﬁts are used for extrapolation to obtain the ﬁssion probability in the Z = 85 to the Z = 88 region. In the actinide region for high-Z nuclei, Zi ≥ 89, the ﬁssion barrier is relative constant at about 6 MeV, and the probability for ﬁssion, Pf is not strongly dependent on the excitation energy E ∗ (see, e.g., Gavron et al. [415]). Therefore, the RAL model assumes Pf = 0 for E ∗ ≤ 6 (MeV) and Pf independent of E ∗ above 6 MeV. Neither the ﬁssion width f is calculated nor Eq. (3.70) is employed for the ﬁssion probability Pf . Instead a semiempirical expression is obtained in the RAL model by approximating the experimental values of n / f published by Vandenbosch and Huizenga [389] to calculate the ﬁssion probability

log n / f = C(Zi )(Ai − D(Zi )),

(3.77)

where C(Zi ) and D(Zi ) are functions depending on the nuclear charge Zi only. The expression is used for 89 ≤ Zi ≤ 99 with ﬁssion not considered for higher Zi . The values of these constants can be found in the current version of LAHET [110, 111, 193]. 3.7.3.1 Postﬁssion Parameters of the RAL Model If ﬁssion has occurred for a nucleus of charge Zi , atomic mass Ai , excitation energy Ei∗ , and recoil energy Ei-recoil the corresponding parameters for each of the ﬁssion fragments have to be determined (cf. Section 3.4.5). (1) Mass distribution:

(a) The selection of the masses for the ﬁssion fragments depends on whether the ﬁssion is symmetric (a wide, single peak for the fragment mass distribution) or asymmetric (two peaks). (b) For Zi2 /Ai ≤ 35 only symmetric ﬁssion is allowed for a preﬁssion nucleus, and the mass A1 is selected from a Gaussian distribution of mean A1 = Ai /2 with the index i as fragment type and width σm-RAL . σm-RAL = 3.97 + 0.425 · Ui − 2.12 × 10 − 3 · Ui2

(3.78)

with Ui = Ei∗ − Bf as the excitation energy above the ﬁssion barrier Bf . This symmetric ﬁssion mass distribution is based on the systematics given by Neuzil and Fairhall [416]. (c) If Zi > 88 the ﬁssion energy barrier Bf is determined in the RAL model based on the work of Seaborg and Vandenbosch [417, 418], Bf = C − 0.36 with C = 18.8 for odd–odd nuclei, C = 18.1 for even–odd nuclei, C = 18.1 for odd–even nuclei, and C = 18.5 for even–even nuclei.

(3.79)

173

174

3 Evaporation and High-Energy Fission

(d) For Zi2 /Ai > 35 both symmetric and asymmetric ﬁssion are allowed, depending on the excitation energy E ∗ of the ﬁssioning nucleus. For symmetric ﬁssion, A1 is selected from a Gaussian distribution of mean Af = Ai /2. With A1 determined , the mass of the other ﬁssion fragment is A2 = Ai − A1 . Whether the ﬁssion is symmetric or not is determined by the asymmetric ﬁssion probability Pasy Pasy =

4870 · exp(−0.36E ∗ ) . 1 + 4870 · exp(−0.36E ∗ )

(3.80)

For asymmetric ﬁssion, the mass of one of the postﬁssion fragments A1 is selected from the Gaussian distribution of mean Af = 140 and width σm-RAL = 6.5. Consequently the second mass is A2 = Ai − A1 . (2) Charge distribution: (a) The charge distribution of the ﬁssion fragments is assumed to be a Gaussian distribution of mean Zf and width σZ = 2. Zf is expressed as Zf =

Zi − Z1 − Z2 2

with Zi =

65.5Ai 2/3

131 + Ai

,

i = 1, 2.

(3.81)

(3) Energy distribution: (a) The total kinetic energy of the ﬁssion fragment in the c.m. system, Etotal , is selected from a Gaussian distribution having a mean kinetic energy Ef and a width σEf , 1/3

Ef = 0.133 · Zi2 /Ai

− 11.4

σEf = 0.084 · Ef .

(3.82)

These relations are based on the evidence of the strong correlation of the ﬁssion fragment kinetic energies with the Coulomb repulsion parameter 1/3 Zi2 /Ai of the ﬁssioning nucleus (e.g., [414]). The kinetic energy of each fragment in the c.m. system is given by E1 = A2 · Ef /Ai

and

E2 = Ef − E1 .

(3.83)

Isotropic emission in the c.m. system is then assumed to obtain the kinetic energies in the laboratory system. (b) The excitation energies of the ﬁssion fragments are then determined by an energy balance E1∗ = (A1 /Ai ) · (Ei∗ + B1 + B2 − Bi − Ef ) and

E2∗ = E1∗ · A2 /A1 , (3.84)

where B denotes the binding energies.

3.7 High-Energy Fission Models

100

Probability of fission

100 MeV −2

10

20 MeV

10−4 50 MeV

10−6 175

200

225

250

Atomic mass number A Fig. 3.10 Probability of ﬁssion simulated using the RAL model for various isotopes arbitrarily selected over the atomic mass range A = 175–250. The top, middle, and bottom curves are for assumed excitation energies of 100, 50, and 20 MeV, respectively.

Figure 3.10 shows the ﬁssion probability simulated with the RAL model for various arbitrarily selected isotopes covering the atomic mass range from 175 to 250. The ﬁgure shows that the ﬁssion probability is very small for masses A ≤ 200, accounting for a peak in this region, which is shown in Figure 3.11. Figure 3.11 illustrates the prediction of mass distributions with and without high-energy ﬁssion taken into account for protons of 1.0 GeV incident on a 238 U target. The RAL model predicts three peaks in the mass distribution: The ﬁssion fragment peak at a mass about A ≈ 110, the spallation product peak at a mass of A = 238, and an intermediate peak at a mass of about A ≈ 200. This intermediate peak apparently results from spallation products which ‘‘survive’’ de-excitation through the mass region of high-ﬁssion probability into a lower mass region where further de-excitation by neutron emission is much more likely than ﬁssion. This intermediate peak in the mass distribution is probably most evident at ‘‘medium’’ incident beam energies, e.g., at low beam energies of about ∼100 MeV where there is no sufﬁcient excitation energy to produce many nuclei in the lower mass region of low-ﬁssion probability (see Figure 3.10), whereas at high beam energies there is sufﬁcient excitation energy that spallation products can be produced with very low masses which overlap with the higher mass ﬁssion fragments.

175

3 Evaporation and High-Energy Fission

Residual nuclei distribution per mass number per nonelastic collision

176

10−1 1 GeV protons on a 238 U target

With fission Without fission

10−2

10−3

10−4 0.0

40.0

80.0 120.0 160.0 200.0 240.0 Mass number A

Fig. 3.11 Comparison of mass distributions with and without high-energy ﬁssion simulated with an EVAP-RAL [380] model combination taken into account for protons of 1.0 GeV incident on a 238 U target.

3.8 Fermi Breakup for Light Nuclei

As mentioned in Sections 3.1 and 3.2, the decay of the compound nucleus is usually treated by statistical models using sequential emission. The models of Weisskopf and Weiskopf–Ewing [8, 320] and of Hauser–Feshbach [363] are useful. However, the level density formalisms employed in evaporation models are, in general, poor approximations for light nuclei. Furthermore, cascade residuals or evaporation residuals may de-excite by a simultaneous statistical breakup into multiparticle exit channels [419–422] rather than by sequential evaporation of light particles. The breakup mechanism was originally proposed by Fermi [263] to describe highenergy hadronic collisions due to the multiple production of particles in NN and in πN collisions. The Fermi breakup mechanism (FBM) is particularly applicable for the de-excitation of light nuclei which have a lower density of states, fewer degrees of freedom of the nucleons, and lower Coulomb barriers. Excited light primary fragments left as residuals after the intranuclear cascade have often values of the excitation energy E ∗ per nucleon comparable with the nucleon binding energy. In this case one can assume that the principal mechanism of de-excitation is an explosive decay of the excited nucleus into several separate clusters and isolated nucleons [422]. Several high-energy particle transport models and codes, e.g., CEM [249], FLUKA [423], GEANT4 [100, 424], MCNPX [194], are replacing the evaporation models by a Fermi breakup model for the disintegration of light nuclei mainly with atomic masses A < 17 to predict the ﬁnal states (cf. Chapter 5). The condition for the Fermi breakup A breakup decay is allowed if the total kinetic energy E for all fragments of a given channel at the moment of breakup is positive.

3.8 Fermi Breakup for Light Nuclei

The total kinetic energy E for a breakup into n fragments is calculated using the expression E = U + M(A, Z) − EC −

n

(mb + E ∗ ),

(3.85)

b=1

where mb and E ∗ are the masses and excitation energies of the fragments, respectively. EC is the Coulomb barrier for the appropriate channel b and is given by n 3 · e2 1/3 −1/3 2 1/3 2 , EC = · Z /A − Z /Ab (1 + V/V0 ) 5 · r0

(3.86)

b=1

where the relation V/V0 = 1 is normally used. V0 is the volume of the system corresponding to the normal nuclear matter density. The total probability The total probability for the residual nucleus for separation in n components, e.g., nucleons, d, t, 3 He, 4 He, in the ﬁnal state in channel b is given by the expression

P(E, n) = (V/)n−1 ) · ρn (E),

(3.87)

where V is the decay volume of the system, = (2π)3 is the normalization volume of the system, and ρn (E) is the density of ﬁnal states. The density can be deﬁned as a product of three factors ρn (E) = Mn (E) · Sn · Gn .

(3.88)

The different terms in Eq. (3.88) are deﬁned as follows: • the phase factor7) Mn (E) Mn (E) =

+∞

−∞

···

+∞

−∞

δ

pb

b=1n

n n 2 2 δ E− p + mb · d3 pb (3.89) b=1

b=1

where pb is the fragment b momentum. • the spin factor Sn : Sn =

n

(2sb + 1),

b=1

which gives the number of states of the fragment b with different spin orientations. 7) In the nonrelativistic case the integration of Eq. (3.89) can be evaluated analytically [425].

(3.90)

177

178

3 Evaporation and High-Energy Fission

• the permutation factor Gn : Gn =

k 1 , nj !

(3.91)

j=1

which takes into account the identity of the fragments. The value nj is the number of components of the j-type particle and k is deﬁned by n = kj=1 nj . By substituting in Eq. (3.89) the corresponding functions for the density, the phase space factor, the fragment momentum, and the spin orientation and solving the integrals of Eq. (3.89), the probability P(E, n) for a nucleus with energy E disassembling into n fragments with masses mb , where b = 1, 2, 3, n is expressed as [422] P(E, n) = Sn · Gn · ·

V

n−1 · n

1 1

b=1

3/2

b=1 mb

3(n−1)/2

(2π) · E (3n/2)−(5/2) , (3(n − 1)/2)

(3.92)

where is the gamma function. It is important to note that the Fermi breakup model has only one free parameter, the volume V. The volume V is the volume of the decaying system and can be calculated as follows: V = 4π · R3 /3 = 4π · r03 · A/3

(3.93)

where r0 = 1.4 fm may be used. The application of the Fermi breakup model is necessary to accurately describe the de-excitation process of light excited nuclei, e.g., by using the EVAP model. Results show that the GEM evaporation model has a comparable prediction power as a combination of the EVAP model and FERMI breakup model (see [426] and Figure 3.12).

3.9 Photon Evaporation and Gamma Ray Production

There are two main mechanisms for photon or gamma ray production during or after the cascade and the evaporation process in spallation reactions in the GeV energy range. One source of photons is the produced neutral pions, π 0 , which decay immediately after their production in high-energy photons (cf. Section 1.2 on page 6 and Table 1.1). The other source of photons is generated from the decay of residual nuclei left after the cascade and the evaporation. Here the usual assumption is made that all particle decay modes have been exhausted, thus photon or gamma emission does not compete with particle emission.

Cross section [mb]

3.9 Photon Evaporation and Gamma Ray Production

102

102

100

100

14

10−2 101

N(p,X)11C

102

16

10−2 103

101

O(p,X)13N 102

103

Incident proton energy [MeV]

Fig. 3.12 Excitation functions of carbon 11 C and nitrogen 13 N production. (a) The ﬁgure shows the reaction of incident protons on a nitrogen target, and (b) shows the reaction of protons on an oxygen target (solid lines are the simulation using an INCE-BERTINI/GEM model, dotted lines are an INCE-BERTINI/Fermi breakup model, and open squares are the experimental data given in Ref. [426]).

There are several models for gamma emission employed together with particle transport codes, e.g., the PHT model in the LAHET code and in the MCNPX system [113, 193, 194, 304, 328], the NDEM model in HERMES [88]. A model with similar physics assumptions is used in GEANT4 [100, 424]. The general assumptions are shortly described. The probability of gamma emission is given by Pγ =

γ γ + i ·i

(3.94)

where γ is the width for γ -emission and the i are the transitions widths for different open channels, e.g., n, p, d, t, 3 He, 4 He, etc., and ﬁssion for the emission. Discrete photon evaporation It is assumed that there exist a range of known energy levels given by the Gilbert–Cameron formulas [336]. The discrete photon transitions such as E1 , M1 , and or E2 transitions are used from tabulated isotopic libraries, e.g., the BNL data ﬁle [317] or the Lund/LBNL data ﬁle [427]. These libraries contain a large number of isotopes with experimentally measured excited level energies, spins, parities, and relative transition probabilities. The most probable transition is the E1 or electric dipole transition which is the main source of photons from highly excited nuclei [428, 429]. For an E1 transition to occur between two states, the change in the angular momentum should be 1, corresponding to the emission of one photon. If the change in angular momentum between the states is very large, then the lower order or most probable transitions such as electric dipole E1 or electric quadrupole E2 or magnetic dipole M1 cannot occur. In this case the difference in angular momentum is so large that the state is very long lived. Although an M2 decay is less probable, it does occur ﬁnally. Table 3.6 summarizes the multipolarity types of photon transmissions. The multipole character of photon or gamma radiation is discussed in more detail in standard textbooks, e.g., [430].

179

180

3 Evaporation and High-Energy Fission Tab. 3.6

Types of gamma or photon transitions.

Multipolarity

Electric dipole Magnetic dipole Electric or Magnetic quadrupole Electric or Magnetic octopole Electric or Magnetic 24 -pole

Transition

Change in angular momentum

Change in parity

E1 M1 E2, M2

1 1 2

Yes No Yes, no

E3, M3

3

Yes, no

E4, M4

4

Yes, no

If the excitation energy is above the maximum known level, the level is assumed to be in the continuum. Total probability for photon evaporation The probability of either evaporating or alternatively of emitting photons in the energy interval (Eγ , Eγ + dEγ ) is given by

Pγ (Eγ ) =

1 π 2 (c)3

· σγ (Eγ ) ·

ρ(E ∗ − Eγ ) 2 · Eγ , ρ(E ∗ )

(3.95)

where σγ (Eγ ) is the inverse absorption cross section of the photon, and ρ is a nucleus level density deﬁned as ρ(E) = C · exp 2 a(E ∗ − δ ,

(3.96)

where C is a constant and δ is the pairing energy correction of the daughter nucleus evaluated by Gilbert and Cameron [336]. The probability of a transition between levels is assumed to be proportional to the Weisskopf single-particle estimates (cf. [430] page 414), unless speciﬁed by the isotope libraries. The calculation by Weisskopf [431] and Blatt and Weisskopf [432] is based on a nuclear model which assumes such a weak coupling between the constituent nucleons that in a photon or gamma transition only a single nucleon experiences a change in its quantum state. Internal conversion electron emission The GEANT4 [100, 424] particle transport system uses in addition to photon emission another important competitive channel namely the internal conversion electron emission8) . This is done including into 8) Internal conversion is a radioactive decay process where an excited nucleus interacts directly with one or more orbital electrons within the nuclear region. The nucleus imparts its excess energy to the conversion

electron in a one-step process and causes it to be injected from the atom with a comparatively high energy, where Eγ = Ee + EB .

3.10 Vaporization and Multifragmentation

the photon evaporation database internal conversion coefﬁcients such as those evaluated by R¨osel [433], and Hager and Seltzer [434]. A review of the reliability these data evaluations is given by Ryˇsav´y and Dragoun [435]. As conversion and photon decay compete, the branching ratio provides a measure of the relative probability in a given transition. Therefore, a conversion coefﬁcient CC can be deﬁned as CC =

λe conversion probability N ≡ = e γ -emission probability λγ Nγ

(3.97)

in terms of the decay constants λ, where Ne and Nγ are the number of conversion electrons and photons, respectively. The applicability of spallation reactions of photon evaporation or induced gamma ray spectra (cf. page 179) to analyze planetary surface compositions is shown in Part 3 on page 653.

3.10 Vaporization and Multifragmentation

Depending on the thermal excitation energy E ∗ dissipated into the nucleus, there exists beyond evaporation and ﬁssion also more ‘‘exotic’’ decay modes such as, e.g., vaporization and multifragmentation. Although they set in only at higher temperatures, and therefore compete with evaporation or ﬁssion only marginally in the E ∗ regime under consideration here, we devote for the matter of completeness this section to these speciﬁc decay modes. Deﬁnition For the so-called thermal multifragmentation (MF) the formation of intermediate mass fragments(IMFs) at higher temperatures is a consequence of increasing thermal motion linked with increasing mean distance of the nucleons. An excited remnant achieves the thermal equilibrium state and then expands, eventually reaching the freeze-out volume. At this point it fragments into neutrons, light charged particles, and IMFs. Due to the short ranging nuclear forces of nucleons the mean ﬁeld collapses and IMFs are formed by condensation. This unique phenomenon can be observed only for nuclei. Dynamical fragmentation in contrast is caused by high angular momenta, compression of the nuclear density, large momentum transfer and the formation of noncompact deformed nuclei. In this case the whole system and its parts (projectile and target remnants) never pass through states of thermal equilibrium. As schematically illustrated in Figure 3.13, the multifragmentation (MF) is observed in the E ∗ domain between spallation-evaporation and the ‘‘explosive’’ fragmentation regime. As mentioned in the previous section the global properties of nuclear matter are well described by the LDM for E ∗ /A ≤ 1 MeV/nucleon. In this domain the basic decay mechanism is the successive emission of particles via evaporation from the surface of the compound nucleus (left picture in Figure 3.13) and ﬁssion. In the case of evaporation a heavy residual remains which is comparable in size to the original target nucleus.

181

182

3 Evaporation and High-Energy Fission

Multifragmentation

Excitation energy E*

Fig. 3.13 Schematic sketch of the three decay modes such as spallation-evaporation, multifragmentation, and vaporization. The circle drawn indicates the original size of the target nucleus.

Many models [232, 422, 436–438] predict for nuclei A > 150 the multifragmentation within a range of the excitation energy from 3 to 5 MeV/nucleon. It is open so far whether one may regard the emission of IMFs by the conventional description of the evaporation from an equilibrated source, or whether other simultaneous decay characteristics need to be taken into account [437]. In this intermediate energy region the system fragments into many spallation products, having a size no longer comparable with the target mass (Figure 3.13, center). There is no accurate deﬁnition of the IMFs, however for heavy targets around A ≥ 150 fragments of mass 5 ≤ A ≤ 40 or atomic number 3 ≤ Z ≤ 20 are generally considered as IMFs. For E ∗ in the range of the entire binding energy of the target nucleus (7.5 MeV/nucleon) vaporization (right representation in Figure 3.13) begins to set in. Vaporization is a speciﬁc case of MF and is deﬁned as a decay in which all reaction products have atomic numbers A ≤ 4. In particular for MF, the time scale of fragment emission in general and the question of sequential or simultaneous decay of highly excited nuclei is the focus of theoretical [439, 440] and experimental [441–443] studies. Models have been developed based on the chemical equilibrium [229, 444], phase transitions with simultaneous evaporation during the dynamical expansion [445] or a dynamic of statistical decay [446]. Alternatively Moretto [442, 447], Tso [448], and Botvina [437] propose as a signature of statistical nature of MF the linear dependence between the natural logarithm of the decay ratios of an n-body decay as a function of (E ∗ )−1/2 ∝ 1/T (Arrhenius plots). However, so far no clear-cut answer could be given to the question whether the MF is subject to a prompt or sequential decay mechanism [379]. Also different model approaches try to ﬁnd an answer whether the multifragmentation mechanism is dominated by dynamical or statistical decay. Some of them describe the multifragmentation by instabilities in the gas–liquid phase of the nuclear matter [436, 445]. Analog to a Van der Waals liquid, nuclear matter having a density of ∼ 0.17 nucleons/fm3 in the ground state (T = p = 0) can be described by phase diagrams (Figure 3.14).

3.10 Vaporization and Multifragmentation

1.5

1.0 Pressure [MeV fm−3]

T = 20

0.5 Tc = 17.9

16 12

0

0.05

Nuclei

0.10

0.25

Density [fm−3] 8

−0.5

4

Spinodal Fig. 3.14 Solid lines (isotherm) indicate the pressure of the nuclear matter as a function of nuclear density for different ﬁxed temperatures (in MeV). The unstable states of the homogeneous inﬁnitely expanded (and thus idealized) system is represented by the broken area. A nucleus in the ground

state resides in the condition p = T = 0. The dashed curve shows the expansion of a hot, expanding nuclear system (see the text). The line at Tc = 17.9 MeV represents pressure and density for which liquid and gas phases co-exist (ﬁgure adapted from [436]).

In the ground state the nucleus resides at p = T = 0 and in the liquid phase. After an initial compression induced, e.g., by a heavy ion reaction the hot nucleus expands. The hot nuclear matter follows the dashed line (isotherm) of Figure 3.14 and ends ﬁnally as a diluted system in the spinodal region. In this region the compression coefﬁcient κ is given by ρ κ = (∂p/∂V)T = − V

∂p ∂ρ

,

(3.98)

T

where κ exhibits positive values. Under these conditions (ρ = 0.2–0.5 ρ0 ) density ﬂuctuations may easily lead to fragmentation. The phase diagram, as represented in Figure 3.14, applies only for inﬁnitely expanded homogeneous matter, in which no Coulomb interactions are considered. Therefore, the diagram is at most valid for hot neutron stars, but certainly not for real nuclei. This model is not quantitatively being established in detail and would reveal MF as a sudden phenomenon. The formation of cluster in the region of low nuclear density was studied theoretically also by Chomaz et al. [449]. They showed that – due to the ﬁnite range of strong nuclear forces – ﬂuctuations of the system do not have short wavelength components. Consequently the production of fragments of almost

183

184

3 Evaporation and High-Energy Fission

same intermediate size is more probable than the formation of small fragments. Theoretically the process of MF can also be described by the percolation theory. Percolation models treat the nucleus as a lattice with nucleons located at nodes of the lattice. It has been found that results of perculation calculations depend signiﬁcantly upon the details of the lattice structure. For reasons of computational convenience, the simple cubic lattice has most frequently been used in MF simulations [450], but several studies [451, 452] have found that the face-centered-cubic lattice more accurately reproduces the experimental distributions of fragment masses and their energy spectra. A detailed analysis on fragmentation of excited remnants using the face-centered-cubic lattice model of nuclear structure is given in Ref. [453]. Finally also statistical models are used for the description of the fragment emission. They are based either on the sequential binary statistical decay [229] or the simultaneous splitting of the system. The breakup of the system strongly depends on the so-called freeze-out volume [439, 444, 445] and shows a rising probability with increasing excitation energy. Decay models describing the simultaneous breakup take as a basis the accessible phase space, which determines the probabilities of different decay channels. These ‘‘phase-space models’’ describe both for low excitation energies the evaporation and for higher energies (based on the assumption of an increasing phase space) the breakup into 3, 4, 5 and more fragments of intermediate mass.

185

4 The Particle Transport in Matter 4.1 Introduction

Particle transport in matter became an increasing importance in many ﬁelds of basic science, technology, and applications in the recent years. The investigation of hadronic and electromagnetic cascades is of considerable interest for all aspects of radiation physics around, e.g., • particle sources, e.g., high-intensity neutron spallation sources and neutrino complexes; • particle accelerators; • biological shielding against high-intensity particle radiation for radiation protection for personnel and for components; • study of radiation damage of materials in a high-intensity radiation ﬁeld; • radiation therapy in cancer treatment with hadron, light ion, electron, gamma, and neutron radiation; • astrophysics, cosmic ray reactions, and space applications; • accelerator transmutation of radioactive waste (ATW); • sustainable energy production by accelerator-driven systems (ADS). As discussed earlier, the simulation of particle transport in matter and their interaction with matter involves a huge variety of particles like protons, neutrons, light and heavy ions, electrons and photons, muons, and neutrinos, etc., with energies starting from meV – the energy of ultracold neutrons – up to the energies of high-energy accelerator collider systems or cosmic rays at about several tens of TeV or even higher.

4.2 Hadronic and Electromagnetic Showers

In spallation and particle physics, a shower is a cascade of secondary particles produced as a result of a high-energy particle interacting with dense matter, e.g., with a heavy metal target as used by spallation neutron sources or by acceleratordriven systems, with the shielding material of iron or concrete to shield particle Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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4 The Particle Transport in Matter

accelerators or with high-energy physics calorimeters. The incoming particle interacts with the target matter and in producing multiple new particles with lesser energy. The process ends if the secondary particles are absorbed and stopped in the matter or escape from the target system. There are two basic types of showers. Hadronic showers are produced by hadrons (i.e., nucleons and other particles made of quarks), and proceed mostly via the strong nuclear force and obey the quantum chromo dynamic (QCD theory). Electromagnetic showers in contrast are produced by a particle that interacts primarily or exclusively via the electromagnetic force, usually a photon or electron, and are well described by quantum electrodynamics (QED theory) over a wide energy range. (1) A hadronic shower is produced by a high-energy hadron such as a nucleon, pion, or atomic nucleus. Some such particles have electric charge, and so produce showers that are partially electromagnetic, but they also interact with nuclei via the strong force. Although the details are more complex for this force, such an interaction involves one hadron interacting with a nucleus and producing several lower energy hadrons. This continues, as with the electromagnetic shower, until all particles are stopped or absorbed in the material. (2) An electromagnetic shower begins when a high-energy electron or photon enters a material. At high energy, photons interact with matter primarily via pair production, that is, they convert into an electron–positron pair, interacting with an atomic nucleus or electron in order to conserve momentum. High-energy electrons and positrons primarily emit photons, a process called bremsstrahlung. These two processes continue in turn, until the remaining particles have lower energy. Electrons and photons then lose energy via scattering until they are absorbed by atoms. The development of electromagnetic showers with their principal production processes – bremsstrahlung for electrons and positrons, pair production for photons, becoming energy dependent above 1 GeV. In order to visualize typical hadronic and electromagnetic shower propagation in nuclear matter, Figures 4.1 and 4.2 exhibit in different colors the tracks of particles generated by 1 and 10 GeV incident energy of protons, photons, and µ− in a lead target (Figure 4.1) and a target of plastic scintillator material (Figure 4.2), respectively. The Monte Carlo simulation has been performed by GEANT4 [100], hadronic interaction, multiple scattering, bremsstrahlung, ionization, pair production, photo-, Compton-effect, electroweak decays, and annihilation have been taken into account. The particle beam is coming from left in both the Figures 4.1 and 4.2. For the purpose of comparability the tracks of 20 primary incident particles in the bulk of the Pb material and of plastic material of target geometry of 100 × 80 × 80 cm3 are represented, respectively. The target materials have been chosen to compare a high density material (Pb with ρPb = 11.35 g/cm3 , with a radiation length of rlPb = 5.612 mm), and a hydrogen containing low density material, (plastic scintillator material1) with ρscin = 1.032 g/cm3 , with a radiation length of rlscin = 42.549 cm). 1) Assumed is a molecule H10 C9 .

4.2 Hadronic and Electromagnetic Showers

(a) Shower events of protons with energy of 1 GeV on a Pb target

(b) Shower events of protons with energy of 10 GeV on a Pb target

(c) Shower events of photons with energy of 1 GeV on a Pb target

(d) Shower events of photons with energy of 10 GeV on a Pb target

(e) Shower events of muons (m−) of energy of 1 GeV on a Pb target

(f) Shower events of muons (m−) with energy of 10 GeV on a Pb target

Fig. 4.1 Particle tracks following a GEANT4 [100] simulation for 20 events of 1 and 10 GeV energy of protons, photons, and µ− -induced spallation reactions on a Pb target with the dimensions 100 × 80 × 80 cm3 . The color coding is as follows: protons are blue, neutrons are yellow, photons are gray, µ− are red, and e− are magenta.

187

188

4 The Particle Transport in Matter

(a) Shower events of protons with energy of 1 GeV on a target of scintillator material

(b) Shower events of protons with energy of 10 GeV on a target of scintillator material

(c) Shower events of photons with energy of 1 GeV on a target of scintillator material

(d) Shower events of photons with energy of 10 GeV on a target of scintillator material

(e) Shower events of muons (m−) with energy of 1 GeV on a target of scintillator material

(f) Shower events of muons (m−) with energy of 10 GeV on a target of scintillator material

Fig. 4.2 Particle tracks following a GEANT4 [100] simulation for 20 events of 1 and 10 GeV energy of protons, photons, and µ− -induced spallation reactions on a target of scintillator material with the dimensions 100 × 80 × 80 cm3 . The color coding is as follows: protons are blue, neutrons are yellow, photons are gray, µ− are red, and e− are magenta.

4.2 Hadronic and Electromagnetic Showers

As a general tendency the showers penetrate deeper into the material, the higher the incident energy or the smaller the density of the material is. For 1 GeV incident energy charged particles as representatively shown in Figure 4.1 for protons and µ− are stopped in Pb after few cm, but may penetrate the low density plastic scintillator material as it is shown in Figure 4.2. For 10 GeV incident energy protons and µ− are neither stopped in Pb nor in scintillator material via electromagnetic processes. Due to their hadronic interactions protons – but also neutrons, not shown here – produce along their trajectory a huge number of secondary particles mainly neutrons (see Figures 4.1(a) and (b)) including photons, electrons, pions, kaons, and a long list of other mesons and baryons. For identical incident energy the hadronic shower produced by neutrons penetrates slightly deeper into the material, because neutron do not suffer any energy loss as the primary protons do. The electromagnetic shower of photons shown in Figures 4.1 and 4.2 gets quickly extinct even for incident energies as high as 10 GeV in particular in Pb material known as highly efﬁcient photon or γ absorber due to its high charge number Z. At deeper penetrations the photons are inducing an electromagnetic shower starting even only after a few cm, which is observed in the plastic scintillator material (cf. Figures 4.2(c) and (d)). Since as mentioned above at high energy, photons interact with matter primarily via pair production and high-energy electrons and positrons likewise emit photons via bremsstrahlung when passing through matter, the electromagnetic showers caused by electrons and photons resemble. The lepton µ− does not undergo hadronic interactions and as a 200 times heavier relative of the electron much less photons are created via bremsstrahlung processes. As mentioned in the case of extended targets, the reaction scenario includes secondary and higher order reactions induced by the reaction products themselves and, therefore, the calculations must include a three-dimensional simulation of internuclear cascades. Such a three-dimensional description of the propagation of the internuclear cascade and the transport of particles in thick targets is a rather complex problem that involves various boundary conditions. The propagation of protons and neutrons is considered separately in longitudinal and radial directions in the following. The energy losses of high-energy particles (≥ 1 GeV) traveling through matter are mainly determined by the production of secondary particles and not due to electronic stopping which is dominating at lower bombarding energies. Thus, the main feature of the cascade is an initial increase of the particle intensity with depth and time. If the energy of these produced secondary particles is high enough, they in turn knock out additional particles. There exists however a physical limit for the development of further cascades, because the initial energy of the primary particle is distributed among the produced particles. Therefore, the multiplicities tend to decrease again during the cascade process and fade away because the average energy of the cascade particles decreases and a greater fraction of the individual particle energy is now dissipated by ionization losses. At the end of the internuclear cascade process, subsequent emission of many low-energy particles, mainly neutrons, takes place, known as evaporation process [320].

189

4 The Particle Transport in Matter Neutron flux 0.07 p−1 cm−2

Proton flux

6

Ep = 2.5 GeV

4

0.002 p−1 cm−2

2 Target radius R [cm]

190

0 6

0.07 p−1 cm−2

4

Ep = 1.2 GeV 0.002 p−1 cm−2

2 0 Ep = 0.4 GeV

6 Protons

4 0.07 p−1 cm−2

2 0

0 (a)

10

0.002 p−1 cm−2

20 30 0 10 20 Target depth L [cm] (b)

30

Fig. 4.3 Neutron (a) and proton (b) ﬂux (per square centimeter and source proton, cm−2 p−1 ) of a hadronic shower in a cylindrical target of 35 cm × 15 cm lead as a function of incident energy of the protons (2.5, 1.2, and 0.4 GeV, top to bottom). Sequent lines are separated by factors of 1.5. Calculations have been performed using the HERMES simulation package (see the text).

As an example, the simulated propagation of three-dimensional hadronic showers following the bombardment of cylindrical lead targets of length (l = 35 cm) and diameter (d = 15 cm) by 0.4, 1.2, and 2.5 GeV protons is illustrated in the contour plots of Figure 4.3. The simulations have been done with the HERMES particle transport system taking into account the development of all shower processes. (cf. Chapter 5). The complexity and entanglement of all intra- and internuclear cascade and electromagnetic processes ﬁnally also causing the production of spallation neutrons requires a complex record keeping of all particles actually participating in terms of energy, direction, and location. In the example of Figure 4.3, the HERMES Monte Carlo particle shower simulations produced the data for Figure 4.3 in a cylindrical target divided into cylindrical zones of 0.5 cm spatial resolution in radial direction and of 1 cm spatial resolution in longitudinal direction. The particle ﬂux for neutrons and protons is estimated by the track-length estimator2) . The symmetry axis of the cylinder is oriented in the z direction and pointing downstream of the proton beam. The 2) The track-length ﬂux estimator is deﬁned in Eq. (4.18) on page 197.

4.3 The General Transport Equation

track-length ﬂux of neutrons (left) and protons (right) reﬂects the radial and longitudinal propagation of particles involved in the intra- and internuclear cascades inside the target volume. The track-length ﬂux comprises both, cascade and evaporation particles. The primary beam protons are not included for the proton track-length ﬂux in Figure 4.3. Multiplying the proton beam current, measured in protons per second, by the track-length ﬂux speciﬁed in Figure 4.3, the particle ﬂux, generally used in units of (particles cm−2 s−1 ), is obtained for neutrons and protons. As also shown for the individual tracks in Figures 4.1 and 4.2 as a general tendency one observes in Figure 4.3 that a deeper and deeper penetration into the target the higher the kinetic energy of the incident proton is. The maximum of the evolution in the radial direction is found after the hadronic cascade has already propagated 5 to 10 cm in the longitudinal direction. Neutrons tend to spread out radially much more than protons do, because especially low-energy protons experience high electronic stopping power and consequently short range. That is also why protons develop along their trajectory in a more narrow cone. Note the difference in the absolute track-length ﬂux of more than one order of magnitude between neutrons and protons. For low incident proton energies (0.4 GeV) it is well shown that the cascade rapidly becomes extinct, since the leading particles are stopped before being able to convert their energy effectively into the production of neutrons or protons. Whereas for large kinetic energies (≈GeV) the range due to the stopping power of protons in the lead target is larger than the dimension of the cylinder in z. Although the presentation of hadronic cascades in the r, z-plane is illustrative to explain phenomenologically the interplay of intra- and internuclear cascade descriptions and the well-known consequences of stopping powers applied to charged particles, a more quantitative analysis would include the study of kinetic energy and multiplicity spectra or angular distributions of particles released. The next section is devoted to the theoretical background of the particle transport.

4.3 The General Transport Equation

Phenomena in radiation physics and particle transport in matter of leptons, baryons, mesons, and energetic photons are described by the Boltzmann integrodifferential equation (4.2). It was derived by Ludwig Boltzmann in 1872 to study the properties of gases. The important processes involved in the equation will be brieﬂy described and some solutions are presented to introduce the nomenclature of frequently used important parameters, which are describing the particle transport in various spallation environments. More details are given in the literature for reactor physics and neutron transport [63, 150, 454]. The Boltzmann equation (4.2) is a continuity equation in phase space, which is made up of three space coordinates of euclidian geometry, the kinetic energy and the direction of motion, Ω, of the particle. The vector, Ω, is a unit vector in the particle’s direction of motion. Its three components, in Cartesian form, in terms of

191

192

4 The Particle Transport in Matter x Ω Θ

Y

y

z

Fig. 4.4

The coordinate system of the Boltzmann equation (4.2).

the so-called polar angle and the azimuthal angle are given as x = cos y = sin cos z = sin sin .

(4.1)

The coordinate system of the Boltzmann equation is given in Figure 4.4. The Boltzmann’s equation or transport equation (4.2) is expressed in terms of − → the variable i (r , E, , t), called the angular ﬂux. The angular ﬂux is the number of particles of a given type (nuclei, protons, neutron, leptons, mesons, etc.) in the volume element dxdydz about r in the energy element dE with the direction of the motion dΩ about Ω, multiplied by the velocity of these particles. The velocity is in terms of the scalar v = (p · c)/Etotal , where p is the particle momentum (see 1/2 Eq. (1.19)) with p = (E 2 + 2 · E · mi ) , c is the velocity of light, Etotal is the total particle energy E + mi , and mi is the particle mass (cf. Section 1.3.5.4 on page 30. The Boltzmann equation in its general form is given by 1 · vi

∂i ∂t

= − Ω · grad i +

i

· j (r , EB , Ω , t) −

dΩ · dEB · σi,j (r , EB → E, Ω → Ω )

dΩ dEB

· σi,j (r , E → EB , Ω → Ω ) · j (r , E, Ω, t)

− σi (r , E) · i (r , E, Ω, t) + (∂/∂E)(i (r , E, Ω, t) · S(r , E)) 1 − · i + Yi (r , E, Ω, t). (4.2) λi It follows a discussion of the meaning of different terms of the Boltzmann equation (4.2). The density of the particle radiation in a volume of the phase space may change in ﬁve ways:

4.3 The General Transport Equation

(1) uniform translation, with changing the spatial coordinates of the vector r with the Cartesian coordinates x, y, z, but the energy-angle coordinates remain unchanged; (2) collisions, with changing the energy-angle coordinates, but the spatial coordinates remain unchanged; (3) continuous slowing down of the particle energy, a process where a uniform translation is combined with a continuous energy loss; (4) decay, with a changing of particles through radioactive transmutation into other particles; (5) external source, the direct emission of particles into the volume of phase space of interest, e.g., a spallation neutron source, a ﬁssion source, other radioactive sources as electrons and photons, and cosmic rays, etc. The ﬁrst process (1) results in a particle current reducing the phase-space density 1 ∂i (r , E, Ω, t) = −div[Ω · i (r , E, Ω, t)] = −Ω · gradi (r , E, Ω, t). vi ∂t (4.3) The second process (2) results in a change in energy, angle, and particle type as a result of the collisions between the particle radiation and the nuclei of the matter 1 ∂i (r , E, Ω, t) (2) = · dΩ · dEB · σi,j (r , EB → E, Ω → Ω) vi ∂t j · j (r , EB , Ω , t) − dΩ dEB · σi,j (r , E → EB , Ω → Ω ) · j (r , E, Ω, t) (1)

− σi (r , E) · i (r , E, Ω, t).

(4.4)

In Eq. (4.4), the term σi,j (r , EB → E, Ω → Ω) represents the cross section which is the probability of producing an i-type particle with the phase-space coordinates (r , E, Ω, t) as a result of a collision with a j-type particle with the phase-space coordinates (r , EB , Ω , t). The energy EB is higher than the energy E, and therefore this ﬁrst term in the square brackets is called the down scattering integral. The cross-section term in Eq. (4.4) σi,j (r , E → EB , Ω → Ω ) represents the probability of the production of a particle with higher energy at the energy EB from a lower energy particle. This so-called up-scattering integral is important for all moderation processes in matter. Up-scattering is especially signiﬁcant in treating thermal neutrons with energies low enough to gain energy in colliding with the atoms of matter. Both processes – down/up-scattering – play an important role in the moderation of neutrons in reactor physics and technology. The physics and technology of cryogenic moderator systems are especially considered for the neutronic performance of high-intensity spallation neutron sources. The third process (3) is connected with the stopping power S of particles by traversing matter. Particles will loose energy continuously at a rate S(r , E) per unit path length.

193

194

4 The Particle Transport in Matter

The densities of particles at an energy EB and on slowing down to the energy E are given as – (a) i (r , EB , Ω , t) · S(r , EB ) and – (b) i (r , E, Ω , t) · S(r , E), respectively. (3)

1 ∂i ∂(i S) = vi ∂t ∂E

(4.5)

As seen from Eq. (4.5), the energy loss of a particle in matter is associated with the motion of the particle through the matter. The fourth process (4) is connected with the decay probability λi of a particle. In the decay process is a simple removal process where the particle i disappears. (4)

1 1 ∂i = − · i , vi ∂t λi

(4.6)

where the decay probability λi is given per unit path-length by λ = τi · c

βi , (1 − βi )1/2

(4.7)

with τi as the mean lifetime of the rest frame of the particle, c as the velocity of light, and βi as the particle velocity relative to the velocity of light. The ﬁfth process (5) describes the application of an external source. This means the direct emission of particles into the volume of phase space of interest, e.g., a spallation neutron source, a ﬁssion source, other radioactive sources as electrons and photons, and cosmic rays, etc. (5)

1 ∂i = Y(r , E, Ω, t). vi ∂t

(4.8)

The combination of the ﬁve processes given by Eqs. (4.3), (4.4), (4.5), (4.6), (4.7), and (4.8) results in the Boltzmann equation in its general form given by Eq. (4.2). The general form of the Boltzmann equation (4.2) is written in the stationary form with ∂i /∂t = 0. The subscripts and the arguments have been dropped in the following description: Ω · grad + σ · + (/λ) − [∂(S)/∂E] = Q + Y,

(4.9)

where Q is the sum over the up- and down-scattering integrals in the square brackets in Eq. (4.4). Another often used abbreviated form in operator notation is given as B · = Q + Y,

(4.10)

where B = Ω · grad + σ + λ−1 − (∂S/∂E). The general form and also the stationary form of the Boltzmann equation are difﬁcult to solve. Therefore, a large number of numerical methods and special techniques were developed to yield for different particle transport cases useful

4.3 The General Transport Equation

results. These numerical techniques are the straight-ahead approximation [455, 456], the method spherical harmonics [457, 458], the method of discrete ordinates, often named SN -method [459, 460], and the Monte Carlo method [146, 149, 150], which is capable of treating very complex three-dimensional conﬁgurations of multiparticle transport problems. The Monte Carlo method is a stochastic model in which the expected value of a certain random variable is equivalent to the value of the physical quantity to be determined. The expected value is estimated by the average of many independent samples representing the random variable. Particle tracks or histories3) are generated by simulating the real physical situation. There is not even the need to invoke the transport equation for more elementary operations. Only the complete mathematical description of probability relationships is needed that govern the track length of individual particles between interaction points, the choice of interaction type, the new energies and directions and the possible production of secondary particles. Especially for three-dimensional problems, SN methods and Monte Carlo techniques turned out to be most advantageous. Because the transport of particles through matter obeys stochastic processes, the application of Monte Carlo solutions of particle transport problems in matter are the favorable methods nowadays. 4.3.1 The Angular Flux, Fluence, Current, and Energy Spectra

As mentioned earlier, Eq. (4.2) is a system of coupled transport equations, which is, in general difﬁcult to solve. Solving the equation for hadronic cascades is more difﬁcult than, for instance, for neutrons in the core of a nuclear reactor, because of secondary particle production. Thus the solution involves solving the ﬂuxes for many different particle types. The angular ﬂux or ﬂux spectrum, i (r , E, Ω, t), gives the number of particles per cm2 per MeV per steradian per second of a given kind at a given location at a given time. In the following there are some useful relations determined with the angular ﬂux characterizing the radiation ﬁeld of particles. • The integral quantity (actually used to deﬁne the angular ﬂux i (r , E, Ω, t) in units of (cm−2 s−1 sr−1 MeV−1 ) is the ﬂuence i (r ). i (r ) =

dE

E

i (r , E, Ω, t).

dΩ 4π

(4.11)

t

The ofﬁcial deﬁnition of ﬂuence by the International Commission on Radiation Units and Measurements (ICRU), 1993 [461] is based on crossing of a surface and deﬁnes the ﬂuence as the quotient of dN by dα, where dN is the number of particles incident on a sphere of cross-sectional area dα, i (r ) = dN/dα. This deﬁnition is the source of frequent mistakes. It is not to be interpreted as ‘‘ﬂow’’ or ‘‘ﬂux’’ of particles through a surface, but to be understood as a density of particle path lengths in an inﬁnitesimal volume: i (r ) = limV→0 i si /V 3) The experience a particle undergoes from the time it leaves its source until it is absorbed or

until it leaves the system is called the particle’s history.

195

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4 The Particle Transport in Matter

(cm× cm−3 = cm−2 ), where i si is the sum of path-length segments. The ﬂuence is therefore a measure of the concentration of the particle path in an inﬁnitesimal volume element around a space point. If the particle’s path length is measured in units of mean free path λ = 1/σ , the expression of ﬂuence is equivalent to the density of collisions σ · i (r ). The most important ﬂuence estimator is the track-length estimator (see Section 4.3.2), which represents the average ﬂuence in a space region when the sum of track lengths is divided by the volume). Frequently the ﬂuence is calculated because it is proportional to the effect of interest, since many effects can be expressed as volume concentrations of some quantity proportional to the ‘number of collisions’. • The ﬂuence rate or ﬂux density is also referred to as scalar ﬂux is expressed in terms of the sum of path segments transversed within a given volume per time unit:

i (r , t) =

dEi (r , E, Ω, t).

dΩ 4π

(4.12)

E

In Monte Carlo calculations with a source given in units of particles per unit time, the scalar ﬂux represents a ﬂuence quality. • The particle current J or the boundary crossing estimator is

J i (r , t) = 2π

π

sin θ dθ

0

dE cos θ i (r , E, Ω, t).

(4.13)

E

To estimate the average ﬂuence on a boundary, the factor 1/ cos θ for each particle has to be added, where θ is the angle between the particle’s direction and the normal to the surface at the crossing point. Therefore, the current is equal to the ﬂuence only if all particles pass perpendicular to the surface. • The ﬂux density of particles or number of particles per volume element dxdydz is n(r , t) =

dEi (r , E, Ω, t)/v.

dΩ 4π

(4.14)

E

• The energy spectrum of particles can be expressed by i (r , E, t) =

dΩi (r , E, Ω, t).

(4.15)

4π

An often used nomenclature for the ﬂux density of particles having a kinetic energy in the range E and E + dE in radiation ﬁelds is written as (E)dE, and the parameter (E) as a function of E is named the differential energy spectrum. The ﬂux density, , over all energies is given by = 0

∞

(E)dE,

(4.16)

4.3 The General Transport Equation

and the integral ﬂux density, (>E ), is given by (> E ) =

∞

E

(E)dE.

(4.17)

4.3.2 Monte Carlo Estimation of Particle Fluxes and Reaction Rates

As discussed earlier, the particle ﬂux is a function of the spatial position, the energy, the time, the direction, etc. In many practical problems one only needs the particle ﬂux as a function of a spatial position and energy. There are, e.g., in general four methods to calculate particle ﬂuxes of particles transported through matter using Monte Carlo methods. These are referred to as track length estimation, collision density estimation, boundary crossing estimation, and statistical estimation. The formalisms of estimators are usually named ‘detectors’ by analogy with particle detectors to measure particle ﬂuxes by an experiment or named ‘tallies’ to register the particles traversing the matter (more details can be seen in standard textbooks about Monte Carlo [149, 150] or in manuals of modern Monte Carlo particle transport code systems GEANT4 [100, 424], FLUKA [197, 423, 462], and MCNPX [194, 463]). (1) The track length estimator: The energy-dependent ﬂux per unit source particle is calculated in an arbitrary volume in space by N

(r , E) =

li · wti

i=1

V · E · M

,

(4.18)

where • li is the track length of the ith particle in the volume, • wti is the statistical weight of the ith particle, which is one in analog Monte Carlo, • V is the volume traversed by the particle, • M is the total number of source particles, • N is the total number of track-lengths in the volume V by particles of energy E about E. The volume V can be of any size and shape. Large volumes may be needed to improve the statistics. (2) The collision density estimator: The collision density estimator counts the number of particle collisions within a given volume. But it only approximates the total track length. This detector works well if there is a large number of particle collisions in the volume of interest. The collision density estimation of the particle ﬂux is given by (r , E) =

N i=1

total

wti , (E) · V · E · M

(4.19)

197

198

4 The Particle Transport in Matter

where • wti is the statistical weight of the ith particle producing the collision, which is one in analog Monte Carlo, • (E) is the total cross section in cm−1 of the matter where the collision takes total

place, • V is the volume traversed by the particle, • M is the total number of source particles, • N is the total number of track-lengths in the volume V by particles of energy E about E. (3) The boundary crossing estimator: The boundary crossing estimator calculates the particle ﬂux through a given surface A in a position of interest in a geometry. The energy- and spatial-dependent particle ﬂux per unit source particle is calculated as (r , E) =

N wti · (|n · Ω|−1 )i i=1

A · E · M

,

(4.20)

where • wti is the statistical weight of the ith particle transverses the surface A, which is one in analog Monte Carlo, • A is the surface area, • n · Ω is the cosine of the angle between the direction of the particle and the normal vector n of the surface area A at the point the particle crosses the surface, • N is the total number of particles crossing the surface area with energy E about E, • M is the total number of source particles. Numerical problems may occur in Eq. (4.20) if the product |n · Ω| ≈ 0. So one has to control the magnitude of the cosine of the angle near π/2. (4) The statistical estimator or the ﬂux at a point estimator: This method allows for estimating the ﬂux at a point in space. The detector is extremely powerful for deep penetration problems, e.g., radiation shielding calculations of thick shields, for particle streaming through beam holes, etc. (cf. Chapter 7 on page 233). The statistical estimator is composed of two contributions, the ﬁrst one is the uncollided response representing the source particles and the produced particles, and the second one is the collided response representing all scattered particles leaving a collision site. The uncollided response is given as (r , E)uncollided =

N exp(− i=1

· |r i − r |) wti , 4π|r i − r |2 M total (E)

(4.21)

4.3 The General Transport Equation

where • wti is the weight of the source or the produced particle, which is one in analog Monte Carlo, • r i are the coordinates of the source or the produced particles, • r are the coordinates of the detector, • (E) is the total cross section in cm−1 of the matter of interest, total

• N is the sum over all source and produced particles of energy E about E, • M is the total number of source particles. The collided response is given as (r , E)collided =

N g(E → E, → ) · exp(− |r i − r |2

i=1

total (E)

· |r i − r |) wti , M (4.22)

where • g(E → E, → ) is the probability that a particle of energy E and direction will scatter to energy E and direction , which is toward the detector located at position r , • N is the total number of particle collisions, • wti weight of the particle producing the collisions • M is the total number of source particles. • r i are the coordinates of the source or the produced particles, • r are the coordinates of the detector, • (E) is the total cross section in cm−1 of the matter of interest. total

(5) The nuclear response function: The estimated particle ﬂux spectra and particle currents may be used to calculate or to analyze further important nuclear quantities which are the reaction rates or the nuclear response in matter applying the particle ﬂuxes in phase space together with a macroscopic response function (r , E)j,k , which is a function of the spatial coordinates and the energy E. The index j stands for the particle under consideration and the index k considers the material of interest, respectively. The reaction rate Ri can be given by

Ri =

i+1 (r , E)j,k · (r , E, Ω, t)dE, i

(4.23)

i

where (r , E, Ω, t) is the angular particle ﬂux distribution and (r , E)j,k is the macroscopic cross section of a certain nuclear reaction to estimate, e.g., radioactivity, energy deposition, material damage, dose, and other nuclear-induced properties of materials. Databases of nuclear response functions could be retrieved by using the following databases, e.g., the National Nuclear Data Center (NNDC),

199

200

4 The Particle Transport in Matter

Brookhaven, USA [464], the Nuclear Energy Agency (NEA) Nuclear Data Bank, Paris, France [465], the International Atomic Energy Agency (IAEA) Nucleus-Data Center, Vienna, Austria, [466], and the Radiation Safety Information Computational Center (RSICC-ORNL), Oak Ridge, USA, [467]. 4.4 Range Straggling

Because of ﬂuctuations in energy loss (cf. Section 1.3.6.1 on page 33) a beam of charged particles will have at the end of range a distribution of ranges in the medium. In some applications in spallation research involving low-energy charged particle sources in which the fraction of the beam particles that slow down and stop from ionization losses rather than undergo nuclear collision is signiﬁcant, it is necessary to take into account the statistical ﬂuctuations in energy loss at the end of range. This also yields for detectors, e.g., for high-energy physics calorimeters segmented of heavy-metal absorber and scintillator plates. These ﬂuctuations result in a variable range distribution at the end of range called range straggling. Calculations have shown that these range distributions for protons in various metals are nearly Gaussian [468]. The probability of energy loss – the straggled range distribution – is taken to be Gaussian about the mean range with a variance given, e.g., by Ref. [469]

σR2i (E

E

→ E ) = 4π · e · 4

Zi2

·N· E

(1 − 1/2β 2 ) · K(E) (Si (E))−3 dE, (1 − β 2 ) · (1 + (2me /mi ) · γ )

(4.24) where σR2i (E → E ) is the variance of the range distribution for a charged particle of type i slowing down from a kinetic energy E to E , • e is the electron charge, • Zi is the charge of the particle slowing down, • N is the electron density of the stopping medium, – the number of electrons per unit volume in the medium4) , • K(E) is the binding correction factor which takes into account the effects of binding on the atomic electrons at low energies of the incident particle. The expression of K(E), Eq. (4.25), has been derived by Livingston and Bethe [95]. • β 2 is given by [(E + 1)2 − 1]/(E + 1)2 , • E is given by E/mi · c2 , • me is the electron mass, • γ is given by (1 − β 2 )−1/2 , • Si is the stopping power of the medium i (cf. Section 1.3.6.1 on page 33). 4) N = NAA·Z·ρ , with NA the Avogadro number, ρ the density of the medium, and Z, A the atomic and the mass numbers of the medium,

respectively. For example, 26 56 Fe is N ≈ 2, 28 × 1024 electrons cm−3 .

4.5 The Elastic Scattering of Protons and Neutrons

The factor K(E) is given by K(E) =

kn I n Z n

2mv 2 Zeff + · ln , 2 Z mv In n

(4.25)

where Zn is the number of electrons in the nth shell of the atoms of the stopping material, In is the corresponding effective excitation potential for the nth shell, kn is a constant taken as 4/3 for all shells [95], the sum over n extends over all shells for which In < 2mv 2 , and Zeff is the effective number of electrons participate in the stopping process at the incident velocity v considered, e.g., Zeff is the sum of the Zn for the shells for which In < 2mv 2 . Typical values of K(E) are, e.g., for Al at Eproton = 5 MeV K(E) = 1.27, at Eproton = 10 MeV K(E) = 1.19, Eproton = 100 MeV K(E) = 1.04, and for Pb Eproton = 5 MeV K(E) = 1.31, Eproton = 10 MeV K(E) = 1.22, Eproton = 100 MeV K(E) = 1.16, Eproton = 200 MeV K(E) = 1.11. K(E) decreases rapidly toward 1 with increasing kinetic energy of the incident particle. The ranges Ri of a particle i are chosen from a probability distribution P(Ri ) P(Ri )dRi =

σR2i

(R − R )2 1 i 1+1 · exp − dRi , √ 2 · σR2i · 2π

(4.26)

where Ri is the mean range of the particle under consideration.

4.5 The Elastic Scattering of Protons and Neutrons

Nuclear elastic scattering at high energies (≥20 MeV) is a mechanism which is often neglected in high-energy radiation transport calculations of neutrons and protons because the energy losses and angular deﬂections from such interactions are small. However, there are several situations related to accelerator and spallation neutron source shielding, visible energy in high-energy physics calorimeters, heat deposition in material, etc., where elastic scattering affects in the propagation of cascades in matter. For example, small angular changes can affect shield attenuation for very deep penetrations [380]. An example of the elastic scattering cross sections for protons is already given for the materials C, Al, Fe, and Pb on page 50 in Figure 1.31. The data are taken from the NASA compilation [116] and from an evaluation given by [88]. These cross sections are available only for incident proton energies ≥ 100 MeV and are compiled up to energies E ≤ 22.5 GeV. The lower limit for protons is not an important restriction because for most applications protons in this energy range predominately slow down and stop due to ionization energy losses rather than undergo nuclear collisions. The proton elastic cross sections values are assumed essential the same as for neutrons. Neutron-induced elastic cross sections in the energy range from 15 to 100 MeV may be found in the re-evaluated HILO transport cross-section

201

4 The Particle Transport in Matter

101

5 Total neutron elastic cross section [b]

202

2 Pb 100

5

Fe

Al 2 C

10−1

101

2

5

5 103 2 102 2 Neutron energy [MeV]

5

104

Fig. 4.5 Energy dependence of the total neutron elastic cross section for C, Al, Fe, and Pb in the energy range from 15.0 MeV to 10.0 GeV as used in the elastic scattering model of the HERMES system [88].

library [470] developed originally at ORNL, and also in the NASA compilation of Wilson et al. [116] for higher energies up to 22.5 GeV. The energy dependence of the neutron elastic cross sections as a function of the target material is illustrated in Figure 4.5. A double logarithmic interpolation of the database in the HERMES system [88] is used for both energy and target atomic mass number interpolation. Figure 4.6 illustrates the target atomic mass number interpolation and extrapolation for several energies. Several approaches may be considered for obtaining the angular distributions for the elastically scattered neutrons and protons either to use an approximate optical model, e.g., Marmier and Sheldon [471] or a semiempirical formula based on measurements at very high energies as used in GEANT4 [100, 424]. A rather simple form for the elastic scattering differential cross section is predicted by dσ/d ≈ R4 /λ2

J · [2 · R · sin (/2)/λ] 2 1 , 2 · R · sin (/2)/λ

where • c.m. is the center-of-mass scattering angle • J1 is the Bessel function of ﬁrst kind, ﬁrst order

(4.27)

4.5 The Elastic Scattering of Protons and Neutrons

5

Total neutron elastic cross section [b]

2 100 5 50MeV 2 100MeV

10−1 5

400MeV 2

1100MeV

10−2 100

2

5

2 5 101 102 Atomic mass number

2

Fig. 4.6 Target mass dependence of neutron elastic cross sections for several energies. The points are used in the database of the HERMES system [88] for the elastic scattering model, and the lines show the interpolation and extrapolation used within the model for the target mass range.

• • • •

R = r0 · A1/3 + λ and r0 = 1.4 fm λ = h/p is the de Broglie wavelength h is the Planck constant p = 1/c · [E · (E + 2m)]1/2 .

The approximate optical model angular distribution of Eq. (4.27) may be used for both neutron and proton scattering5) . To determine the neutron or proton scattering angle, a random selection is ﬁrst made of the variable x from a probability distribution function P(x) ∝ [J1 (x)/x]2 , where a series expansion is used for evaluating the Bessel function J1 J1 (x)/x ∼ 1/2 − x2 /16 + x4 /3.84 × 102 − x6 /1.8432 × 104 ,

(4.28)

where the range of x is from 0 to the ﬁrst zero crossing of J1 , which is xmax = 0.610 · 2π. 5) Details are given in the HERMES program report [88] on pages 99–116.

203

4 The Particle Transport in Matter

104

103

102 ds/dΩ [mb/sr]

204

101

100

10−1

10−2 0.0

5.0 10.0 15.0 20.0 Proton scattering angle Θ [degree]

25.0

Fig. 4.7 Proton differential elastic scattering cross section on 12 C at 1 GeV as a function of the scattering angle c.m. in the center of mass system as used in GEANT4 (solid line) [424]. The experimental data are measured at Saclay, France [476].

The random number selections are made from a cumulative histogram of P(x) from x = 0 to xmax . The center-of-mass scattering angle c.m. estimated by using the center-of-mass cosine for a nucleon of energy E scattering from a nucleus of atomic mass A is then 1 . cos c.m. = 1 − x2 · −3 1/3 (2 · [7.093 × 10 · A · E(E + 1.878 × 103 ) + 1]2 ) (4.29) The GEANT4 [424] simulation transport system uses a different approach compared to that given in HERMES [88] to estimate hadron–nucleus elastic scattering cross sections. The Glauber model [472] is used as an alternative method of calculating differential cross sections for elastic and quasielastic hadron–nucleus scattering at high and intermediate energies. Scattering of protons of an energy of 1 GeV on nuclei, e.g., 9 Be, 11 B, 12 C, 16 O, 28 Si, 40 Ca, 58 Ni, 90 Zr, and 208 Pb are reviewed in Ref. [473] and also given for 4 He in Refs. [474, 475]. The examples in Figures 4.7 and 4.8 show a comparison of phenomenological cross sections with experiments for protons at 1 GeV energy elastically scattered on 12 C and 208 Pb. The experimental data were obtained at Gatschina [473], Russia, and at CEA-Saclay [476], France.

4.6 The Treatment of Pion Transport in Matter

106 105

ds/dΩ [mb/sr]

104 103 102 101 100 10−1

0

2

4 6 8 10 12 Proton scattering angle Θ [degree]

14

Fig. 4.8 Proton differential elastic scattering cross section on 208 Pb at 1 GeV as a function of the scattering angle c.m. in the center of mass system as used in GEANT4 (solid line) [424]. The experimental data are measured at Saclay, France [476].

4.6 The Treatment of Pion Transport in Matter

Because of the short mean lifetime of pions, the pion transport in matter and their decay has to be taken into account during their transport through matter. Neutral pion decay Neutral pions π 0 s have a very short half-life or mean lifetime of about 0.87 × 10−16 s and are assumed to decay at their collision site where they are created. Within the intra/internuclear cascade usually the source distribution of the π 0 ’s is provided. Therefore, the photons from the π 0 -decay can be obtained either from electromagnetic shower models or codes, e.g., as EGS [477], or in special auxiliary codes taking into account the γ γ - and the Dalitz-decay channels. Charged pion decay For the charged pions ‘‘in ﬂight’’, e.g., before coming to rest due to ionization loss, both decay and nuclear collisions have to be taken into account. π ± -particles which comes to rest may be assumed to decay or undergo nuclear capture. This may depend on the material or the matter in which their transport is considered. Pion decay in-ﬂight is usually determined by deﬁning a ‘‘macroscopic decay cross section,’’ which is in analog to the macroscopic cross section used for nuclear collisions. The capture or decay products have to be treated or transported using other models especially the production of neutrinos. The properties of pions and their decay products are already described in Eqs. (1.1) on

205

206

4 The Particle Transport in Matter Tab. 4.1

Decay properties of pions and muons.

Particle

Mean lifetime τ0 (s)

Mean path length c · τ0 (m)

π+ π− µ±

2.6 × 10−8 2.6 × 10−8 2.2 × 10−6

7.8 7.8 ∼ 660.0

π0

0.87 × 10−16

∼ 10−8

Decay model

π + → µ+ + νµ π − → µ− + ν µ µ+ → e+ + νe + ν µ µ− → e− + ν e + νµ γγ (98.799 %) γ e+ e− (1.198 %)

page 7 and in Table 1.11 on page 29. Important for the decay in-ﬂight is the mean lifetime or mean decay time in the rest frame and the mean free path for decay which are given in Table 4.1. The macroscopic decay cross section is given as D (E) = 1/λdecay with the decay mean path λdecay = v · τ = v · γ · τ0 , where τ = γ · τ0 , and γ = [1 − (v/c)2 ]−1/2 = [1 − (β)2 ]−1/2 . According to Table 4.1 the mean free path for decay can be written as • for pions: Lπdecay = 7.8[(E/139.6 + 1)2 − 1]1/2 (m) • and for muons: µ Ldecay = 660[(E/105.7 + 1)2 − 1]1/2 (m).

207

5 Particle Transport Simulation Code Systems 5.1 Introduction

This chapter summarizes the currently state-of-the-art particle transport simulation code systems used in spallation research and in particle transport through matter. With the advent of high-intensity spallation neutron sources with a proton beam power in the MW range, the SINQ – Switzerland, [478], the SNS – USA [479], the JPARC – Japan, [145], with research projects as the long pulsed European Spallation Neuron Source (ESS) [480], accelerator-driven systems (ADS) for nuclear waste transmutation and energy production [481–483], with the application of radioactive beams, with the detectors and experiments at medium- and high-energy accelerators, and with cosmic and space applications detailed particle production and transport models realized in computer code systems have to be used to demonstrate feasibility and utilization, to optimize the design conﬁgurations, and to support the engineering layout. One main goal of the simulation methods is the determination of the particle ﬂuxes for different applications in a three-dimensional complex multimaterial geometry. Particle ﬂuxes and energy deposition inﬂuence the engineering design criteria on cooling of targets, windows, and containments. Radiation damage produced by different mechanisms as displacements per atom (dpas), gas production, and nuclide transmutation worsens the mechanical properties and limits the lifetime of structure materials and components. Activation and radiation lead to global hazards rating the different components of the accelerator and the experiments. Shielding in spallation-induced reactions is different compared to nuclear reactor systems and fusion devices due to the high-energy neutron component which inﬂuences the safety protection and the environment. Finally the uncertainties of the complex simulation methods have to be assessed based on validation with experiments. The comparison to experiments serves to get conﬁdence in the complex simulations of the physics processes on a level of a broad range of coincident observables, putting strong constraints to the quality and accuracy of modeling (cf. Part 2 on page 277). In Section 5.2, the most useful and recent particle transport simulation code systems and event generator codes for spallation research and applications are summarized. Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

208

5 Particle Transport Simulation Code Systems

5.2 Particle Transport Code Systems and Event Generators

Several particle transport code systems with high-energy capabilities were developed in parallel in the late 1960s and early 1970s. All employ three-dimensional Monte Carlo methods. The most general are: • the HETC (High Energy Transport Code) of Armstrong and Chandler [192], which is a descendant of the NMTC code (Nuclear Meson Transport Code) [484], developed in the late 1960s for space radiation transport. • the FLUKA/KASPRO system of Ranft and Routti [485], • the CASIM code of Van Ginneken [486], and • the DUBNA code of Barashenkov et al. [487]. The ideas and models realized in these early particle transport codes were further developed and have been partly a basis of all modern simulation systems for particle transport through matter. Today computer simulation opens up new potentials of describing and studying physical and technical issues. In certain circumstances, computer simulation is the only way to understand the complexity of physical phenomena. The classic categories – theory and experiment – are completed or assisted by a third category, the computer simulation. The method of this third category is a realistic simulation by Monte Carlo and the instrument used is the super computer. In many respects, the computer simulation of particle transport in matter looks like an experiment. Not to misunderstood, computer simulation is not to substitute the experiments, but it extends the ﬁeld of science and enables experiments in a hypothetical world. Because vector and parallel computer systems have tremendous capabilities today, it is possible to simulate and to study a large number of cases and parameters in a very short time. Many complex systems that could not be veriﬁed by classical methods are now accessible and can be studied in great detail. Therefore, utilization of supercomputers in science and technology is an important tool and an advantage in parallel to traditional experimental and theoretical research work. The particular challenge requested to the particle-transport codes in spallation research is due to the description of hadronic and electromagnetic phenomena over ten orders of magnitude ranging from the incident particle energies of some GeV down to the energy of the subthermal neutrons in meV energy range. There is one caveat concerning the neutron reaction mechanisms with matter in the low-energy region. The complex features of neutron cross sections in the low-energy region cannot be calculated from ﬁrst principles using the properties of the nucleus. Hence data must be determined empirically as a function of energy for each nuclide and for each reaction. In general, these data cannot be interpolated over large energy intervals, because of the irregular resonance structure, although Breit–Wigner resonance parameter or other semiempirical relations often allow a characterization of the cross sections in terms of few empirical parameters per resonance. Cross sections of neutron–nucleus reactions as well as their energy and angular distributions of the resulting secondary particles for hundreds of isotopes

5.2 Particle Transport Code Systems and Event Generators

over an energy range from 10−5 eV to 150 MeV and neutron scattering kernels with energies in the meV energy range have been evaluated and have been stored on nuclear data ﬁles. These data evaluations are restricted to at best to energies of about up to 150 MeV. Nuclear data for all kinds of applications may be retrieved through the international nuclear data centers links such as ANL, LANL, LBNL, LLNL, ORNL, and TUNL (USA), IAEA (Austria), NEA (France), and JAEA-Tokai-mura (Japan). The main evaluator and distributor is the ‘‘National Nuclear Data Center’’ (NNDC), Brookhaven, USA [464], which is responsible for the evaluation of the ENDF library (Evaluated Nuclear reaction Data File) [488] and for the ENSDF library (Evaluated Nuclear Structure Data File) [317]. A useful index of the available nuclear data libraries which can be retrieved through the nuclear data services of the IAEA is given in Ref. [489]. Where multiple channels on particle production via spallation reactions are opened, e.g., above energies of 150 MeV, differential cross sections at higher energies (cf. Eq. (5.1)) need to be described as a function of the energy and the direction of secondary particles of type j produced when a hadron of type hi and energy Ei interacts with a target nucleus of Atarget . dσ/d Ej , j |hi , Ei , Atarget .

(5.1)

This information is not known accurately from measurements over the wide parameter range of interest for practical spallation-research applications, nor is it likely to be because of the large amount of data that would be required. For example, for a target calculation of a spallation neutron source one would need correlated energy and angular distributions for about ﬁve emitted particles types (p, n, π ± , π 0 ) produced by four incident particles (p, n, π ± ), at energy points over a range from about 20 MeV to 3 GeV, for over, e.g., ten target nuclei. Furthermore, to predict the residual nuclei mass and charge distributions for induced radioactivity values, it would require additional cross sections for the multiplicities of heavier particles produced (d, t, α, etc.), correlated with the nucleon and pion production. Thus, the state-of-the-art approach is to use theoretical nuclear model codes for generating the spallation reactions with model validation as possible for speciﬁc sets of parameters. Furthermore, with such models incorporated in particle transport codes to treat the subsequent collisions generated by spallation reactions, and using Monte Carlo techniques, explicit handling of the vast amount of data can be avoided in spallation reaction calculations. The available particle transport codes and the event generators and models used for spallation research are summarized in the following section. 5.2.1 Particle Transport Systems and Event Generators

The following tables summarize the most advanced Monte Carlo particle transport code systems for beam material interaction studies. Table 5.1

209

210

5 Particle Transport Simulation Code Systems A general overview of the most advanced Monte Carlo particle transport code systems.

Tab. 5.1

MCNPX

PHITS

FLUKA

GEANT4

MARS

Version Institution

2.6 LANL

2.09 RIST GSI

2006.3 CERN INFN

15 FNAL

Cost Manual pages Language Parallel processing

Free 470 Fortran 90/C Yes

Free 180 Fortran 77 Yes

Free 390 Fortran 77 Yes

4.9.1 CERN INFN KEK/SLAC Free 280 C++ Yes

Free 150 Fortran 95/C Yes

Website or contact MCNPX http://mcnpx.lanl.gov/ PHITS http://rcwww.kek.jp/research/shield/phits.html FLUKA http://ﬂuka.org GEANT4 http://geant4.web.cern.ch/geant4/ MARS http://www-ap.fnal.gov/MARS/

gives an overview of the frequently used systems considered in spallation research – mainly MCNPX and PHITS – and in high-energy physics detector simulation – mainly FLUKA and GEANT4. Other more special purpose code systems are summarized in Table 5.3. In Tables 5.2 and 5.4, the implemented physics models and other processes are given which are already described in detail in Chapters 2, 3, and 4. The different tallies and analysis strategies of the particle histories are described in different manuals of the code systems referred to in Tables 5.1 and 5.3 and references therein. Section 5.2.2 gives a short overview about the three-dimensional geometry systems implemented in Monte Carlo particle transport codes. For more details on geometry applications, the interesting reader is referred to different manuals of the code systems summarized in Table 5.1. 5.2.2 The Three-Dimensional Geometry Systems of Particle Transport Code Systems

All general purpose particle transport codes make use of geometry routines and systems deﬁning complex material geometries easy of access by the user. The user can apply either a standard conﬁgured geometry package or self-programmed special geometry. Monte Carlo programs typically divide a problem into a number of elementary regions or cells. Each of such regions has a speciﬁed composition of isotopes – representing the material in question – and has surfaces that are determined by ﬁrst- or second-order algebraic equations in a Cartesian coordinate

5.2 Particle Transport Code Systems and Event Generators Physics models, processes, and nuclear data libraries for spallation reactions implemented in particle transport codes.

Tab. 5.2

MCNPX

PHITS

FLUKA

GEANT4

MARS

Particles Energy loss Scattering Straggling Cherenkov

34 Bethe-Bloch Rossi Vavilov No

38 id. Moliere Vavilov No

68 id. Moliere custom Yes

68 id. Lewis Urban Yes

41 id. Moliere custom No

Low-energy neutrons

Cont. ENDF

Cont. ENDF

72 multigroup

Cont. ENDF

Cont. ENDF

Low-energy protons Used models e.g.,

Cont. ENDF Models

Models models

Models Models

Models Models

Models Models

Bertini ISABEL INCL/CEM LAQGSM FLUKA89

Bertini GEMJAM JAM/JQMD >3GeV

PEANUT DPMJET Glauber neutrinos

Bertini INCL ABLA GEM GHEISHA

CEM LAQGSM DPMJET

n s/γ s

n s

βs / γ s

α s/β s/γ s

γ s

Yes Yes Yes

No No Yes

No No Yes

No No Yes

No No Yes

Other features Delayed decay of Eigenvalue Burn-up Fields E, B

Tab. 5.3

Special purpose transport code systems.

Name

Purpose of the system

Main authors

References

CALOR

Calorimeter design/spallation sources

Gabriel et al.

[195, 490]

EA-MC

ADS and energy amplifying

Kadi et al.

[491–493]

HERMES

Spallation sources/calorimeter design

Cloth et al.

[88]

LCS

Spallation sources/general purpose

Prael et al.

[304]

SHIELD

General purpose/spallation

Sobolevsky et al.

[270]

TIERCE

General purpose/spallation

Bersillon et al.

[196]

system. Third-order surfaces, e.g., toroidal-shaped surfaces are also frequently applied. Examples of three-dimensional multipurpose geometry packages are the BOX-concept of the code KENO [503], the Combinatorial Geometry (CG) concept and its further development used in the codes, e.g., MORSE [504], HERMES [88], EGS4 [477] or FLUKA [505] (Table 5.5). The CG-package describes complex threedimensional conﬁgurations by the use of unions, differences, and intersections

211

212

5 Particle Transport Simulation Code Systems Tab. 5.4

A summary of important particle event generators for spallation reactions.

INC (intranuclear-cascade) ≤3 GeV

QMD (quantum-molecular-dynamic)

Bertini CEM INCL ISABEL

JQMDa QMD-SDM QMD, BUU SMM

Refs. [183, 184] Ref. [184] Refs. [189, 495, 496] Ref. [497]

GEM GEMINI JULIAN PACE

Refs. [255, 308] Refs. [229, 256] Refs. [499, 500] Refs. [499, 500]

Refs. [12, 77, 153, 158] Refs. [41, 173–175] Refs. [168–170, 172, 210–212] Refs. [162, 164, 167, 236]

Evaporation and ﬁssion ABLA/ABRABLA Refs. [221, 222, 351] ALICE/ASH Ref. [498] EVAP-versions Refs. [88, 299, 301, 304] ORNL-ﬁssion Ref. [314] RAL-ﬁssion Refs. [311–313] Intranuclear-cascade + evaporation BRIC Refs. [260, 261] DISCA Refs. [501, 502] MICRES Refs. [275–277]

a The JQMD and QMD-SDM are applications for spallation reaction calculations implemented in PHITS [494]. Some remarks about QMD and BUU models are already given in Section 2.7 on page 127.

Tab. 5.5

Examples of three-dimensional geometry packages. MCNPX

PHITS

FLUKA

GEANT4

MARS

System

MCNP-based

MCNP-based MORSE-CG

CG

MCNP-based ﬁxed shapes

Viewer and debugger

Built-in

Built-in

Built-in

Solids CSG, boolean, etc. Built-in

Built-in

(OR and AND boolean algebraic equations) of simple geometric bodies. Further developments of the CG-concept are the MARS-Multiple Array System [506] to describe lattices and the CCG (Complex Combinatorial Geometry) [507] where hierarchical structures – lattice inside a lattice – can be designed. HERMES in addition considers inside the CG-package a three-step search algorithm to search for redundant surfaces to save CPU time, which is important for layer geometries often used for spallation target systems or for calorimeter detectors. The three-dimensional geometry scheme developed for MCNP [508] and MCNPX [194, 463, 509] considers a concept based on a combination of regions built from simple surfaces. The concept also allows operators as unions, differences, and intersections, etc. Surfaces of second- and third-order for toroidal-shaped surfaces in three dimensions are used. For complex detector geometry descriptions for medium- and high-energy physics experiments the GEANT4 [284, 424] system

5.2 Particle Transport Code Systems and Event Generators

make use of a geometry package built by single three-dimensional bodies without intersections. The GEANT4 geometry system is very ﬂexible by using an objectorientated approach and allowing an easy interfacing of self-programmed geometry modules. For more speciﬁc details about the different geometry packages, the interested reader is referred to the user manuals of the program systems summarized in Table 5.1 and the literature therein.

213

215

6 Materials Damage by High-Energy Neutrons and Charged Particles 6.1 Introduction

Radiation effects induced by neutrons were extensively studied in ﬁssion reactors. Their radiation environment differs, however, in several important features from that of accelerators, spallation neutron sources, accelerator-driven systems (ADS) for transmutation and energy production, and galactic and cosmic radiation ﬁelds in space 1) , e.g., by • the presence of high-energy (several hundreds of MeV) charged particles from the accelerators, usually protons and light heavy recoil products; • a much harder neutron spectrum induced by spallation reactions than a typical ﬁssion spectrum (cf. Figure 6.1); • spallation reactions induced by high-energy particles produce a large number of impurities in materials in the form of spallation, ﬁssion, and transmutation products which alter their physical and chemical properties. A detailed review of these radiation effects can be found in Refs. of Ullmaier et al. [511–513] and in a recently published report by Broeders and Konobeyev [514]. The accelerator structures and target systems with their associated components such as containment vessel, windows etc. are subject to radiation damage in variousdegrees. Figure 6.1 clearly shows that a neutron energy spectrum for a 0.8-GeV proton beam on a stopping length solid tungsten target has on average a much larger kinetic energy as compared to a ﬁssion neutron spectrum. There are several phenomena for damage production, which may change the materials of interest: • atomic displacements induced by recoiling nuclei leading to microstructural defects; • production of hydrogen and helium isotopes in p, n, and d reactions; • formation of heavier chemical impurities caused by spallation-, ﬁssion-, and transmutation products. 1) Galactic and cosmic particles produce in spacecrafts single event effects (SEE), classiﬁed in three categories: SEU (Single Event Upset),

SEL (Single Event Latch-up), and SEB (Single Event Burnup), NASA Ref. [510].

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

6 Materials Damage by High-Energy Neutrons and Charged Particles

Energy [MeV] 4

Nucleon emission probability density

216

100

2

10

10−2

100

10

10−4

Spallation protons 10−1

Fission neutrons

10−2

Spallation neutrons

10−3

10−4 −6

−4

−2

0

2

4

6

8

Lethargy Fig. 6.1 The probability of observing a nucleon with energy E in a W target bombarded by 0.8 GeV protons. The corresponding quantity for a typical LWR is shown for comparison. The curves are normalized to unity (after Ref. [515]).

These processes affect many properties of solids. In a nuclear environment the dimensional and mechanical stability of materials is of utmost importance. The irradiation-induced changes in the mechanical properties depend on materials parameters and irradiation parameters in a complex way. General statements can only be made for the temperature ranges where different effects occur, if the temperatures T are normalized to the melting point Tm of the materials (Figure 6.2). It should be mentioned that the evaluations shown in Figure 6.2 are mainly based on extrapolations from ﬁssion and fusion research experience since high-dose experimental data on the behavior of materials under conditions of radiation ﬁelds of high-intensity spallation neutron sources are not available.

6.2 Displacement of Lattice Atoms

One important type of radiation damage to materials stems from the displacement of lattice atoms resulting from the collision of the projectile particle upon the target atom or from the recoil energy that the atoms of the materials receive when bombarded by nuclear particles – charged particles and neutrons – produced from spallation reactions. Figure 6.3 illustrates the primary knock-on atoms (PKAs) displacing secondary knock-on atoms. The PKAs slow down over distances much larger than a typical lattice distance and can displace more than one atom. The secondary recoils in turn displace other atoms, producing a displacement

6.2 Displacement of Lattice Atoms

Hardening Irradiation creep (+Growth*) Void swelling Helium embrittl.

Hydr. embrittl.

0

0.4

0.2

0.6

0.7

1

T Tm AL

−200

200

0

400

600°C Steel

0

400

600

1200°C W ≈ Ta**

0

800

* In noncubic metals

1600

2400

3200°C

** In hydride-forming metals

Fig. 6.2 Approximate ranges of normalized temperatures T/Tm where the main radiation damage effects occur. In the lower part of the ﬁgure the actual temperature scales for three typical materials are given. The cross-hatched areas indicate the ranges of operating temperatures of these materials (after Ullmaier and Carsughi [512]).

cascade2) [513]. This is a hierarchy of secondary, tertiary, etc. displacements, from which, after some atomic rearrangements, a stable defect pattern evolves. The whole process occurs in the order of picoseconds (ps) and cannot be investigated experimentally with present techniques. However, in the last years computer simulation using molecular dynamics methods have clariﬁed many details of the defect production mechanisms by atomic displacements cascades. The displaced atoms ﬁnally end up as interstitials and leave vacancies at their original location. The ﬁrst stage of the damage starts when a PKA is produced. The whole process is ﬁnished when the primary and other knock-on atoms have slowed down to energies below the so-called displacement threshold energy, typically in the range between 20 and 90 eV for most metals (cf. Table 6.1). It should be noted here that Seitz [516] introduced the idea of an ionization limit, below which energy losses by electron excitation may be neglected. Kinchin and Pease [517] involved the ionization limit model for estimates of the defect number produced in metals (cf. Eq. (6.6)). 2) Note: A displacement cascade is an interaction of particles – charged particles or neutrons – with the atoms of a solid, whereas

an intranuclear cascade is an interaction of charged particles or neutrons with the nucleons of a nucleus.

217

218

6 Materials Damage by High-Energy Neutrons and Charged Particles

Incident p / n

Incident p/n

Interstitial atom

Vacancy

Transmuted atom

Helium atom

Fig. 6.3 The interaction of high-energy particles with nuclei of a solid leads to primary and secondary knock-on atoms resulting in interstitials, vacancies, and to transmutation products, e.g., helium. Values for the threshold energies for displacements recommended by the ASTM/E 521-89 [538].

Tab. 6.1

Element

Be, C

Na, Mg Al, Si

K, Ca, Ti, V Cr, Mn, Fe, Co Ni, Zr, Nb

Cu

Mo

Ag

Ta, W

Au

Tthreshold (eV)

31

25

40

30

60

40

90

30

Pb

25

An example of the result of a 10 keV atomic displacement cascade simulated by molecular dynamics simulation (MDS) is illustrated in Figure 6.4. One sees in the center of Figure 6.4, a highly disordered liquid-like region surrounded by the well-preserved lattice structure. The transfer of the recoil energy to the lattice atoms leads to the production of point defects, either as single Frenkel pairs or defect clusters. A measure of the irradiation load to a material is the total dpa number (displacements per atom). The displacement rate is given by

5 nm

y

6.2 Displacement of Lattice Atoms

x 5 nm Fig. 6.4 Example of an atomic conﬁguration at 1 ps after a 10-keV PKA event in Au. The atom positions within a cross-sectional slab of three atomic planes near the center of a 10-keV atomic cascade are projected

dpa =

Emax

σdisp (E) · (E) · dE,

on a {100} plane (MDS) by Gahly and Averback. Note that the computer printout of the picture has slightly different scales in x and y directions of the atomic positions (ﬁgure adapted from Ref. [513]).

(6.1)

0

where σdisp (E) is the energy-dependent damage cross section in b, often referred to displacement cross section, (E) is the irradiation particle ﬂux in particles · cm−2 s−1 . The details are given by Eqs. (6.3), (6.7), and (6.9), respectively. The two basic measures of material damage produced by charged particles and neutrons are damage energy and atomic displacements. To estimate damage energy the main formalisms needed are those that describe the energy loss ‘‘partitioning’’ between electron and atomic collisions , e.g., the energy dissipated by atomic collisions – producing PKAs, and atom displacements – versus that part of the charged particle energy which is deposited by interactions with the atomic electrons, which is ionization and excitation. The latter effects do not produce displacement damage in metals. The other key relation needed is the total number of displacements created by further secondary displacement collisions from the slowing down of the PKA (cf. Eq. (6.1) and Figure 6.3). The systematic aspects of atomic scattering theory to study radiation damage in metals has been extended primarily by Lindhard and coworkers. Therefore to determine damage energy and total displacements the theory of Lindhard et al. [518–520] and the semiempirical formula of Robinson [521–523] may be used. These relations are rather ‘‘standard’’ in that they have been often used in predicting materials damage from ﬁssion and fusion neutron spectra (e.g., Refs. [524–526]) also taking into account the damage by fast neutrons. The physics of the radiation-induced degradation properties of spallation appears to be similar to those of reactor or fusion neutron irradiation. The exposure for materials in spallation sources, high-intensity accelerators or ADS, however, are of a severity in

219

220

6 Materials Damage by High-Energy Neutrons and Charged Particles

terms of neutron and proton ﬂuxes and energies that has no parallel in previous experience (cf. Figures 6.1 and 6.13). In the following, the relations of the parameters determining the radiation damage in matter by spallation reactions are described. 6.2.1 Damage Energy and Displacements

To estimate the radiation damage dose rate in terms of dpa/s, the total displacement cross sections given by Eq. (6.2) σdtotal (E) = σ elastic d (E) + σ nonelastic d (E),

(6.2)

has to be known. The term σ elastic d (E) is the elastic damage cross section which may be evaluated at energies above 20 MeV with various forms of optical models (Refs. [527]), whereas σ nonelastic d is the nonelastic damage cross section which may be evaluated at energies above 20 MeV with the event generators summarized in Table 5.4 on page 212. Below an energy of 20 MeV displacement cross sections especially for neutrons could be retrieved from the evaluated nuclear reaction data ﬁle (ENDF) [488] library. Above energies of 1 or 20 MeV displacement cross sections, hydrogen, and helium production cross sections for incident protons and neutrons on target materials from aluminum to uranium are evaluated and published by Lu and Wechsler [528] and by Lu et al. [529], by Korovin et al. [530, 531] and by Konobeyev et al. [532, 533]. Recently, Broeders and Konobeyev et al. [501, 527, 534] published improved displacement cross sections and helium production cross sections for the materials iron, copper, tantalum, and tungsten irradiated with intermediate and high-energy protons and neutrons. Furthermore, Konobeyev et al. [527] performed calculations to compare the different event generators and models given in Table 5.4. To estimate the damage cross sections the NRT formalism of Norgett, Robinson, and Torrens [535] and Robinson [523] is employed as a standard to determine that fraction of the energy of the PKA which will produce damage, e.g., further nuclear displacements. The displacement cross sections can be evaluated from the following expression: σdamage (Eparticle ) =

· i

Timax

Tthreshold

dσ (Eparticle , Ztarget , Atarget , Zi , Ai , Ti ) dTi

× ν(Ti , Ztarget , Atarget , Zi , Ai ) · dTi ,

(6.3)

where • σdamage (Eparticle ) is the damage energy cross section as a function of the incident particle energy Eparticle in (b keV), dσ (Eparticle ,Ztarget ,Atarget ,Zi ,Ai ,Ti ) • is the heavy ion primary recoil spectrum for the ith dTi reaction type as a function of the recoil energy Ti and of the incident particle energy Eparticle ,

6.2 Displacement of Lattice Atoms

• Ztarget , Atarget is the atomic number and mass number of the target, and Zi , Ai are the numbers for the recoil atoms, respectively. • ν(Ti , Ztarget , Atarget , Zi , Ai ) is the number of Frenkel pairs produced by the PKA with the kinetic energy Ti , where Timax is the maximum kinetic energy of the PKA produced in ith reactions. The function ν(Ti ) is the Robinson cascade damage function, here known as the NRT standard. It is that fraction of the recoil energy Ti , which will produce further nuclear displacements. • i is summation over all recoil atoms produced in the irradiation, • Tthreshold is the effective threshold displacement energy. The number of Frenkel pairs or the number of defects ν(Ti , Ztarget , Atarget , Zi , Ai ) produced in irradiated material for spallation reactions using the NRT formalism of Refs. [523, 535] is determined in the following way: Let Ti , Ai , and Zi be the recoil energy, atomic mass number, and charge number of the ion i, respectively, created as a secondary charged particle from a spallation collision. The target material is described by its average mass and charge numbers Atarget =

j

nj · Aj /

nj

and Ztarget =

j

j

nj · Z j /

nj ,

(6.4)

j

where nj is the atom density for the jth element. Based on the Kinchin and Pease formula modiﬁed by Norgett et al. [521, 523] and using the Lindhard slowing-down theory [518, 519], the number of defects produced in irradiated material is calculated ν(Ti , Ztarget , Atarget , Zi , Ai ) = NNRT ,

(6.5)

where NNRT is the number of defects calculated by NNRT =

0.8 · Tdamage . 2 · Tthreshold

(6.6)

The constant 0.8 in the formula is the displacement efﬁciency given independent of the PKA energy, the target material, or its temperature. The value is intended to compensate for forward scattering in the displacement cascade of the atoms of the lattice. Tdamage is the ‘‘damage energy’’ transferred to the lattice atoms reduced by the losses for electronic stopping in the atom displacement cascade and is given by Norgett, Robinson, and Torrens [535]. Tdamage =

Ti , 1 + k · g()

(6.7)

221

6 Materials Damage by High-Energy Neutrons and Charged Particles

where the parameter k, g(), , and α are as follows: 2/3

k=

[0.0793 · Zi 2/3

[(Zi

1/2

· Ztarget · (Ai + Atarget )3/2 ] 2/3

3/2

+ Ztarget )3/4 · Ai

1/2

· Atarget ]

,

g() = + 0.40244 · 3/4 + 3.4008 · 1/6 , = α · Ti × 106 , α=

(0.8853 · Atarget ) 2/3

[27.2 · Zi · Ztarget · (Zi

2/3

+ Ztarget )1/2 · (Ai + Atarget )]

.

(6.8)

The factor α has the unit (eV−1 ), and Ti and Tdamage are given in units of (MeV). The threshold energy Tthreshold is the minimum energy above the PKA that must be transferred to a lattice atom to produce a stable defect. This threshold energy can depend on numerous factors, e.g., such as the directional dependence due to the lattice structure of the target material, material impurities, and the temperature of the material. This is discussed in detail by Jung in Ref. [536]. Therefore, Tthreshold usually represents an ‘‘effective’’ threshold. Values for Tthreshold based on the ASTM standard are given for different materials in Table 6.1. Considerable variations of these values for Tthreshold are found in the literature (e.g., [537]). As an example, Figure 6.5 shows the displacement damage efﬁciency, Tdamage /T, as a function of the primary recoil energy for several elements calculated from Eqs. (6.7) and (6.8). It shows the effect of electronic losses on the energy available for atomic displacements. Numerous relations have been proposed for relating damage energy to the total number of displacements or defects created and estimating damage cross sections for structure materials in reactor, fusion, and spallation neutron source technology.

Damage efficiency –Tdamage / T

222

1.0 0.8

U Al

0.6 0.4

Au Nb

C Be

0.2 0.0 101

Cu

102

103 104 Recoil energy [eV]

105

Fig. 6.5 Displacement damage efﬁciency Tdamage /T as a function of the transferred recoil energy T (after Robinson [521]).

106

6.2 Displacement of Lattice Atoms

The following relations in Eqs. (6.9) have been recommended by several evaluation groups [501, 523, 525, 527, 531, 535, 539–542] to calculate the number of produced defects: ν(Ti , Ztarget , Atarget , Zi , Ai ) = η · NNRT , with the relations Tdamage < Tthreshold : NNRT = 0 Tthreshold ≤ Tdamage ≤ 2 · Tdamage : NNRT = 1 0.8 · Tdamage 2 · Tthreshold 0.8 Ti =η· · 2 · Tthreshold 1 + k · g()

Tdamage > 2 · Tthreshold : NNRT = η ·

(6.9)

where • NNRT , Tdam , and Ethreshold are as deﬁned before, • η is the defect production deﬁciency additional introduced by Caturla et al. [541] and studied by Broeders and Konobeyev [542]. The introduction of the defect production deﬁciency η in Eq. (6.6) is based on recent investigations by Stoller et al. [540] and by Caturla et al. [541] who have shown that the NRT model (cf. Eq. (6.6)) overestimates the number of displacements. This has been concluded from the analysis of the discrepancy between experimental measurements and calculations using MD (molecular dynamic) models. The most probable difference is related to the excitation energy distributions and recoil kinetic energies of charged residuals computed by intranuclear cascade models. The authors therefore introduced in addition a defect production efﬁciency η (cf. Eq. (6.9)) evaluated by MD simulations. It was observed that for most metals the value of η decreases as the energy increases, and reaches an asymptotic value of η ∼ 0.2 for recoil energies Ti ≥ 25 keV, e.g., for recoil energies relevant for spallation applications (cf. Figure 6.6). Simulations by other authors have shown that the efﬁciency η converges to a mean value ofapproximately 0.2–0.4. The relation between the displacement cross section and the damage energy cross section is given by Eq. (6.9). σdisplacement = η ·

0.8 · σdamage energy (b), 2 · Tthreshold

(6.10)

where σdamage energy and Tthreshold in units (b keV) and (keV). In summary, it can be concluded that only a part of the total recoil energy T, deposited in the material by an irradiation particle leads to displacement damage effects, because: (1) The fraction of T going into electronic excitation and ionization does cause displacements (cf. displacement efﬁciency in Figure 6.5),

223

6 Materials Damage by High-Energy Neutrons and Charged Particles

1.0

0.8 Efficiency h

224

0.6 Tungsten Copper 0.4

0.2 0

20

40 60 Energy [keV]

80

100

Fig. 6.6 Atomic displacement cascade efﬁciency η for copper and tungsten as a function of the recoil energy. Data are adopted from Caturla et al. [541].

(2) and spontaneous recombination processes in displacement cascades lead to a further reduction of the number of stable defects (cf. cascade efﬁciency η in Figure 6.6). (1) and (2) operate even at low temperatures where the defects are ‘‘frozen in.’’ At elevated temperatures, thermal migration of the defects enables additional recombinations which further reduce the number of defects causing macroscopic radiation damage effects (cf. Figure 6.2).

6.3 Hydrogen and Helium Production

Hydrogen and its isotopes are soluble in many metals. The effect of hydrogen in metals is well documented in literature related to nuclear technology. More important than hydrogen production is the formation of helium. It is known that especially He produced, e.g., by (p,α)- and (n,α)-type reactions can lead to drastic property changes of the materials even at concentrations in the parts-per-million range. Helium atoms are insoluble in most, if not all, metals. The helium atoms tend to migrate and form bubbles that embrittle the irradiated metal. This effect of helium in metals has been extensively studied. A useful database of measured data is given in [543] recently. The various spallation reactions producing H and He gas atoms within the materials alter the material properties. Thus the atomic parts per million (appm) of H and He are measures of radiation damage via transmutation. It is conventional to relate the H and He production and total displacements in dpa in terms of appm/dpa (cf. Table 6.2 on page 225).

6.3 Hydrogen and Helium Production Comparison of numerical values of evaluated displacement, damage energy, and helium production cross sections for aluminum, iron, and tungsten from incident protons with energies of 0.8, 1.0, and 2.0 GeV of various authorsa .

Tab. 6.2

Incident protons Proton energy (GeV)

Displacement cross section σ disp (b)

Damage energy cross section σ dam (b×keV)

Helium production cross section σ He (b)

[529]

[529]

appm/dpab

Aluminum Refs.

[529]

0.8 1.0 2.0

768 764 708

– – –

53 52 49

– – –

0.43 0.44 0.45

– – –

559 575 635

– – –

151 190 359

194 220 339

76 97 181

115 126 –

Iron Refs.

[529]

[527]

[529]

[527]

[529]

[534]

0.8 1.0 2.0

3298 3131 2878

2610 2610 2380

330 313 287

261 261 238

0.469 0.596 1.035

0.507 0.580 0.807

Tungsten Refs.

[529]

[546]

[529]

[546]

[529]

[534]

0.8 1.0 2.0

9277 10544 13582

6960 7730 –

2087 2372 3056

1566 1739 –

0.706 1.025 2.459

0.805 0.978 1.680

a

It is conventional to relate the He production and total displacements in terms of appm/dpa. b The appm/dpa ratio is determined by the formula (σ /σ 6 He disp ) × 10 .

Investigations on helium production in spallation reactions induced by intermediate and high-energy protons and neutrons are important to adjust the property changes of materials designed for high-intensity spallation sources, ADS applications, and other emerging nuclear systems. There is a signiﬁcant spread of experimental He cross sections and deﬁciencies in the model calculations (Refs. [501, 514, 528, 534]). Several experiments are undertaken to measure He

225

Helium production cross section [mb]

6 Materials Damage by High-Energy Neutrons and Charged Particles 104

181

Ta(p,x)He

103

102 Enke (99) Hilscher (01) Systematics ALICE /ASH CASCADE / INPE

101

100 101

103 102 Incident proton energy [MeV]

104

Fig. 6.7 Comparison of measured and evaluated He production cross sections of 181 Ta. (Refs. shown in the ﬁgure are: Enke (99) [114], Hilscher (01) [544], Systematics (Ref. [514] on page 105), ALICE/ASH [498], and CASCADE/INPE [78, 340, 532]) (after Broeders and Konobeyev [514]).

production cross sections induced by protons in the spallation energy range between 0.1 GeV and 2.5 GeV in the recent years. These experiments are described in Part 2. Broeders and Konobeyev [514] have recently compiled He production data for incident protons on nat Fe, 197 Au, 181 Ta, and nat W targets. A comparison of measured and model predictions in Figures 6.7 and 6.8 tantalum and tungsten shows a remarkably good agreement in applying the CASCADE/INPE model [514].

Helium production cross section [mb]

226

104

W(p,x)He

103 Green (88) Enke (99) Hilscher (01) Systematics JENDL-HE ALICE /ASH CASCADE / INPE

102

101

100 101

103 102 Incident proton energy [MeV]

104

Fig. 6.8 Comparison of measured and evaluated He production cross sections of nat W. (Refs. in the ﬁgure the same as in Figure 6.7 and Green (88) [537], JENDL-HE [545]) (after Broeders and Konobeyev [514]).

6.4 Cross Section Examples

It should be mentioned that the radiation damage induced by spallation reactions is particularly characterized by a large He/dpa ratio in appm/dpa (cf. last two columns in Table 6.2) compared to about 0.5 appm/dpa observed in ﬁssion reactors.

6.4 Cross Section Examples

Based on the above-discussed formalisms, proton and neutron-induced displacement cross sections, hydrogen, and helium production cross section were evaluated by several authors [528, 529, 531, 533, 534, 546] applying the INCE-NRT model and the binary collision approximation model with MD methods (the -BCA-MD) model. Although it is essential to evaluate the radiation damage for spallation sources, for ADS projects, and for space applications, the simulation of radiation damage parameters as displacements, gas production, and transmutation species are often inconsistent and differs due to the various models and codes, which are used for their evaluation. As indicated by Konobeyev et al. [527] there are remarkable differences within a factor of 2 between different models – BCA-MD and NRT – in estimating displacement cross sections, whereas the helium production estimation is much close together. Therefore, it is important to compare the calculated parameters with experimental results and reconsider the currently used methods for calculating spallation damage [527, 528]. A database in ENDF format for neutron-induced displacement cross sections, as well as hydrogen and helium production cross sections from aluminum to bismuth from about 10 MeV up to 1 GeV incident neutron energies is published by Korovin et al. [531]. In addition, improved proton-induced displacement cross sections and helium production cross sections using BCA-MD models are published recently by Konobeyev et al. [527] and Broeders et al. [501, 546] considering iron, tantalum and tungsten, respectively. Lu, Wechsler and Dai [528, 529] have evaluated a radiation database – the NCSU radiation damage database – for 23 target elements irradiated by protons and neutrons for an energy range for incident protons from 1 MeV up to 3.2 GeV and an energy range of incident neutrons from 1.0 × 10−10 MeV up to 3.2 GeV. The contents of the NCSU database considers damage energy cross sections, displacement cross sections, hydrogen-, helium production cross sections, and transmutation cross sections. The data are derived employing different intranuclear-cascade-evaporation and cascade-exciton models (cf. Table 5.4), a multistage-preequilibrium (MPM) model [194], and evaluations taken from ENDF libraries [488]. For low-energy incident protons, e.g., ≤100 MeV damage cross sections calculated with the SRIM model [547] of Biersack and Ziegler et al. [548–550] are employed. The SRIM model uses a more realistic approach for the interatomic potential including Coulomb screening [518, 520], quantum mechanical treatment of ion–atom collisions, and an exchange and correlation interactions between overlapping electron shells. But intranuclear cascades and spallation is not taken into account.

227

6 Materials Damage by High-Energy Neutrons and Charged Particles

Figures 6.9–6.12 illustrate neutron- and proton-induced damage energy cross sections in b keV of Al, Fe, Cu, Nb, W, Au, and Pb, whereas Figure 6.13 shows the helium production cross section from incident protons for Al, Fe, Cu, Nb, W, Au, and Pb target materials. 3 ×103 3

10 Damage energy cross section [b keV]

Al Tthr 27 eV Fe Tthr 27 eV

2

10

Cu Tthr 30 eV Nb Tthr 60 eV

1

10

0

10

10−1 −2

10

−3

10

−11

10

−10

10

−9

10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10

0

10

1

10

2

10

3

10 5×103

Incident neutron energy [MeV]

Fig. 6.9 Examples of damage energy cross sections in b keV as a function of the incident neutron energy up to 3.2 GeV for thin target materials of Al, Fe, Cu, and Nb with threshold energies Tthr of 27 eV, 27 eV, 30 eV, and 60 eV, respectively. The data are taken from the NCSU radiation database [528, 529].

2 ×104 Damage energy cross section [b keV]

228

Al Tthr 27 eV Fe Tthr 27 eV Cu Tthr 30 eV Nb Tthr 60 eV

104

103

102

101 100

101 102 103 Incident proton energy [MeV]

Fig. 6.10 Examples of damage energy cross sections in b keV as a function of the incident proton energy up to 3.2 GeV for thin target materials of Al, Fe, Cu, and Nb with threshold energies Tthr of 27 eV, 27 eV, 30 eV, and 60 eV, respectively. The data are taken from the NCSU radiation database [528, 529].

5 ×103

6.4 Cross Section Examples

Damage energy cross section [b keV]

5×104 10

4

10

3

W Tthr 90 eV Au Tthr 30 eV Pb Tthr 25 eV

102 10

1

10

0

10

−1

10−2 10−3 10−4 10−5 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 5×103 Incident neutron energy [MeV]

Fig. 6.11 Examples of damage energy cross sections in b keV as a function of the incident neutron energy up to 3.2 GeV for thin target materials of W, Au, and Pb with threshold energies Tthr of 90, 30, and 25 eV, respectively. The data are taken from the NCSU radiation database [528, 529].

Damage energy cross section [b keV]

5×104 W Tthr 90 eV Au Tthr 30 eV Pb Tthr 25 eV 104

103

100

101

102

103

5 × 103

Incident proton energy [MeV] Fig. 6.12 Examples of damage energy cross sections in b keV as a function of the incident proton energy up to 3.2 GeV for thin target materials of W, Au, and Pb with threshold energies Tthr of 90, 30, and 25 eV, respectively. Data are from the NCSU radiation database [528, 529].

Table 6.2 shows examples of estimated displacement cross sections, hydrogen, and helium production cross sections from different references for some materials in the spallation energy regime for incident protons. The numbers in Table 6.2

229

6 Materials Damage by High-Energy Neutrons and Charged Particles

101 Helium production cross section [b]

230

100 10−1 10−2 10−3 Al Fe Cu Nb W Au Pb

10−4 10−5 10−6 10−7 10−8 10−9 100

101

102

103

5×103

Incident proton energy [MeV] Fig. 6.13 Examples of helium production cross sections in b as a function of the incident proton energy up to 3.2 GeV for thin target materials of Al, Fe, Cu, Nb, W, Au, and Pb. The data are taken from the NCSU radiation database [528, 529].

referring to [529] are calculated with the NRT model whereas the numbers [527, 534, 546] are evaluated using BCA and MD models. There are, at least, several origins of the difference in estimating damage energy, or displacement, or gas production cross section, e.g., hydrogen and helium: • Differences occur by using different models for the defect production. The results obtained using BCA-MD (or MD) are usually different from the displacement cross sections calculated by using INCE codes applying the NRT model. The differences are some times large especially comparing the number of defects. • Displacement cross sections calculated for incident neutrons and protons below the primary energy 100 MeV can be noticeably different (e.g., different INCE models, BCA or MD, etc.). One main reason is the difference in the contribution of the elastic scattering of protons and neutrons in the total displacement cross section. In case of protons there are contributions from the screened Coulomb [518, 520] and nuclear scattering, and their interference. Also above about 100 MeV the INCE, the BCA-MD, and QMD models may use different physical assumptions that yield to a different cross section estimation especially for calculating the number of defects. • The use of a different effective threshold displacement energy (Tthreshold ) in the NRT formula (6.9) produces also different results in the damage cross section calculation. But this could be corrected by a renormalization to a comparable threshold displacement energy using the formulas (6.9) and (6.10).

6.5 Radiation Damage Effects of High-Intensity Proton Beams in the GeV Range

6.5 Radiation Damage Effects of High-Intensity Proton Beams in the GeV Range

The following example shows a dpa calculation for a high-power neutron spallation source of 5 MW beam power, with a proton current of 5 mA, with a proton beam energy of 1.0 GeV for one year of operation: • the integrated proton ﬂux should be about · t = 2.0 × 1022 protons/cm2 , • the displacement cross section for an iron window is assumed to be about σdisplacement = 3000 b at 1.0 GeV (cf. Table 6.2), • this yields using the formula (6.1) a number of displacements per year: dpa = 3000 b × 2.0 × 1022 cm2 = 60 Figure 6.14 shows estimated dpa numbers, hydrogen (cH ) and helium (cHe ) concentrations as a function of the irradiation time t in the center of a stainless steel proton beam entry window of the spallation source ESS [551] with an incident proton beam energy of 1.3 GeV and a beam power of 5 MW compared to a ﬁrst wall of a fusion reactor (CTR) with 1 MW/m2 . The helium concentration cHe increases with time as shown by the dash-dotted lines. The values for the hydrogen concentration cH are somewhat ﬁctitious since hydrogen is highly mobile and most of the produced amount will diffuse out of the material. Compared to fast ﬁssion systems the dpa rates are similar to the fusion Time 1 day

1 week

1 month

1 year

102

101 100

dpa (ESS)

10−1

dpa (CTR)

100

H (ESS)

10−1

10−2 He (ESS)

10−2 10−3 104

10−3

H (CTR) He (CTR)

105

106 Time [s]

107

10−4 108

Fig. 6.14 Comparison of the number of displacements per atom (dpa) hydrogen concentration cH and helium concentration cHe as a function of the irradiation time t in the center of a stainless steel proton beam entry window of the spallation source ESS [551], incident proton beam energy 1.3 GeV and beam power 5 MW, and in the ﬁrst wall of a fusion reactor (CTR) with 1 MW/m2 .

CHe,CH [atomic fraction]

Displacement [dpa]

101

231

232

6 Materials Damage by High-Energy Neutrons and Charged Particles

case while the concentration of hydrogen and helium are negligibly small. At operating temperatures of target components of high-intensity spallation sources most of the irradiation-induced defects are mobile and can react with each other and/or with defects already present in the unirradiated material [512]. It is important to note that only a small fraction of the initially produced defects considered by the displacement number dpa contributes to the ﬁnally observed property changes of the irradiated material, since the pertinent fraction not only depends on the material, temperature and recoil energy, but also on some other properties illustrated in Figure 6.2. This means the overall ‘‘damage’’ cannot be characterized by a single value. Nevertheless, the dpa number is a useful measure in correlating results determined by different particles and ﬂuxes in an irradiation environment. The temperature during irradiation plays an important role for several reasons: (a) the amount of spontaneous recombination, (b) and the mobility of certain species in the lattice, which is strongly temperature dependent. At material temperatures T ≥ 0.55 · Tm , the melting temperature, the He embrittlement often dominates the mechanical behavior of materials as tensile, creep, and fatigue. In general, displacement effects could diminish with increasing temperature of the material, whereas helium effects gain importance at high temperatures. Experimental investigations on helium production in irradiated materials and material issues on spallation neutron sources and ADS are presented in Parts 2 and 3.

233

7 Shielding Issues 7.1 Introduction

The shielding problem of high-current particle accelerators, high-intensity spallation neutron sources, and ADS systems in the spallation energy regime is unique in terms of the general requirements because of a relatively high-energy and intense particle source, large shielding dimensions, and geometric-material complexities. The solution is usually called the deep penetration problem applied to particle radiation transport. Monte Carlo methods cannot generally be used to determine the radiation paths of particles through a geometrically very complicated shield, although the computer power is available nowadays. Some a priori knowledge of the shield design must be available before beginning a detailed calculation. Therefore, different methods are applied which are semiempirical estimation based on the Moyer model, discrete ordinates, Monte Carlo coupling with discrete ordinates, and Monte Carlo methods using variance and appropriate biasing techniques to direct particles along the ‘‘important’’ paths [552–561]. The general shield design concerns include • bulk shielding for the target stations, • effects of beam holes, collimators, shutters, and other openings inside the bulk shield, • neutron beam line shielding and collimators external to the bulk shield, • accelerator shielding, shielding due to beam losses during acceleration as losses at normal operation, accidental losses, and losses under shutdown conditions of the accelerator, beam dump systems, • groundshine and skyshine phenomena, • energy deposition, heating, material damage, and activation. With the advent of high-energy accelerators, e.g., the Cosmotron, a 3-GeV proton synchrotron [562] at BNL, USA, ﬁrst operated in 1952 and the Bevatron, a 6.3-GeV synchrotron [563], at Lawrence Berkeley Laboratory (LBL), USA, which ﬁrst achieved full energy at an intensity of about 1010 protons per pulse in 1954, leads to the development of Moyer model [564, 565]. Moyer developed a phenomenological model capable of estimating the additional shielding required as part of the Bevatron improvement program during 1962–1963. At the time Moyer invented Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

234

7 Shielding Issues

his model ‘‘the design of shielding for high-energy accelerators was thought to be more an art than a science’’ [566]. The interesting reader is referred to the book of Patterson and Thomas [102] on the history of accelerator shielding and their radiation protection and the recently published article of Thomas [567]. In 1973 these authors postulated that it might eventually be possible to simulate the precise details on shielding and radiation levels via computer calculations, but they argued that such calculations, however, are difﬁcult, expensive, and perhaps several years in future ([102] page 381). Various computer programs to simulate the development of high-energy particle transport in matter are now available (cf. Chapter 5). The explosive development of computer capabilities, the operating experience gained with high-energy proton accelerators and with small- and medium-spallation neutron sources lead to a detailed knowledge on the physics and technology of all aspects of shielding needed for accelerators, high intensity neutron spallation sources and irradiation facilities in the last 10–15 years. Details could be ﬁnd in proceedings of numerous conferences and workshops, e.g., the International Collaboration of Advanced Neutron Sources, ICANS-I-XVIII, the NEA SATIF 1-7 and SARE 1-6 workshops, or the International Conferences on Radiation Shielding, ICRS 1-11. A collection of computer codes and data sets for accelerator shielding calculations and analysis are collected at the ‘‘Radiation Safety Information Computational Center’’ (RSICC) [467] and the ‘‘NEA Data Bank’’ (NEA DB) [465]. A comprehensive report about radiation physics and protection around accelerators was recently published by Cossart [568]. In the following, the basic assumptions and methods, used nowadays, for the shield design of accelerators and spallation sources are summarized.

7.2 The Attenuation Length and the Moyer Model

The Moyer model [564, 565] in its early form provides a formalism to estimate the high-energy neutron ﬂuxes and the associated biological dose rates at the surface of transverse very thick shields of accelerators with the general assumption that at this local position, the internuclear cascade is well developed and in equilibrium. Although high-energy neutrons are not the only particles propagating the hadronic cascade in matter Moyer assumed that it was sufﬁcient to treat all particles in the cascade as ‘‘neutron like.’’ The fact that those neutrons with energies ≤150 MeV contribute much larger to the dose equivalent as those neutrons with energies >150 MeV which propagate the cascade has led to some confusion in understanding the Moyer model and the early literature ([569] on page 14). The main factors governing the required bulk shield thickness are the attenuation of the high-energy particles and the material density. This is because the particle ﬂux or dose attenuation approximately depends on these factors, and only linearly on the source strength and the dose rate criterion (cf. Eq. (7.1)). This means that the particle ﬂux spectrum at large distances – several mean free paths – from the

7.2 The Attenuation Length and the Moyer Model

Target

Particle beam θ

R D

d1 d2

d

r

d3 d4

Shielding material Fig. 7.1

Secondary particle surface leakage

Coordinates P(r,θ)

Shielding geometry model for the generalized Moyer model.

source is approximately represented by (x, E) ∝ S · B(E) ·

exp(−x · ρ/λatt ) , x2

(7.1)

where • (x, E) = particle ﬂux spectrum at position x, S = source term, • B(E) = build-up factor, x = distance to source in cm, ρ = shielding material density in g/cm3 • λatt = attenuation length in g/cm2 or in cm. 7.2.1 Accelerator Shielding and the Generalized Moyer Model

A generalized formulation for the ﬂux or the radiation level [568, 570] outside a shield is given by Eq. (7.2) considering a neutron source produced by protons interacting on a thick target, e.g., a magnet structure in an accelerator tunnel, as illustrated in Figure 7.1. Assuming that neutrons are the only secondary particles produced, then the number of neutrons dNneutrons /dE at the point P(r, θ ) outside a shield of material thickness d, which are emitted into a given element of solid angle d at angle dθ in an energy interval E + dE relative to a beam by a number of Nproton protons is given by −d · csc(θ ) d2 Y dNneutrons = Nproton · B(E) · d · exp , dE dEd λatt (E) where • B(E) is the buildup factor, • λatt (E) is the effective energy and material-dependent attenuation length,

(7.2)

235

7 Shielding Issues

• d2 Y/dEd the yield of neutrons per solid angle per unit energy interval at energy E, • the exponential function accounts for the attenuation of the radiation ﬁeld by a shielding thickness d, at an angle θ . In Figure 7.1 the distance of the target interaction point to the coordinate P(r, θ ), where the neutron ﬂux emerges the shield surface, is determined by D = (R + d) · 1/ sin(θ ) = (R + d) · csc(θ ) = r · csc(θ ). Including the factor 1/D2 in Eq. (7.2), the total ﬂuence (E) is then given at point P(r, θ ) by (E) =

Nproton · D2

Emax

B(E) ·

Emin

−d · csc(θ ) d2 Y · exp dE. dEd λatt (E)

(7.3)

In the original formulation, Moyer approximated Eq. (7.3) by a single energy group because of the characteristic functional dependence of the neutron attenuation length shown in Figure 7.2. As seen in Figure 7.2, the neutron attenuation lengths above 150 MeV are approximately independent of the energy, but diminish rapidly with energies below 100 MeV. This consideration is not totally right because the lower energy particles do have a small but ﬁnite attenuation length (cf. Figure 7.2). However, for thick shields and for deep penetrations of the particle cascade, the total neutron ﬂux density and as a consequence also the dose equivalent or dose rate are proportional to the high-energy hadron ﬂux density. Because the low-energy particle components are produced by the interactions of the high-energy particles inside the shield, their intensity decreases through the shield in an exponential manner. The general conclusion from the Moyer model, therefore, is that the dose equivalent at any Attenuation length λatt [g·cm−2]

236

150 High-energy limit 100

Concrete ρ = 2.4 g·cm−3

500

0

1

10

100

Neutron energy [MeV] Fig. 7.2 The variation of the attenuation length for monoenergetic neutrons in concrete as a function of neutron energy. Full circles are data from Ref. [571] and open circles are data from Ref. [572]. The dashed line shows the high-energy limit with an attenuation length λatt = 120/2.4 cm = 48.75 cm (after Thomas and Stevenson [570]).

1000

7.2 The Attenuation Length and the Moyer Model

point outside an accelerator shield is mainly governed by a simple line-of-sight propagation of the cascade-generating particles at the ﬁrst interaction with a target and a kind of multiplication factor accounting for the particle build up. The cascadegenerating particles have an attenuation length that is approximately independent of the energy (cf. Figure 7.2). Therefore for practical accelerator shield calculations (7.3) can be simpliﬁed after Moyer in the following way: (1) λatt (E) = constant = λ for E ≥150 MeV and λatt (E) = 0 for E <150 MeV. Thus Eq. (7.3) can be written as (Eneutron > 150 MeV) −d · csc(θ ) Emax Nproton d2 Y dE. exp B(E) · = 2 D λatt dEd E150 MeV

(7.4)

(2) The neutrons emitted at angle θ can be written as a simple function f (θ ) multiplied by a multiplicity factor m(Emax ) that depends only on the incident proton energy [570], thus −d · csc(θ ) Nproton · m(Emax ) · f (θ ) exp D2 λatt −d · csc θ Nproton = · g(Emax , θ ), exp (7.5) 2 D λatt

(Eneutron > 150 MeV) =

where g(Emax , θ ) is an angular distribution function that is constant for a given value of Emax and for a particular target material. (3) The dose rate or dose equivalent per ﬂuence, usually written as H, for neutrons is not strongly dependent near the energy E ≈ 150 MeV (cf. Figure 7.3). Therefore, the dose equivalent outside the shield due to neutrons with about 150 MeV can be written as H150 ≈ C150 · (Eneutron > 150) MeV,

(7.6)

where C150 is the value of the ﬂuence-to-dose conversion factor at 150 MeV. The total dose equivalent, Htotal , is then given by Htotal = k · H150 , where k ≥ 1.

(7.7)

The relation of Eq. (7.7) assumes that the low-energy neutrons are in equilibrium with the neutrons having energies E > 150 MeV after several mean paths in the shield. This is valid for a neutron spectrum in a shield more than a few mean free paths thick. Thus, with the above assumption the dose rate or the dose equivalent Htotal is given by Htotal =

−d · csc(θ ) k · C150 · Nproton · g(Emax , θ ) . exp (R + d)2 · csc2 (θ ) λatt

(7.8)

237

7 Shielding Issues

104 Effictive dose conversion factor [pSv cm2]

238

Protons Pions+

3

10

Muons 102

101

100

Photons

Neutrons

10−10 10−8

10−6

10−4

10−2

100

102

104

Particle energy [GeV] Fig. 7.3 Fluence-to-effective dose conversion factors for AP irradiation as a function of the energy of neutrons, protons, photons, and muons [19].

To calculate the dose rate for personal protection purposes the ﬂuence-to-effective dose factors for the various particles must be known. These conversion coefﬁcients are given in Figure 7.3 for anterior–posterior (AP) irradiation1) and various particles [19, 573]. Other evaluations of conversion factors can be found in Refs. [574– 576] and in periodically published reports of the International Commission on Radiological Protection (ICRP). For example, the effective dose rate from an AP irradiation in a ﬁeld with neutrons of an energy of 1 MeV with a ﬂuence of 1 neutron cm−2 is about 300 pSv. Using a multilayer shield system shown schematically in Figure 7.1, the ratio d/λatt in formula (7.8) can be replaced by η=

n di , λi

(7.9)

i=1

where the sum is over n shielding layers with thicknesses di and attenuation lengths λi . 7.2.2 The Moyer Model Parameters

The Moyer model parameters are usually determined by an analysis of measurements related to practical shielding conﬁgurations at existing accelerators. Basically the function f (θ ) (cf. Eq. (7.5)) must be known. Stevenson et al. [569] and Thomas and Thomas [577] determined from experimental data over a wide energy range 1) AP is a standard irradiation geometry of the human body in radiology for calculations of ﬂuence-to-effective dose conversion

coefﬁcients. AP means the direction of the irradiation – front to back – of the human body.

7.2 The Attenuation Length and the Moyer Model Recommended values of H0 (Eproton ) and Eproton is the proton energy in GeV.

Tab. 7.1

H0 (Eproton )(Sv m2 )

Reference

((2.84 ± 0.14) × 10−13 ) · E 0.80±0.10 ((2.00 ± 0.14) × 10−14 ) · E 0.50±0.10 ((6.90 ± 0.10) × 10−15 ) · E 0.80±0.10 ((7.00 ± 0.14) × 10−15 ) · E 0.80±0.10 ((1.30 ± 0.14) × 10−14 ) · E 0.80±0.10 ((1.30 ± 0.14) × 10−14 ) · E 0.80±0.10 ((1.50 ± 0.14) × 10−14 ) · E 0.80±0.10

[568] [578] [578, 579] [579] [579] [579] [579]

that the function f (θ ) is well described by f (θ ) = exp(−β · θ ),

(7.10)

where θ is given in radians, β is in radians−1 , and β −1 ≈ 2.3 rad−1 for (Eneutron > 150 MeV) and for incident proton energies in the GeV range (1 rad ≈ 57.2958%). This leads to a parameterized expression to determine the dose equivalent H at the surface of a thick shield (cf. Figure 7.1) H=

H0 (Eproton ) · exp(−β · θ ) · exp(−η · csc(θ )) , (r · csc(θ ))2

(7.11)

with r = R + ni=1 di . The expression H0 (Eproton ) · exp(−β · θ ) is determined from target yield data and measurements at accelerators. A best ﬁt for the values of H0 (Eproton ) is by the power law: H0 (Eproton ) = k · E n .

(7.12)

Several values of H0 (Eproton ), k, and n of Eq. (7.12) are given in the literature and summarized in Table 7.1. The Moyer model of Eq. (7.11) is applicable for relatively ‘‘thick’’ targets for 0.80±0.10 Sv m2 as given in Table 7.1. It a H0 (Eproton ) = ((2.84 ± 0.14) × 10−13 ) · Eproton should be mentioned that the Moyer model was further developed by several authors to use this model for shielding estimates around accelerators and spallation neutron sources [553, 559, 580] to overcome the restrictions , e.g., in geometry, energy dependence of the attenuation lengths, variation of H0 (Eproton,θ ) with d/λatt , etc. This could be considered to evaluate certain Moyer parameters with the help of transport codes and Monte Carlo methods (cf. Section 7.3 on page 242). Without going into detail, the Moyer model can be extended to beam losses described by a line source [568]. Using a formulation known as the Tesch approximation [581], this leads to the following equation estimating the dose equivalent: H=

H0 (Eproton ) · 0.065 · exp(−1.09 · η), r

(7.13)

239

240

7 Shielding Issues Earth shield 5.0 m 1.0 m

Accelerator structure

Accelerator tunnel

Concrete shield 2.5 m

Fig. 7.4

Shielding example geometry model for the generalized Moyer model.

where the dose equivalent H is measured in Sv per interacting proton per unit length. The other parameters are the same as before. It should be noted here that the Moyer principle was further developed by Armstrong et al. [553] concerning a semiempirical model code for shielding layout and assessment (CASL, Computer Aided Shield Layout) with a rather general source and 3D material and geometry capabilities. While this model uses approximately, semiempirical physics treatment based on internuclear-cascadeevaporation models and parameters depending upon source energy and shielding thickness, the model provides sufﬁcient accuracy for many practical problems and parameter variation for shielding issues. Applications will be discussed in Part 3. In the following example results are given for transverse shielding estimation for a high-energy linear accelerator applying Eqs. (7.11) and (7.13). Accelerator shielding example A typical shielding geometry arrangement for a high-energy linear accelerator is illustrated in Figure 7.4 with a tunnel built of concrete for the accelerator components and surrounded by an earth shield (concrete thickness d1 = 1.0 m, a tunnel radius tr = 2.5 m, and a thickness of the soil of the top shield of d2 = 5.0 m). (1) LINAC parameters: – proton energy Eproton = 1.5 GeV, – average beam power Pbeam = 5 MW and an average proton current Iproton = 3.33 mA, – number2) of protons = 2.16 × 1016 protons/s. (2) Assumed proton beam losses: – point losses about (10−6 ) = 2.16 × 1010 protons/s= 7.78 × 1013 protons/h, – continuous beam loss during operation assumed 1 Wm−1 or 4.3 × 109 protons s−1 m−1 = 1.55 × 1013 protons h−1 m−1 . 2) 1 mA = 6.24 × 1015 protons/s.

7.2 The Attenuation Length and the Moyer Model

(3) Assumed shield material parameters: – concrete density = 2.4 g/cm3 , assumed attenuation length λconcrete = 0.50 m, – soil density = 1.8g/cm3 , assumed attenuation length λsoil = 0.70 m. To calculate the dose equivalent H with Eqs. (7.11) and (7.13) the following parameters are used: H0 (Eproton ) = 2.84 × 10−13 × E 0.80 Sv m2 ; β ≈ 2.3 rad−1 ; θ = 90◦ = π/2 = 1.57 rad; csc(θ ) = 1.12; r = 2.5 + 1.0 + 5.0 m = 8.5 m; η = d1 /λ1 + d2 /λ2 = 1.0/0.50 + 5.0/0.70 = 9.14. The dose equivalent results for point losses Hpoint and for continuous losses Hcontinuous are then given by Hpoint = 4.21 × 10−21 · 7.78 × 1013 = 0.33 µSv/h , Hcontinnuous = 1.41 × 10−19 · 1.55 × 1013 = 2.18 µSv/h.

(7.14)

7.2.3 Attenuation Lengths

Small uncertainties in the attenuation length λatt may lead to unacceptable errors concerning the shield thickness and therefore the radiation protection goals of a facility by using Eq. (7.1). The following example demonstrates this fact: • A high-intensity spallation neutron source may need a total attenuation provided by the bulk shield of about ∼1012 . • Assuming an iron shield of a thickness of 500 cm with an attenuation coefﬁcient λatt = 20 cm = 156 g/cm2 (shielding material iron with a density ρ = 7.8 g/cm2 ), yields a material attenuation factor alone of about e−25 ≈ 1.4 × 10−11 , or 25 mean free paths of shielding material. • A 10% uncertainty in λatt then corresponds to about e−2.5 , or more than one order of magnitude error in the prediction of particle ﬂuxes or dose rates. One might expect that since λatt is so fundamental to shield design for highenergy radiations, accurate values for common shielding materials would be available from experiments and accelerator facility designs. This is not the case in general. For example, previous measurements of attenuation lengths for iron range from about 120 to 180 g/cm2 . There is also a wide range of measured λatt values reported for concrete ≈ 110–172 g/cm2 . A summary of measured values for λatt and descriptions for most of the experiments are given in the book by Patterson and Thomas [102], and more recently published measurements are summarized by Nakamura [582]. In Table 7.2 some estimates of attenuation lengths are given. There are several reasons for these considerable variations of the measured values for λatt . One reason is that simple measurements for the decrease in radiation intensity with shield thickness may involve some unaccounted values for geometric attenuation as well as material attenuation, e.g., an invalid assumption of a point source attenuation, whereas the actual beam distribution incident on the shield may constitute an extended source. This leads, of course, to a misinterpretation of

241

242

7 Shielding Issues Approximate nominal values for the attenuation length λatt for some shielding materials for accelerators and spallation sources sources. Tab. 7.2

Material

Density (g/cm3 )

Al Fe

2.7 7.8

Steel

∼7.8

Pb

11.3

W U Normal concrete

19.3 18.95 2.4

Heavy concrete

4.0–4.3

Soil Air

1.8 1.2 × 10−3

Attenuation length λatt (g/cm2 ) ± 1σ 135 ± 3 (theory [583]) 119 ±10 − 179 ± 12 ([102, 584]) 164 ±2 (theory ([583]) 161.1 ± 2.1 (exp. ([582, 585]) 150, 3 ± 5.8 (theory ([582, 585]) 200 264 ± 3 (theory([583]) 192 258 ± 3 (theory [583]) 108 ± 20–172 ([102, 584]) 125.4 ± 5.1 (exp [582, 585]) 116.7 ± 3.4 (theo [582, 585]) 133 ± 3 (theory [583]) 130–169 ([102] p. 379) 117 ([102], p. 413) (KENS [586])

cm 50.0 15.2–22.9 21.0 20.7 19.2 17.7 23.3 9.9 13.6 45–72 52.2 48.6 55.4 32.5 (30.2) −39.3 (42.3) 65 8.5 × 104

the proper value of λatt , which is used to represent only material attenuation. Also, λatt has a spectral dependence or a certain energy dependence below the high-energy limit, where the attenuation length is constant. This is shown in Figure 7.2 for the variation of the neutron attenuation length for monoenergetic neutrons in concrete as a function of the neutron energy [570]. The value of λatt measured along the beam axis of an accelerator is different from off-axis measurements of differences in particle spectra, e.g., measurements in 90◦ direction. It may be also different because of the anisotropy of the source term and the spectral differences of the leakage distributions of the targets.

7.3 Advanced Shielding Methods for Spallation Sources

Although the Moyer model has been widely used for accelerator shielding estimates, for high-intensity spallation neutron sources and ADS more sophisticated calculational methods have to be applied, which have been developed with the rapid evaluation in computer technology in the recent years. Table 7.3 shows the relative merits of the basic methods and models. The scheme of performance in Figure 7.5 illustrates the possibilities by using full Monte Carlo or Monte Carlo with discrete ordinates coupling for advanced

7.3 Advanced Shielding Methods for Spallation Sources Tab. 7.3

Relative merits of computational methods on shielding of spallation sources.

Method

Advantage

Disadvantage

Monte Carlo

Three-dimensional, transport of all particle types, generation of high-energy cross sections

Stochastic and time consuming

Monte Carlo coupling with SN -transport

Three-dimensional and deterministic, well suited for deep penetration transport

high-energy cross sections needed, coupling-procedures

1–3 dimensional SN -transport

Deterministic, well suited for deep penetration transport

High energy, cross sections needed, only neutron, gamma transport

Semiempirical formalisms

Easy to use, overview estimates

Attenuation concept, in general only with simple material constants

shielding calculations. Monte Carlo with 1D discrete ordinates3) coupling was ﬁrst considered by Armstrong et al. [552, 553] and further developed and applied for shielding calculations at the 2.5 GeV proton cooler synchrotron COSY at J¨ulich, Germany, [555]. Systematic investigations were performed with the Monte Carlo/1D discrete ordinates coupling approach during the study phase of the high intensity European Spallation Neutron Source (ESS) project [551, 556, 558, 559]. The Monte Carlo with discrete ordinates coupling approach was then further extended developing connection methods for the two- and three-dimensional DORT [587] and TORT [588] discrete ordinates codes by several authors [589–591]. A new system named DOORS, 1, 2, and 3D discrete ordinates system for deep penetration neutron and gamma transport [592] is also a useful tool to couple Monte Carlo simulation tools with discrete ordinates. A comprehensive summary of computer codes and data sets for accelerator shielding analysis is given at the SATIF-3 and SATIF-5 workshops by Kirk et al. [593] and Satori et al. [594]. It is important to note that for applying the discrete ordinates transport methods high-energy neutron/gamma transport cross section data are needed. For this purpose, two different cross-section libraries are available for such calculations, the LAHI / LAHIMACK library [338, 555, 556, 595, 596] and the HILO2k library [470, 590, 597, 598]. 3) The discrete ordinates method is the dominant numerical solution to the integro-differential form of the transport

equation, often retained in a shorthand designation SN of historic reasons.

243

244

7 Shielding Issues

3D geometry proton beam parameter

Monte Carlo recommended system MCNPX, PHITS, CALOR, HERMES, FLUKA

3D shielding calculations using biasing techniques

3D geometry calculations angle dependet neutron fluxes/currents at coupling surfaces inside shield

Results dose equivalent energy deposition radioactivity

Surface flux in legendre expansion for discrete ordinates -SN - calculations

n,γ transport cross section libraries HILO/LAHI 10−4 eV − 2.5 GeV

1D/2D/3D discrete ordinates neutron/gamma transport discrete ordinates codes ANISN, DORT, TORT

1,2,3D shielding calculations using discrete ordinates

Results dose equivalent energy deposition radioactivity

Fig. 7.5 Scheme of performance for shielding calculations of accelerators and target stations of spallation sources using Monte Carlo and Monte Carlo discrete ordinates coupling.

High-energy transport library descriptions (1) LAHI / LAHIMACK is a coupled multigroup library of 62 neutron and 21 photon group cross sections and response functions for neutron energies up to 2800 MeV. – The original LAHI library developed during the German spallation source J¨ulich SNQ project during the 1980s is a combination of the HILO [408] and a high-energy neutron multigroup library from Ref. [599]. The library was updated up to an energy of 2800 MeV during the COSY accelerator project and the ESS project by [555, 558]. The LAHIMACK version of this library contains, additionally, multigroup response functions and reaction cross sections, secondary particle production yields, kerma factors obtained

7.3 Advanced Shielding Methods for Spallation Sources

by HERMES intranuclear-cascade-evaporation calculations [596] above energies of 20 MeV and below 20 MeV from Ref. [600]. – The library contains neutron cross sections for H-1, C, O, Al, Si, Fe, and Pb in 62 energy groups from 0.1 eV up to 2800 MeV and 21 gamma groups from 0.01 up to 14.0 MeV. The library contains Legendre expansions up to P3 for the scattering cross sections (2) HILO2K is a coupled 83 neutron and 22 photon group cross sections for neutron energies up to 2 GeV. – HILO2k is a high-energy neutron and photon transport cross-section library containing neutron cross sections to 2 GeV and photon cross sections to 20 MeV. It represents the updating and extending of the HILO86 transport cross-section library developed by Alsmiller et al. [597] in the mid-1980s. – HILO2k was developed as a part of the neutronics research associated with the design of the Spallation Neutron Source (SNS) currently under construction at ORNL. The HILO2k multigroup cross sections are in the form needed for the DOORS3.2a [592] (ANISN, DORT, and TORT) discrete ordinates codes. In addition to transport cross sections, the HILO library contains ﬂux-to-dose conversion factors, kerma factors, dpa, hydrogen, and helium gas production response functions. – The library contains transport cross sections for 32 nuclides commonly found in the target, reﬂector, and shielding materials used at spallation neutron source facilities. The high-energy portion (E > 20 MeV) of HILO2k is based on neutron elastic and nonelastic interaction and production data generated using the nuclear collision models in MCNPX [194]. The low-energy portion was derived from ENDF data for all nuclides except Hg. The high-energy neutron interaction and production cross sections were also normalized to the nonelastic cross sections for those nuclides treated in the recently evaluated Los Alamos National Laboratory (LANL) 150-MeV library. Data are provided for H-1, H-2, He, Be, B-10, B-11, C, N, O, Na, Mg, Al, Si, S, K, Ca, Cr, Mn, Fe, Ni, Cu, Zr, Nb, Cd, Ba, Gd, Ta, W, Hg, Pb, U-235, and U-238. – Two versions of the HILO2k library are distributed. In the standard version, all high-energy particle interaction and production data were taken into account to obtain the group total cross section (interaction cross section) and the group-to-group Legendre scattering coefﬁcients (scattering cross sections). In the modiﬁed version, neutrons that exited collisions almost straight ahead with more than 95% of the incident neutron energy were treated as uncollided neutrons. Both the libraries contain 105 total energy groups (42 high-energy neutron, 41 low-energy neutron, and 22 photon groups). The modiﬁed version of the new HILO library contains P9 Legendre expansions for the scattering cross sections, whereas the standard version contains P10 expansions.

245

246

7 Shielding Issues

7.3.1 Monte Carlo Discrete Ordinates Coupling

As discussed earlier, the particles which cause the radiation problems around accelerators and high intensity spallation neutron sources are the deep penetrating neutrons with energies above 100 MeV up to the energy of the proton beam of the accelerator. These neutrons determine the dose rate at each point inside and outside the shield because they produce via the cascade propagation a neutron spectrum with energies down to thermal energies. This spectrum is far inside the shield more or less an equilibrium spectrum if the shielding material is not changed. The advantage of the Monte Carlo discrete ordinates coupling for shielding calculations is as follows: in the vicinity of the neutron spallation target one uses the Monte Carlo method to treat all important particle types in that area and to calculate the spatial and angular distribution of generated high-energy neutrons at the outer edge of that region. This distribution is handed over to a deterministic transport code, which calculates the attenuation of the high-energy neutron ﬂux inside the shield far away from the target. The incoming proton beam and all particles produced in the spallation process and in the target vicinity are treated exactly by Monte Carlo allowing a proper design of the geometries in three dimensions. Therefore, one gets the correct fast neutron ﬂux distributions inside and at the edge of the target region or the accelerator structure, respectively. The coupling procedure works in the following manner: The particle transport via Monte Carlo has to be used until a depth sufﬁciently large inside the shield, where the neutrons are the dominant high-energy particles rather than protons, but not deeper than necessary to satisfy the criterion so that the statistics from the Monte Carlo are as good as possible. The Monte Carlo calculated neutron current across this boundary then constitutes the discrete ordinates angular neutron for further calculations. All neutrons from the Monte Carlo calculations crossing this coupling plane in the ‘‘positive’’ direction – larger depth inside the shield – for the ﬁrst time then constitute a surface source. This is illustrated in Figure 7.6. The experience has shown that a sufﬁcient depth for the coupling plane inside the shield is about several mean free paths or several attenuation length. To analyze the results from the Monte Carlo estimations at the ‘‘coupling plane’’ the boundary source for the 1D discrete ordinates code ANISN is considered here as an example in the following way: • Let MC i,g denote the Monte Carlo calculated neutron ﬂux at the coupling plane for the ith angular interval and gth energy interval, which can be computed as S Wi,g,k /(ωk · N0 ), (7.15) MC i,g = k S is the statistical weight4) of the kth neutron in the Monte Carlo where Wi,g,k calculation which crosses the scoring plane – the coupling surface – in the

4) cf. Section 4.3.1 on page 195.

7.3 Advanced Shielding Methods for Spallation Sources

Monte Carlo

Discrete ordinates Neutron current J (E,µi)

Incident protons

x Z

Coupling surface

End of Monte Carlo history

Fig. 7.6 Schematic of the contribution of a particle to the surface source at its ﬁrst cross-over point on the coupling surface between Monte Carlo and discrete ordinates.

direction ωk > 0 within the ith angular group and with an energy of the gth group. The direction cosine ωk = k · z, where z is a unit vector along the +z axis (taken to be the beam direction). The index k refers to individual contributions, and the summation over k is for all contributions made for N0 incident beam protons. The contribution to is zero if ωk ≤ 0. • In discrete ordinate calculations, e.g., 1D ANISN, the angular ﬂux is assumed to be directed along a ﬁnite number of ‘‘discrete directions,’’ denoted by the cosine µi between the neutron direction and z with a weighting factor wi associated with each direction, e.g., the scalar ﬂux is given by i i,g · wi . Thus ANISN expects as a source from the Monte Carlo calculations the angular ﬂux per unit weight, Si,g = MC i,g /wi .

(7.16)

Note that the source ﬂux is not divided by the energy interval, only the energy group index g, is needed (g = 1 corresponding to the highest energy group in the group cross section library). Thus, the energy boundaries for the Monte Carlo ﬂux tabulation correspond to the energy intervals of the used cross section group structure used for the discrete ordinates calculations. What remains is to deﬁne the angular boundaries around the discrete directions for tabulating the Monte Carlo results. Values for µi and wi are deﬁned from the quadrature set used. Normally, classical quadrature sets with µi representing the zeros of Legendre polynomials and wi the weighting factors for Gaussian integration are used, as can be found in numerical analysis handbooks. An example (to only three signiﬁcant digits) for an SN = S8 quadrature is given in Table 7.4. (By ANISN convention, µ1 = −1 and w1 = 0.) The weights can be envisioned as fractional solid angles ( i wi = 1). (a) µi = zeros of Legendre polynomials, the discrete direction cosines used in discrete ordinates calculation. (b) θi = cos−1 ·µi in degrees

247

248

7 Shielding Issues Example (for S8 quadrature) of deﬁning angular boundaries for neutron source calculations.

Tab. 7.4

Discrete directions and weights (a) µi (= cos θi ) −1.000 −0.960 −0.797 −0.526 −0.183 +0.183 +0.526 +0.797 +0.960

(b) θi (◦ )

(c) wi (weight factor)

180 164 143 122 100 79.5 58.5 37.5 16.5

0.000 0.051 0.111 0.157 0.181 0.181 0.157 0.111 0.051

Source boundaries (d) µi

−1.000 −0.899 −0.662 −0.355 0.000 0.355 0.665 0.899 1.000

+1 (c) wi = weight factors for Gaussian integration −1 (µ)dµ ≈ ni=1 wi · (µi ) (d) µj = boundaries for calculating angular ﬂux source distributions in Monte Carlo calculations = µi−1 + 2 · wi , µi = −1. Apparently, there is no unique method for deﬁning the values µi for the angular source boundaries about the µi directions. One way is to set the interval width about each µi as µi = 2 · wi , then µi = µi−1 + 2 · wi , with µi = −1. The resulting va1ues for the S8 quadrature (given in Table 7.4 are numerically very close to simply taking the midpoints of the µi interva1s, which suggests that the Monte Carlo directions could approximately be scored according to the closest µi . The procedure for coupling with the 2D and 3D discrete ordinates is similar to that described above for the 1D case except that a (R, Z) or a (R, θ ) dependence in the two-dimensional case of the ﬂux and in the three-dimensional case a (X, Y, Z) or (R, θ , Z) must be obtained. Some solutions are given in Refs. [589, 591, 592]. For deep penetration problems, asymmetric quadrature sets are usually required, where more discrete angles are used in forward direction than in backward direction. During the German spallation neutron source, J¨ulich SNQ project during the 1980s, detailed studies were investigated to show the feasibility of the anticipated nuclear parameters of a high-power neutron spallation target station of 5 MW proton beam power and an incident proton energy of 1.1 GeV [601]. Deep penetration bulk shield calculations utilizing Monte Carlo discrete ordinates coupling with the high-energy neutron/gamma LAHI library [338, 595] mentioned above where done the ﬁrst time. One concern was that whether the bulk shield thickness of the neutron spallation target station would be the same in the forward direction as in the backward direction for the 1.1 GeV incident proton beam on a water cooled lead target system. The inner part of the shield was composed of cast iron while

7.3 Advanced Shielding Methods for Spallation Sources

Dose equivalent [µSv/h] per 5 mA

1011 1010

Incident proton energy 1.1 GeV on target

107

Forward

Backward

104

Concrete 101

Iron

Concrete Iron

5 µSv/h 10−2 0.5

1

2

3 4 Shield radius [m]

5

5.5

6

6.5

Fig. 7.7 Comparison of the dose equivalent per hour in forward and backward directions in an iron–concrete bulk shield for a proton beam energy of 1.1 GeV and beam power of 5 mA [601].

the outer part was composed of concrete [601]. Figure 7.7 shows a comparison of the space-dependent dose equivalent in µ Sv/h per 5 mA beam power in forward and backward direction to the incident proton beam. It was found by the Monte Carlo 1D discrete ordinates coupling that in forward direction 5.5 m of cast iron and 1 m of concrete and in backward direction 4 m of cast iron and 1 m of concrete are sufﬁcient to reduce the dose rates of less then 5 µ Sv/h outside the shield5) . The difference in the dose rate distributions is the fact, that the energy spectrum in the forward direction is much harder than in the backward direction and the angular distribution is strongly peaked in the forward direction. An example of this anisotropy is shown in Figure 7.8. 7.3.2 Monte Carlo Techniques and Deep Penetration

The Monte Carlo method is a very useful tool for solving a large class of radiation transport problems of complicated three-dimensional geometry and material systems. However, the Monte Carlo method in all its forms involves some sort of random process. Most of the Monte Carlo systems summarized in Table 5.1 are using models in analog fashion. The analog process of ‘‘pure’’ Monte Carlo methods for deep penetration calculations is inefﬁcient because only macroscopic quantities are important. These quantities are often a result from contributions of statically rare events. In thick shields, needed for radiation protection of high-energy 5) It should be noted here that the dose criterion given here is only an example. It depends of the rules of the licensing procedures in

different countries and the radiation protection legislation. Nowadays a much lower value, e.g., 0.5 µ Sv/h, will be assumed.

249

7 Shielding Issues

10° 10

30°

1 dΦ(E)/dΩ [neutrons cm−2 sr−1 p−1]

250

60° 8

1

7 0.1

6

5

4

3

2 90°

0.1

120°

1

150° Beam

1 all neutrons 2> 1 MeV 3> 6 MeV 4> 20 MeV 5> 50 MeV 6> 100 MeV 7> 250 MeV 8> 500 MeV

Fig. 7.8 The measured angular distribution of neutrons in different energy groups for a 20-cm diameter lead target bombarded by protons of an energy of 2 GeV (after Bauer [57]).

and high-intensity spallation sources, particles have to travel a large number of mean free paths to go through, whereas the average number of collisions that particles undergo during their lifetime until their energy has fallen below a certain level is considerably smaller. Neutral particles, e.g., neutrons, however, can travel long distances between collisions, of course, with a low probability for larger path lengths. Thus a few particles can penetrate a thick shield. The calculation of this small fraction is the deep penetration problem. Besides the bulk shielding problems there exist other issues at high-intensity spallation neutron sources e.g., the streaming of neutrons through gaps and ducts in a shield, and the neutron beam line shielding, the instrument shielding, shutters, and collimators which are of high importance. The neutron albedo and multiple scattering of neutrons within the neutron beam line or in the ducts are very important. High-energy neutrons entering a duct in a neutron shield become thermalized and have been able to scatter many times, allowing to stream along

7.3 Advanced Shielding Methods for Spallation Sources

the duct, even with several bends. Also the steel walls of a pipe for cooling water inside a shield can act as a duct for steaming of high-energy neutrons. Unlike low-energy Monte Carlo codes as MORSE [506] or MCNP inside the MCNPX code [509], where a large experience on particle transport biasing exists in reactor and fusion technology shielding [602, 603], this is in general not the case for high-energy intensity spallation sources. Only recently Monte Carlo methods were applied for high-intensity source shielding of spallation sources, e.g., in [560, 561, 604–609] and ADS assemblies [610]. In the following a short overview is given on the available biasing methods in high-energy particle transport system (cf. Table 5.1 on page 210). Details about the main mathematical and statistical considerations can be found in the textbooks by Lux and Koblinger [149] and by Lewis and Miller, Jr. [150]. (1) Russian Roulette and surface splitting: The simplest biasing method is a very well-known Russian Roulette and splitting procedure. The method is based on a region ‘‘importance’’ concept, where a numerical value to each geometry region is assigned, which may be dependent on the particle under consideration. During the transport of the particles through the geometry the number of the selected particle types crossing a given region boundary is decreased or increased by a factor equal to the ratio of the importance on either side of the boundary. Here the relative importance of different regions not their absolute values are considered. In simple deep-penetration calculations with one main attenuation path this biasing procedure is easy to use and very effective [197]. (2) Weight window: The weight window biasing reduces ﬂuctuations of the particle weight within predeﬁned limits. It is also based on Russian Roulette and splitting of the particle weight. It refers to the absolute particle weight and is not linked with geometrical boundaries. It can be ﬁnely tuned by region, particle and energy and increases the effectiveness of all other biasing techniques. (3) Leading particle biasing: Leading particle biasing is important for electrons, positrons, and photons. It is used to avoid the geometrical increase with energy of the number of particles in electromagnetic showers. (4) Nonanalog absorption: This biasing method is used mainly for low-energy neutrons. It is the choice between analog absorption with the actual physical probability and a systematic survival with a reduced weight. (5) Biased decay and interaction length: This biasing method is useful to decrease, e.g., the inelastic interaction length in a given material by a particle dependent factor which is useful to increase

251

7 Shielding Issues

the probability of interaction in a low density material. The average decay length of unstable particles can be shortened without stopping the parent particles. (6) Biased down-scattering: This biasing method is used to bias the group-to-group transfer probabilities used in the transport of low-energy neutrons. The method accelerates or slows down the moderation process. The method needs some experience, but can save considerable computer time in systems where the moderation process plays an important role. An impressive example of a deep penetration Monte Carlo calculation for thick bulk shield using the weight window biasing method was given by Koprivnikar and Schachinger [560] recently. The geometry model of the used MCNPX Monte Carlo system [509] was adopted from the JESSICA cold moderator experiment [551, 611], a 1:1 mockup of the target–moderator–reﬂector system similar to the high-intensity European Neutron Spallation Source (ESS) [551] of 5 MW proton beam power equal to 3.75 mA proton current or 2.34 × 1016 protons/s, and an incident proton energy of 1.334 GeV on a mercury target. The very detailed inner part of the ESS target station is surrounded by a cylindrical bulk shield of iron and concrete, whereas at the outer edge of this inner part at

Target - moderator reflector system x

Iron shield

60°

Incident proton beam

Sampling surface

50

z

∅1

252

Shielding is not to scale

Target

Reflector

Concrete

Fig. 7.9 Horizontal cut through the used Monte Carlo 3D geometry of the target station of an inner diameter of 3 m showing the sampling surface for the incident neutron source incident in a cone into the bulk shield. The target station is surrounded by an iron shield of a thicknesses between 475 cm in forward, 425 cm in backward direction and in addition by a 50-cm thick concrete layer (after [560]).

7.3 Advanced Shielding Methods for Spallation Sources

a radius of 150 cm an energy and angle-dependent sampling surface source was determined for the deep penetration calculations (cf. Figure 7.9). A combination of two biasing techniques, available in the MCNPX system, was used. One is the energy-dependent weight window technique, and the other one is the source biasing. The weight window is a space-energy-dependent splitting and Russian Roulette method in which each space-energy phase-space cell deﬁnes a window of a certain acceptable particle weight. If this weight is below a speciﬁed weight, then Russian Roulette is played and the particle is eventually killed from the history. If the weight of the particle is above the speciﬁed weight, then splitting occurs. All split particles are again within the weight window. For this kind of biasing technique the shield system geometry has been divided into sections. Therefore, the shielding part of the geometry of Figure 7.9 was divided into concentric spherical shells of an incremental radius of 25 cm. The neutron equivalent dose attenuations in (µ Sv/h) as a function of the depth inside the shield are given in Figure 7.10 for 0◦ , 45◦ , and 90◦ directions to the incident proton beam. Assuming a 5 µ Sv/h design criterion for the edge of the shield at 0◦ this yields 475 cm of iron plus 50 cm of concrete, at 45◦ 460 cm of iron plus 50 cm concrete, and at 90◦ about 425 cm of iron plus 50 cm of concrete, respectively. From these calculations the authors [560] determined from the dose distributions, given in Figure 7.10, with the help of an exponential function, neutron attenuation lengths in the energy range between 10 MeV and 1.334 GeV for iron as 22 ± 1 cm and for concrete as 38 ± 2 cm. 1010

Neutron dose equivalent [µSv/h]

Concrete layer 45° Concrete layer 90° Concrete layer 0°

105

100

10−3 100

Total neutron dose rate, 0° direction Total neutron dose rate, 90° direction Neutron dose rate due to neutrrons >10 MeV, 90° direction Total neutron dose rate, 45° direction Neutron dose rate due to neutrrons >10 MeV, 45° direction

150

200 250 300 350 400 450 Distance from inner iron shield surface [cm]

Fig. 7.10 The attenuation of the neutron dose equivalent is plotted in (µ Sv/h) in different directions 0◦ , 45◦ , and 90◦ to the incident proton beam through the bulk shield assuming a thickness of iron to be 475 cm and that of concrete of 50 cm (after [560]).

500

550

253

254

7 Shielding Issues

7.4 Sky- and Groundshine Phenomena

Increased neutron and photon radiation ﬁelds have been observed in the vicinity of accelerator and reactor facilities [102, 612], which may produce a radiation hazard for the laboratory staff and the surrounding population. The spatial distributions of these external dose levels are usually affected by the sky- and groundshine effects, due to backscattering of the radiation from the atmosphere, of the secondary radiation from the ground, and of neighboring buildings. Figure 7.11 illustrates these phenomena. The interesting point is that dose rates caused by sky- and groundshine effects are usually measured not directly adjacent to, but at higher distances from a facility. Another problem is caused by the possible contamination of the surrounding air and ground water by the induced radioactivity. These effects can occur at facilities with not adequate roof shielding or by the leakage of radiation underneath the high-density shielding. Its solution is to improve the roof shielding or reduce the scattered radiation by extending the high density shielding into the lighter density foundation of the ground. An overview about evaluation methods of neutron and photon skyshine is given by Hayashi [613] recently. Rindi and Thomas [612] have summarized experimental and theoretical studies from high-energy particle accelerators and suggested a simple formula (cf. Eq. (7.17)) to estimate the neutron ﬂuence at distances up to about 1000 m from the source. (x) =

a·Q · exp(−r/λatt ), 4π · r 2

(7.17) Skyshine

Shielding

Target Direct Ground shine

Ground Fig. 7.11

Sketch of the sky- and groundshine phenomena around a spallation facility.

7.4 Sky- and Groundshine Phenomena 1000

latt in air [m]

800 600 400 200 0 0 10

101 102 103 104 105 Upper energy of neutron 1/E spectrum [MeV]

Fig. 7.12 The attenuation length λatt in air as a function of the neutron energy assuming a 1/E neutron leakage spectrum (after [615]).

where (x)= neutron ﬂuence at a distance r from the source, Q = neutron source strength, a = 2.8 an empirical buildup factor, and the neutron attenuation factor in air is assumed as λatt > 830 m for neutrons with energies E > 150 MeV. Alsmiller et al. [614] calculated ‘‘importance function” for neutron skyshine up to 400 MeV by 2D discrete ordinates adjoint calculation. Stevenson and Thomas [615] extended Eq. (7.17) of Rindi and Thomas using Alsmiller’s response functions. Under the assumption that the leakage neutron spectrum of the facility under consideration is 1/E spectrum, Stevenson and Thomas estimated the attenuation length λatt in air as a function of upper neutron energy Ecut . This functional dependence is given in Figure 7.12. The extended formula is given by Eq. (7.18) and is only valid for distances r > 100 m. H(r) ≈

(1.5 ∼ 3.0) × 10−15 · exp(−r/λatt ), r2

(7.18)

where H(r) is the equivalent dose rate at a distance r from the leakage source in (Sv/per source neutron), r is the distance from the source, and λatt the attenuation length in (m) for high-energy neutrons. To estimate the total dose equivalent H(r) the number of leakage neutrons must be known. Besides these simple methods, nowadays neutron- and photon skyshine distributions are precisely calculated by using Monte Carlo, by multidimensional Sn transport or by Monte Carlo methods coupled with discrete ordinates including the facility and building structure directly, or concatenating leakage calculations from the facility building and air transmission calculations (cf. Figure 7.5). Coupled Monte Carlo discrete ordinates calculations on sky- and groundshine are investigated for the high power neutron spallation target station of 5 MW proton beam power and an incident proton energy of 1.1 GeV of the German SNQ project E[601]. Based on the same geometry used for the attenuation calculations

255

7 Shielding Issues 102 5 2 1

10 5 2 100 5 2

101

Vertical

Horizontal

Relative contribution to dose equivalent

Average neutron energy [MeV]

256

−1

Low-energy neutrons

10−1

Gamms

10−2 −3

10

10−4 10−5

High-energy neutrons

10−6

10 (a)

100

101 2 5 102 2 5 103 2 5 104 Horizontal/verticale distance [m]

101 2 (b)

5 102 2 5 103 2 5 104 Horizontal distance [m]

Fig. 7.13 (a) Average energy of skyshine neutrons versus distance from the targetstation. (b) Relative contribution to the dose equivalent of high-energy neutrons (> 20 MeV), low-energy neutrons (< 20 MeV), and gammas versus the horizontal distances from the target station.

given in Figure 7.7 and using the neutron–gamma transport cross section library LAHI [338, 595, 596] a coupled neutron–photon leakage radiation transport is possible. Zazula et al. [616] have shown for this high-current spallation source facility some interesting features resulting from sky- and groundshine calculations. Up to a distance of 100 m from the station, it is not possible to describe the decrease of the radiation levels proportional to 1/4πr 2 or by an attenuation proportional to exp(−x/λatt ). Numerical ﬁts of the results with semiempirical formulas developed for the description of the skyshine effect were not performed here, since such expressions do not have a universal character and are strongly dependent on the source energy and the geometry details of the facilities considered. The differences of the attenuation lengths are caused by different energy ranges of the secondary particles at different distances. To explain this behavior, the relative contributions to the dose equivalent from different kinds of secondary radiation are compared in Figure 7.13(b). The neutron spectrum distribution in air is equal to the distribution of neutrons at the surface of the shielding, and thus, the low-energy neutrons dominate. Farther away these slow neutrons are absorbed, and the fast neutrons, penetrating the air to large distances (hundreds of meters) in air, are not slowed down very much. Thus, at a distance of about 1000 m and more, the high-energy neutron and gamma components contribute more to the dose. This hardening of the skyshine radiation spectrum was also described by Rindi and Thomas [612]. This effect is clearly shown in Figure 7.13(a), for both, the horizontal as well for the vertical average neutron energy. Another issue is the photon sky- and groundshine problem, where also many theoretical work and measurements including benchmark experiments were done by many investigators. Examples of shielding experiments will be given in Part 2 on page 481. Problems on safety and radiation protection are discussed in Part 3 on page 554. Properties of shielding materials are given in the appendix on page 689.

257

8 The Basic Parameters of Spallation Neutron Sources 8.1 Introduction

The emphasis of this chapter is focused on the basic matters related to the parameter scheme of spallation neutron sources due to their estimated use. As already discussed in Section 1.3 on page 12, besides ﬁssion or fusion, spallation is an efﬁcient process for producing neutrons and other particles in large numbers. However, in contrast to ﬁssion spallation is an endothermal process and can therefore, a priori not be used for energy production. Compared to ﬁssion, spallation has its own technology issues, which need a careful selection of a variety of physical variables. The spallation process is responsible for some technical constraints concerning the neutron producing target as, e.g., the selection of target and structure materials, particle type and kinetic energy of the incident beam, moderators and reﬂectors, target heating, induced radioactivity, etc. The worldwide operating, under construction and planned facilities of highintensity spallation neutron sources, including the realized accelerators and target systems, are described in Chapters 16,17 on pages 497, 505.

8.2 Parameter Regime for Spallation Neutron Sources 8.2.1 The Particle Type

In considering the merits of protons versus heavier ions as projectiles for spallation sources, a primary consideration is the desire to transfer the beam energy into secondary particle production rather than into deposition power or heating through ionization. The rate of ionization energy loss, or stopping power Si (Ai , Zi , Ei ) for an ion of mass Ai , charge Zi , and kinetic energy Ei can be written in terms of the proton stopping power, Sproton , evaluated at the energy per nucleon, Ei /Ai , of the ion Si (Ai , Zi , Ei ) = Zi2 · Sproton ·

Ei . Ai

(8.1)

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

258

8 The Basic Parameters of Spallation Neutron Sources

Also, the ion range Ri (Ai , Zi , Ei ) can be scaled from the proton range Rproton evaluated at the energy per nucleon of the ion Ri (Ai , Zi , Ei ) =

Ai Ei · Rproton · . 2 Ai Zi

(8.2)

Proton range curves for iron, tungsten, and lead spallation target materials are shown in Figure 8.2. The nuclear collision cross section is approximately constant with energy and increases slowly with increasing ion mass, 1/2

σin ∝ (Ai

1/3

+ Atarget )2 ,

(8.3)

where Atarget is the mass number of the target nucleus. Thus, to maintain an ion range sufﬁciently long to allow nuclear collisions to occur requires increasing kinetic energies with increasing ion masses. As an example, consider a lead target with protons and oxygen ions as projectiles. For protons, the nuclear collision mean free path is λ ≈ 200 g/cm2 , and if one speciﬁes a range so that essentially all of the beam protons can interact, say 3 · λ, then the corresponding beam energy needed is ≥1 GeV. For oxygen ions, λ ≈ 135 g/cm2 , and a 3 · λ range requires the beam energy to be about 30 GeV. Once a nuclear collision occurs, the neutron multiplicity will, of course, be higher for higher mass ions, but it is clear that much higher beam energies are involved with higher mass ions, with higher costs and technology requirements for acceleration. Measurements of neutron yields Yneutron per charge number Zi for a lead target bombarded with protons, deuterons, 3 He, 4 He, and 12 C are published by Vassil’kov [617] and shown in Figure 8.1 as a function of the incident energy per ion charge number Ei /Zi . The deuteron is somewhat of a special case in considering ions heavier than protons because: • The deuteron and proton have the same charge, so the Z2 factor in ionization loss is not relevant. • The nucleons of the deuterons are weakly bound and easily ‘‘stripped’’ in nuclear collisions, resulting in a source of neutrons and protons, each with about one-half the deuteron energy, at rather shallow target depths. For 1 GeV beams and a lead target Barashenkov et al. [618] calculated about 15% greater neutron yield for deuterons over protons with essentially no difference in heat deposition. With deuterons a slightly higher neutron yield is produced. This small difference in the neutron yield between incident protons and deuterons is also shown in Figure 8.1. Bauer et al. [619] reported measurements of neutron leakage ﬂuxes from hydrogenous moderators of a realistic target–moderator–reﬂector conﬁguration as the function of protons and deuterons impinging on lead and uranium targets. The measured neutron ﬂuxes represent not the total fast neutron yield given by Barashenkov et al. [618] and therefore contain some physical parameters as a function of the target–moderator geometry, penetration depth of the primary protons and deuterons, and the coupling efﬁciency for fast neutron

8.2 Parameter Regime for Spallation Neutron Sources

150 Deuteron

100 Yi /Zi

Proton 3He 12C

50

0

4He

0

1

2

3

4 5 Ei /Zi [GeV]

6

7

8

Fig. 8.1 Measured neutron production yield per incident particle charge, Yi /Zi , of a cylindrical Pb target (diameter = 20 cm, length = 60 cm) as a function of the incident particle energy per ion charge Zi , Ei/Zi , of protons, deuterons, 3 He, 4 He, and 12 C (after Vassil’kov [617]).

from the target into the moderator. A comparison of the ﬂux measurements of Bauer et al. shows a gain for incident deuterons to incident protons on lead at beam energies of 0.4 GeV of about 10% and at an incident beam energy of 0.75 GeV a gain of 23%. For the uranium target experiment, the gain at these incident energies is about 13% and 16%, with a larger value of about 24% at an incident energy of 0.6 GeV, respectively. Theoretical evaluations of Ridikas and Mittig [620] done in the context of ADS studies have shown that there is some advantage to use deuterons instead of protons in ADS devices depending on the choice of the neutron producing target system. They found bombarding beryllium spallation targets, placed inside the same ﬁssionable fuel assembly, with deuterons of an energy at 0.6 GeV, an average energy gain, e.g., the ratio of the energy produced by ﬁssions in the device to the energy delivered by the beam – Eﬁssion /Ebeam – of about 28 compared to incident protons of the same energy of about 16 for beryllium. In addition, this study considers for incident deuterons that an energy ampliﬁer could therefore be operated with deuteron beam energies of the order of 0.4–0.8 GeV, e.g., at lower beam energies than suggested for a proton beam, and give a comparable energy gain factor. 8.2.2 The Kinetic Energy

The rationale for the minimum kinetic energy of proton beams appropriate for spallation sources is basically the same as discussed above for particle masses,

259

8 The Basic Parameters of Spallation Neutron Sources

104

Proton range [g /cm2]

260

103

102

26

Fe, r = 7.87 g/cm2 2

74

W, r = 19.30 g/cm

82

2

Pb, r = 11.35 g/cm

101

100 102

103

104

Proton energy [MeV] Fig. 8.2

Proton energy range curves for target materials Fe, W, and Pb.

i.e., the proton range, a monotonically increasing function of energy, should be sufﬁciently large compared to the nuclear collision mean free path, which is constant with energy above about 100 MeV. The range dependence on energy is shown in Figure 8.2 for iron, tungsten, and lead. The nuclear mean free path for nonelastic collisions of incident protons for E ≥ 100 MeV and A > 1 and the probability of nuclear collisions Pnuclear-collsion before the proton reaches the end of range are given as λ = 33 · A1/3 (g/cm2 ) Pnuclear-collision = 1 − exp(R/λ).

(8.4)

Figure 8.3 shows for a lead target, the proton range divided by the proton nuclear collision length λnuclear-collision-PB ≈ 192 g/cm2 ≈ 16.9 cm and the probability of nuclear collisions Pnuclear-collsion before the proton reaches the end of range as a function of the proton incident energy on the target. Thus, the probability of obtaining nuclear collisions to produce neutrons is not substantial unless the beam energy is several hundred MeV, or more. This is approximately independent of the target material. For the maximum appropriate neutron production yield, there is no advantage for energies much greater than about 1–2 GeV because, • as mentioned above, essentially all of the beam protons interact if the energy is about 1–2 GeV, • pion production becomes increasingly signiﬁcant for beams much above 1–2 GeV, and the energy is partly lost for neutron production, in particular the π ◦ decay in 2γ s is not be efﬁciently converted to neutron production (cf. via the electromagnetic drain already discussed in Section 1.3.8 on page 57),

8.2 Parameter Regime for Spallation Neutron Sources

Proton range / l

101

Proton range / l

101 Lead target

100

100 Probability P

10−1

10−1

10−2 101

102

103

104

Pnuclear collision = 1-exp(-range / l)

102

102

10−2 5 × 104

Incident proton energy [MeV]

Fig. 8.3 Values for the probability of nuclear collisions for a Pb target before the proton reaches the end of its range.

• the spatial dependence of neutron production becomes somewhat less concentrated for higher energies, which may reduce the maximum density of neutrons attainable, • and higher beam energies require larger accelerator systems. Within the above-deﬁned general energy range of about 0.5 up to about 1–2 GeV, the neutron production is directly proportional to the beam energy, which is illustrated in Figure 8.4. The energy dependence of the yield data in Figure 8.4 can be described by a simple empirical relation (see also Section 1.3 on page 12) x Mneutron /proton = M0 + M1 · Eproton ,

(8.5)

where Mneutron /proton is the multiplicity per incident proton with an energy Eproton in GeV. The numerical values for the parameters in Eq. (8.5) are given in Table 8.1. Carpenter et al. [625] have discussed ‘‘The 10,000,000,000-Volt question.’’ What is the advantage to use higher proton beam energies for pulsed spallation neutron sources, e.g., in an energy range of about 10 GeV? Some of the conclusions are as follows: • losses of the neutron yield at higher incident proton beam energies have to be compensated with some higher beam power, • higher incident proton beam energy reduces radiation damage problems in accelerator and target beam windows, • potentially lower beam losses and operating costs of the accelerator, • different shielding problems, e.g., considering neutrons with higher energies and gamma rays produced by electromagnetic cascades, • detailed engineering studies are needed to reach a certain level of conﬁdence.

261

262

8 The Basic Parameters of Spallation Neutron Sources

200

Mean neutron multiplicity per incident proton

(1)

(2)

150

(3)

100

Hilscher et al. Vassil′kov et al. Arai et al.

50

Protons on cylindrical Pb targets

0

0

5

10

Incident proton energy [GeV] Fig. 8.4 Mean neutron multiplicity per incident proton of Pb targets as a function of the incident proton energy. Data from Hilscher et al. [621] and Filges et al. [622] are for a cylindrical target with diameter 15 cm and length 35 cm, data from Vassil’kov and Yurevich [617] refer to

moderator measurements with a target of diameter 20 cm and length 60 cm, and the data of Arai et al. [623] are for a target of diameter of 20 cm and length 60 cm, respectively. The solid, dotted, and dashed lines correspond to a parameterization (1), (2), (3) given in Table 8.1.

Parameters for Eq. (8.5) to estimate the average neutron yield as a function of the incident proton energy on thick targets, where A is the atomic mass of the target material [621].

Tab. 8.1

Line

(1) (2) (3)

Target material A Pb Pb

Dimension ∅, length (cm)

Ep (GeV)

10, 100 20, 60 20, 60

≤ 1.5 ≤ 3.7 ≤ 8.1

M0

M1

x

−(A + 20) · 0.012 −4.8 ± 1.0 −8.2 ± 1.6

(A + 20) · 0.1 28.6 ± 2.5 29.3 ± 1.3

1.00 0.85 0.75

Reference

[59] [624] [617]

8.2.3 The Target Material

Desirable ‘‘physics properties’’ of target materials for spallation sources are high neutron production, low heating, and low induced radioactivity; a summary of these features are discussed below. There are, of course, other important factors, not discussed here, which enter into target design considerations, such as thermal properties, e.g., conductivity, melting point, mechanisms for heat removal, material damage under irradiation and thermal cycling (affecting target life time), safety, economics, etc. Thus, the overall problem of target design involves tradeoffs of various materials properties, and ﬁnal selection depends on the magnitude of the

8.2 Parameter Regime for Spallation Neutron Sources

particular proton beam intensities and neutron output goals being considered. The issues and solutions on materials for spallation sources are discussed in more detail in Part 3. 8.2.4 The Neutron Production

One factor in considering appropriate target materials for spallation sources is the total neutron production in phase space produced per beam proton. The determination of this neutron yield, and its dependence upon target material mass number and proton beam energy, has been the objective of several experimental and theoretical studies. It should be noted that values for neutron yields appearing in the literature are not always reported on the same basis. They may refer to neutron absorptions in a moderator surrounding the target, to moderator plus target absorptions, or neutrons escaping from a ‘‘bare’’ target without surrounding the moderator. The numerical difference due to these different deﬁnitions can be appreciable, making the interpretation of comparisons between experiments difﬁcult in some cases. Experimentally, the ﬁrst study of neutron yields for spallation neutron sources was carried out by Fraser et al. [59] at the Brookhaven Cosmotron accelerator in connection with the proposed Canadian ING concept [58] (cf. Section 1.3 on page 1.3) and by Bercovitch et al. [626]. Recent measurement were extensively undertaken together with the research and design of highintensity spallation neutron source projects SNQ [142], SINQ [478, 627], ESS [551], J-PARC [628, 629], LANSCE [630], and in relation with international research on ADS [133, 543]. All these measurements exploit either the neutron time-of-ﬂight (TOF), the moderation and activation, or the threshold method. The various experimental results on thick target measurements can be condensed to a quantity which expresses the ‘‘economy’’ of neutron production, i.e., the number of neutrons produced per incident proton and per unit of beam energy. This number is displayed as a function of the incident proton energy Eincident in Figure 8.5. The presentation could be a useful guideline on neutron generation in the context of new concepts of high ﬂux neutron sources. The neutron number increases sharply with increasing incident proton energy or decreasing electronic loss of the proton in the material and culminates at about 0.8–1.0 GeV when the minimum of ionization is approached. Tungsten gives a 10% higher yield than lead for the same target size, length of 35 cm and diameter 15 cm. Data on mercury give, not shown in the ﬁgure, similar results compared to lead. As for example, HERMES simulations reproduce the measured yield for lead and tungsten reasonably well. A calculation for a larger lead cylinder with length of 60 cm and diameter 20 cm is also indicated in order to show the possible gain of some 20% with a larger target and because this has been the standard target in previous investigations [623, 624]. Data from Ref. [624] lie close to the latter simulation. Beyond the maximum near an incident energy of 1 GeV the yield diminishes very slowly, which is corroborated by a recent Mn -bath experiment [623] with a Pb target

263

8 The Basic Parameters of Spallation Neutron Sources

25

Number of neutrons [np−1 GeV−1]

264

20

15

10 NESSI (Pb, l = 35 cm, d = 15 cm) NESSI (W, l = 35 cm, d = 15 cm) PS208 (Pb, l = 35 cm, d = 15 cm) ORION (Pb, l = 25 cm, d = 12 cm) HERMES (Pb, l = 35 cm, d = 15 cm) HERMES (W, l = 35 cm, d = 15 cm) HERMES (Pb, l = 60 cm, d = 20 cm)

5

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Incident proton energy [GeV] Fig. 8.5 The average number of neutrons produced in Pb and W cylindrical target per incident proton and per energy unit (1 GeV) as a function of the incident proton energy. Data from NESSI, PS208 [631], and ORION [632] are shown. Results of simulations with

the HERMES code [88, 622] for different targets (Pb: diameter = 15 cm, length = 35 cm, Pb: diameter = 20 cm, length = 60 cm, W: diameter = 15 cm, length = 35 cm)-, are indicated by solid, dashed, and dotted lines.

at incident proton energies at 12 GeV, because at energies well above 1 GeV pion production becomes a dominating process [633] as already discussed. 8.2.4.1 Spatial Leakage Distribution of Neutrons and Target Shape The spatial distribution and intensity of the leakage neutron current from a thick target depend not only on the target radius or thickness but also on the target shape and of course, on the target material. Only an optimal leakage neutron spectrum in space and energy ensures a maximum neutron ﬂux utilization for the spallation neutron source. The leakage current distributions are important for an optimum location of neutron moderators in wing position above and below the target (cf. Section 8.3). Figures 8.6, 8.7, and 8.8 [551] compare calculated axial distributions of leakage neutrons from cylindrical and ﬂat targets of Hg and PbBi bombarded by 1.5 GeV [634, 635] and 1.334 GeV protons [636], respectively (Figure 8.8). The comparison of the neutron leakage ﬂux distributions of Figure 8.7 shows different target geometries and beam shapes where neutron moderators may be located most efﬁciently. The ﬂat targets give higher leakage neutron ﬂuxes than the cylindrical ones, whereas the rectangular Hg target with a width of 14 cm and a height or thickness of 9.88 cm gives the highest leakage neutron ﬂux. Figure 8.8 shows a comparison of calculated neutron leakage distributions of reﬂected ESS target geometries of mercury, and water-cooled tungsten and tantalum

8.2 Parameter Regime for Spallation Neutron Sources

Cylindrical targets (Ø [cm], L [cm]) (16.23, 60), (12.36, 60)

Rectangular targets (W × H × L cm3) (14 × 9.88 × 60), (24 × 6.44 × 60)

Proton beam (uniform distribution)

Proton beam shape Cylindrical (Ø [cm])

13.23, 9.36 10 × 6.88, 20 × 3.44

Rectangular (W × H cm)2

Fig. 8.6 Target geometries and beam shapes for neutron leakage distribution calculations. The calculations are given in Figure 8.7.

0.04 Neutron leakage current [neutrons cm−2 protons−1]

14W × 9.88H cm2 (Hg) 24W × 6.44H cm2 (Hg)

0.03

14w × 9.88H cm2 (Pb–Bi) 24W × 6.44H cm2 (Pb–Bi) f 12.36 cm (Hg) f 12.36 cm (Pb–Bi)

0.02

0.01

0

0

10

20

30

40

50

Distance from target surface [cm]

Fig. 8.7 Comparison of calculated axial neutron leakage distributions in (neutrons/cm2 /proton) of bare Hg and PbBi targets bombarded by a 1.5 GeV proton beam with a uniform proton current distribution [634].

(with a 10% average water content) [551, 636] bombarded by a proton beam of 1.334 GeV energy, 5 MW beam power and assuming an elliptical beam proﬁle of 6 × 20 cm2 with a parabolic beam density distribution. The highest neutron current at the target surface is produced by the mercury target and is more than 30% higher compared to the tantalum target . Especially along the target surface, the current gradient in the case of mercury is lower than that of the tungsten target. This means that downstream moderators receive an even higher percentage of neutrons in case of mercury.

265

8 The Basic Parameters of Spallation Neutron Sources

Total neutron leakage current J [neutrons cm−2 s−1]

266

6× 1014 Target materials Hg W Ta

4× 1014

2× 1014

0

0

20

40

60

Target depth [cm] Fig. 8.8 Comparison of calculated neutron leakage from a lead reﬂected mercury target and water cooled tantalum and tungsten targets [551, 636].

8.2.5 The Target Heating

The energy carried by the incident beam is dissipated in a spallation source target system in the following way: • target material heating, which is rather concentrated spatially and due to a variety of different deposition mechanisms occurring during the hadronic cascade, • production and emission of high energy particles, mainly neutron, escaping from the target, which deposit energy over a relatively large volume about the whole target station complex, • the binding and mass energies associated with secondary particle production. The amount of energy or heating power in the spallation target depends upon the target dimensions, but since the size of targets for spallation sources are designed to contain most of the cascade collisions approximate comparisons of various heating estimates can be made somewhat independent of the exact dimensions. In Figure 8.9, a comparison of target heating estimates for various spallation target concepts is given in terms of F, the fraction of the proton beam energy which goes into target heating. All of these results are from calculations except for the measurements for U-238 at 300 and 500 MeV and for tungsten at 500 MeV made at the Argonne ZING-P’ facility [637]. Most of the data points are from the calculations of Coleman and Alsmiller [638, 639] and the AECL calculations were made in connection with the Canadian Intense Neutron Generator (ING) study [58], both made for 10.2 cm diameter × 60 cm long geometry. The data point designated ISIS is an estimate by Rutherford Laboratory for a 10 × 10 × 30 cm3 target [640]; those labeled SNQ were computed in the German spallation neutron source study [601] for a ‘‘target wheel’’ geometry with a wheel diameter of 254.8 cm and thickness 10 cm. Results for other spallation source projects are as follows: the Argonne IPNS [641], the Rutherford and Appleton Laboratory ISIS [642, 643],

Fdeposition-heat (energy depositon in spallation targets) (beam energy)

8.2 Parameter Regime for Spallation Neutron Sources

2.2

= Aecl report = Coleman

ZING-P′ (MEAS.)

2.0

SNQ (U) IPNS

1.6

Depleted uranium targets

ISIS (U) ISIS (U)

1.2

ZING-P′(W) (MEAS.) SINQ (Pb-Bi) SNQ (Pb) TRIUMF (Pb-Bi) KENS (W) ¤ SNS (Hg)

0.8 0.4

Lead targets, except as noted

ESS (Hg)

JSNS (Hg)

0 0

500

1000

1500

2000

2500

3000

Incident proton beam energy [MeV]

Fig. 8.9 Fractional heat deposition as a function of the incident beam energy of different existing and projected spallation sources.

the Canadian TRIUMF facility [59], the Japanese KENS source at KEK [644], and the SINQ source [627, 645]. As is evident from Figure 8.9, the estimates for nonﬁssionable targets are rather consistent. The heating fraction estimates for depleted uranium, which are higher than for lead by factors of about 2 over the energy range from 500 to 1500 MeV because of the energy deposition from ﬁssion fragments, show much larger variation. The energy deposition for natural uranium targets is not as simply characterized because the contribution from ﬁssions induced by low-energy neutrons becomes very important, making heating estimates more sensitive to target dimensions and to the presence of moderating materials around the target. Heating for natural uranium targets can be much higher than for depleted uranium (e.g., a fraction of about 6 for a very large natural uranium target and 1 GeV proton beam [268]). The maximum volumetric deposition or peak energy deposition during the pulse train inside the target of a pulsed spallation source depends upon the details of the hadron cascade, the incident beam proﬁle, the pulse frequency and the pulse length. Results for the spatial distributions of energy deposition inside different targets of spallation sources are given in Part 3. 8.2.6 The Induced Radioactivity

Since the binding energy for ejecting a nucleon from the nucleus is about 10 MeV, and since spallation neutron sources need beam energies of about 1–2 GeV and heavy target nuclei with an atomic mass Atarget of about 200 or more, the mass numbers of residual nuclei from spallation collisions can have a wide range of values, extending to about 50 to 100 mass units below the target mass Atarget . These residual spallation nuclei are generally radioactive and neutron deﬁcient relative to the valley of stability. Furthermore, for ﬁssionable target materials, there are additional contributions to the radioactivity from high energy ﬁssion reactions,

267

268

8 The Basic Parameters of Spallation Neutron Sources Induced radioactivity at saturation for an incident proton beam of an energy of 1.1 GeV and an average beam current of 5 mA.

Tab. 8.2

Radioisotope production yield per incident beam proton

Induced radioactivity at saturation Bq

Target material Pb–H2 O–Al 3.0

Pb–H2 O–Al 93.6 × 1012

Depleted U–H2 O–Al 15.4

Depleted U–H2 O–Al 960 × 1012

induced by nucleons ≥15 MeV and pions, and from ﬁssion induced by low-energy neutrons ≤15 MeV. Also, there can be signiﬁcant contributions from other lowenergy neutron reactions, such as (n,γ ), (n,2n), etc., for certain target material compositions. One measure of the radioactivity produced by spallation neutron sources is the ‘‘saturation activity,’’ which corresponds to the total decay rate after a very long, e.g., inﬁnite, irradiation at the time-irradiation stops, e.g., for a zero ‘‘cooling’’ time. For these conditions, the rate of decay is proportional to the production rate. Using the conversion factors 6.2 × 1018 protons/s per ampere and 1.0 decay/s per Becquerel1) , the saturation activity, in Peta Becquerel per milliampere of beam current, can be written as Asaturation = 6.24 · G · N ∗ (PBq/mA),

(8.6)

where N ∗ is the number of radio nuclides produced in the total volume, e.g., the target volume, per beam proton. Nominal values for N ∗ for spallation neutron source beam energies are about 3 for nonﬁssionable target materials and about 5 for ﬁssionable target materials, e.g., depleted uranium (Armstrong et al. [646]). The factor G takes into account the contribution from the decay of daughter or subsequent products. The factor G ≈ 1 for nonﬁssionable materials, and about 2–3 or more for uranium. Thus, the general magnitude of the induced radioactivity for spallation neutron targets is Asaturation ≈ 18.7 (PBq/mA), nonﬁssionable targets Asaturation ≈ 62.4 (PBq/mA), ﬁssionable targets.

(8.7)

As an example in Table 8.2 calculated production rates of radioisotopes by an intranuclear cascade model for a water-cooled lead and a water-cooled depleted uranium target [601] are given with the estimated corresponding ‘‘saturation radioactivity’’ using Eq. (8.6). There are several approaches that have been developed and used for estimating the radioactive species produced in spallation targets: 1) 1 Bq = 1 disintegration rate per second = 27 × 10−9 Ci = 27 pCi.

8.3 The Spallation Neutron Source Facility

• the use of measurements, • empirical formula, for ‘‘thin’’ target cross sections, e.g., partial microscopic cross sections for particular spallation product nuclei, and then the integration of these energy-dependent cross sections over thick target particle spectra calculated by a hadronic cascade code, • the use of Monte Carlo methods and the intranuclear cascade model to directly obtain the isotopes produced during the hadronic cascade and depletion codes with evaluated decay libraries. The semiempirical formula for spallation product isotopes, based on sparse experimental data and parametric ﬁts, such as the Rudstam formula [42] or extensions thereof [45, 47], however, can be very inaccurate by an order of magnitude or more. Therefore, Monte Carlo methods are likely to be more accurate coupled with depletion codes and considering evaluated data libraries. Details of these methods [647–651] are given with applications on high-intensity spallation neutron producing targets in Part 3.

8.3 The Spallation Neutron Source Facility

A spallation neutron source is usually built of two different systems, a particle accelerator which accelerates charged particles, mainly protons, of energies from about 0.4 GeV up to several GeV and a target station where the charged particle beam interacts with a heavy metal target and produces via the spallation process (cf. Section 1.3.4 on page 21) mainly neutrons and other particles, protons, pions, etc. All these particles are the source for further applications. Without going into detail, Figure 8.10 illustrates possible arrangements for accelerator–target–station systems to produce high-intensity neutron beams. Linear accelerators are an attractive choice to produce the required high-intensity proton currents. They operate most efﬁciently with duty cycle factors of a few percent in long pulse or continuous wave (cw) mode. Also the development of rapid cycling synchrotrons have enabled their use as high current accelerators. For short pulse spallation neutron sources either a full energy linear accelerator feds an accumulator or a storage ring or a rapid cycle synchrotron is used for proton beam extraction with a cycling frequency between 10 and 60 Hz and pulse duration in the range of ns–µ s. A spallation neutron source fed directly from a pulsed linear accelerator with pulse length of several milliseconds is referred to as a long pulse source. Continuous spallation sources are fed from accelerators with no-macro time structure such as a cyclotron or a cw linear accelerator. The only existing source of this type is the 1 MW SINQ spallation source at PSI, Switzerland [627]. Continuous spallation sources are favorable to accelerator-driven systems (ADSs) as accelerator transmutation of radioactive waste (ATW)s and energy amplifying systems (EASs). The main characteristics of existing spallation sources are discussed in Chapter 17 on page 505 and summarized in Table 17.17 on page 559.

269

270

8 The Basic Parameters of Spallation Neutron Sources

Compressor ring

Linear accelerator

Ion source (a)

Short-pulse target station

Long-pulse target station

Neutron beam lines Ion source

Injector

(b)

Rapid cycling synchrotron

Short-pulse target station

Fig. 8.10 Principle of accelerator–target–station arrangements of spallation neutron sources. Reflector: - Material (Be, C, Pb) - Cooling (H2O, D2O) - Openings, beam holes - Dimension

Target: - Material (Hg, W, Ta, Pb, U) - Cooling (H2O, D2O) - Dimension, geometry

Proton beam: - Energy - Beam profile

Moderators: - Material (H2O, H2, methane, etc.) - Temperature (300 K, 100 K, 20 K) - Premoderator, coupling / decoupling, poisoning

- Position on target, wing, flux-trap, composite - Dimension

Fig. 8.11 The schematics of a TMR arrangement and the main parameters determining the optimal magnitude of the neutron ﬂux.

Figure 8.11 illustrates the principal arrangement of a target-moderator-reﬂector system (TMR) to produce thermal or subthermal neutron beams via moderation of fast neutrons generated by a high-intensity proton beam of GeV energy impinging on a heavy metal target. The TMR systems is embedded in a thick bulk shield with openings for neutron beam lines guiding the neutrons to the experiments (cf. Figure 8.10). The different parameters which determine the optimal neutron utilization of the TMR system are also depicted in the ﬁgure. It is obvious that the construction and the optimization of a TMR system and in general of a spallation

8.3 The Spallation Neutron Source Facility Wing geometry Moderator Target Proton Beam Neutron current to expreiments Slab geometry

Flux-trap geometry

Slab configuration

Proton beam

Fig. 8.12

Slab target configuration with two wing moderators

Basic target–moderator conﬁgurations.

neutron source is a very complex process concerning the possible parameter space given in Figure 8.11. As shown in Figure 8.12, there are about three basic target moderator conﬁgurations to obtain thermal or cold neutrons from a moderator, the so-called wing-, slab-, or ﬂux-trap conﬁguration [652]. The wing geometry conﬁguration together with a slab target is widely used at the existing or projected high-intensity spallation neutron sources, SNS, USA, J-PARC, Japan, and ESS, Europe (cf. Table 17.17 on page 559 and more in detail in Part 3). It should be noted, that moderators in a slab geometry conﬁguration provide about two times higher neutron ﬂuxes [635]. No experiment views the target directly, therefore a background contamination in the low-energy neutron beam by high energy neutrons from the target may be minimized. In combination with a slab target system, as shown in Figures 8.6 and 8.12, additional moderators with lower intensity could be positioned [551].

271

272

8 The Basic Parameters of Spallation Neutron Sources

Three classes of spallation sources can be distinguished depending of the accelerator parameters as the driving source, the layout of the target station and the considered applications: continuous, long-pulse, and short-pulse spallation sources [57].

8.3.1 Continuous Spallation Neutron Sources

The goal of these sources is to produce a high average neutron ﬂux. Therefore, an accelerator with no macro time structure of the proton beam is used. The use of low-absorption material around and in the TMR system is crucial to produce a long life time of the moderated neutrons and a high thermal neutron ﬂux. Such a system is comparable to a high-ﬂux reactor core-reﬂector arrangement as ILL [653]. Typically, a 2-m diameter D2 O system acting as moderator and reﬂector surrounds a target system of low-absorbing target material, e.g., PbBi. The only existing continuous spallation neutron source of this type is the SINQ source [627]. Some issues of continuous spallation sources are also relevant in ADS. Details are given in Part 3.

8.3.2 Short-Pulse Spallation Neutron Sources

Their characteristic feature is that they generate fast neutron pulses. These sources favor neutron application techniques with TOF experiments and are working in pulsed mode with a high neutron peak ﬂux and a short pulse duration at an appropriate repetition rate (cf. Table 17.17 on page 559). Figure 8.13 shows as an example a typical pulse shape of a short neutron pulse with a FWHM of about 100 µ s. The optimization criterion of this type of neutron source is a short pulse duration without disproportionate losses in the peak ﬂux intensity. Examples of these sources are the spallation neutron sources IPNS, ISIS, MLNS, SNS, JPSNS-JPARC. Details are given in Part 3.

8.3.3 Long-Pulse Spallation Neutron Sources

The pulse width of the produced neutron pulse of these sources is essentially determined by the proton pulse duration of the accelerator. Figure 8.13 shows as an example a typical pulse shape of a long neutron pulse with a duration of about 2 ms. High-intensity time averaged neutron ﬂux is an important optimization criterion and a ﬂat top pulse shape as shown in Figure 8.13. Therefore, it is important to ﬁnd a compromise between high-peak ﬂux and neutron lifetime in the moderator.

Neutron current density [n/cm2 sr Angström]

8.3 The Spallation Neutron Source Facility

5× 1013 Peak intensity

4× 1013 Short pulse Exponential pulse decay with decay constant t

3× 1013

2× 1013

Long pulse

1× 1013

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time t [ms] Fig. 8.13 Examples of typical pulse shapes of short- and long-pulse spallation neutron target stations.

8.3.4 Scattering of Neutrons by Matter

The pulsed spallation sources make use of the pulse state of the produced neutrons using TOF methods (cf. Figure 8.14). Their merits can be shortly characterized as follows: • A range of wavelengths and corresponding energies of the neutrons can be used at the same time. • The instantaneous luminosity is large enough for signals to be detected with high precision. • It is easy to perform neutron scattering experiments under special condition, e.g., such as pulsed magnetic ﬁelds and high pressures. Figure 8.14 illustrates the principle of a neutron experiment applying the time-of ﬂight method. A pulse of protons is injected into a spallation target every 50 ms, shown by the lines of the upper part of Figure 8.14. Accordingly, the neutrons are also produced every 50 ms. The neutrons produced by the spallation process have a broad range of energies. It is possible to determine their energies and wavelengths by using the pulsed nature of the source. The neutrons with energies E1 , E2 , and E3 in Figure 8.14 leave the source at the same time but with different velocities. The neutron with energy E1 is the ﬁrst one to reach the detector because it has a higher velocity than the neutrons with energies E2 or E3 . Using the distance to the target and the time the neutron reaches the detector, it is possible to determine the velocity, and hence the wavelength and energy of the neutron. The method uses the simple equations as shown in the insert of Figure 8.14.

273

8 The Basic Parameters of Spallation Neutron Sources

20 Hz 50 ms

Assuming thermal neutrons at T = 293 K:

Proton pulse injection

V = L/t = 2200 m/s E = 1/2 mv2 Energy: = 25.3 meV Wavelength: l = h/mv = 1.798 Å Velocity:

Distance L from the target [m]

274

E1 > E2 > E3

E1

E2

E3

0.0

50.0 Time t [ms]

Fig. 8.14

The neutron time-of-ﬂight method.

The relation between energies and wavelengths of neutrons makes it possible to obtain microscopic information about matter. This depends on the sample which will be analyzed by the low-energy neutrons in the meV energy range. Basically from elastic or inelastic scattering processes of neutrons with matter, information is obtained to determine the relation between the wavelength and energy of scattered neutrons emitted from the sample. As shown from the insert of Figure 8.14, the neutron wave properties obey some relations of quantum mechanics as already given in Section 1.3.5.4 on page 30 which are shortly repeated here. 2π λneutron 1 2 energy: E = mneutron · v 2 = k2 = · ω 2 2mneutron 2π · h neutron wavelength: λneutron = = mneutron · v mneutron · v 3950 ˚ (A), or ≈ v momentum: mneutron · v = p = · k =

(8.8)

where k is the wave vector, mneutron is the neutron mass given in 939.56 MeV/c2 , = h/2π = 6.58212 × 10−22 (MeV s), and λneutron in A˚ is the wavelength of the neutron given by its momentum. With the formulas given in Eq. (8.8) the wavelength of the neutron can be written in a abbreviation form of Figure 8.15 considers the basic ingredients of a neutron scattering experiment [654, 655]. A

8.3 The Spallation Neutron Source Facility

Neutron scattering experiment Detector bank Pulsed source from moderator

ki ,

ki ,

Ef

L2 Scattered neutrons

Ei L1 Sample

With the scattering triangle kf

Scattering direction Q,w

Beam direction

2q ki

Fig. 8.15 The principle of a neutron scattering experiment with the use of low-energy neutrons to analyze the structure of a matter.

neutron scattering event can be described by six independent parameters for the initial k initial (kx , ky , kz ) and ﬁnal neutrons k ﬁnal (kx , ky , kz ) with the energy E as a function of k . The function Q is known as the scattering vector depicted in the scattering triangle given in Figure 8.15. It represents the momentum transferred to the sample with the momentum conservation Q = k i − k f . Thus, a neutron spectrometer must be able to determine the k i , k f . A neutron scattering experiment measures the number of scattered neutrons as a function of (Q , ω). The parameter space is 4D. The intensity or number of scattered neutrons is proportional to the scattering function S(Q , ω) which depends only on the sample and not on the neutron spectrometer. The scattering function S(Q , ω) gives information about the structure of the sample, whereas the variable ω gives information about the dynamics or motion as elastic, quasielastic or inelastic depending of the momentum Q transferred to the sample by the interacting neutrons. Figure 8.15 illustrates the principle of a neutron scattering experiment. In both elastic and inelastic scattering events, the neutron is scattered through the angle 2θ , Figure 8.15. For elastic scattering, the scattering vector Q can be calculated by the following simple trigonometry relation:

sin θ =

Q/2 k

Q = 2k · sin θ =

4π · sin θ . λ

(8.9)

275

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8 The Basic Parameters of Spallation Neutron Sources

kf kf

Q

Q

kf

Q

ki ki

ki ki = kf

ki > kf

ki > kf

w=0

w>0

w>0

Elastic scattering

Inelastic scattering (w can vary independly of Q)

Fig. 8.16 The scattering triangles showing the relation between elastic and inelastic scattering.

Comparing elastic versus inelastic scattering the following relations between the wave vector components ki , kf , the momentum Q, and ω are shown by the scattering triangles of Figure 8.16. The energy conservation is given by the following relation: Eneutron = −Esample Esample = Einitial − Eﬁnal =

2 · (k2initial − k2ﬁnal ). 2m

(8.10)

From the scattering triangles in Figure 8.16 it is shown that in an elastic scattering event in which the neutron is deﬂected, the neutron does not lose or gain energy (so that ki = kf ) and in inelastic scattering events in which the neutron either loses energy (so that ki > kf ) or gains energy (so that ki < kf ) during the interaction, respectively. The issues on moderator neutron performance, moderator technology, research with neutrons and examples on neutron instrumentation for spallation sources are described in the experimental Part 2 and in the application Part 3.

Part II Experiments

279

9 Why Spallation Physics Experiments? 9.1 Introduction

Contributions in the ﬁeld of experimental spallation research have been extended and accumulated in the literature over the past 40 years in a vast but scattered array of publications in journals, conference proceedings, in reports and monographs. The following part overviews the most important experiments in spallation research, which were the driving source for the theoretical understanding of the physics of spallation phenomena and have supported applications and developments of spallation neutron sources, of accelerator technology, of accelerator-driven sources as ATWs or energy ampliﬁers, of detectors for medium- and high-energy particle physics, of space science and astrophysics, etc. The overview given here can only be a selection of some topic experiments, which may be partial to the authors. In the following sections, some arguments are given for the considerable needs to investigate spallation physics by experiments.

9.2 Application-Driven Motivation

Spallation neutron sources for condensed matter research, nuclear transmutation or new concepts for energy production consist basically of a high-energy and highintensity proton accelerator and of target systems or complex target stations for the neutron generation. The spallation neutron sources exploit the thermal excitation of the heavy target nuclei by GeV protons and their subsequent de-excitation by evaporation of neutrons mainly with energies of a few MeV. Typically only 20% of the incident kinetic energy is dissipated in the ﬁrst reaction into intrinsic excitation giving rise to the emission of about 15 neutrons (for 2 GeV protons impinging on a Pb target, as for example). The larger fraction of the energy, instead, is carried off during the initial intranuclear cascade (INC) by a few energetic (hundreds of MeV) particles, mainly nucleons. These cascade and pre-equilibrium particles in turn initiate further nuclear reactions in the extended target, thereby increasing the total number of neutrons created per incident proton to about 40. Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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9 Why Spallation Physics Experiments?

The best proton energy for the accelerator is still subject of some consideration. From a material’s point of view (e.g., radiation damage) it seems advantageous to use higher energies (some GeV) with the beneﬁt of lower currents, which could also be reasonable from the physics point of view, if the neutron production was indeed to grow linearly with incident proton energy. The latter assumption is not unconﬁned true for energies far beyond 1 GeV as already discussed in Section 8.2.4 on page 263. One goal of the experiments is to increase the reliability of the models in the GeV energy range where only few and moreover quite diverging data exist. The economic design and operating of new high-current proton accelerators and spallation neutron sources is strongly dependent on the accurate knowledge of neutron, proton, pion, and radioisotope production data, since these reaction products are on the one hand important for the optimal layout of all the systems and on the other hand cause the main technological problems related to shielding, radiation damage, safety, and maintenance aspects. More speciﬁcally, it is the aim to accomplish spallation physics experiments for various proton energies in the range from 0.2 up to several GeV to investigate, e.g., • the double differential production cross sections d2 σ/dEd for neutrons, for light particles (p, d, t, and He isotopes), and residual spallation products and their radioactive species of target, window, and structural materials (cf. Section 10.2 on page 288), • the multiplicity distributions of n, p, d, t, and He from the nuclear-evaporationcascade production (cf. Section 10.3.2.2 on page 342), • the neutron multiplication in thick targets, e.g., neutron leakage multiplicity distributions and total inelastic cross sections for ‘‘thick’’ targets of various dimensions, where the incident energy is converted as efﬁciently as possible into neutron production yield (cf. Section 11 on page 379), • the heat deposition and induced radioactivity in targets and structural materials (cf. Chapter 11 on page 379), • the features and the neutron behavior of ambient temperature water moderators and advanced cold moderators (cf. Chapter 13 on page 431), • the efﬁciency of shielding in particular for high-energetic neutrons (cf. Chapter 15 on page 481). The experimental efforts contribute to the increasing conﬁdence and in ﬁxing the parameters in the nuclear models currently available. Recently at an international conference on nuclear data for science and technology, an overview about the progress in nuclear data accelerator applications and accelerator-based facility design was given by Goldenbaum [656] and Takada [657]. 9.3 Space Science and Astrophysics-Driven Motivation

Spallation reactions are also important from an astrophysical point of view (cf. already discussed in Section 1.2 on page 5). A large variety of stable and radioactive

9.4 Nuclear Physics Driven Motivation

nuclides is produced by the interaction of cosmic rays and solar particles with extraterrestical matter. To interpret these cosmogenic nuclides in lunar samples, in meteorites, in cosmic dust, and in dense matter, a detailed knowledge of the cross sections of the respective nuclear reactions is necessary. The basic experiments are the measurement of integral excitation functions and depth-dependent radionuclide proﬁles induced by protons and alpha particles in matter. Experiments can be performed at proton accelerators considering proton energies similar to the energies of the cosmic or solar ray spectrum incident on targets of matter made of elemental compositions identical to extraterrestical matter. Also the measured induced radioactivity in various spacecraft components provides information on the radiation exposure and about single-event-effects (SEE) concerning materials damage in space electronics. The simulation of shielding experiments concerning cosmic ray energies and particle spectra at proton accelerators can be used as part of the safety considerations in the design and operation of long-term space missions, e.g., manned missions to Mars. Experiments in the ﬁeld of cosmogenic nuclide production and space science are discussed in Chapter 23 on page 653. Spallation reactions and experiments are in addition also important from another astrophysical point of view. Due to their low binding energies Li, Be, and B nuclei are highly unstable especially at temperatures and pressures encountered during stellar nucleosynthesis. The experimental determination of the spallation cross sections for C, N, and O targets will provide a valuable data set to improve the understanding of the anomalous abundance of light elements in the cosmic rays and astrophysical questions of nucleosynthesis of the light nuclei in general. As for example the abundance of Li, Be, and B in cosmic rays is only several times smaller than the abundance of neighboring nuclei C, N, and O, whereas this abundance is 5–6 orders of magnitude smaller when observed in the solar system (the ‘‘LiBeB puzzle’’) (cf. Section 1.2 on page 5). However, to account for all details of the relative abundances of all isotopes on the ground of astrophysics models it is required to thoroughly test their predictions. Therefore, not only the values of the total production cross sections, relevant in the context of the abundance problem have to be determined experimentally, but also the energy distributions should be known precisely enough to allow checking of the applied models. The experiments described in Chapter 23 on page 653 are an approach to ﬁll this serious lack of such data in the intermediate energy range.

9.4 Nuclear Physics Driven Motivation

Properties of hot nuclear matter can not be described by elementary nucleon– nucleon scattering, because even knowing the hadronic interactions the solution of the many-particle system would cause serious problems for heavy nuclei. Instead generally matter is described by macroscopic observables like temperature, density, and pressure. For inﬁnite nuclear matter, the relation between thermodynamic observables pressure, energy, density ρ, and temperature T is given by the equation

281

282

9 Why Spallation Physics Experiments?

of state [190]. Except of the saturation density ρ0 and the energy at this density the form of the equation is not well understood. When expressed in form of a caloric equation of state the energy EB per Baryon is written as EB = E(ρ, T) = ET (ρ, T) + EC (ρ, T = 0) + E0 (ρ = ρ0 , T = T0 ), A

(9.1)

with the thermal energy ET and the compression energy EC taking the dependency on ρ and T into account and E0 reﬂecting the energy in the ground state. The relation between the equation of state and the mean nuclear potential U is expressed by the kinetic energy density tv and the density of the total energy hv : EB /A = hv /ρ ∂ (hv − tv ). The equation of state for nuclear matter gives, e.g., insights and U = ∂ρ in phase transitions. At low density (ρ < ρ0 ) and high T due to the superposition of nuclear and Coulomb forces, nuclei can coexist in liquid and gaseous phase analogous to the Van-der-Waals gas. For extremely high T and ρ a quark–gluon plasma is expected. In this new phase of nuclear matter the quarks are supposed to be (quasi-)free. With the energies typically discussed in spallation reactions in this book (few GeV), neither T nor ρ of such high-density phases is approached and the nuclear matter in the form of an ensemble of A nucleons is neither inﬁnitely expanded nor to be reduced to nucleon–nucleon interactions. However, also on the way to this high-density phase numerous interesting phenomena exist. The nuclear physics aspect concerns the decay modes (as being discussed in Chapter 3) of very highly excited nuclei and has been intensively investigated during the last decade mostly with heavy-ion accelerators – with moderate success, however. At high excitation energy one expects more diverse decay modes than evaporation and ﬁssion (Section 3.7) to become accessible to the nucleus: multibody fragmentation (Section 3.10) with the emission of many intermediate-mass fragments (IMF), and, when the excitation exceeds notably the binding energy of the nucleus, also even more violent vaporization (Section 3.10) into single nucleons and light nuclei not heavier than alpha particles (complete disintegration of the nuclei into light fragments). In the past heavy-ion collisions in the energy range of up to several 100 MeV/A have often been investigated [658–660] and new decay phenomena or novel and relatively scarce modes have indeed been observed. These exotic modes might be due to the unique feature of nuclear matter – namely the superposition of short range nuclear forces and extremely long ranging Coulomb forces. However at the same time these modes represent the superposition of statistically and dynamically driven fragmentations. Also the exact deﬁnition of the decaying source from the correct theoretical description point of view is rather ambitious. These phenomena raise a variety of open questions: Is the multifragmentation driven by thermal excitation of the nuclei, by repelling Coulomb forces or by deformations and high spins? The interpretation of these sequential or possibly simultaneous decay modes requires a clear distinction of statistical and dynamical fragmentation. The driving forces for these fragmentations still remain obscure,

9.4 Nuclear Physics Driven Motivation

because too many dynamic distortions are inevitably introduced by the heavyion reaction together with the thermal excitation, like large angular and linear momenta, density compression or the formation of peculiar unstable noncompact shapes. Reactions with protons, instead, are much less likely to induce collective excitations in the target nucleus and may thus allow to come closer to what is called statistical fragmentation: the decay of a compound nucleus stocked with purely thermal and equilibrated excitation. The knowledge of these purely statistical decay mechanisms is a prerequisite or key to the understanding of the more complicated effect of collective excitations on the fragmentation. Fundamental properties of hot nuclear matter like heat capacity, speciﬁc heat, viscosity and phase transitions are by far not thoroughly explored. Since in this kind of reactions a minimum of compression to the nucleus is induced, the experimental investigation of Eq. (9.1) is enabled for high T at densities ρ ≈ ρ0 . In order to reduce the inﬂuence of the entrance channel on the decay modes also the nuclear excitation following annihilation of energetic antiprotons has been investigated as will be illustrated in Chapter 12 on page 425. Detailed discussions on antiproton-induced reactions can also be found in Refs. [379, 661–670]. In short, antiprotons annihilate on a single nucleon at the surface of, or even inside the nucleus, thereby producing a pion cloud containing an average of about ﬁve particles. Due to the high center-of-mass velocity (βc.m. ≈ 0.6 in GeV antiprotoninduced reactions) of this cloud it is focused forward into the nucleus. Since the pion momenta are comparable to the Fermi momentum of the nucleons in the nucleus, the pions heat the nucleus in a soft radiation-like way [671], even softer and more efﬁcient than in proton- or other light-ion-induced spallation reactions, which have also been exploited recently for this purpose [114, 219, 622, 672–675]. Due to the small radius of interaction volume of 1.8 fm and a coherence length of cτ ∼1.5 fm in elementary NN annihilation reactions extremely high local energy densities are obtained. For antiproton-induced reactions, INC calculations have been found to provide a reasonable description of the underlying mechanism. They predict that the spin remains low (below maximum 25) and that shape distortion and density compression are negligible [676], in contrast to what is expected in heavy-ion reactions. The reaction time for the achievement of equilibrium conditions is only about 30 fm/c or 10−22 s [169], which is much shorter in general than the dynamical period in heavy-ion reactions [677]. This is all the more important at high temperature (T ≈ 6 MeV) when the characteristic evaporation time reduces to t < 10−22 s, implying little cooling of the compound nucleus during heating. Summarized light-particle-induced reactions – and therefore also protons generally employed in spallation reactions – represent the softest way of producing hot nuclei with the advantage of: • small compression and shape distortions; • small transfer of linear and angular momenta; • good deﬁnition of mass and charge of the decaying compound nucleus;

283

284

9 Why Spallation Physics Experiments?

• fast excitation (much faster than nonrelativistic heavy- ion collisions. Therefore, only little cooling during the formation of the hot nuclei). • existence of reliable reaction models. From previous experiments at Saturne/Saclay [678] (cf. Section 10.2.2.1) and at LEAR1) /CERN2) [379, 663] it is known on the other hand that light projectiles are less effective in energy dissipation than heavy ions and that therefore even with, e.g., the maximum energy at COSY, 2.5 GeV, only about 1000 MeV of excitation with reasonable cross section in heavy target nuclei and somewhat less excitation (but higher temperatures) in lighter nuclei (cf. Chapter 10) is reached. Thus ﬁssion and evaporation in heavy ﬁssile nuclei and the new fragmentation phenomena, or rather their onset, in lighter nuclei can be explored. Even the conventional decay modes, evaporation and ﬁssion, studied as function of excitation energy become new territory above 200 or 300 MeV of excitation: First, the occurrence of ﬁssion up to about 1000 MeV of excitation indicates, by its slow collective nature, that the nucleus has survived this tremendous excitation as a self-bound system which moreover has reached thermal equilibrium [379, 663, 665]. Beyond that, from the competition with the faster and well-known particle evaporation a time scale can be established for ﬁssion (and this separately for the motion from equilibrium deformation to the saddle point and from the saddle to scission) [62, 381, 403, 665]. This ﬁssion time is related to one of the basic properties of nuclear matter, the nuclear viscosity or dissipation (cf. Section 3.7). The multifragmentation or vaporization phenomena can be observed in lighter nuclei like Cu or Ag [670]. Here it seems important not only to observe the phenomena and deduce a probability or cross section as a function of E ∗ for them, as has been mostly done in the past, but also to specify the phenomena more closely. In this respect, a particular advantage of the NESSI-charged particle detection system described in Chapter 10 can be exploited, namely that it registers not only light particles and lighter fragments (IMFs), but also all heavier residues from each reaction. This allows to built a complete mass- and linear-momentum balance for each reaction and thereby to test the completeness of the multifragmentation process. The need for complete measurements of IMFs at these energies is emphasized by the lack of data measured at incident proton energies below 1 GeV. Drawing conclusion on features of nuclear matter from experimental observations is possible only by an intense comparison between the experiments and the theoretical descriptions. Only using theoretical models assumptions concerning nuclear matter and their inﬂuence on observables can be tested. Furthermore, models provide to some extent an insight into the dynamics of processes which is generally scarcely or not possible with the ‘‘static’’ observables accessible in the experiments. Therefore, the primary intention of the experimental investigation in nuclear physics is to provide exclusive data rather than only to improve the database of 1) LEAR – Low- Energy-Antiproton-Ring.

2) CERN – Centre Europ´een pour la Recherche Nucl´eaire, European Laboratory for Particle Physics.

9.4 Nuclear Physics Driven Motivation

inclusive cross sections. With these exclusive data it is possible for instance not only to reconstruct for each initiated reaction the distribution of the deposited thermal excitation energy [663], but also to investigate pre-equilibrium emission for peripheral and central collisions. This in turn allows to test a variety of critical model parameters (cf. Chapter 3) which, e.g., determine the equilibration point after the fast intranuclear cascade stage and deﬁne the transition from the INC model to an evaporation model for the statistical decay of the equilibrated nucleus (cf. Section 2.3.1.7).

285

287

10 Proton-Nucleus-Induced Secondary Particle Production – The ‘‘Thin’’ Target Experiments 10.1 Introduction

With the advent of the ﬁrst spallation neutron sources KENS at KEK, Japan [644, 679], at IPNS at ANL, USA [641], at LAMPF-WNR at LANL, USA [680], and the high-intensity spallation source project SNQ J¨ulich/Karlsruhe, Germany [142] however, much more strong constraints to the quality and accuracy on spallation reaction data, especially on differential cross-section data, are required to consider the performance of the design parameters. In the context of new sources with high beam intensity, which are built, constructed and planned e.g. SINQ, Switzerland, [627], SNS, USA [681], J-PARC, Japan [629], ESS, Europe [480, 551], numerous projects for accelerator-driven systems (ADS) [483, 682], and high-power targets, e.g., EURISOL [683] more accurate data and a more detailed description of the underlying particle reaction processes are needed [656]. Recently a new neutron facility – the n TOF facility – became available at CERN, Switzerland, well suited for high-quality measurements for capture and ﬁssion data for fertile and ﬁssile isotopes for ADS applications. The n TOF facility produces intense neutron beams with a wide energy range of 1 eV to 250 MeV by spallation of a 20-GeV proton beam from the CERN-PS accelerator on a lead target [684–686]. ‘‘Thin’’ target cross-section measurements reduce the uncertainties on the nuclear and other parameters upon which the design and operation of high-intensity spallation sources are based. This demand led to a worldwide effort to extend the experimental database on spallation-induced reactions, e.g., on differential cross sections and multiplicities of neutrons, protons, pions, light charged particles, and residuals nuclei measured over a broad range of target masses, emission angles, and secondary energies well suited to provide a better understanding of the spallation process. Experiments of this kind are called ‘‘code validation experiments’’ using so-called thin targets where the energy loss of the incident proton beam is very small compared to the proton beam energy. The ratio should be of the order Eloss /Eproton ≤ 5%. The produced secondary particles inside the target generally do not undergo further collisions inside the target. In contrast in ‘‘thick’’ targets the energy loss of the incident beam could be large and the produced secondary particles undergo further collisions. These collisions create additional secondary particles and result in an internuclear cascade (INC) (cf. see also Section 1.3.4 on Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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10 Proton-Nucleus-Induced Secondary Particle Production

page 21). The experiments presented in the following section are considered to be a representative selection of ‘‘thin’’ target measurements, although they reﬂect only a small selection of the numerous investigated ones. Thick target measurements will be discussed in Chapter 11.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

Above the pion production threshold the majority of existing differential data are charged particle data, which experimentally are easier to detect than neutrons. The detection of neutrons with kinetic energies above several 100 MeV is not trivial caused by the low efﬁciencies and low time resolutions of suitable detector systems. Until 1980, secondary double-differential neutron measurements at incident proton energies above 100 MeV were rather scarce and cover only a few points in the double-differential scale [125, 126, 687–690]. More systematic studies and measurements were started as part of a study project for the SNQ spallation source [142] by Cierjacks et al. [691] at the PSI cyclotron in 1981. The publication and the controversial discussion concerning the high-energy resolution of these measurements (cf. Refs. [127, 128, 692] led then to a collaborative effort between LANL, Los Alamos, USA, and the research center J¨ulich, Germany, to measure systematically double-differential neutron-production cross sections of various targets between 0.1 and 0.8 GeV at the Los Alamos LAMPF-WNR facility during 1984–1990. A second research program concerning neutron double-differential production at incident beam energies higher than 0.8 GeV was started at the SATURNE accelerator in France, mainly as a collaboration between Bruy`eres-le Chˆatel, SATURNE, Saclay (DAPHNIA), France, and the Uppsala University, Sweden in 1994 [693]. Incident protons and deuterons on different thin target in an energy range between 0.8 and 1.6 GeV were used. The main aim of these investigations was to measure neutron-production cross sections for ADS applications. In addition, during 1995–1998 at the 12 GeV proton synchrotron of KEK, Japan, double-differential neutron-production measurements at incident proton energies from 0.8 GeV up to 3.0 GeV were measured for various targets for applications concerning the design and development of the 3 GeV spallation neutron source at J-PARC in Japan [265, 694] currently being commissioned. There are only few experiments where pion double-differential cross sections in proton–nucleus collisions were measured, which are useful to validate spallation reaction models. This early measurements were originally accomplished to provide sufﬁcient data to allow the optimal design of secondary pion and muon beams at three proton beam ‘‘pion factories’’ as LAMPF, USA, TRIUMPF, Canada, and SIN (now PSI), Switzerland, during 1970–1980. Measured charged pions produced by incident proton energies of 0.585 GeV and 0.730 GeV on various thin targets were reported by Crawford et al. [695] and by Cochran et al. [124].

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Start time t0

Stop time tL

Neutron kinetic energy En

L t = tL - t0 = time to traverse distance L

Fig. 10.1 The kinetic energy Eneutron of the neutron is measured by the stopping t to traverse the ﬂight path of length L.

10.2.1 The Double-Differential Neutron-Production Measurements at the LAMPF-WNR Facility

During the years 1984–1990, a physics program was implemented to measure double-differential neutron-production cross sections at the Los Alamos LAMPFWNR time-of-ﬂight (TOF) facility [680] of various targets up to incident proton energies of 800 MeV. The principle of high-energy TOF measurements of neutrons will be described and the application of this method to measure high-energy neutron-production cross sections will be demonstrated. The principle of the TOF method for relativistic velocities β = v/c is given in Figure 10.1. The kinetic energy of the neutron is measured by stopping the time t to traverse the ﬂight path of lengths L. The kinetic energy Eneutron is then derived using relativistic kinematics by the formula (10.1) Eneutron = m ·

= 939.6 ·

1

1 − β2

−1 1

1 − 11.13[L2 /t2 ]

−1 ,

(10.1)

where Eneutron is given in (MeV), L in (m), the time t in (ns), and m = 939.6 MeV/c2 the mass of the neutron. The relativistic expression of Eq. (10.1) is required above approximately 10 MeV as Figure 10.2 demonstrates. Also from Figure 10.2 it follows that there is certainly a limitation to the TOF method at high energies. For neutrons this is in the several GeV kinetic energy region, where the speed of a neutron is almost same as the speed of light. As an example, typical ﬂight times – as inverse velocities – are 102.286 ns/m at 0.5 MeV, 23.045 ns/m at 10 MeV, and 3.964 ns/m at 800 MeV. The time scale in the experiments is calibrated against the arrival of the prompt gamma ﬂash produced by the incident protons from the target. The inverse speed of light is 3.336 ns/m. For neutrons, the start time has to be taken from the accelerator pulse arrival because neutrons have to be detected by nuclear recoils produced in the

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10 Proton-Nucleus-Induced Secondary Particle Production

104 Non relativistic

102 101 100 10−1

100 10 1 7.8

1

23.0

10 Inverse speed [ns/m]

72.4

103 Inverse speed of light

Kinetic energy [MeV]

290

100

Fig. 10.2 The kinetic energy of a neutron versus its inverse speed. The inverse speed of light is 3.336 ns/m.

detector and, therefore, change their energy by the method of detection. Generally organic scintillators are used as stop detectors with hydrogen-to-carbon ratios of approximately one. In these detectors, neutrons are detected by proton recoils, predominantly at the lower energies, or by inelastic reactions with carbon nuclei. The used detectors are given in Tables 10.3 and 10.4 on pages 297, respectively. Because the slowest neutrons from one initiating process could be mistakenly identiﬁed as fast neutrons in the following initiating process, the time spacing between two successive beam bursts has to be long enough to eliminate such misidentiﬁcations. For organic scintillation detectors, the practical lower limit of detection is approximately 0.5 MeV which is just above a typical photomultiplier equivalent noise. From this the micropulse spacing required follows as 102.286 ns/m times the length L of the ﬂight path, i.e., approximately 1 µs per 10 m. Employing the experimental uncertainties in total time and ﬂight path uncertainty, the fractional energy resolution of the TOF method can be estimated by the following approximate formula [127]: Eneutron = γ · (γ + 1) · [(L/L)2 + (t/t)2 ]1/2 , Eneutron

(10.2)

where γ = 1/(1 − (v/c)2 )1/2 is the Lorentz contraction factor, and L and t are the ﬂight path length and the neutron ﬂight time, respectively. At nonrelativistic energies γ ∼ 1, the energy resolution is two times the time resolution for (L = 0) and at high relativistic particle energies, the resolution is quadratic in energy. 10.2.1.1 The Time-of-Flight Experiment at the LAMPF-WNR Facility Looking at the accelerator-speciﬁc needs for high-energy neutron TOF experiments, the Los Alamos WNR facility is unique in the world because all requirements as the beam intensity and beam time structure are met. An artist’s view of the WNR facility is shown in Figure 10.3. Proton pulses are accelerated in the LAMPF linear accelerator up to an energy of 0.8 GeV. A certain part of the beam is diverted by a

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

Los Alamos National Laboratory WNR Facility 4 3

6 2 1

5

1. High-current target area 2. Low-current target area 3. Proton storage ring 4. Control/data center 5. Neutron time-of-flight path 6. Proton beam from LAMPF Fig. 10.3

5

7

An artist’s view of the WNR facility (Courtesy LANL).

set of kicker magnets down to the WNR area and handed over to the WNR control system (cf. Figure 10.3 label 6). The beam is then transported to the low current target area (label 2 in Figure 10.3) for the high-energy neutron TOF experiments. The characteristics of the proton beam for TOF experiments at the WNR Figure 10.4 shows, in general, the beam structures of the LAMPF accelerator and the WNR macropulses and micropulses. The LAMPF accelerator delivers of macropulses 800 µs in length at rates up to 60 Hz and consists a series of micropulses separated by 5 ns [696]. Each macropulse contains up to ∼ 1.6 × 105 micropulses. These macropulses are repeated at a rate of 120 Hz. Each micropulse has a full width at half maximum (FWHM) of about 80 ps at LAMPF accelerator but is broadened to approximately 180–200 ps at the WNR facility. For the neutron TOF experiments, a low-energy chopper has to be used to select micropulses separated by 12 µs, which prevents frame overlap at the longest ﬂight path for neutrons above a 250 keV minimum energy. By using this fast chopper located in the injector area of LAMPF accelerator individual micropulses can be selected out of the LAMPF accelerator macropulse for individual applications. Separation between micropulses can be as short as 1 µs over the duration of the LAMPF accelerator macropulse. The chopped macropulses can be repeated at a rate up to 12 Hz or 40 Hz recurrence suitable for neutron energies of 0.256 or 0.8 GeV. The maximum average repetition rate is approximately 8.4 × 103 micropulses per second with 2–3×108 protons per micropulse, corresponding to approximately 40–250 nA. The TOF experimental area Figure 10.3 illustrates the details of the WNR TOF experimental area and the arrangement of different components. The target area is a 12-m diameter dome-shaped room (label 2 in Figure 10.3), which provides a

291

292

10 Proton-Nucleus-Induced Secondary Particle Production

80ps

5ns 800 µs

LAMPF macropulses – 120 Hz

81 3 ms

Time [ms]

WNR macropulses – 12 Hz

83 1 3 ms Time [ms]

~200ps

≥1µs

800 µs

WNR micropulses structures Fig. 10.4 The beam structure of the LAMPF accelerator and the beam pulse structure used for the TOF experiments.

low-scatter environment with a minimum distance of approximately 5.5 m from the central target location to the nearest shield wall. Shielding is provided by a 14-m thick compacted tuff wall surrounding the experimental area. The beam stop is embedded into the tuff wall. Six ﬂight paths could be used and penetrate the shield wall to allow angular distributions to be measured at 7.5◦ , 15◦ , 30◦ , 60◦ , 120◦ , and 150◦ . The detector stations are setup outside allowing ﬂight path lengths of at least 60 m. Full details of the experimental setup are shown in Figure 10.5. A detailed description is as follows. The proton beam is transported to the center of the experimental room where the target is located. On its way, the arrival is signaled in a capacitive time pickoff. The

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

150°

Proton beam

Target

60°

A B

A-E:Filters NeutronC collimator

Time pickoff Secondary Electron monitor Charged particle Collimator Charged particle Sweep dipoles 1kG

120°

D

15°

Compacted tuff

Beam stop

7.5

E

30°

Detector station with veto and neutron detector

Fig. 10.5 The experimental layout of the high-energy neutron TOF experiments at Los Alamos (after Howe [690]).

total charge applied of the proton beam to the target is measured using a secondary emission monitor (SEM). The principle plan view of the arrangement of the neutron TOF lines is shown in Figure 10.6. For most of the experiments the beam lines with 30◦ , 60◦ , 120◦ , and 150◦ are used, whereas Stamer and Scobel et al. [131] experienced measurements in addition with the ﬂight path under 7.5◦ with incident proton energies of 0.256 and 0.8 GeV. The cylindrical tubes of the ﬂight paths have roughly a diameter of 75 cm to minimize the number of in-scattered neutrons. Their clearance assured that all neutrons produced by the target would be seen by the neutron detectors.

293

294

10 Proton-Nucleus-Induced Secondary Particle Production

7.5° detector station 50 m 30° detector station 30 m Collimation

120° detector station 60 m Collimation

60° detector station 60 m Target

Protons from LAMPF 150° detector station 60 m Fig. 10.6 The principle plan view of the arrangement of the neutron TOF lines with their distance to the target. The locations of the target in the center and the collimators are also indicated.

The secondary emission monitor SEM (cf. Figure 10.5) is calibrated by measuring its rate relative to the production of 27 Al(p,3pn)24 Na, 27 Al(p,x)22 Na, and 27 Al(p,x)7 Be in irradiating Al foils located at the target position. The dominant uncertainty in this calibration is about 5% cross sections uncertainty for the production of Na. The total uncertainty in the number of protons normalization turns out to be less than 7%, whereas the relative error of the calibration is about 1%, consistent with the TOF system stability [129] and the statistics of counting the calibration foils. Behind the target a collimation system deﬁnes the neutron beam in a quasi open geometry. In this system two sets of collimators are separated by a few meters. The ﬁrst collimator is the charged particle collimator of 50 cm thickness, 1.3 m away from the target. Its aperture is wider than the following neutron collimator, so its surface is not seen by the neutron detector. The charged particle collimator serves to produce a given charged particle beam spot diameter between the poles of the following of the charged particle sweep or clearing magnet which has approximately a 0.1 T magnetic ﬁeld strength of length 1 m (SmCo permanent magnets). The following neutron collimator is 2.4 m thick. Its aperture deﬁnes the neutron beam in such a way that the neutron beam spot at the detector station is larger than the detector, but smaller than the beam pipe diameter to prevent small-angle scattering of neutrons into the detector by the material surrounding the pipe. The design of the shielding between detector and target consists of a 0.5-m concrete wall of the target room and a 14-m compacted tuff wall as indicated in Figure 10.5. Table 10.1 summarizes the parameters for the ﬂight-path collimators and used ﬁlter systems used for the beam lines of 30◦ , 60◦ , 120◦ , and 150◦ . Uranium ﬁlters were inserted into the ﬂight paths to scatter energetic charged particles out of the beam by successive small-angle scattering. Neutrons interacting

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Parameters of ﬂight paths, collimators, beam diameter at detector, and uranium ﬁlter [130].

Tab. 10.1

Scattering angle Flight path length (m) Target to collimator distance (m) Collimator aperture (cm) Beam diameter at detector (cm) Beam/detector solid-angle ratio Iron collimator thickness (cm) Uranium ﬁlter (nuclei per mb)

30◦ 28.71

60◦ 58.46

120◦ 23.19

150◦ 30.22

4.80 8.52

4.80 6.95

12.00 7.95

4.80 9.64

25.66

27.86

10.63

33.79

40.06

23.61

6.87

69.49

209.60

248.90

335.28

188.00

138.42

87.69

87.40

1.52

Tab. 10.2 Examples of experimental typical uncertainties for the TOF experiment to measure double-differential production cross sections for 597 MeV protons as given by Amian et al. [130].

Correction Time-dependent background Target-produced background Shadowbar-background Air transmission Uranium transmission < 20 MeV Uranium transmission > 20 MeV Detector efﬁciency Live time Charge normalization

Magnitude

Uncertainty (%)

< 0.01 < 0.05 < 0.08 > 0.45

<5 20 <3 < 2.5

> 0.32 > 042 0.03–0.20 > 071 1.0

5 < 20 5–20 <5 5

with these ﬁlters are removed out of the beam because this effect of secondary neutron production is negligible due to the very small solid angle subtended by the detector. To correct the attenuation effects, the transmission of uranium ﬁlters with a polyethylene wrapping was measured between 1 and 800 MeV neutron energy and the corresponding attenuation cross sections generated. The experimental uncertainties are summarized in Table 10.2. Figure 10.7 gives the energy resolution in percent for a 30-m ﬂight path versus energy with the time resolution as the parameter. The experiments at the WNR had ﬂight paths of 30–60 m and time resolutions of better than 200 ps. From Figure 10.7, the worst energy resolution of less than 1% follows. In practice, the TOF method is limited by accelerator-speciﬁc considerations like beam structure and instantaneous beam intensity, by the time jitter related to the response of the

295

10 Proton-Nucleus-Induced Secondary Particle Production

102 Energy resolution in % per 30 m flight path

296

TOF resolution

101 100 10−1

1000 400 200 100 ps time resolution

10−2

800 MeV

10−3 10−1

100 101 102 Neutron energy [MeV]

103

Fig. 10.7 The neutron energy resolution of the TOF method for a 30-m ﬂight path length. The time resolution is introduced as a parameter.

neutron detection system and the time spread associated with the thickness of the detector itself. For instance, for a typical 2 thick detector the best time resolution, that can be attained is 200 ps at a neutron energy of 800 MeV and of a ﬂight path length of 30 m. This is because of the point of interaction, and, therefore, the total ﬂight path length, is uncertain within the detector thickness. In Figure 10.7, the uncertainty in the ﬂight path length is assumed to be zero. But note, however, that the thickness of the neutron detector corresponds to such an uncertainty, which has to be included. The used detectors, energy resolutions and ﬂight path timing Different detector systems were used by different groups to accommodate with different neutron energies from 113 MeV up to 800 MeV, different ﬂight path lengths, and scattering angles at the WNR TOF facility. The detectors used in the experiments by Amian and Meier et al. [129, 130, 696–698] are the following: For all incident proton energies of 116, 256, 597, and 800 MeV cylindrical BC-418 plastic scintillators with a diameter of 5.08 cm were used. Depending on the ﬂight path length, the incident proton energy and the maximum neutron energy different detector length as 5.08 cm or 2.54 cm were used. The longer ﬂight paths required a length of 5.08 cm. The detectors were machined from the BC-418 scintillator (Pilot U), which has a density of 1.032 g/cm3 and a hydrogen-to-carbon ratio of 1.100. Neutrons were incident perpendicular to the cylindrical axis of the detector. Thin plastic scintillators with a thickness of 0.3 cm at a 10 cm distance from its center were placed in front of each detector and were operated in veto coincidence to prevent charged particle contamination in the neutron TOF spectra. Table 10.3 summarizes the detector characteristics, the ﬂight path timing, and the energy resolutions as derived from the gamma ﬂash assigned to different ﬂight paths. The parameters for the 800-MeV incident proton

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

297

Neutron detector data of the experiments at the WNR by Amian et al. [130] at incident proton energy 597 MeV (ﬂight path timing and energy resolutions).

Tab. 10.3

Flight path Flight path length (m) Material dimension Diameter × thickness (cm) Energy/time resolution FWHM in %/ns at 597 MeV Incident protons Maximum neutron energy (MeV)

30◦ 28.71 BC-418

60◦ 58.46 BC-418

120◦ 23.19 BC-418

150◦ 30.22 BC-418

5.08 × 2.54

5.08 × 5.08

5.08 × 2.54

5.08 × 2.54

8.2 MeV 2.3 ns

4.7 MeV 3.1 ns

7.3 MeV 2.3 ns

5.2 MeV 2.6 ns

600

500

400

300

Tab. 10.4 Neutron detector data of the experiments at the WNR by Stamer et al. [131] at incident proton energies of 256 and 800 MeVa .

7.5◦ 50.36 BC-501

30◦ 29.76 NE-213

60◦ 58.61 BC-501

120◦ 23.34 BC-501

150◦ 30.99 BC-501

25.4 × 5.1

10.2 × 10.2

30.5 × 20.3

25.4 × 5.1

30.5 × 20.3

Energy/time resolution at 256 MeV Incident protons (ns)

16 MeV 5.8

16 MeV 53

15 MeV 6.5

29 MeV 4.9

26 MeV 5.9

Energy/time resolution at 800 MeV Incident protons (ns)

22 MeV 1.1

36 MeV 1.0

49 MeV 2.7

164 MeV 3.6

72 MeV 2.1

Flight path Flight path length (m) material Dimension Diameter × thickness (cm)

a The H/C-ratios are for the NE-213 detector material 1.213 and for the BC-501 detector material 1.287.

experiments are similar. The overall neutron detection efﬁciency of the plastic scintillator detector was determined to an accuracy of ≤ 20% [699, 700], which has to be taken into account to generate absolute cross sections. The detectors used in the experiments by Stamer and Scobel et al. [131] are given in Table 10.4 assigned to different ﬂight paths. Several experiments were performed for the efﬁciency calibration of the cylindrical BC-418 plastic neutron detectors with a diameter of 5.08 cm and a length of 5.08 cm for monoenergetic neutrons of 30, 55, 90, 140, and 200 MeV [699] at the IUCF beam swinger facility [701] using a 43.5-m long ﬂight path and at neutron energies between 135 and 800 MeV [700] at the LAMPF-WNR facility carried out at 241 m long ﬂight path [680]. Also Howe et al. [702] have studied the efﬁciency

10 Proton-Nucleus-Induced Secondary Particle Production

0.14 Van de Graaff data 0° Pb(p,n) Bonner data 0° 7Li(p,n) 7Be(g.s. + 0.43 MeV) Cecil et al. code

0.12 0.10 Efficiency

298

0.08 0.06 0.04 0.02 0.00

1

10 100 Neutron energy [MeV]

Fig. 10.8 Efﬁciency of the cylindrical BC-418 plastic neutron detectors with a diameter of 5.08 cm and a thickness of 5.08 cm used for TOF experiments at the LAMPF-WNR facility. The triangles are data generated by a Van de Graaff accelerator, the open circles

1000

are obtained from the 7 Li(p, n0−1 )7 Be reaction, the solid circles are data from Bonner et al. [689], and the solid line is the result of calculations with the Monte Carlo model of Cecil et al. [703]. All data are taken from [700].

behavior of organic scintillators of NE-213 material in the same energy range during earlier experiments at the WNR facility [690]. For both energy ranges up to 200 MeV and up to 800 MeV the efﬁciency was determined utilizing monoenergetic neutrons produced by the 7 Li(p, n0−1 )7 Be (ground state + 0.43 MeV) reaction at zero degrees. A comparison with standard Monte Carlo of Cecil et al. [703] up to the energy of 200 MeV agrees fairly well with the measurements. For the energy range from 135 MeV up to 800 MeV an energy-dependent efﬁciency was also determined using published data of the zero-degree differential cross section for the Pb(p, n)-reaction reported by Bonner et al. [689]. This lead to a calibration efﬁciency illustrated in Figure 10.8. It could be seen in Figure 10.8 comparing the efﬁciencies generated using the Pb(p, n) data and those that use the 7 Li(p, n0−1 )7 Be (ground state + 0.43 MeV) reaction a disagreement at energies above 200 MeV. As discussed in Refs. [131, 700] using the reaction 7 Li(p, n0−1 )7 Be (ground state + 0.43 MeV) as reference has the advantage that the L = 0 transition is characterized by a prominent peak at small angles that can be resolved from the continuum in TOF experiments. The good agreement between the Monte Carlo simulation with the model of Cecil et al. [703], a slightly modiﬁed version of the original code, is also supported by the agreement between measured and calculated efﬁciencies by Cierjacks et al. [127]. For the efﬁciency correction at energies above 400 MeV therefore the measurements of the zero-degree 7 Li curve (cf. Figure 10.8) was used.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Tab. 10.5

Measured target materials at the WNR TOF facilitya .

Incident proton energy (MeV)

Target materials

Scattering angle (◦ )

Measurements of Amian and Meier [129, 130, 696–698] 113 (stopping length targets) 256 (stopping length targets) 256 (near, stopping length targets) 597 (thin targets) 800 (thin targets)

Be, C, O, Al, Fe, W, Pb, 238 U C, Al, Fe, 238 U

7.5, 30, 60, 150

C, Al, Fe, 238 U

7.5, 30, 60, 120, 150

Be, BeO, B, BN, C, Al, Fe, Pb, depleted 238 U (> 99.75%) Be, BeO, B, BN, C, Al, Fe, Cd, W, Pb, depleted 238 U (> 99.75%

30, 60, 120, 150

7.5, 30, 60, 120, 150

30, 60, 120, 150

Measurements of Stamer and Scobel [131] 256, 800 (thin targets)

7 Li, 27 Al, nat Zr, nat Pb

7.5, 30, 60, 120, 150

a

All target materials selected are in their natural isotopic abundances, if not otherwise indicated. For oxygen and nitrogen targets of BeO and BN were used, again with their natural abundances. The contributions of the Be and the B spectrum were subtracted.

10.2.1.2 The Experimental Results of Double-Differential Neutron-Production Cross-Section Measurements The measurements and also validations with intranuclear-cascade-evaporation models have been published in journals during 1989–1993 [129–131, 696– 698] and conference proceedings [704–708]. Table 10.5 summarizes the studied target materials selected for incident proton beam energy and scattering angle. For the beam energies of 597 and 800 MeV, all targets caused energy loss of less than 3 MeV to the incident protons (cf. Amian et al. [129, 130] Table 10.6). The speciﬁcations of the thin targets studied by Stamer et al. [131] at proton beam energies of 256 and 800 MeV are also shown in Table 10.6. For the experiments of incident beam energies of 113 and 256 MeV, the target characteristics are given in Table 11.12 and in Refs. [696–698]. Because these targets are stopping-length or near stopping-length targets the neutron-production spectra are related to thick target experiments and will be discussed in Chapter 11 on page 379. The ‘‘thin’’ target cross sections presented here are retrieved from NNDC experimental nuclear reaction database (EXFOR /CSISRS) [709]. The general behavior of proton-induced double-differential neutron-production cross sections is already

299

300

10 Proton-Nucleus-Induced Secondary Particle Production Tab. 10.6 Thin target materials and thicknesses used at the 597 and 800 MeV proton beam experiments.

597 and 800 MeV incident protons (Amian et al. [129, 130]) Target material thickness (g cm−2 )

Be 1.18

BeO 0.85

B 1.00

BN 0.86

C 0.56

Al 1.29

Fe 1.56

Pb 0.89

238 U 0.78

256 and 800 MeV incident protons (Stamer, Scobel et al. [131]) Target material thickness (mg cm−2 )

7

27 nat Li Al Zr nat Pb Thin metallic foils 70–150

discussed in Section 1.3.7.6 on page 54. Some examples of the measurements of Amian et al. [129, 130] at the LANL-WNR facility for incident proton energies of 597 and 800 MeV and C, Fe, Pb, and U targets are displaced in a double logarithmic scale in Figures 10.9 and 10.10. The total uncertainties of the experimental results are determined by ±1σ = 10–15% and thus are of the order of the data point sizes. The cross-section curves are seem to be very much alike. The absolute double-differential cross sections are seen to increase with increasing target mass number and incident proton energy, e.g., from C to U and from 597 to 800 MeV, for all neutron emission angles. Furthermore, the fraction of cascade neutrons in the total emission spectra increases with decreasing mass number for all laboratory angles. In Table 10.7, a subset of the results of Amian et al. [130] is compared with the measurements of Cierjacks et al. [127] for an incident proton energy of 597 and 585 MeV, scattering angles of 30◦ and 150◦ , and targets of uranium, lead, iron, aluminum, and carbon. Figures 10.11 and 10.12 compare cross-section measurements of Amian et al. [130] and of Cierjacks et al. [127] of uranium and lead at a scattering angle of 30◦ . In the ﬁgures the vertical scale uses an energy multiplied cross section, which is equivalent to the cross section per logarithmic energy unit d ln(E). With such a representation discrepancies and agreements between measurements are better illustrated as the commonly used representation in a double logarithmic scale using units of (b sr−1 MeV−1 ]. The error bars depicted in Figures 10.11 and 10.12 on the Amian data are mainly uncertainties due the counting statistics, time-independent and time-dependent backgrounds, whereas the error bars on the Cierjacks data are in general 11% uncertainties referred in [127]. The examples in Figures 10.11 and 10.12 show only an agreement for the evaporation region, whereas at high energies some of the discrepancy might be a result of the short ﬂight paths of the experiments of Cierjacks et al. [127]. These discrepancies are also indicated in Table 10.7.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments 100

100 Eproton = 597 MeV

10−2 10−3 10−4 10−5 10−6 10−7

C - 30° C - 60°

10−8

C - 120° 10−9

Eproton = 597 MeV

10−1 d2s / dΩdE cross section [b sr−1 MeV−1]

d2s/ dΩdE cross section [b sr−1 MeV−1]

10−1

10−2 10−3 10−4 10−5 10−6 10−7

27

Al - 30°

27

10−8

Al - 60°

27

Al - 120°

10−9

C - 150°

10−10

27

Al - 150°

10−10 10−1

100

101

102

10−1

103

Neutron energy [MeV]

Eproton = 597 MeV

10−2 10−3 10−4 10−5 10−6 Fe - 30° 10−7

Fe - 60° Fe - 120°

10−8

Fe - 150°

Eproton = 597 MeV

10−1 d2s / dΩdE cross section [b sr−1 MeV−1]

d2s / dΩdE cross section [b sr−1 MeV−1]

103

100

10−1

10−2 10−3 10−4 10−5 10−6

Pb - 30°

10−7

Pb - 60° Pb - 120°

10−8

Pb - 150°

−9

−9

10

10−10

−10

10

10−1

100

101

102

10−1

103

Reaction proton (597 MeV) + Fe target

100

101

102

103

Neutron energy [MeV]

Neutron energy [MeV] (c)

102

Reaction proton (597 MeV) + Al target

(b)

100

10

101

Neutron energy [MeV]

Reaction proton (597 MeV) + C target

(a)

100

(d)

Reaction proton (597 MeV) + Pb target

Fig. 10.9 Proton-induced experimental double-differential neutron-production cross sections at scattering angles of 30◦ , 60◦ , 120◦ , and 150◦ – measurements of Amian et al. [129, 130]. Each successive curve, starting from the smallest angle 30◦ , is scaled by a multiplication factor of 10−1 , e.g., 60◦ × 10−1 , 120◦ × 10−2 , and 150◦ × 10−3 .

301

10 Proton-Nucleus-Induced Secondary Particle Production 100

100 Eproton = 597 MeV

10−2 10−3 10−4 10−5 10−6 U - 30° 10−7

U - 60° U - 120°

10−8 10

Eproton = 800 MeV

10−1 d2s/ dΩdE cross section [b sr−1 MeV−1]

d2s/ dΩdE cross section [b sr−1 MeV−1]

10−1

U - 150°

−9

10−2 10−3 10−4 10−5 10−6 Fe - 30° 10−7

Fe - 60° Fe - 120°

10−8

Fe - 150°

−9

10

−10

10−10

10

−1

10

0

10

1

10

2

10

10−1

3

10

Neutron energy [MeV]

102

103

100 Eproton = 800 MeV

10−1

d2s / dΩdE cross section [b sr−1 MeV−1]

10−2 10−3 10−4 10−5 10−6

Pb - 30°

10−7

Pb - 60° Pb - 120°

10−8

Eproton = 800 MeV

10−1

Pb - 150°

−9

10−2 10−3 10−4 10−5 10−6

238

U - 30°

238

10−7

U - 60°

238

U - 120°

10−8

238

U - 150°

−9

10

−10

10−10

10

−1

10

0

10

10

1

2

10

10−1

3

10

Neutron energy [MeV] (c)

101

Reaction proton (800 MeV) + Fe target

(b)

100

10

100

Neutron energy [MeV]

Reaction proton (597 MeV) + U target

(a)

d2s / dΩdE cross section [b sr−1 MeV−1]

302

Reaction proton (800 MeV) + Pb target

100

101

102

103

Neutron energy [MeV] (d)

Reaction proton (800 MeV) + U target

Fig. 10.10 Proton-induced experimental double-differential neutron-production cross sections at scattering angles of 30◦ ,60◦ , 120◦ , and 150◦ – measurements of Amian et al. [129, 130]. Each successive curve, starting from the smallest angle 30◦ , is scaled by a multiplication factor of 10−1 , e.g., 60◦ × 10−1 , 120◦ × 10−2 , and 150◦ × 10−3 .

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Energy-integrated neutron-production cross section of thin targets – U, Pb, Fe, Al, C – for an incident proton energy of 597 MeV evaluated by Amian et al. [130] compared with data evaluated by Cierjacks et al. [127] with an incident proton energy of 585 MeV.

Tab. 10.7

Experiment Experiment 597 MeV protons 585 MeV protons Amian et al. [130] Cierjacks et al. [127] target

dσ/d (mb sr−1 ) 0.9–20 MeV

dσ/d (mb sr−1 ) 20–597 MeV

dσ/d (mb sr−1 ) 0.9–20 MeV

dσ/d (mb sr−1 ) 20–585 MeV

Scattering angle 30◦ Uranium Lead Iron Aluminium Carbon

2428.0 ± 64.1 1866.0 ± 71.1 283.9 ± 7.01 129.5 ± 2.4 51.9 ± 3.71

396.0 ± 1 373.0 ± 1 131.3 ± 0.1 81.2 ± 0.1 39.0 ± 0.1

3129.0 ± 255.2 2226.0 ± 178.4 537.5 ± 44.1 198.0 ± 22.2 92.7 ± 7.7

861.0 ± 96 693.0 ± 77 278.2 ± 31.1 146.6 ± 16.4 52.3 ± 5.8

Scattering angle 150◦ Uranium Lead Iron Aluminium Carbon

1420.0 ± 54 1110.0 ± 47 64.0 ± 2.31 27.2 ± 0.41 5.5 ± 1.3

13.7 ± 0.2 14.6 ± 0.3 2.9 ± 0.1 2.0 ± 0.1 0.93 ± 0.1

1685.3 ± 173.7 1147.0 ± 115.8 116.9 ± 10.7 39.7 ± 3.3 11.0 ± 0.93

64.4 ± 7.2 53.5 ± 6.0 10.8 ± 1.2 7.0 ± 0.78 1.83 ± 0.20

10.2.2 The Double-Differential Neutron-Production Measurements at the SATURNE Facility

The double-differential neutron-production measurements at the SATURNE accelerator, France, during 1994–1997, extend the energy of the incident protons up to an energy of 1.6 GeV and made it possible to measure double-differential neutron-production cross sections in an angular range from 0◦ up to 160◦ . A detailed description of the measurements and the different experimental apparatus is given by Leray et al. [132] and in Refs. [220, 710–713]. In the course of the experimental program several different techniques were developed to measure the double-differential neutron production spectra. The slow extraction of the proton beam of the SATURNE accelerator did not allow a TOF method using a highfrequency pulse from the accelerator as used at the Los Alamos WNR experiment. Therefore, two independent methods were used to measure the neutron spectra in the low-energy range 3 ≤ E ≤ 400 MeV (cf. Figure 10.13) and in the high-energy range 200 ≤ E ≤ 1600 MeV (cf. Figure 10.14). Both methods overlap in the energy range of about 200–400 MeV thus providing also a check on their consistency.

303

10 Proton-Nucleus-Induced Secondary Particle Production

Energy x d2s / dΩdE cross section [MeV b sr−1 MeV−1]

1.2 238U (p,xn), 30° Cierjacks et al.

1.0

238U (p,xn), 30° Amian et al. Ep = 585/597 MeV

0.8 0.6 0.4 0.2 0.0 10−1

100

102 101 Neutron energy [MeV]

103

Fig. 10.11 Comparison of measured double-differential cross section of Amian et al. [129] and Cierjacks et al. [127] at a scattering angle of 30◦ for the reactions proton (597 MeV) + 238 U and proton (585 MeV) + 238 U. The vertical scale uses an energy multiplied cross section, which is equivalent to the cross section per logarithmic energy unit d ln(E). 1.2 Energy × d2 s/dΩdE cross section [MeV b sr−1 MeV−1]

304

Pb - 300 Cierjacks et al.

1.0

Pb - 300 Amian et al. Eproton = 585/597 MeV

0.8 0.6 0.4 0.2 0.0 10−1

100

101

102

103

Neutron energy [MeV]

Fig. 10.12 The same as Figure 10.11 but for the reactions proton (597 MeV) + Pb and proton (597 MeV) + Pb.

The SATURNE accelerator was a synchrotron located in the CEA Research Centre in Saclay, France. SATURNE could accelerate protons up to 2.95 GeV with a maximum intensity of 8 × 1011 particles per second and heavy ions up to krypton with 1.15 GeV/u with a charge-to-mass ratio of 0.5 [693]. The synchrotron delivers pulses during the beam spill with a pulse length of about 0.5 s with a repetition rate between 1 and 0.25 Hz.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Charged particles

Collimator Anticoincidence

Magnet

S3 Neutrons

Protons Targets

Scintillator for neutrons

S2

S1

Shadow bars Stop

Start

Time-of-flight 13.4 m

Fig. 10.13 The principle of the TOF arrangement at SATURNE. As an example, an arrangement in the zero degree direction is displayed here [711]. Spectrometer

Collimator Magnet

C2

T2

C3

C1

Proton Neutron Targets

T1 M1 Shadow bars 4.5 m

M3 Hydrogen

Anticoincidence 8.0 m

2.0 m 1.8 m

2.7 m 1.6 m

Fig. 10.14 The principle setup of the spectrometer for high-energy neutron spectra measurements for energies ≥ 200 MeV. As an example, an arrangement in the zero degree direction is shown here.

10.2.2.1 The Experimental Apparatus at the SATURNE Accelerator The low-energy method The principle arrangement for the low-energy measurements for 3 ≤ E ≤ 400 MeV is described by Borne et al. [711] and is shown in Figure 10.13. In the ﬁgure the TOF method is shown for a 0◦ measurement, which is adopted with some minor modiﬁcations for other angles as shown in Figure 10.15. The TOF is measured between the incident proton beam of an intensity of 106 protons per second tagged by a 1-mm thick plastic scintillator (S1) and a cylindrical neutron liquid scintillator detector (S2) called the Demon detector (cf. Figure 10.15). Beam protons that do not interact with the target and other charged particles emitted in the forward direction are swept out by a magnet about 50 cm downstream of the target. The ‘‘Demon’’ detectors (cf. Figure 10.15) are surrounded by a parafﬁn shielding loaded with borax and lithium to reduce the background of

305

306

10 Proton-Nucleus-Induced Secondary Particle Production M3 ‘Demon’detectors liquid scintillator

Spectrometer Vé

‘DENSE’ low-energy detectors liquid scintillator

s

M2 Protons

0

115

1000

1350 1150

850

Vé 0

s nu

Rotation 00 – 850

550

70

1450 160

nu

400

0

Liquid hydrogen target

250 100

Neutron beam

00

Concrete

Proton Beam

Target area Beam stop Stop time-of-flight Magnet area scintillator M1

Fig. 10.15 The experimental area at the SATURNE accelerator with the spectrometer and the TOF arrangement to measure angle-dependent neutron-production spectra (after Borne et al [711], Martinez et al. [712], and Leray et al. [132]).

ambient gamma rays. In addition a 3 mm thick plastic scintillator of NE102 (S3) is placed in front of each neutron detector to tag events induced by charged particles. A 1-m shadow bar placed between the sweep magnet and the collimator is used to measure effectively the background produced by the collimator. Measurements with the shadow bar in place found only a small difference in the spectra between target ‘‘in’’ and target ‘‘out’’ of about ≤ 1%. Therefore, the shadow bar is not used for all target-energy combinations. To investigate in addition neutron spectra measurements at lower energies between 2 and 14 MeV, smaller detectors, called ‘‘Dense,’’ are also used as indicated in Figure 10.15. The ﬂight-path length of 13.4 m depicted in Figure 10.13 for the TOF method is reduced to 8 m utilizing the TOF method for the apparatus as shown in Figure 10.15. The main characteristics of the used neutron detectors are summarized in Table 10.8. The high-energy method The principle arrangement for the high-energy measurements is a proton recoil spectrometer for 200 ≤ E ≤ 1600 MeV described Tab. 10.8

The detector parameter of the neutron detectors DENSE and DEMON.

Characteristics Liquid scintillator Diameter Length Photomultiplier Detector threshold

DENSE detector NE-213 127 mm 51 mm 9390 KB 1.0 MeV

DEMON detector NE-213 160 mm 200 XP 4512 1.9 MeV

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

by Martinez et al. [712] and is illustrated in Figure 10.14 for the 0◦ direction. Figure 10.15 shows the utilization of the spectrometer for angle-dependent measurements. The method is based on the detection of recoil protons produced by the scattering of high-energy neutrons via (n,p) reactions in a liquid hydrogen converter target which is based on an experimental technique published by Bonner et al. [689]. The neutrons emitted from the target are collimated through an 8-m thick concrete shield to an angular aperture of ±25◦ . Behind the collimator the neutrons interact with a liquid hydrogen converter target with a thickness of 1 g/cm2 and a diameter of 14 cm. The spectrometer system (cf. Figure 10.14) contains several components, e.g., a dipole magnet and three double-plan (X–Y) wire chambers indicated in the ﬁgure by C1, C2, and C3, to reconstruct the deﬂected trajectories of the protons. The spectrometer magnet has a ﬁeld strength of 0.5 T on a 160 × 160 cm2 aperture with a length of 140 cm. The wire chamber C1 covers a 20 × 20 cm2 surface, whereas the chamber C2 covers a surface of 80 × 40 cm2 , and chamber C3 a surface of 100 × 80 cm2 . The wires have a spacing of 1.27 mm for C1 and 2 mm for C2 and C3. The overall XY-resolution gives a 1-mm accuracy on the position measurement for the proton trajectories. From the reconstruction of the trajectories, it is possible to determine the momentum of the protons, which are emitted within the spectrometer acceptance. The wire chambers C1 and C2 measure the emission angle of the protons. The neutron momentum is deduced assuming that the proton is produced by an elastic scattering event in the hydrogen converter target. In the hydrogen converter target several other types of charged particles are produced: np → np, np → npπ ◦ , np → ppπ − , np → dπ ◦ , np → 2nπ + . The charged particles with different masses are identiﬁed using the biparametric representation of the TOF of the T1 scintillator-wall versus the momentum measured with the wire chambers and the spectrometer M3 [132]. The plastic scintillator T1 behind the hydrogen converter and a 200 × 200 cm2 plastic scintillator hodoscope T2 of NE102 behind the spectrometer serve in coincidence to provide the trigger for the data acquisition. Both scintillation detectors are also used to measure the TOF of particles crossing the spectrometer identifying the protons from other charged particles produced in the hydrogen converter target. The hodoscope T2 is made of 20 horizontal slats with photomultipliers on each side. Figure 10.15 illustrates the ﬁnal construction of the experiment, which allows 12 neutron beam lines to measure at neutron scattering angles from 0◦ to 160◦ by steps of 15◦ . In the ﬁnal setup of the experiment a second magnet M2 is positioned before the hydrogen converter target, which deviates the charged particles created in the target in the horizontal plane. As indicated in Figure 10.15 the whole spectrometer could rotate from 0◦ to 85◦ . This is sufﬁcient, because at larger scattering angles only some few neutrons with energies higher than 400 MeV are produced. At these scattering angles, the spectra could be measured with the TOF method applying the DEMON and DENSE detector systems. The beam intensity is limited to about 1010 protons/s with an average number of 400 triggers/s by dead times of 20% for reading out the wire chamber information.

307

10 Proton-Nucleus-Induced Secondary Particle Production 40.0 NE-213 detector efficiency of the DENSE detector

Neutron efficiency [%]

308

(threshold 1.0 MeV)

30.0

20.0

Experimental datas

10.0

Measured efficiency Corrected efficiency

0.0

1

10 Neutron energy [MeV]

Fig. 10.16 The efﬁciency of the neutron detector ‘‘DENSE.’’ The triangle symbols are the measured values, whereas the dashed line is a ﬁt of these values. The solid line is the ﬁnal parameterization used in the data analysis (after Leray et al. [132]).

The number of protons was monitored by two scintillator telescopes viewing a 50-µm thick Mylar foil placed upstream in the beam. The absolute calibration of the telescopes is obtained by irradiated a thin disk of carbon by counting the beta decay of 11 C. The production cross section 12 C(p,11 C) is well known. An estimation of the systematic error of the beam monitoring results in the energy range between 0.8 and 1.6 GeV of about 5.8% [132]. Also the standard beam monitoring with Al foils was used. The detectors, efﬁciency, energy resolution, and systematic errors in the TOF method Experiments and calculations were performed to estimate the detector efﬁciency over the whole energy range. Several experiments are investigated with quasi monoenergetic neutron beams to determine the neutron detectors’ efﬁciencies as a function of the incident neutron energy. Details are described by Leray et al. [132] and in references therein. The characteristics of the DENSE and the DEMON detectors are summarized in Table 10.8. The estimated efﬁciency functions of the ‘‘DENSE’’ and ‘‘DEMON’’ detectors are adopted from [132] and shown in Figures 10.16 and 10.17. The efﬁciency measurements were performed for the following energy ranges: • from 2 up to 17 MeV at the Bruy`eres-le-Chatel Van de Graaff accelerators, France [711] using quasi monoenergetic neutron-production reactions as 7 Li(p,n)7 Be, 3 H(p,n)3 He, 3 H(d,n)4 He, and 2 H(d,n)3 He, • from 30 ≤ E ≤ 100 MeV at the TSL Uppsala accelerator, Sweden [714], • from 100 to 180 MeV using the 7 Li(p,n)7 Be reaction, • from 150 up to 800 MeV at SATURNE using the (d+Be)-breakup reaction to produce quasi monoenergetic neutrons.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments 70 NE-213 detector efficiency of the DEMON detector (threshold =1.9 MeV)

Detector efficiency [%]

60 50 40

Bruyeres-le-Chatel Saturne Uppsala O5S Simulation Modified KSU simulation Efficiency as measured Corrected efficiency

30 10 20 0 1

10 100 Neutron energy [MeV]

1000

Energy resolution [%]

Fig. 10.17 The efﬁciency of the neutron detector ‘‘DEMON.’’ The black symbols are the measurements at Bruy`eres-le-Chatel, TSL Uppsala, and SATURNE. The gray symbols are simulations based on the codes O5S [715] and the code KSU a modiﬁed version of Cecil et al. [703]. The solid line is the ﬁnal parameterization used in the data analysis (after Leray et al. [132]). 20 18 16 14 12 10 8 6 4 2 0

Total resolution Time component Geometrical component

1

10

102

103

Neutron energy [MeV]

Fig. 10.18 The different contributions to the energy resolution E/E as a function of the neutron energy for the DEMON detector. Estimated for a TOF path length of 8.5 m. The time resolution uncertainty is 1.5 ns and the uncertainty in the ﬂight-path length is about 6 cm (after Leray et al. [132]).

The ‘‘DENSE’’ detectors are only used in the energy range of 2 to 14 MeV. The efﬁciency calculations for the ‘‘DEMON’’ detector with the KSU code of Cecil et al. [703] are in good agreement with the measurements, which was also found for the efﬁciency calibration of the LANL-WNR detectors investigated by Amian et al. [129] (see Section 10.8 on page 298). The neutron energy resolution E/E depends on a time and a geometrical component as already discussed in Section 10.2.1 and given by Eq. (10.2) on page

309

310

10 Proton-Nucleus-Induced Secondary Particle Production Tab. 10.9 The estimation of the main systematic errors as a function of the incident proton beam energy for neutron measurements above 0.4 GeV (data are based on Ref. [132]).

Incident beam energy (GeV) Error of

0.8 and 1.2

1.6

Beam intensity Spectrometer Response function Unfolding procedure and analysis

≤5.8% ≤4.0%

≤5.8% ≤11.5%

≤5.8%

≤8.6%

Total uncertainty

≤9.1%

≤15.5%

290. Figure 10.18 shows the energy resolution as a function of the neutron energy for the applied TOF method of the SATURNE experiment. Above 400 MeV (see Figure 10.18) the TOF method does not allow a better resolution than 12%. This was the reason to develop and use a complementary experimental setup for neutron measurement above an energy of 400 MeV, as described in Figures 10.14 and 10.15. Table 10.9 summarizes an estimation of the systematic errors as a function of the incident proton beam energy determined for neutron measurements above 400 MeV applying the spectrometer experimental setup. 10.2.2.2 The Experimental Results of Double-Differential Neutron-Production Cross Section Measurements The measurements at SATURNE and also validations with intranuclear-cascadeevaporation models have been published in journals during 1997–2006 [132, 172, 220, 711, 712] and conference proceedings, reports, and PhD theses [543, 693, 710, 713, 716]. Table 10.10 summarizes the studied target materials selected by incident proton beam energy and scattering angle. The ‘‘thin’’ target cross sections presented are already retrieved again from NNDC experimental nuclear reaction database (EXFOR /CSISRS) [709]. Summary of proton energies, scattering angles, and used targets (the targets are all of natural abundance (data are based on Refs. [132, 220]).

Tab. 10.10

Incident proton energies (GeV)

0.8, 1.2, 1.6

Scattering angles (◦ )

0, 10, 25, 40, 55, 85, 100, 115, 130, 145, 160

Target material Target thickness (g cm−2 ) Target diameter (cm)

Al 8.1 3.0

Fe 23.6 3.0

Zr 19.4 3.0

W 19.3 3.0

Pb 22.7 3.0

Th 39.8 3.0

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments 103 Eproton = 800 MeV

d 2 s/dΩdE cross section [mb sr −1 MeV−1]

102 101 100 10−1

10

0

LANL - Pb - 30 Saclay - Pb - 550

−3

×10−2

LANL - Pb - 600

10−4 10−5

×10−1

Saclay - Pb - 250

10−2

LANL - Pb - 1500 Saclay - Pb - 1600

10−1

100

101 102 Neutron energy [MeV]

103

Fig. 10.19 Comparison of SATURNE data of Ledoux et al. [220] with measurements at LANL-WNR of Amian et al. [129] of the reaction proton (800 MeV) + Pb. As indicated in the ﬁgure, the different curves are scaled successively by a factor of 10−1 . The symbols have a different size to distinguish between the measurements.

Some representative examples of double-differential neutron-production measurements at the SATURNE facility for incident proton energies of 0.8 GeV, 1.2 GeV, and 1.6 GeV for C, Al, Fe, Pb, and Th targets and scattering angles of 0◦ ,10◦ , 25◦ , 85◦ , and 160◦ are displaced in a double logarithmic scale in Figures 10.20, and 10.21 [132, 220]. The total uncertainties of the experimental results are determined by ±1σ = 10–15% and thus are of the order of the data symbol sizes. In Figure 10.19, a subset of the results at SATURNE of Ledoux et al. [220] is compared with measurements at LANL-WNR of Amian et al. [129] for an incident proton energy of 800 MeV and scattering angles of (25◦ , 30◦ ), and (55◦ , 60◦ ), and (150◦ ,160◦ ), and for the reaction proton (800 MeV) + Pb). The data comparison is made for the closest possible angles. It is seen that the SATURNE data fully agree with the LANL-WNR data. For other targets, e.g., Fe, there are some minor differences below neutron energy ≤ 4 MeV. These differences are probably a consequence of the target-enhanced thickness. The employed targets at the SATURNE experiments are not really ‘‘thin’’ compared with the targets used at the LANL-WNR experiment (cf. Tables 10.10 and 10.6). As pointed out by Leray et al. [132] the thickness of the used targets at the SATURNE experiments may produce some distortions in the measured spectra induced by secondary reactions of the particles from the spallation process. The result is a slight shift and a broadening of the quasielastic and inelastic peak at very forward scattering angles and the increase of the number of low-energy emitted neutrons. These peaks vanishes at higher emission angles about ≥ 30◦ as seen in the ﬁgures. The LAN-WNR experiments did not show this structure because it was not possible to measure at scattering angles ≤ 30◦ . In contrast to

311

312

10 Proton-Nucleus-Induced Secondary Particle Production

SATURNE measurements, the LAN-WNR experiments (cf., for e.g., Figure 10.19) with their lower detection threshold of about 0.525 MeV illustrate much more pronounced broad evaporation region in the neutron-production spectrum which strongly dominates for heavy mass targets, being less pronounced at low masses where the nucleon–nucleon mechanisms dominate. As mentioned earlier, the cross-section curves are seem to be very much alike. The absolute double-differential cross sections increase with increasing target mass number and incident proton energy, e.g., from Al to Th and from 0.8 to 1.6 GeV, for all neutron emission angles. Furthermore, the fraction of cascade neutrons in the total emission spectra increases with decreasing mass number for all laboratory angles. 10.2.3 The Double-Differential Neutron-Production Measurements at the KEK Facility

The TOF method developed at π2 beam line of the 12 GeV proton synchrotron at the National Laboratory for High Energy Physics, KEK, Japan, is to use a very weak secondary proton beam up to 3.0 GeV, which leads to a short ﬂight length of 1 m. The experiments were started with some test experiments by Nakamoto et al. [694] at incident proton energies of 0.8 and 1.5 GeV during 1995 and ﬁnished in 1997 by Ishibashi et al. [265]. 10.2.3.1 The Time-of-Flight Method with a Short Flight Path The double-differential neutron-production spectra are measured by the TOF method with detectors of liquid NE-213. The length of ﬂight paths for such experiments has usually been taken to be several 10 m up to 60 m as used at the LAMPF-WNR and the detectors have been heavily been shielded by materials of iron, concrete, etc., against background radiation. However, the proton beam used for the KEK experiments is generated as a secondary particle beam by an internal target, which is placed in the synchrotron accelerator ring. The beam intensity for the experiment was very weak at a level of about 105 protons per 2.5 s. Because of this very low-intensity pulsed proton beam the protons could individually be counted [265]. The experimental arrangement is illustrated in Figure 10.22. As shown in Figure 10.22, a TOF method is used with a pair of Pilot-U scintillators located at a ﬂight distance of 20 m for the separation of incident protons and pions, because of the nature of the used secondary beam. The protons in the beam are contaminated by pions of the same momentum. A time resolution of about 0.25 ns could be achieved to resolve the pions from the incident protons. As indicated in Figure 10.22, NE-102A plastic scintillators were used to deﬁne the incident beam of protons on the targets. The coincidence of the scintillators signals of P1 and P2 determines the number of protons. The weakness of the intensity of the incident proton beam comprises not only a short ﬂight paths but also thicker targets (cf. Table 10.12) to maintain the measurement efﬁciency to a reasonable degree.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments 103

102

Eproton = 0.8 GeV

1

Fe

10

102 d2 s/dΩE cross section [mb sr −1 MeV−1]

d2 s/dΩE cross section [mb sr −1 MeV−1]

103

100 −1

10

10−2 −3

10

10−4 −5

10

00

−6

10

10−7

100

10−8

25 85

10−9

0

0

Eproton = 0.8 GeV Pb

101 100 10−1 10−2 10−3 10−4 10−5 10−6

00

10−7

100 250

10−8

850

10−9

1600

10−10

1600

10−10 100

101

102

103

100

Neutron energy [MeV] Reaction proton (0.8 GeV) + Fe target

(a)

d2 s/dΩE cross section [mb sr −1 MeV−1]

d2 s/dΩE cross section [mb sr −1 MeV−1]

102

Eproton = 1.2 GeV

1

Al

100 −1

10−2 10

−3

10

−4

10−5 10−6

00

10−7

10

0

10−8

25

0

850

10−9 10

−10

10

100 10−1 10−2 10−3 10−4 10−5 10−6

00

10−7

100 250

10−8

10 101

Eproton = 1.2 GeV Pb

1

850

10−9

1600

100

102

103

1600

−10

100

Neutron energy [MeV] (c)

103

103

102

10

102

Reaction proton (0.8 GeV) + Pb target

(b)

103

10

101

Neutron energy [MeV]

Reaction proton (1.2 GeV) + Al target

101

102

Neutron energy [MeV] (d)

Fig. 10.20 Proton-induced experimental double-differential neutron-production cross sections at scattering angles of 0◦ , 10◦ , 25◦ , 85◦ , and 160◦ –measurements of Ledoux et al. [220] and Leray et al. [132]. Each successive curve, starting from the smallest angle 0◦ , is scaled by a multiplication factor of 10−1 , e.g., 10◦ × 10−1 , 25◦ × 10−2 , 85◦ × 10−3 , and 160◦ × 10−4 .

Reaction proton (1.2 GeV) + Pb target

103

313

314

10 Proton-Nucleus-Induced Secondary Particle Production

103

103 Eproton = 1.2 GeV

101

102 d2 s/dΩE cross section [mb sr −1 MeV−1]

d2 s/dΩE cross section [mb sr −1 MeV−1]

102

Fe

100 10−1 10

−2

10−3 10

−4

10−5 00

10−6

10

10−7

0

250

10−8

85

10−9

0

160

10−10

0

Eproton = 1.2 GeV Th

101 100 10−1 10−2 10−3 10−4 10−5 10−6

00

10−7

100 250

10−8

850

10−9

1600

10−10 100

101

102

103

100

Neutron energy [MeV] Reaction proton (1.2 GeV) + Fe target

(a)

103

103 d2 s/dΩE cross section [mb sr −1 MeV−1]

Eproton = 1.6 GeV

102 d2 s/dΩE cross section [mb sr −1 MeV−1]

102

Reaction proton (1.2 GeV) + Th target

(b)

103 Fe

101 10

101

Neutron energy [MeV]

0

10−1 10−2 10−3 10−4 10−5 10−6

0

0

0

10

10−7

250

10−8

850

10−9

1600

10−10

102

Eproton = 1.6 GeV

101

Pb

100 10−1 10−2 10−3 10−4 10−5 10−6

00

10−7

100 250

10−8

850

10−9

1600

10−10 100

101

102

103

100

Neutron energy [MeV] Reaction proton (1.6 GeV) + Fe target

(c) Fig. 10.21

The same as Figure 10.20.

101

102

Neutron energy [MeV] (d)

Reaction proton (1.6 GeV) + Pb target

103

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments NE102A (veto)

Ø 12.7 cm × 12.7 cm NE213

90°

60°

120°

30°

150° NE102A (beam definition) S01

Proton beam

S02

20m

15°

Target area

P02

Pilot U (p -p discrimination and particle counting)

1.5m

1m

P01

P1 P2

0.6m

0.9m

Proton beam line 15° 30°

150° 120° NE102A (veto)

90°

60° Ø 5.08 cm × 5.08 cm NE213

Fig. 10.22 The arrangement of the KEK time-of-ﬂight experiment (after Ishibashi et al. [265]).

Test experiments referred by Nakamoto et al. [694] were mainly investigated to check the signal-to-background ratio. For this purpose, the NE-213 detectors were shielded with iron blocks with a thickness between 0.5 and 1 m. Measurements with and without shielding of the detectors showed a relatively good agreement at neutron energies above several MeV and a large disagreement below 4 MeV caused by the generation of secondary neutrons produced by high-energy particles in the iron shield surrounding the detectors. Therefore, the KEK TOF experiment was operated in a bare detector condition. Another issue was the background scattering of particles from the concrete ﬂoor because of the low beam line height of 1.7 m. Particle transport calculations for estimating the ﬂoor particle scattering effects into the detectors and shadow bare experiments showed that the effect of ﬂoor scattered neutron is clearly negligible in the energy range up to several 100 MeV [694]. As shown in Figure 10.22 two different sizes of the NE-213 neutron detectors (∅5 × 5 , ∅2 × 2 ) were used simultaneously for the scattering angles of in 150◦ , 300◦ , 600◦ , 900◦ , 1200◦ , and 1500◦ direction. In front of each neutron detector, a NE-102A plastic scintillator is mounted and works as veto detector in anticoincidence to eliminate charged particle background events. The larger detectors are used with ﬂight-path lengths of 1–1.5 m measuring the high-energy neutrons and the smaller ones with 0.6–0.9 m measuring low-energy neutrons, respectively. Table 10.11 summarizes the detector data of the NE-213 detectors. The neutron detector efﬁciencies were determined by simulations with the standard code of Cecil et al. [703] for neutron energies up to several 100 MeV (cf. see also Sections 10.2.1.1 on page 296 and 10.2.2.1 on page 305) and the SCINFUL code of Dickens [717, 718] for neutron energies below 80 MeV. The results of the simulation with the Cecil code are adjusted together with the SCINFUL results at

315

10 Proton-Nucleus-Induced Secondary Particle Production Tab. 10.11

Summary of the detector data of Refs. [265, 694].

Flight path Flight path length (m) Detector material (liquid) dimension Diameter × thickness (cm) Time resolution (ns) Energy resolution ± 1σ (%)

15◦ , 30◦ , 60◦ , 90◦ , 120◦ , 150◦ 1.5–1.0 NE-213

15◦ , 30◦ , 60◦ , 90◦ , 120◦ , 150◦ 0.9–0.6 NE-213

12.7 × 12.7(5 × 5 ) 0.5–1.0 5.7 for 10 MeV neutrons 14.0 for 300 MeV neutrons

5.08 × 5.08(2 × 2 )

60 Am

Cs

Co

AmBe

Am-bias by SCINFUL for NE213 (5.08 cm) Cs-bias by SCINFUL for NE213 (12.7 cm) Co-bias SCINFUL for NE213 (12.7 cm) AmBe-bias by CECIL (corr.) for NE213 (12.7 cm)

50 Detector efficiency [%]

316

40 30 20 10 0 10−1

100

101 102 Neutron energy [MeV]

103

Fig. 10.23 Determined neutron detector efﬁciencies for liquid scintillators of NE-213. The Cecil code simulations are normalized to the 80 MeV simulations determined by the SCINFUL code. The energy ranges for different biases are indicated in the upper part of the ﬁgure [265].

an energy of 80 MeV. The results are shown in Figure 10.23 for four bias levels considering Am, Cs, Co, and AmBe-biases1) . The 241 AmBe-bias is used for the smaller NE-213 detector of 5.08 × 5.08 cm2 whereas the other biases are used for the larger detectors of 12.7 × 12.7 cm2 . 10.2.3.2 The Experimental Results of Double-Differential Neutron-Production Cross Section Measurements Double-differential neutron-production cross section were measured for C, Al, Fe, In, and Pb targets at incident proton beam energies of 0.8, 1.5, and 3.0 GeV. The data presented in the following examples are retrieved from the EXFOR database [709]. Table 10.12 shows the target characteristics and the incident proton beam energy 1) The light output in terms of the scintillator’s response to electrons of energy in MeV is expressed in the electron equivalent MeVee.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Tab. 10.12

Summary of the target characteristics (data are taken from [265]).

Target material

C

Al

Fe

Fe (1.5 GeV)

In

Pb (plate)

Diameter (cm) 5.0 Thickness (g cm−2 ) 17.5 Density (g cm−3 ) 1.75

5.0 4.9 10.7 23.6 2.69 7.87

4.9 15.74 7.87

4.9 10 × 10 × 1.2 cm3 17.76 13.6 7.31 11.34

Proton energy loss (MeV) : At energy 0.8 GeV At energy 1.5 GeV At energy 3.0 GeV

37 33 33

20 18 18

40 – 36

– 24 –

26 23 23

18 16 16

Mean excitation energya (eV)

73.8

160

278

278

483

819

a The mean excitation energy is the mean excitation and ionization potential in the proton energy loss process in the targets.

Time-of-flight energy resolution [%]

100

80

60

40

20

0 100

Fig. 10.24

101 102 Neutron energy [MeV]

103

The resulting energy resolution of the KEK TOF experiment.

loss because the targets are not really ‘‘thin.’’ All targets have a cylindrical shape except the Pb target. The energy resolution of the TOF experiment is important for cross-section measurements. The energy resolution of the KEK experiment is derived from the time resolution and from the neutron detection efﬁciency. The resulting energy resolution is shown in Figure 10.24. The uncertainty of the neutron detection efﬁciency was determined to be about 10% in the energy region below 80 MeV, whereas above 80 MeV it was estimated to be about 15% [694]. The time resolution in conventional TOF experiments, e.g., the LANL-WNR experiment, is mainly determined by the pulse width of the incident particle beam usually about several nano seconds. Because in the KEK experiments the protons are counted event by event, the uncertainty of the TOF measurements

317

10 Proton-Nucleus-Induced Secondary Particle Production

102

103 Eproton = 0.8 GeV Fe

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10

Ishibashi-15° Ishibashi - 30° Amian - 30° Ishibashi - 60° Ishibashi - 120° Ishibashi - 150° Amian - 150°

−9

10−1

100 101 102 Neutron energy [MeV]

103

(a) Reaction proton (0.8 GeV) + Fe target

Fig. 10.25 Proton 0.8 GeV induced experimental double-differential neutronproduction cross sections on Fe and Pb targets at scattering angles of 15◦ ,30◦ , 60◦ , and 150◦ – measurements of Ishibashi et al. [265] in comparison with measurement of

d2s/dΩdE cross section [mb sr−1 MeV−1]

103 d2s/dΩdE cross section [mb sr−1 MeV−1]

318

102

Eproton = 0.8 GeV Pb

101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−1

Ishibashi-15° Ishibashi - 30° Amian - 30° Ishibashi - 60° Ishibashi - 120° Ishibashi - 150° Amian - 150°

100 101 102 Neutron energy [MeV]

103

(b) Reaction proton (0.8 GeV) + Pb target

Amian et al. [129] of angles at 30◦ and 150◦ . Each successive curve, starting from the smallest angle 15◦ , is scaled by a multiplication factor of 10−1 , e.g., 30◦ × 10−1 , 60◦ × 10−2 , 120◦ × 10−3 , and 150◦ × 10−4 .

is mainly determined by the time resolution of the neutron detectors. The time resolution of the detectors is estimated from the FWHM of the gamma ray peak ﬂash and is obtained to be 0.5–1.0 ns [265]. Then the time resolution have to be converted into the energy resolution considering the uncertainty of the ﬂight path’s length. It is seen from Figure 10.25 that there is a remarkable good agreement between the data of Ishibashi and Amian although the targets studied at the KEK facility are not really ‘‘thin’’ compared to the target characteristics given in Tables 10.5 and 10.12 on page 299 and 317, respectively. The good agreement is also given at other measured scattering angles not shown in Figure 10.25. To visualize the comparison the plotted symbols have different sizes. Figure 10.26 shows examples of the double-differential neutron production for reactions proton (3.0 GeV) + Fe and Pb targets for scattering angles of 15◦ , 30◦ , 60◦ , 90◦ , and 150◦ at the KEK facility of Ishibashi et al. [265]. The energy and angle dependence of the neutron-production cross sections show the expected trend. 10.2.4 The Double Differential Pion Production Measurements

Double-differential pion production measurements of proton–nucleus (p,A)-reactions are very scarce. The production of pions is a major ﬁeld of intermediate energy physics to validate the secondary particle production channels.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

102

103 Eproton = 3.0 GeV

30° 60°

101 10

90° 150°

0

10−1 10−2 10−3 10−4 10−5 10−6 100

Eproton = 3.0 GeV

15°

Fe

101 102 103 5×103 Neutron energy [MeV]

(a) Reaction proton (3.0 GeV) + Fe target

d2s/dΩdE cross section [mb sr−1 MeV−1]

d2s/dΩdE cross section [mb sr−1 MeV−1]

103

102

15°

101

60°

10

30° 90° 150°

0

10−1 10−2 10−3 10−4 10−5

Pb

10−6 100

101 102 103 5×103 Neutron energy [MeV]

(b) Reaction proton (3.0 GeV) + Pb target

Fig. 10.26 Proton 3.0 GeV induced experimental doubledifferential neutron-production cross sections on Fe and Pb targets at scattering angles of 15◦ ,30◦ , 60◦ , 90◦ , and 150◦ – measurements of Ishibashi et al. [265]. Each successive curve, starting from the smallest angle 15◦ , is scaled by a multiplication factor of 10−1 , e.g., 30◦ × 10−1 , 60◦ × 10−2 , 90◦ × 10−3 , and 150◦ × 10−4 .

Only few experiments of double-differential pion production cross-section measurements are reported for incident protons [124, 695, 719–721] and incident neutrons [722] in the GeV energy range. The most comprehensive data sets are published by Cochran et al. [124] for incident protons of 730 MeV, and by Crawford et al. [695, 719] for incident protons of 585 MeV for a large variety of scattering angles and target materials. More recently, the HARP collaboration [723] measured double-differential pion production spectra for incident protons in the energy range between 3 and 12 GeV/c for Be, C, Al, Cu, Sn, Ta, and Pb targets. As already discussed in Sections 1.3.7.6 on page 54 and 1.3.8 on page 57, highpower spallation facilities may provide intense neutrino beams. The main scientiﬁc and technical issues investigating an intense neutrino source involve the construction of very intense proton beams, targeting effective capture of produced particles and an accurate knowledge of the pion production mechanisms in proton-induced spallation reactions (cf. e.g., the NuFact-07 conference [724] and references therein). 10.2.4.1 The Double Differential Pion Production Measurements at the Berkley Cyclotron with Incident Protons of 730 MeV The general setup of the pion spectrometer at the Berkley 184-inch cyclotron investigated by Cochran et al. [124] is shown in Figure 10.27.

319

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10 Proton-Nucleus-Induced Secondary Particle Production

Rotation for angles 15, 20, 30, 45, 60, 75, and 90 degree, and 90, 105, 120, 135, and 150 degree

Beam from 184’’ cyclotron Spectrometer

Premagnet collimator Steering magnet

Q 1 Q2

Circe Beam monitors 4.72m

2.65m

Diana

Sic T1 target

T2 target

5.74m

Fig. 10.27 Sketch of the pion spectrometer at the Berkley 184-inch cyclotron using 730 MeV protons of Cochran et al. [124].

The experiment used a low-intensity extracted proton beam of an intensity of about 5–20 nA passing through an adjustable magnet collimator, a steering magnet, and a quadrupole doublet Q1 , Q2 and through a proton beam pipe in the concrete shield into the experimental area. The quadrupole doublet CIRCE is used to focus the beam at the target on position T1 , and the quadrupole doublet DIANA is considered to focus the beam when the target is used at position T2 . Experience has shown that the setting of the premagnet collimator could be used for both the forward- and the backward-angle measurements. As depicted in Figure 10.27 there are a large number beam channels from the target positions of T1 to deﬁne scattering angles at 15◦ , 20◦ , 30◦ , 45◦ , 60◦ , 75◦ , and 90◦ with respect to the incident beam, and scattering angles of the target position T2 of 90◦ , 105◦ , 120◦ , 135◦ , and 150◦ . The spectrometer could be moved radially to cover the forward and backward angles. The ﬂight path channel openings are 10 cm horizontally by 12.5 cm vertically and with inserted lead collimators 5 × 7.5 cm2 . The collimators were used to test and estimate the scattering of particles from the channel walls into the spectrometer. The spectrometer was constructed by modifying an existing ‘‘C’’ magnet of the Berkley cyclotron which had a 33 cm × 61 cm pole face and a 15 cm gap. The central ﬁeld was chosen to be 1.1 T. Further information of the spectrometer itself with the used counters of Ne-102 each 3.8 cm wide and 3 mm thick to assure that a charged particle had entered the spectrometer within its acceptance and had traversed the magnet ﬁeld, the electronics, the particle identiﬁcation procedure, and the off-line data reduction is given in great detail in the publication of Cochran et al. [124].

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments Used targets and target densities given by [124] (the ‘‘thin’’ targets were either 7.5 cm or 10 cm in diameter).

Tab. 10.13

Target material liquid H2 CD2 Be C Al Ti a

Density (g cm−2 )

Target material

densitya 1.13 0.90 1.10 0.97 0.76

Cu Ag Ta Pb Th

Density (g cm−2 ) 0.97 1.08 1.28 1.90 1.01

The density for liquid H2 is given in 1.59 × 1023 protons cm−2 .

Examples of the double-differential pion production measurements Doubledifferential pion production cross sections d2 σ/ddE by 730 MeV protons at 11 scattering laboratory angles in the interval 15◦ –150◦ and at 12 energies in the interval 25–550 MeV were measured. The used targets are summarized in Table 10.13. The systematic errors in the beam current measurements affecting all cross sections are estimated to be about 10%. The above-discussed ﬂight-path channel in-scattering into the spectrometer gives an average uncertainty of about 10% and is included in the cross-section errors. The statistical uncertainty is typically of the order of 3%. The produced positrons and electrons arise from π and µ decay in ﬂight and from π ◦ –γ decay and subsequent pair production in the region of the target system. It was shown that the (e− /π − ) ratio is in general equal to the (e+ /π + ) and is an order-of-magnitude indication for the background for the experiment [124]. Examples of ratios for e− /π − are selected for the angles 15◦ , 90◦ , and 150◦ and shown in Figure 10.28. Figures 10.29, 10.30, and 10.31 show some examples of double-differential production cross sections of positive- and negative-charged pions at different angles by protons of 730 MeV incident on hydrogen, carbon, aluminum, copper, and lead targets. Note that compared to the production cross sections of neutrons typically in the order of mb, the production cross sections of pions in proton–nucleus (pA) reactions are only in the order of several µ barns. The cross-section production data for π + data of the reaction 1 H(p, π + )X (cf. Figure 10.29) show a very strong forward peaking at all energies. The maximum cross section is seen at 15◦ and about 300 MeV. This behavior is also expected in isobar models, where the (1236) formation and decay dominates the production process. The production cross section of the reaction 1 H(p,π − )X is only a few + − percent of that of the positive pions also shown by the ratio of πtotal /πtotal in − Table 10.16. The production of π from hydrogen comes from the reaction p + p → π + + π − + p + p. The examples of Figures 10.30 and 10.31 show that positive pion production is predominantly at forward angles, and the spectrum peaks at about 250–300 MeV. The shape of the spectra and the angular distributions are essentially the same from the lighter elements to the heavier ones for π + or π − , respectively.

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10 Proton-Nucleus-Induced Secondary Particle Production 100 15°

Ratio (electron /p−)

90° 150°

10−1

Target Cu ratio: e− / p−

10−2

10−3 2×102

102

3×102

4×102 5×102 6×102

Electron energy [MeV]

Fig. 10.28 Ratios of the number of electrons to the number of negative pions – (e− /π − ) at the same energy. The plotted data are from Ref. [124]. 25 Cross section d2s/dΩdE [µb sr−1 MeV−1]

322

20

15°

20°

30°

90°

120°

150°

Proton 730 MeV 1 H(p, p+)X

15

10

5

0 −1 101

5×101 102 Pion energy [MeV]

Fig. 10.29 π + production spectra from liquid hydrogen for the reaction 1 H(p,π + )X, Eproton = 730 MeV. The pion cross section are plotted in a log-linear scale to show the peaking at the forward angles of 15◦ , 20◦ , and 30◦ . The data are taken from Ref. [124].

5×102

103

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

102 Cross section d2s/dΩdE [µb sr−1 MeV−1]

Cross section d2s/dΩdE [µb sr−1 MeV−1]

102

101

100

10−1

15° 30° 120° 150°

C-target p− 10−2 101

101

100 15° 30° 120° 150°

10−1

Al-target p− 10−2

102

101

6×102

102

Pion energy [MeV] (a) Reaction C (p, π−)X, Eproton = 730 MeV

(b) Reaction Al (p, π−)X, Eproton = 730 MeV 102 Cross section d2s/dΩdE [µb sr−1 MeV−1]

Cross section d2s/dΩdE [µb sr−1 MeV−1]

102

101

100

10−1

15° 30° 120° 150°

Al-target p+ 10−2 101

6×102

Pion energy [MeV]

101

100 15° 30° 120° 150°

10−1

Cu-target p+ 10−2

102

6×102

101

Pion energy [MeV] (c) Reaction Al (p, π+)X, Eproton = 730 MeV

102 Pion energy [MeV]

6×102

(d) Reaction Cu (p, π+)X, Eproton = 730 MeV

Fig. 10.30 Proton-induced double-differential π ± production cross sections for C, Al, and Cu targets at scattering angles of 15◦ , 30◦ , 120◦ , and 150◦ at an incident proton energy of 730 MeV. Data are from Ref. [124].

323

324

10 Proton-Nucleus-Induced Secondary Particle Production

102 Cross section d2s/dΩdE [µb sr−1 MeV−1]

Cross section d2s/dΩdE [µb sr−1 MeV−1]

102

101

100 15° 30° 120° 150°

10−1

Pb-target p+ 10−2

101

100 15° 30° 120° 150°

10−1

Pb-target p− 10−2

101

102

2

6×10

101

Pion energy [MeV] (a) Reaction Pb (p, π+)X, Eproton = 730 MeV Fig. 10.31

102 Pion energy [MeV]

6×102

(b) Reaction Pb (p, π−)X, Eproton = 730 MeV

The same as Figure 10.30 but for lead targets.

Figure 10.32 shows a comparison of the measured double-differential π + production cross section for incident protons on aluminum with several intranuclear-cascade models, e.g., the Bertini model, the NUCRIN model, and the MICRES model described in Sections 2.2 on page 64 and 2.6.3 on page 123. The Bertini and the MICRES model predictions are in good agreement with the measurements, which is also shown for other target materials in [275]. On page 327, the experimental data of Cochran et al. are compared with the data of Crawford et al. which are described in Section 10.2.4.2. For both the experiments, the total cross sections for the production of charged pions by protons with energies of 585 and 730 MeV are summarized in Tables 10.15 and 10.16. The π + cross sections are normalized to Z1/3 and the π − cross sections to N 2/3 . The Z1/3 law for the π + suggests that the measured π + are produced peripherally. They escape the nucleus with relatively little scattering or energy loss. Therefore, the π + production spectrum peaks at forward angles. The formation of the π − production indicates a more complicated mechanism which is a function of π ◦ formation and the charge-exchange reaction π ◦ + n → π − +p as an important source of π − production. The charge-exchange scattering lowers the energy of the produced π − , broadens the angular distribution , decreases the π + /π − ratio, and makes the total cross section proportional to the nuclear area times N/A, or about N 2/3 . The functional dependence of the total cross sections of π + and π − on Z and N is shown in Figures 10.36 and 10.37 on pages 330 and 331, respectively.

10.2 Neutron, Pion, and Proton Double Differential Measurements and Experiments

15°

102

101

×10 30°

100

d2a/dΩdE [mb sr−1 GeV−1]

×102 10−1 45°

×103 10−2

60°

10−3 ×104 90°

10−4

×105

10−5

120° 10−6 0

0.1

0.2

0.3

0.4

Pion (p+) energy [GeV] Fig. 10.32 Double-differential π + production spectra for incident protons on aluminum at 730 MeV (p+Al → π + + X) at scattering angles of 15◦ , 30◦ , 45◦ , 60◦ , 90◦ , and 120◦ . Each successive curve, starting from the smallest angle 15◦ , is scaled by

a multiplication factor of 10, e.g., 30◦ × 10, 45◦ × 102 , 60◦ × 103 , 90◦ × 104 , and 120◦ × 105 . Circles are experimental data of Cochran et al. [124], full line Bertini model code, dotted line MICRES model code, and dashed line NUCRIN model code.

10.2.4.2 The Double Differential Pion Production Measurements at the Cyclotron of the Paul Scherer Institut (PSI) The double-differential production spectra of charged pions in proton–nucleus (p,A) collisions were measured from various nuclei at the Paul Scherer Institut (PSI, formerly named as SIN) by Crawford et al. [695, 719] during 1980. The experiment was performed at a proton beam energy of 585 MeV and covered a similar data set as that of Cochran et al. [124]. Pions were measured at energies above 24 MeV [695] and at low energies from 6 to 36 MeV [719]. In Figure 10.33,

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10 Proton-Nucleus-Induced Secondary Particle Production

Scintillation counter P1 P2

Central trajectory incident protons

CH3 target

Superconducting solenoid

Ce of ntra sp l tr ec aje tro ct me ory Sp ter ec tur trom nt ab eter le

Magnet

xr Pion production target

Shielding

326

yr q

Scintillation counter p1

Lead Collimators

p2

1m

p3 Scintillation counter

Fig. 10.33 The experimental arrangement to measure the production of charged pions from various nuclei at the PSI accelerator at an incident proton energy of 585 MeV by Crawford et al. [695, 719].

the general setup of the pion spectrometer is shown. The unpolarized extracted proton beam for the experiment was scattered in an 8-mm thick Be target through an angle of 8◦ and was transverse polarized of about 41.65 ± 0.40%. The transverse polarization of the beam could be rotated through 180◦ using the 1-m long solenoid magnet. The intensity of the proton beam was 5 × 109 protons per second during the experiment. The beam energy of 585 MeV was calibrated with an absolute uncertainty of 1 σ = ± 2 MeV and an energy band Eproton /Eproton of 0.4% FWHM. The beam was monitored with a multiwire proportional chamber near the pion production targets. The beam geometry at the pion production targets was 14 mm horizontally and 9 mm vertically FWHM. The superconducting solenoid magnet (Figure 10.33) has a longitudinal magnetic ﬁeld of 4.5 T along the beam direction. The beam was monitored by the scintillator hodoscopes P1 and P2 scattered at 30◦ from a 5-mm thick CH2 target. For the calibration of the intensity the beam has to be reduced during the experiment with a factor of about 103 –104 without changing the beam dimensions. The charged particles produced from the target were momentum analyzed in 1 m spectrometer magnet. The TOF through the spectrometer was determined using the scintillator counters π1 , π2 , and π3 indicated in Figure 10.33. The TOF measurement between the detectors π1 and π2 allowed a clear separation of electrons and pions emitted from the targets. The spectrometer could be rotated through the center of the target system to cover backward scattering angles up to 135◦ . The acceptance momentum of the spectrometer is p/p0 = 18.8% (FHWM),

10.3 Proton Cooler Synchrotron COSY at J¨ulich Tab. 10.14

Pion scattering angles and measured pion energies.

Scattering angle θπ (degree)

Energy Eπ (MeV)

23 45 60, 90, 135

24, 35, 88, 151, 254 24, 35, 88, 151, 192 24, 35, 88, 151

where p0 is the momentum of a particle traveling along the central trajectory of the spectrometer. Examples of the double-differential pion production measurements Pions were measured at the following scattering angles θπ = 23◦ , 45◦ , 60◦ , 90◦ , and 135◦ in the laboratory system with respect to the direction of incident proton beam. Table 10.14 summarizes the studied pion energies and the covered scattering angles. The following pion production targets were used: • CH2 , C6 D12 , Be, Al, Al2 O3 , Ni, Cu, Mo, and Pb. • The CH2 , C6 D12 , and Al2 O3 targets are used to determine the pion production cross sections for the proton, the deuteron, and the oxygen. • The targets were plates with a surface of 5 × 7 cm2 , a thickness of about 1 g/cm2 and were mounted on a remote-controlled target ladder with an empty position to measure the background.

Figures 10.34 and 10.35 show proton-induced π ± production spectra at scattering angles of 23◦ , 60◦ , and 135◦ for C, Al, Cu, and Pb targets. Comparison of total π + and π − cross sections Tables 10.15 and 10.16 summarize the total cross sections determined from of the measured cross-section distributions + − /πtotal π + and π − using the formula σtotal ≡ (d2 σ/ddE)ddE. The ratios of πtotal change from 8.4 of deuterium to 2 of lead for the PSI data of Crawford et al. and rapidly from 45 of hydrogen to 1.9 of thorium for the data of Cochran et al. As mentioned earlier, the functional dependence of the total cross sections of π + and π − on Z and N is shown in Figures 10.36 and 10.37.

10.3 The ‘‘Thin’’ Target Particle Production Measurements at the 2.5 GeV Proton Cooler Synchrotron COSY at J¨ulich

In this section, the emphasis will be on the description of nuclear data taken by the NESSI (NEutron Scintillator and SIlicium detector) and the PISA (Proton Induced SpAllation) experiment installed at the Cooler Synchrotron COSY in J¨ulich, Germany. To this, ﬁrst the accelerator COSY used by both experiments is brieﬂy introduced. The typical energy range of incident protons is 150 MeV–2.5 GeV with luminosities for the internal experiment PISA up to 6 × 1034 cm−2 s−1 . The

327

10 Proton-Nucleus-Induced Secondary Particle Production

70

70 Scattering angle 23°

60 50 40 30 20 Pb target Cu Al C

10

Cross section d2s/dΩdE [µb sr−1 MeV−1]

Cross section d2s/dΩdE [µb sr−1 MeV−1]

Scattering angle 23°

1

60 50 40 Pb target Cu Al C

30 20 10 1

50

50

100 150 200 250 300

Pion p+ energy [MeV]

100 150 200 250 300

Pion p− energy [MeV]

(a) Reaction C, Al, Cu, Pb(p, p+)X, qp = 23°

(b) Reaction C, Al, Cu, Pb(p, p−)X, qp = 23°

70

70 Scattering angle 60°

60

Pb target Cu Al C

50 40 30 20 10

Cross section d2s/dΩdE [µb sr−1 MeV−1]

Scattering angle 60° Cross section d2s/dΩdE [µb sr−1 MeV−1]

328

60

Pb target Cu Al C

50 40 30 20 10 1

1 50

100

150

200

50

Pion p+ energy [MeV] (c) Reaction C, Al, Cu, Pb(p, p+)X, qp = 60°

100

150

200

Pion p− energy [MeV] (d) Reaction C, Al, Cu, Pb(p, p−)X, qp = 60°

Fig. 10.34 Proton-induced double-differential π ± production cross sections for C, Al, Cu, and Pb targets at scattering angles of 23◦ and 60◦ at an incident proton energy of 585 MeV. Data are from Ref. [695].

10.3 Proton Cooler Synchrotron COSY at J¨ulich 100

Scattering angle 1350

90 80 Pb target Cu Al

70 60

C

50 40 30 20 10

Cross section d2 sdΩE [µb sr −1 MeV−1]

Cross section d 2 s dΩE [µb sr −1 MeV−1]

100

0

Scattering angle 1350

90 80 Pb target Cu Al

70 60

C

50 40 30 20 10 0

1

50

100

150

200

1

Pion p+ energy [MeV] (a)

Reaction C, Al, Cu, Pb (p,p+)X, qp = 135°

50

100

150

200

Pion p− energy [MeV] Reaction C, Al, Cu, Pb (p,p−)X, qp = 135°

(b)

Fig. 10.35 Same as Figure 10.34 pion production cross sections for π + and π − at a scattering angle of 135◦ . Data are from Ref. [695]. Total cross sections for π + and π − , the ra+ − /πtotal , and the normalization σtot (π + )/Z 1/3 and tios of πtotal − 2/3 σtot (π )/N , incident proton energy is 585 MeV, and crosssection data are from Ref. [695]. Tab. 10.15

Target/element

σtot (π + ) (mb ± 1σ )

σtot (π − ) (mb ± 1σ )

Ratio + − πtot /πtot

H D Be C O Al Ni Cu Mo Pb

9.7 ± 1.2 8.7 ± 1.1 22.7 ± 2.8 28.5 ± 3.5 34.6 ± 4.2 43.8 ± 5.4 62.5 ± 7.7 60.0 ± 7.4 69.6 ± 8.5 86.0 ± 11.0

– 1.03 ± 0.13 4.75 ± 0.59 4.72 ± 0.58 6.40 ± 0.79 9.80 ± 1.2 14.70 ± 1.8 18.00 ± 2.2 24.50 ± 3.0 41.50 ± 5.1

− 8.4 4.78 6.04 5.4 4.47 4.25 3.33 2.84 2.07

σtot (π + )/Z 1/3 (mb ± 1σ )

σtot (π − )/N2/3 (mb ± 1σ )

9.7 ± 1.2 8.7 ± 1.1 14.3 ± 1.8 15.7 ± 1.9 17.3 ± 2.1 18.6 ± 2.3 20.6 ± 2.5 19.5 ± 2.4 20.1 ± 2.4 19.8 ± 2.5

1.03 ± 0.13 1.62 ± 0.20 1.43 ± 0.18 1.61 ± 0.20 1.68 ± 0.20 1.50 ± 0.18 1.70 ± 0.21 1.72 ± 0.21 1.66 ± 0.20

experimental setups, detection efﬁciencies, and particularities of the experiments at NESSI and PISA will be discussed and a selection of experimental and theoretical results are shown and compared. The experiments at COSY J¨ulich (and LEAR, PS/CERN) were carried out within an international collaboration between the FZ-J¨ulich, the Hahn-Meitner-Institut Berlin, the research center CERN (Geneva),

329

10 Proton-Nucleus-Induced Secondary Particle Production Total cross sections for π + and π − , the + − /πtotal , and the normalization σtot (π + )/Z 1/3 and ratios of πtotal σtot (π − )/N2/3 , incident proton energy is 730 MeV, and crosssection data are from Ref. [124]. Tab. 10.16

Target/element

H D Be C Al Ti Cu Ag Ta Pb Th

σtot (π + ) (mb ± 1σ )

σtot (π − ) (mb ± 1σ )

Ratio + − πtot /πtot

σtot (π + )/Z 1/3 (mb ± 1σ )

σtot (π − )/N2/3 (mb ± 1σ )

13.50 ± 0.73 11.42 ± 0.55 27.30 ± 1.40 35.00 ± 1.80 53.10 ± 2.90 67.00 ± 3.60 77.30 ± 4.30 91.60 ± 5.10 101.00 ± 5.60 104.20 ± 5.80 107.90 ± 5.90

0.03 ± 0.01 1.12 ± 0.06 6.49 ± 0.37 6.64 ± 0.41 13.17 ± 0.90 21.20 ± 1.60 25.20 ± 2.00 35.00 ± 3.00 51.40 ± 4.70 53.70 ± 4.90 60.40 ± 5.50

45.0 10.2 4.3 5.3 4.0 3.2 3.1 2.6 2.0 1.95 1.9

13.50 ± 0.73 11.42 ± 0.55 17.19 ± 0.9 19.28 ± 0.97 22.55 ± 1.24 23.93 ± 1.29 25.12 ± 1.39 25.37 ± 1.41 24.2 ± 1.34 23.99 ± 1.32 24.08 ± 1.32

0.03 ± 0.01 1.12 ± 0.06 2.21 ± 0.13 2.15 ± 0.13 2.26 ± 0.15 2.42 ± 0.18 2.38 ± 0.19 2.26 ± 0.19 2.27 ± 0.21 2.15 ± 0.22 2.22 ± 0.20

30

25 stotal (p+) / Z1/3 [mb]

330

20

15 Data cochran et al. Data crawford et al. 10

5 0

20

40

60

80

100

Nuclear charge Z

Fig. 10.36 Total pion production for π + from various thin targets divided by Z 1/3 as a function of the nuclear charge Z. The plotted data are given in Tables 10.15 and 10.16, where the data of Cochran et al. are for incident protons of 730 MeV, and the data of Crawford et al. are for proton energies of 585 MeV.

GANIL (Caen), INR (Moscow), Rossendorf (Dresden), INP (Orsay), the universities of Rochester and Warsaw and the TU-Munich. The data compiled by the NESSI and PISA collaborations at COSY are of particular interest also for the EU-FP6 integrated project EUROTRANS – (NUDATRA Nuclear data for transmutation of nuclear waste). The goal of that domain is to improve nuclear data in evaluated

10.3 Proton Cooler Synchrotron COSY at J¨ulich

stotal(π−) / N2 /3 [mb]

3

2

1 Data cochran et al. Data crawford et al. 0

0

20

40

60

80

100

120

140

160

Nuclear neutron number N

Fig. 10.37 Total pion production for π − from various thin targets divided by N2/3 as a function of the nuclear neutron number N. The plotted data are given in Tables 10.15 and 10.16, where the data of Cochran et al. are for incident protons of 730 MeV, and the data of Crawford et al. are for proton energies of 585 MeV.

ﬁles and models, which involves sensitivity analysis and validation of simulation tools, low- and intermediate-energy nuclear data measurements, nuclear data libraries evaluation at low and medium energies, and high-energy experiments and modeling. NUDATRA aims at the investigation of: • pA (spallation) reactions in the GeV regime, • data measured from exclusive experiments for testing, validating and developing theoretical models, • double-differential cross sections (DDXS) dσ/dEd of light charged particles (LCP = p,d,t,3 He,4 He, . . .) and intermediate mass fragments (IMFs, Z ≤ 16) in spallation and fragmentation p-induced reactions (0.1–2.5 GeV, C to Au), • reaction mechanism of pN reactions in terms of time scales, simultaneous or sequential emission of IMFs, origin of pre-equilibrium and evaporation processes. 10.3.1 The COoler SYnchrotron COSY

COSY is the abbreviation for ‘‘COoler SYnchrotron,’’ which means as much as accelerator for ‘‘cold’’ particles. However in COSY not only protons can be accelerated up to 96% of the speed of light, but also can stored for ultra slow or fast extraction. The COSY ring as shown in Figure 10.38 consists a 180-m vacuum tube. Protons in the momentum range between 600 and 3400 MeV/c (corresponding to 175 and 2600 MeV) are accelerated and stored. Protons with the desired energy are available for experiments with the circulating beam (”internal experiments”) as

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10 Proton-Nucleus-Induced Secondary Particle Production

Cavity e-Cooler

ANKE

Cosy-11 Fast quadrupoles Stochastic cooling HE polarimeter EDDA

PISA

TOF

NESSI

NESSI

JESSICA

Exchange

332

TOF BIG KARL

GEM, MOMO

LE polarimeter

10 m Cyclotron

Fig. 10.38 Cooler synchrotron COSY in Julich ¨ with the internal and external experimental beam areas. The locations of NESSI and PISA experiment are indicated.

well as for experiments with the extracted beam (”external experiments”). Detailed reports on the performance and perspectives of the Cooler Synchrotron COSY are given in Refs. [725–727]. Twenty-four electromagnets deﬂect the protons rotating in the COSY around 15◦ each so that a course of approximately 360◦ results. Quadrupoles exert a force on charged particles, which is attractive in one plane and repulsive in the plane perpendicular. These focusing and defocusing planes ensure the protons being held together to a bundle during acceleration.

10.3 Proton Cooler Synchrotron COSY at J¨ulich

For the injection process the debit orbit of the particles rotating in the ring is shifted for a short time. The debit orbit is the position intended for the proton beam for a stable closed course in the ring. The particles are shot in on this disturbed course, and during the injection the circulating proton beam is reset on the original debit course. The disturbance of the debit course is accomplished with the use of so-called bump magnets. The entire injection process takes about 0.01 s. By interaction with electron beams (electron-cooling), the proton beam stored in COSY shrinks on the smallest possible expansion. During the ‘‘stochastic cooling’’ the debit course of the circulating proton jet is measured in pick ups and corrected with the help of the kickers. The position of the jet in COSY is measured by 29 position monitors with an accuracy of approximately ∼ 1 mm. This position measurement takes place without contact, i.e., without direct effect on the jet. For the cold moderator experiment JESSICA [551, 611] discussed in Section 13.3.3.2 on page 454, the accelerator COSY was operating in a speciﬁc mode: In contrast to the slow extraction needed generally for experiments at COSY or the relatively long spills applied for internal experiments, the single turn extraction requested by JESSICA meets some challenges for the COSY crew. Fast beam extraction in the proton energy range of 0.8–2.5 GeV is accomplished by the use of a kicker magnet generally employed for beam diagnostic measurements. The cycle starts in the same manner as for resonant beam extraction for external experiments. A closed orbit bump in the horizontal plane is located near the electrostatic septum. The proton beam is bunched with a bunch length in the ﬂat top of about 200–500 ns. The beam intensity peaks at about 1010 p in the ﬂat top. By means of the kicker magnet the beam bunch is short time (0.75–2 µs in width, rise- and fall-time ≤ 1µ s) deﬂected. The kicker excitation is synchronized with respect to the COSY rf-signal and can be adjusted in time by a programmable delay, so a unique deﬂection of the total bunch can be performed (bunch synchronous excitation). Only horizontal beam deﬂection is possible with the kicker magnet installed at a repetition rate of 1 Hz. The minimal COSY cycle time varied from 5 ms in case of low energy to 2 s in the case of highest energy. In order to extract the whole beam stored in COSY in one single turn, electron cooling is indispensable. The relatively long cooling time needed results in a repetition rate of the extracted proton beam of ≈0.03 Hz. The reliability of the kicker magnet has been shown to be rather high. Details are given in Ref. [728]. 10.3.2 The NESSI Experiment

All previous data on production yields have been obtained by measuring the integral neutron-induced activation in a moderator bath surrounding the target, by integrating double-differential neutron yields (d2 σ/dEd), or by neutron-induced activation in small samples positioned on the target surface. For a summary of such measurements see Ref. [621]. Instead, in the NESSI experiment all neutrons produced in each individual shower induced by an incident energetic hadron are counted. In order to demonstrate the inherent capabilities of the new approach, the

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characteristics of the employed detection method will be described brieﬂy in the following. On one hand emphasis is put on a comparison of model predictions with the data obtained with thick targets (cf. Section 11.2.2), where incident energetic protons in the energy range up to 2.5 GeV at COSY (5 GeV/c hadrons at PS/CERN and up to 1.2 GeV p at LEAR/CERN, (cf. Section 12)) impinging on massive targets give rise to cascades of nuclear reactions within the bulk target material. In these kinds of setups, charged reaction products are stopped within the target volume and only neutrons are detected. Speciﬁcally, of great importance are neutron-production cross sections for various incident hadron energies, various target materials, and different target geometries. On the other hand following the motivation of the fundamental physics aspect, results of production cross sections, particle spectra, angular distributions, etc., for neutrons and charged particles taken at thin target measurements have been compared with the corresponding simulations in order to decouple the primordial spallation reaction from the subsequent INC. The NESSI and former PS208 collaborations have enriched the available information by the event-wise measurement of the number of neutrons (called hereafter neutron multiplicity Mn ) [115, 379, 622, 631, 632, 663, 664, 673, 729, 730] using a high-efﬁcient 4π sr gadolinium loaded scintillator detector [631, 731, 732] and provided a heavyset matrix of benchmark data enabling a validation and possibly an improvement in high-energy transport codes. As mentioned in contrast to previous measurements the event-wise character of the experiment allowed to gain access even to the distributions dMn /dN rather than average values only, thus imposing additional constraints for theoretical models [114, 228, 622, 664, 673, 674]. The ﬁrst experiment that measured neutron multiplicity distributions for 0.475 and 2 GeV proton bombarding thin targets was carried out at the SATURNE accelerator at Saclay by Pienkowski et al. [219]. The NESSI experimental investigations comprised both, the so-called thick-target scenario, as discussed in Section 11.2.2, where only neutrons can be observed in the NESSI experiment and multiple-nuclear reactions per source particle2) might take place as well as experiments using thin targets (only one nuclear interaction in the target) as discussed in the current section. While the ﬁrst aspect is triggered by the application driven motivation, the second issue reﬂects the fundamental physics aspect. The latter enables a code validation not only for neutrons, but also for charged particles or even for correlations between them [114, 228, 664, 673, 674]. Insights into the transport process including all cascade particles in thick targets can be gained only by disentangling intra- and internuclear cascades. In addition to the above-mentioned neutron measurements also light charged particles have been measured with π, p, p,3 He and 4 He projectiles in the energy region of 1–14 GeV [663, 675, 733, 734]. However, most of these studies measured energetic cascade and not evaporative light charged particles as p and He, which are needed to get full information on the reaction process. 2) Not only the intranuclear cascade, but also the INC contributes to the production of neutrons following interactions induced by secondary

particles and therefore resulting in a ‘‘multiplication’’ of neutrons.

10.3 Proton Cooler Synchrotron COSY at J¨ulich BNB+BSiB S3,S5-S8

Beamdump

S10

S1 p

S11-14 Targets 1110 cm

605 cm

574 cm

Fig. 10.39

Schematic setup for thin target measurements at COSY accelerator.

Fig. 10.40

Picture of the NESSI neutron ball detector in the COSY experimental area.

10.3.2.1 Experimental Setup of NESSI The setup for the NESSI experiment at the COSY facility is schematically shown in Figure 10.39. Figure 10.40 shows a picture of the NESSI-BNB (Berlin Neutron Ball) as mounted in the COSY experimental area. Visible is the 1.4 m diameter and 1.5 m3 scintillator sphere with the photomultiplier tubes viewing directly into the liquid scintillator. The support structure allows for lifting the upper hemisphere in order to have access to the inner scattering chamber and the 4π Si-ball for charged particle detection. As indicated in Figure 10.39 the incoming protons were tagged by a thin, 0.3 mm, plastic scintillator S1 mounted 11 m upstream from the center of Berlin Neutron Ball (BNB) [631, 731, 732]. Their rate was adjusted to give a similar reaction rate independent of target thickness, i.e., to some 104 pps for thin targets and down to some 200 pps for the 35 cm targets. The detector S1 served as a beam counter for absolute normalization of measured cross sections and provided the time reference for BNB. The incident protons were also monitored by a set of scintillator detectors S3 –S14 partly serving as veto counters and tagging those protons entering

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‘‘off-axis.’’ As mentioned previously, thin-target experiments are aimed essentially at studying the physics of intranuclear cascades, with reaction products having negligible chance for secondary interactions with the target matter. Both neutrons and charged reaction products are detected using two concentric 4π sr detector devices, the BNB and the Berlin Silicon Ball (BSiB) [114, 664]. In this setup, the target is placed in the common operational center of the BNB and BSiB. The latter detector is mounted inside the BNB reaction chamber as schematically indicated in Figure 10.41. In the following, a brief description of the 4π sr detectors, their efﬁciency and the necessary corrections on the data is presented. For more details confer to Refs. [114, 115, 228, 379, 631, 663, 664, 673, 729, 730, 735]. The most recent and comprehensive technical compilations on the two 4π detectors BNB and BSiB are published in Refs. [228, 674, 735, 736]. The electronics and data acquisition are described in [379]. The 4π sr neutron detector The BNB [631, 731, 732] is a spherical vessel – sketched in Figure 10.41 – with an outer diameter of 140 cm and an active volume of 1.5 m3 , ﬁlled with a gadolinium-loaded organic scintillator NE343 (1,2,4-trimethylbenzol = C9 H12 ). It contains a central reaction chamber of 40 cm diameter connected to a high-vacuum beam pipe. The active detector volume is viewed by 24 fast photomultipliers mounted on the outer shell of the BNB. The technical data of the 4π sr BNB are summarized in Table 10.17. The operation of the BNB is based on the detection of gadolinium γ -rays from the capture of neutrons thermalized within the scintillator liquid as shown in Figure 10.41(b). The thermalization of the reaction neutrons is a relatively fast process, occurring on a 0.1 µs time scale. It is accompanied by a light ﬂash generated mostly by the interaction of the recoiling nuclei (mostly hydrogen, but also carbon and oxygen) with the scintillator. This ﬂash, combined with the light produced in the interaction of reaction γ -rays and charged reaction products with the scintillator, gives rise to a ‘‘prompt’’ signal – one of the observables in the Tab. 10.17

Technical data of the 4π sr BNB.

Manufacturer Volume Diameter of reaction chamber Scintillator liquid Gadolinium Gd σ capturea for 155 Gd and 157 Gd Number of photomultipliers Energy resolution Time resolutionb Lower trigger threshold a b

Hahn-Meitner-Institut Berlin 1.5 m3 140 cm 40 cm NE343 (1,2,4-trimethylbenzol) C9 H12 0.4% (wt%) 6.1 × 104 and 25.4 × 104 b 24 no ≤ 3 ns 2 MeVee (electron equivalent)

Capture cross section for thermal neutrons Relative to start-detector

10.3 Proton Cooler Synchrotron COSY at J¨ulich

Photomultipliers

Reaction chamber BSIB Beam dump

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g e g

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Compton eff,Light

Fig. 10.41 (a) Schematic drawing of the NESSI detector system BNB (Berlin Neutron Ball) and the BSiB (Berlin Silicon Ball) in the reaction chamber. (b) The principle of neutron detection in the BNB in three steps: (i) slowing down/thermalization, (ii) storage, (iii) capture, counting.

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NESSI experiments. This signal is an approximate measure of the total kinetic energy of the detected neutrons. A prompt light ﬂash indicates an energy deposition in the detector by any reaction product. As it is detected with virtually unit efﬁciency, it can be used to measure the total reaction cross section, including reactions without neutron emission. Experimentally, one recognizes prompt signals based on their coincidence with valid ‘‘start’’ signals, which are generated by projectiles traversing the thin scintillation detector S1 placed at the entrance to the BNB reaction chamber. The reaction probability PReac for thin targets is obtained by comparing the number of prompt signals with the number of incident particles. The fast thermalization process is followed by a slow diffusion of the neutrons through the scintillator, before they are eventually captured by the gadolinium nuclei present in the scintillator. There is a statistically distributed time lapse for a thermalized neutron to ‘‘ﬁnd’’ such a gadolinium nucleus and be captured, which occurs on a µs scale. The most abundant isotopes 155 Gd with 14.7% and 157 Gd with 15.7% have capture a cross sections for thermal neutrons of (6.1 ± 0.1) × 104 and (25 ± 0.2) × 104 b, respectively. The subsequent capture of γ -ray cascade, with a total energy of approximately 8 MeV, produces a delayed light pulse. Due to the statistical nature of the thermalization and diffusion process, individual neutrons entering the detector volume at the same time instance, are captured at different times, spread over several tens of µs. It is this spread in capture times that allows one to count one-by-one the individual light pulses produced in different capture events and thus, ideally the number of neutrons Mn that have entered the detector volume3) . Mn , the neutron multiplicity, is the essential observable of the BNB. As summarized – in terms of time the neutron detection principle in the scintillator volume is a three step process: (1) thermalization of the neutrons, (2) storage, (3) capture on Gd-nuclei and counting the number of light ﬂashes. Efﬁciency of the NESSI–BNB detector In applications of the BNB, neutron capture γ -rays are counted within a 45 µs counting gate following each reaction event. Hence, as a neutron multiplicity counter, the BNB is a slow device, prone to event pile-up in high-intensity experiments. It is also important to note that not all neutrons are thermalized within the active volume of the detector. Some, especially high-energy neutrons, escape this volume without being captured. Such neutrons are not counted, leading to an overall capture efﬁciency smaller than unity. In the NESSI experiments, the BNB counts mostly low-energy evaporation neutrons, for which the detection efﬁciency is typically εn 82%. In contrast, for pre-equilibrium and INC cascade neutrons of higher energy (30–50 MeV), the detection efﬁciency is of the order of 20–35%. The theoretical neutron detection efﬁciency ε of the BNB as a function of neutron n is shown in Figure 10.42. This efﬁciency was calculated using a kinetic energy Ekin Monte Carlo simulation code [737], assuming a light detection threshold of 2 MeVee 3) The principle of neutron detection dates back to the investigations of Frederic Reines. In

1995, he got the Noble Prize for the recovery of neutrinos.

10.3 Proton Cooler Synchrotron COSY at J¨ulich

Efficiency [e]

0.9

0.6

0.3

0.0

0

30

60

90

Neutron energy [MeV] Fig. 10.42 Detection efﬁciency ε of the BNB as a function n , as calculated with the DENIS of neutron kinetic energy Ekin code [737]. A parameterization of this curve is given in Ref. [115] and Eq. (10.3).

(MeV electron equivalent4) ). In the simulation calculations, the latter threshold was matched to the experimental one, reproducing correctly the measured efﬁciency (82.6%) for 2.16 MeV ﬁssion neutrons emitted from a 252 Cf-source. The ﬁlter applied for the neutrons, i.e., the efﬁciency for detecting a neutron in the 4π neutron ball NESSI is parameterized by the following polynomial function which could easily be implemented in any code: 2 3 + 0.000370167Ekin (Ekin ) = 0.820652 + 0.00689154Ekin − 0.00423934Ekin 3 4 5 +0.000370167Ekin − 1.80244 × 10−5 Ekin + 5.2007 × 10−7 Ekin 6 7 −8.97261 × 10−9 Ekin + 9.06944 × 10−11 Ekin 8 9 −4.95096 × 10−13 Ekin + 1.12679 × 10−15 Ekin .

(10.3)

This parameterization is published in Ref. [115] and shown in graphical presentation in Figure 10.42. In the NESSI experiments, the observed neutron multiplicities are averaged over neutron energy spectra and weighted with the respective detection efﬁciencies. n Since the information on kinetic energies of individual neutrons, Ekin is experimentally not available, the simulation calculations employ the neutron energy as calculated within the model. Additionally, the neutron detection efﬁciency is n calibrated only at low neutron kinetic energies Ekin . At higher energies, the neutron detection efﬁciency is extrapolated based on Monte Carlo calculations. The neutron multiplicity distributions measured with the above setup contained random and target frame related background. The magnitude of the target frame background was determined in separate measurements made without target and subtracted from the measured ‘‘raw’’ multiplicities. The random background was measured online using a second, 45 µs long counting gate pulse, started at 4) The total reaction cross section measured using the prompt response of the BNB with this

threshold corresponds to an inelasticity of at least 2 MeV.

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10 Proton-Nucleus-Induced Secondary Particle Production Tab. 10.18

Technical data of the 4π sr silicon ball. Individual silicon detectors Eurisys Meßtechnika IPH750-500 HMI C surface depletion layer Ceramics 763 mm2 500 µm 14285 cm ∼100 V ∼3.2 kV/cm < 100 keV < 250 ps

Manufacturer Type Detector-type ‘‘Backing’’ Active area Total thickness (depletion zone) Spec. resistance Applied voltage Maximum ﬁeld strength depl. zone Energy res. (5.5 MeV α-source) Time res. (5.5 MeV α-source)

4π sr silicon ball BSiB Granularity Shape Acceptance Radius Weight a

162 detectors, self-supporting 12 penta-, 90 (ir)regular hexagons 91% of 4π sr 10 cm 600 g

Eurisys Meßtechnik, F-67383 Lingolsheim, France.

400 µs after the primary gate pulse. Subsequently, the experimental multiplicity distributions were corrected for this background by deconvolution techniques [379]. All experimental neutron multiplicity distributions shown in the following [115] have also been corrected for the detector dead time of 35 ns and for multiple scattering, but not for the detection efﬁciency. The latter correction was included in simulation calculations in comparisons to experimental data. The 4π sr silicon detector In addition to the neutrons in the thin-target experiments charged reaction products were detected. Light charged particles (LCP: H and He isotopes), intermediate mass (IMF), and ﬁssion fragments (FF) were detected and identiﬁed by the Berlin Silicon Ball (BSiB) inside the BNB (see Table 10.18). The BSiB [114, 228, 664, 735] is composed of 158 independent, 500 µm thick silicon detectors approximating a 20-cm diameter sphere and covering a solid angle of about 90% of 4π sr. Charged particles (CP: H + He + IMF + FF) were identiﬁed by means of TOF versus energy E correlations with a mass resolution of ±3 units for A = 20 and ±15 units for A = 100. Six of the Si-ball detectors at angles between 30◦ and 150◦ are replaced by E − E telescopes. They consist of two fully depleted E silicon detectors (80 and 1000 µm thick) backed by a 7-cm thick CsI scintillator with photodiode read out. These telescopes allow a fully isotopic separation up to about A = 20 and an extension of the covered range of kinetic energy spectra above the BSiB

10.3 Proton Cooler Synchrotron COSY at J¨ulich

thresholds (cf. following paragraph). For thick-target measurements BSiB can be taken out and replaced by thick targets of up to 40 cm length and 15 cm in diameter. Efﬁciency of the Si detectors Due to the absorption or speciﬁc energy loss of LCPs in the target material being evident in particular close to 90◦ , the overall detection efﬁciency of the BSiB for LCPs, calculated with Monte Carlo simulations [663] is about 79–84%, depending on the atomic number Z of the particle. This already takes into account the active area (94%) of the Si detectors and 11 detectors missing for beam in/out, target in/out, TV-camera, some defect detectors and the six detectors replaced by telescopes. The lower energy threshold of the 500 µm thick Si detectors for all charged particles is 2.2 MeV. Protons and α-particles with energies larger than 8.2 and 32.2 MeV, respectively, are not stopped in the 500 µm silicon detectors. Consequently, the lower detection threshold represents at the same time an upper limit for detecting highly energetic p, d, and t of more than 26, 49, and 76 MeV kinetic energy, respectively. For the same reason minimum ionizing particles, π and K fall below detection threshold. For Z ≥ 2 particles on the other hand practically no such upper energy limit exists. The telescopes used at NESSI allowed for a mass resolution of A ≤ 0.2 amu for E/A > 3.5 MeV/A and A ≤ 0.4 amu for E/A < 3.5 MeV/A [735]. The targets The thin targets nuclei ranging from 12 C up to 238 U have typical thicknesses of the order of some 100 µg/cm2 to g/cm2 . The targets were mounted on a 14 cm long Al ﬂag-pole with 0.5 mm × 5 mm proﬁle and positioned perpendicular to the beam axis. Thinner targets (≤ 1 mg/cm2 ) were generally used to measure proton-induced ﬁssion while thicker targets were employed for the measurement of neutron-production and total reaction or inelastic cross sections. The target thicknesses were measured by weighing the energy loss measurements of αparticles from ThC. For thick targets as discussed in Section 11.2.2 three nuclides, Hg, Pb, and W have been chosen which are representative of the target, structure and core materials of the ADS. All pieces were made from chemically pure (≥ 99.98%) material of Pb, W, and Hg, the latter being encapsulated into 1 mm thick stainless steel containers. 10.3.2.2 Experimental Results of NESSI An example of the capability of the NESSI experiment is presented in Figure 10.43. It shows the eventwise correlation of neutron versus charged particle multiplicities measured with the two almost 4π devices. With the simultaneous measurement of mainly evaporative-like neutrons and charged particles (CP) detailed exclusive information is obtained on an event-by event base. The multiplicity correlations are shown in Figure 10.43 representatively for 2.5 GeV proton-induced reactions on target nuclei ranging from 13 Al to 238 U. The target thicknesses between 0.1 and 1.0 g/cm2 correspond to reaction probabilities of 1–5 × 10−3 . The best description of the coincidence data for multiplicities LCPs vs. the multiplicity Mn can be found in Ref. [233].

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Fig. 10.43 Correlation of measured (NESSI) light charged particle(LCP) vs. neutron multiplicity for 2.5 GeV protoninduced spallation reactions on various targets from Al to U. The color scale gives the relative yield for each target per multiplicity bin; the thermal excitation is following the indicated arrow in the upper left corner of the ﬁgure.

As a general tendency, an increase of both, Mn and MCP , with increasing A and Z of the target is observed. This is mainly due to the fact that larger target nuclei incorporate more energy from the INC and have lower particle separation energies than do lighter ones. Also, at lower excitations for heavy nuclei (Au, Pb, U relative to Al, Fe,...) emission of neutrons is strongly favored over that of LCPs and at higher excitations, when comparing Au to U, one observes again a shift of the measured distributions toward larger neutron multiplicity as a result of a further reduction of neutron separation energies. The total number of evaporative particles is strongly correlated with E ∗ indicated in Figure 10.43 by the arrow for Al. The multiplicities are employed to deduce excitation energy distributions dσ/dE ∗ as described in detail in Ref. [379, 663, 664]. The procedure allows to analyze observables as a function of E ∗ . In ﬁgure 7 of Ref. [233], a comparison of such a correlation between experiment and ﬁltered (cf. Eq. (10.3)) INC+GEMINI calculation has been given. The particular advantage of the presentation in Figure 7 of Ref. [233] is that the correlation is shown both for GEMINI (evaporation only) as well as for the full calculation (INC+ GEMINI). The z-scale in that ﬁgure presents the production cross section expressed in mb per Mn and MLCP units as a function of LCP and neutron multiplicity. Particle multiplicities-neutron production Of signiﬁcant interest for a wide range of applications and fundamental research, in particular at the crux of spallation neutron sources, transmutation of nuclear waste in ADS, and shielding issues

10.3 Proton Cooler Synchrotron COSY at J¨ulich

100

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Fig. 10.44 Measured (symbols) and calculated (histograms) neutron multiplicity distributions of NESSI for 1.2 GeV p+Al,...,U. Note different neutron multiplicities Mn s scales for the left and the right panels.

are also neutron-production double-differential cross sections in GeV protoninduced spallation reactions. In Figure 10.44 neutron multiplicity distributions for 1.2 GeV p+Al,...,U are compared with calculations following the INCL2.0/GEMINI model. These distributions are projections onto the Mn axis of two dimensional presentations like the one given in Figure 10.43. Although generally described satisfying by, e.g., INCE codes, neutrons are more difﬁcult to detect than protons or LCPs. Experimental double-differential neutron-production spectra represent a valuable observable also for validating new model developments or improvements [117, 171, 172, 261]. It is also interesting to look at neutron multiplicities Mn

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10 Proton-Nucleus-Induced Secondary Particle Production

as global properties of neutron spectra which are not easily revealed by their inspection. An extensive overview on the observable Mn for thin targets is compiled in Refs. [115, 172, 622, 631]. In order to compare the calculated with the measured distributions the calculations are shown before (dashed histogram) and after (solid, shaded histogram) folding with the neutron energy dependent detection efﬁciency ε of the BNB (cf. Section 10.3.2.1). Note the different Mn scales for the left and right panels. When taking ε into account, the INCL2.0/GEMINI calculations agree well with the measured distributions. For heavier targets and low Mn there exists a discrepancy between experiment and calculations. A similar discrepancy was reported [730] and ascribed to the sharp cut-off modeling of the nuclear density distribution in INCL2.0. Light charged particle and IMF production The emission of composite particles such as 2,3 H, 3,4,6 He, and Li has long been recognized as an important decay channel in spallation reactions. The pioneering experiments of Poskanzer et al. [738] have shown that the emission of these composite particles could not be accounted for by a single evaporation mechanism. Indeed, the emission is far from being isotropic in the emitter frame and the energy spectra exhibit a high-energy tail in excess of the usual evaporative component. Further experiments [739] have conﬁrmed these ﬁndings at different bombarding energies and for several target nuclei. It was also shown that the neighboring isotopes 3 He and 4 He have very different behaviors with a strong and weak component of nonevaporative particles, respectively. However, in all these studies the underlying reaction mechanisms could not be investigated thoroughly due to the lack of additional experimental information. Taking advantage of the very exclusive data brought by the NESSI detector arrays a detailed study of composite particle emission was conducted. As an example of LCP production, double-differential energy spectra of 1,2,3 H and 3,4 He ejectiles following 1.2 GeV p-induced reactions on Ta target as measured by the NESSI collaboration at COSY-Juelich are shown for different angles with respect to the incident proton in Figure 10.45. The experimental data clearly feature two components: an evaporation component dominant for all angles at low-kinetic energies and a high-energy component; The higher the kinetic energy of the ejectiles the smaller their emission angle on average in respect to the incident proton beam. Here [228] for the theoretical description the INCL2.0 [170] intranuclear cascade code is coupled to the evaporation code GEMINI [229]. Only for protons both the components can be well described. Due to the lack of composite particle emission in the early phase of the reaction in the INCL2.0 model, the high-energy tails of the spectra for d, t, and 3,4 He are not described by the calculations. The shape of the calculated evaporation component (shaded histogram in Figure 10.45) however is also well reﬂected for composite particles. The calculations confronted with the measured total He (3 He+4 He) production cross sections as shown in Figure 10.46 generally tend to underestimate the experimental data because of 5–20% pre-equilibrium emission (not taken into

10.3 Proton Cooler Synchrotron COSY at J¨ulich

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Energy [MeV] Fig. 10.45 Energy spectra of 1,2,3 H and 3,4 He for 1.2 GeV p+Ta. Dots: experimental data, shaded histogram: calculated evaporation spectra, dashed histogram: pre-equilibrium protons as calculated by INCL2.0 (after Herbach et al. [228]).

account in INCL+GEMINI). Although it is obvious that there is some discrepancies between different sets of data, Figure 10.46 clearly exhibits the need to solve deﬁciencies or discrepancies of different models. A comprehensive set of published data and NESSI results for He production cross sections is also compiled in the EU-Hindas Report [543]. Previous measurements essentially exploited mass spectrometry methods [740, 742] for gas extracted from irradiated samples and only a few measurements are based on methods with E − E telescopes for isotope, mass, and energy identiﬁcation [414, 738]. As for example for p+Fe, the measured helium production cross sections in the NESSI experiment (440 ± 44 mb) are about a factor of two

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INCL2 + GEMINI LAHET(RAL)

2 Total helium production cross section s He [b]

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LAHET(ORNL) HERMES 1.5

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0.5 Herbach2005 Michel1995 0

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Fig. 10.46 Total He (3 He+4 He) production cross sections for 1.2 GeV p+X (NESSI). Symbols: experimental data: Herbach2005 [228], Enke1999 [114], Michel1995 [740], Leya2005 [741]; Lines: calculation by INCL2.0+GEMINI, LAHET and new version of INCL (cf. Section 5.2.1 on page 209) (after Herbach et al. [228]).

smaller than the other experiments (792 ± 55 mb) [740]. This corresponds to a discrepancy of a factor of 1.8 or about 6 standard deviations. On the other hand, the present results for Fe and Ni agree quite well with the older measurements of Goebel et al. [742]. A large spread of experimental He cross sections found in literature is also evident when comparing model calculations. The cross sections as calculated with the LAHET (with RAL ﬁssion model) and the HERMES(with RAL ﬁssion model) are somewhat smaller than the NESSI data in case of light targets (Fe,Ni,...) while for heavy targets LAHET (with RAL ﬁssion model) and HERMES predict larger cross sections and LAHET(with ORNL ﬁssion model) smaller ones (cf. Section 5.2.1 on page 209). The calculations with the INCL2.0/GEMINI model combination are in good agreement with the data throughout all nuclei and incident energies [664]. Recent results of measured mass distributions in the reverse kinematic reaction of 800 MeV/nucleon Au+p are also well described [743] by the INCL code coupled, however, to a different evaporation/ﬁssion code [221, 222]. As pointed out above the discrepancies between the data and the HERMES and LAHET calculations are associated with the ﬁnding that these codes overestimate

10.3 Proton Cooler Synchrotron COSY at J¨ulich

Proton (1.2 GeV) + Au

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Fig. 10.47 Angular distributions dσ/d of 1,2,3 H and 3,4 He for 1.2 GeV p+Au. Symbols: experimental data, lines calculation by INCL2.0/GEMINI (after Herbach et al. [228]).

E ∗ after the prompt INC and with different handling of the Coulomb barriers in the employed evaporation codes. For 1.2 GeV p+Au in Figure 10.47(a), the angular distribution of disentangled evaporation and pre-equilibrium components are shown in Figure 10.47(b) (for details see [228]). For all particle species the evaporation exhibits an isotopic behavior, while more directly emitted particles show larger forward/backward asymmetry. The strong declines of the angular distributions for the pre-equilibrium particles are almost identical for all H and He isotopes. Also the differential cross section for particles with equal Z, but different A does not vary substantially. However, as expected, lower kinetic particles (typically from evaporation process) show an almost isotropic angular distribution, and the slopes are similar for the various isotopes (cf. Figure 10.47(a)). The absolute differential cross sections, however, differ considerably since they are governed by the binding energies of the composite particles. The production cross sections of 6,7,8,9 Li and 7,9,10 Be isotopes for 1.2 GeV protons on different targets (C to Au) as well as the total production cross sections of Li and Be are shown in Figure 10.48. Note that for pre-equilibrium protons the angular dependence is well described in the INCL2.0 model. It would be certainly worth to compare the current experimental data [228] with, e.g., the latest version of INCL4.3 [117] including a coalescence

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Fig. 10.48 Production cross section of (a) and 7,9,10 Be isotopes (b) for 1.2 GeV p+X. Bullets •: NESSI [228], triangles: Dostrovsky [744], stars: Michel [740] data, lines: calculation by INCL2.0/GEMINI.

formalism allowing the cluster emission of composite nucleons (d, t, 3,4 He) in the early phase of the reaction. The production of all individual isotopes does not strongly depend on Z. When looking more carefully at the energy spectra of the IMFs (shown in Figure 10.49), ones more as expected the combination of INCL2.0/GEMINI fails to describe the high-energy tails of the energy spectra. Nevertheless in Figure 10.48 the calculated angle and energy-integrated production cross sections agree generally rather well with the NESSI [228, 740, 744] data, because the pre-equilibrium component may amount to the total cross section only on the percent level. The lines representing the model prediction are reﬂecting the ejectiles coming from evaporation model only, i.e., GEMINI. The experimental data on 7 Be and 10 Be ejectiles measured for low Z-targets by mass spectrometry [740] coincide with the systematics of the NESSI experiment [228]. In a similar presentation one observes the multiplicity/production cross sections of the neutron rich 6 He isotope strongly increasing with atomic number Z of the bombarded target (cf. Figure 10.50) – a very similar behavior to the one which is observed for the ‘‘neutron rich’’ triton. In contrast to the 3,4 He isotopes, for 6 He the INCL2.0/GEMINI calculations overestimate the experimental results of Herbach et al. [228] by approximately 30%. Please note that in the NESSI data for 1.2 GeV proton-induced reactions mentioned above [228] all cross sections have been corrected not only for double hits, geometrical efﬁciencies, and background as measured with empty frames and dead times, but also for the contribution below the lower energy threshold (Table 2, page 434 of [228]) of the Si detectors. Indeed this had been done by extrapolating

10.3 Proton Cooler Synchrotron COSY at J¨ulich

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Fig. 10.50 Multiplicity of 6 He isotopes as a function of the target charge number Z, bullets •: [228], line: INCL2.0/GEMINI.

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10 Proton-Nucleus-Induced Secondary Particle Production

to zero energy for the cross-section contribution. The hydrogen and He production cross sections – including errors – are given for Al, Ti, Fe, Ni, Cu, Zr, Ag, Ho, Ta, W, Au, Pb, Th, and U in Table 3 of Ref. [228]. Thresholds are speciﬁed in Table 3. Tables 4 and 5 give the cross sections for the individual p,d,t and 3 He, 4 He and 6 He isotopes, respectively. Table 6 provides the very same targets the production cross sections for 6 Li, 7 Li, 8 Li,9 Li, 7 Be, 9 Be, and 10 Be. Timescale of ﬁssion in GeV proton-induced reactions on Au, Bi, and U Integrated ﬁssion cross sections have been measured for a large variety of projectiles on thorium and uranium. Simbel et al. [745] studied proton-induced ﬁssion on Th and U in the energy range 0.1–30 GeV . These data exhibit an almost constant cross section up to 1 GeV and a decline beyond. This decline is interpreted by Simbel as the onset of multifragmentation [746]. Also for d-, α-induced ﬁssion [747] and heavy ion-induced ﬁssion of U and Th [748] the ﬁssion cross section decreases with incident energy of the projectiles, respectively. This tendency is corroborated by Ar+Th measurements [749], which show complementary an increase of (heavy residual) HR cross sections with increasing incident energy. Ledoux [710] measured the relative ﬁssion probability of 475 MeV –p and 2 GeV – 3 He-induced reactions on U as a function of evaporated neutrons. The experimental challenge is to measure ﬁssion probabilities of hot nuclei at low spin up to highest temperatures as a function of E ∗ , also including nuclei with higher ﬁssion barriers. For this purpose Hilscher et al. [219, 621] proposed to study ﬁssion induced by high energetic light particles using the 4π detector array NESSI. As discussed in Section 9.4 light-ion-induced particles provide an ideal tool for the investigation of ﬁssion and other decay channels almost free of inducing collective excitations in the target nucleus. In this section, the ﬁssion probability Pf (E ∗ ) of highly excited target like nuclei produced in reactions of 2.5 GeV protons on Au, Bi, and U is discussed as a function of excitation energy E ∗ , whereby E ∗ is deduced event-wise from the multiplicity of evaporated light particles[379, 663, 664, 750]. The overall time elapsed from the equilibrium deformation up to the scission (10−20 s) is known to be quite long compared to other processes like the emission of neutrons [751]. Although the entire ﬁssion process is slow, the decision to ﬁssion can be fast. For the three targets, the dependence of the inelastic cross section, σinel , and the ﬁssion cross section, σf , as a function of E ∗ [735, 736] was studied. Their ratio, the ﬁssion probability Pf (E ∗ ) = σf (E ∗ )/σinel (E ∗ ), provides the best possible evidence for the presence of dissipative or transient effects in ﬁssion and is shown in Figure 10.51. Fission fragments have been separated from heavy residues and intermediate mass fragments by constraints as discussed in more detail in Ref. [750]. The total ﬁssion cross sections deduced the amount to σf = 200 ± 60, 320 ± 50, and 1350 ± 120 mb for Au, Bi, and U, respectively, in agreement with Ref. [753]. Despite the large differences in ﬁssility and ﬁssion barriers, Bf ≈ 5, 12, and 21 MeV of the initial nuclei U, Bi, and Au, respectively, at the highest E ∗ of 1000 MeV, Pf amounts to 30% for all three target nuclei. Intranuclear-cascade plus statistical model calculations satisfactorily reproduce the observed evolution of Pf

10.3 Proton Cooler Synchrotron COSY at J¨ulich

Fission probability Pfission

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Fig. 10.51 Comparison of the experimental (symbols) and the simulated (histograms) ﬁssion probability as a function of E∗ . The simulation for p+Au with af /an = 1.05 and τd = 2 × 10−21 s according to Ref. [752] is shown by the chain dotted histogram (after Jahnke et al. [750]).

with E ∗ – provided that no extra transient delay is introduced. A dynamical ﬁssion hindrance or transient time which suppresses ﬁssion at higher E ∗ or reduces σf , might be compensated by a larger value of the level density at the saddle point. As for example the chain dotted line for Au target nuclei in Figure 10.51 shows that for τd = 2 × 10−21 s and af /an = 1.05, the calculation fails to describe the actual Au ﬁssion data. The differential observation of dPf (E ∗ )/dE ∗ allows an independent determination of af /an and τd . Concluding, ﬁssion is decided upon very fast and early in the long deexcitation chain toward scission, e.g., at high excitations. Consequently the large amount of remaining excitation must be carried off, either during the descent from saddle to scission or after scission (cf. Section 3.7.1 and the schematic illustration in Figure 3.9(a)). Indeed according to the calculation at E ∗ = 800 MeV, only between 11%(Au) and 23%(U) of all light particles are emitted before reaching the saddle, or expressed in terms of pre- and postsaddle LCP LCP = 1.9, 1.9, 3.3, and Mpostsaddle = 11.0, 10.4, 7.6 for Au, Bi multiplicities, Mpresaddle and U, respectively. Angular correlations between α-particles and ﬁssion fragments (FFs) and the measurement of pre- and postscission α-multiplicities allow insights into the ﬁssion dynamics. In the NESSI experiment, post-scission LCP emission can be deduced from the angular correlation with the ﬁssion axis. The energy spectra of α-particles for three ranges of emission angles relative to the motion direction of the light ﬁssion fragment is shown in Figure 10.52. The spectra are plotted in the center-of-mass system of the FFs from the reaction 2.5 GeV p+Au at E ∗ = 600–900 MeV. The different contributions from the compound nucleus prior to scission (uncorrelated to the scission axis), and from the two FFs which vary in shape and intensity with θα-LF are indicated. The sum of all components (including the neck emission at 70◦ to 100◦ ) shown in

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10 Proton-Nucleus-Induced Secondary Particle Production

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Fig. 10.52 α-particle energy spectra for three angular domains relative to the motion of the light ﬁssion fragment: θα -LF as indicated in the ﬁgure; dots: experimental data, lines: contribution from compound nucleus prior to scission (thick continuous lines), from the light (dashed lines) and

10

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from the heavy (dotted lines) ﬁssion fragments. At 70◦ to 100◦ , a further component for neck emission is added (thin line). The total calculated spectrum is shown by the histogram. Example: 2.5 GeV p+Au at E∗ = 600–900 MeV (after Jahnke et al. [750]).

Figure 10.52 as histograms provides a good approximation at least to the lower energy (Eα ≤ 35 MeV) part, e.g., to the evaporation part of the spectra. The highenergy tails in the measured spectra, instead, originate partly from pre-equilibrium processes and are, since not taken into account in the simulation, deviating slightly from the experimental data. For further details, the interested reader is referred to [750] and references given therein. Vaporization and multifragmentation Besides the evaporation and ﬁssion, the event group with IMFs as the heaviest detected fragments (cf. deﬁnition of IMFs in Section 3.10) deserves particular attention in the context of multifragmentation (MF). The question is whether these events stem from true MFs, i.e., the complete fragmentation solely into IMFs and light particles, or are only the remnants from events where heavier masses have eluded detection. Such processes can be reliably identiﬁed only by using highly efﬁcient detector arrays like NESSI or the one which is reported by the INDRA collaboration [754–756]. The INDRA collaboration observed the onset of vaporization in the Ar+Ni reaction at an available energy of 12 MeV/nucleon for the excitation of the composite system with an overall probability of 5 × 10−6 . In the following the observations made for 1.2 GeV p-induced reactions on Cu (1.1 mg/cm2 ) and Ag (1.5 mg/cm2 ) targets are discussed as a function of E ∗ . It has been demonstrated in Refs. [663–667, 669] that the maximum thermal excitation energy in heavy nuclei (Ho-U) is about 4–5 MeV/nucleon. The conclusion drawn for such energies was essentially, that the nucleus either survives as a self-bound entity (evaporation residue), or undergoes ﬁssion. However for lighter nuclei such as Cu, excitation energies larger than the total binding energy of the system are expected and thus vaporization might be reached [362, 439, 445]. The reconstructed experimental excitation energy distributions dσ/dE ∗ for Cu and Ag following p-induced reactions are shown in Figure 10.53 as solid dots.

10.3 Proton Cooler Synchrotron COSY at J¨ulich

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Fig. 10.53 Reconstructed experimental excitation energy distributions dσ/dE∗ ; (•) for p (1.2 GeV) + Cu (a) and Ag (b). Lines correspond to INC-calculations [676, 757]. The bottom scale shows E∗ divided by the average mass of the hot nucleus Ahot = AINC at equilibrium, where AINC is taken from INC model simulation.

The experimental results are in good agreement with the predictions on INC model calculations. Both distributions extend beyond the total binding energy (≈ 8 MeV/nucleon) and, hence, processes such as MF and vaporization are energetically possible in both reactions. For both systems studied, a continuous decrease of the heaviest detected fragment is observed with increasing E ∗ . The ‘‘canonical’’ A = 4 limit is reached only for the p + Cu system, at E ∗ of about 350 MeV or 7.5 MeV/nucleon, taking into account the loss of mass in the INC stage of the process. For the p + Ag reaction, however, the heaviest detected fragment is always larger than about 15 mass units. For the p + Cu reaction about 300 good candidates for vaporization events were detected corresponding to a cross section of about 3 ± 1 mb or 0.3% of the total reaction cross section. The angular distribution of evaporated-like LCPs of this event class is almost isotropic, similar to the distribution of particles from other decay modes, indicating the vaporization of a thermalized source. The total probability for vaporization in the current experiment is found to be a factor of 10 larger than the value reported at similar E ∗ by the INDRA collaboration [754–756]. This discrepancy might be associated with the faster heating mediated by p compared to heavy-ion reactions. The ratio of vaporization cross section relative to the reaction cross section is presented for the p + Cu system in Figure 10.54 as a function of E ∗ . Even for the highest E ∗ (600 MeV or 15 MeV/nucleon) this ratio does not exceed 15%. The dashed line illustrates the same observable predicted by the GEMINI code. As already mentioned note that GEMINI predictions should be taken with some care because the fact that the emission times are large compared to the energy

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Fig. 10.54 Top panel: ratio of vaporization cross section, σv , to the reaction cross section σR for 1.2 GeV p+Cu. The dashed line presents the INC-GEMINI simulation. Lower panels: mean multiplicities of neutrons, LCPs (Z = 1, 2) and IMFs as a

function of E∗ for Cu (left panel) and Ag (right panel). The open (ﬁlled) symbols are for all (vaporization) events. The dashed lines illustrate the mean IMF multiplicity for INC plus GEMINI calculations (after Pienkowski et al. [670]).

relaxation times (as is implicitly assumed in sequential-evaporation models) might not be fulﬁlled at E ∗ larger than about 4–5 MeV/nucleon. However, the excitation energy threshold for statistical decay depends mainly on the mass excess balance and Coulomb repulsion energy, so obviously GEMINI model (cf. Section 3.6 on page 159) is at least able to estimate correctly the observed threshold energy for the p + Cu reaction. For the p + Ag reaction the INC+GEMINI calculations predict the onset of vaporization at excitation energies about 9–10 MeV/nucleon, close to the maximum excitation energies observed in this reaction. This ﬁnding corroborates the observed absence of vaporization events among the collected data for the p + Ag system. For both reactions, p + Cu and Ag, the lower panels of Figure 10.54 present the mean multiplicities of neutrons, LCPs (Z = 1, 2) and IMFs (4 ≤ AIMF ≤ 25) as functions of E ∗ . The open and solid symbols in the ﬁgure represent all events and vaporization events, respectively. Near the vaporization threshold the ratio MZ=2 /MZ=1 is approximately one and is considerably larger than for other decay modes at the same E ∗ . Beyond the vaporization threshold MZ=2 is decreasing with E ∗ , while Mn is increasing. This ﬁnding was also observed by the INDRA collaboration for the Ar+Ni system at 12 MeV/nucleon [754–756]. Close to the

10.3 Proton Cooler Synchrotron COSY at J¨ulich

vaporization threshold the INC+GEMINI code also predicts MZ=2 /MZ=1 ≈ 1. The average IMF multiplicity MIMF saturates with increasing E ∗ around MIMF ≈ 1 and MIMF ≈ 2 for the p + Cu and p + Ag systems, respectively. No sudden onset of MF can be observed in the data and the trends in Figure 10.54 do not indicate MF as a conceptually distinct process. Instead the observed multifragment events may reﬂect statistical ﬂuctuations in the decay modes. This conclusion is justiﬁed all the more when looking at the good agreement of multifragment events of the sequential-emission model GEMINI with the experimental data. When deﬁning MF as a process ending with three or more IMFs in the exit channel, one can obtain quantitative characteristics for the so-deﬁned phenomenon. The relative abundances of events with three or more IMFs is discussed in Refs. [664, 670] as a function of E ∗ . A saturation of the probability at about 5% is observed for the p + Cu system, while for the p + Ag system a monotonic increase up to 20% at highest E ∗ is deduced. In agreement with the predictions in Ref. [362], for both systems studied the threshold excitation for such MF is around E ∗ ≈ 4 MeV/nucleon. This agreement, however, does not provide sufﬁcient arguments for a conclusion that the IMF production proceeds in the studied systems according to the general scenario regarded in Ref. [362]. Rather, it is an indication that no exotic scenarios are needed in this case to explain the experimental results. For ion-induced reactions, the phenomenon of MF [658, 675, 734] and the extraction of the time scales [441] have intensively been studied in the past. For p-induced reactions, MF has been measured for the ﬁrst time. The cross section for the MF process as deﬁned is estimated at 20 ± 5 mb and 30 ± 7 mb for the p-induced reactions on Cu and Ag targets, respectively. The latter value for the p + Ag system is very close to the 35 mb reported [758] for MIMF ≥ 3 events in the 3 He+Ag reaction at 3.6 and 4.8 GeV. In any case, the mean IMF multiplicities of the analysis on NESSI data and the values quoted by Kwiatkowski et al. [675] for 4.8 GeV 3 He+nat Ag and 197 Au reactions are substantially smaller than the published data of Lips et al. [734] for relativistic α-particle-induced reactions. The discrepancies may be based on the larger angular momenta involved in ion-induced reaction mechanisms. 10.3.3 The PISA Experiment

The international collaboration PISA (Proton Induced SpAllation) [656, 664, 759–762] aims at the measurement of total and double-differential cross sections for products of spallation reactions on a wide range of target nuclei (C–U), induced by protons of energies between 100 and 2500 MeV. These cross sections are important for testing physical models of the interaction of protons with nuclei what is of crucial importance for planning and constructing any spallation neutron source. The most restrictive tests of the models are provided by data from exclusive experiments. Therefore, coincidence measurements (high-energy protons with other charged

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particles) are performed besides the inclusive experiments. Additionally experiments with light targets up to Fe will provide the data, which are very important for understanding the anomalous abundance of light elements in the cosmic rays. The mass dependence of the cross sections for full range of targets from C to Au should shed light on the competition of various mechanisms of interaction of protons with nuclei. The PISA project is aiming at a quite similar physics program as NESSI, however with a completely different setup and at an internal beam location. At the internal beam of COSY the investigation of the reactions induced by protons on thin targets (50–200 µg/cm2 ) enables to get the cross sections without the absorption and energy loss involved with the propagation of reaction products in the material of the target. The multiple circulation of the beam in the COSY ring is used to compensate for the small reaction rate of beam protons with the thin targets. The advantages of internal experiments are therefore higher statistics and more precise information on the very tails of double-differential energy spectra, which are important particularly for rare decay channels and low-production cross sections of IMFs. PISA is supported by the European Commission through European Community-Research Infrastructure Activity under FP6 ‘‘Structuring the European Research Area’’ program (CARE-BENE, contract number RII3-CT-2003-506395 and Hadron Physics, contract number RII3-CT-2004-506078) as well as the FP6 IPEUROTRANS FI6W-CT-2004-516520. 10.3.3.1 Experimental Setup of PISA The set up of the PISA apparatus is shown in Figure 10.55. Each of the eight detection arms (as shown in detail in Figure 10.55) mounted at the scattering chamber of the PISA experiment consists of two multichannel plates (MCPs) working as ‘‘start’’ and ‘‘stop’’ detectors for the TOF measurement, a Bragg curve detector (BCD) [759, 760] followed by three silicon detectors of 100, 300 and 4900 µm thickness for particle identiﬁcation using E-E techniques and kinetic energy measurement of intermediate-mass spallation products, and a set of double layer scintillation detectors – fast and slow (phoswich detectors) in order to identify light charged evaporation and spallation products like p, d, t, and He. It is shown that the TOF plus BCDs provide identiﬁcation of light heavy ions with mass up to 20–30 and kinetic energy starting from less than 1 MeV/amu. The Bragg curve detector After ﬁrst successful attempts to use ‘‘Bragg curve spectroscopy’’ to identify highly ionizing particles [763, 764] several detectors exploiting characteristic features of the Bragg curve have been built and used for various applications. The appearance of BCDs has allowed to detect fragments with high precision over a broad range of nuclear charges with low registration thresholds. This has also been demonstrated already in former experiments on fragment production cross sections in carbon at GeV proton beams [765, 766]. The design of the BCD is presented in Ref. [767]. The design features of the BCD are very similar to those of Ref. [768] and references therein. Advantages (as e.g., resistivity to radiation damage and insensitivity to minimum ionizing particles)

10.3 Proton Cooler Synchrotron COSY at J¨ulich PISA Setup – october 2002 100°

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40 60 80 100 120 140 160 Time [samples of FADC]

(b) Typical output signal from BCD the whole length of a signal describes the kinetic energy E of the particle. Other parameters like the range of the particle in the detector medium, R, or the partial energy losses DE can also be extracted from the shape of the curve.

of BCDs compared to alternative detectors (gas-semiconductor ionization chamber, solid-state detectors, CsI(Tl)-crystal scintillators, etc.) are outlined in Ref. [768]. The BCD as shown in Figure 10.56(a) is in principle an ionization chamber with a gas volume of 22 cm in length and 5 cm in diameter. It is sealed off at the entrance by a 3 µm thick carbon-coated mylar foil supported by a wire mesh, which will be operated at ground potential and at the rear end by an anode as printed board. The mesh supporting the entrance window is electrically connected to the cathode in order to avoid undesirable charge collection near the window. The Frish grid, which deﬁnes the ionization sampling section in a 2-cm distance from the anode, is made of 20 µm gold plated tungsten wires with 1 mm spacing. The voltage of +1800 V between the Frish grid and the entrance window is divided by a resistor chain, which is connected to nine ﬁeld-shaping rings in order to maintain a homogeneous electric ﬁeld over the active detector volume. All internal parts are

10.3 Proton Cooler Synchrotron COSY at J¨ulich Tab. 10.19

Main parameters of the Bragg curve detector.

Active length Frish grid to anode gap width Cathode voltage Frish grid voltage Anode voltage Number of guard rings Cathode Anode Type of gas Pressure

200 mm 19 mm 0 V grounded 2400 V 2900 V 19 Mylar foil (3.5 µm) Mylar foil (1.5 µm) Isobutane (99.9% purity) 300 mbar

ﬁxed to an isolating skeleton made of plexiglass. The particles enter through the cathode and leave an ionization track parallel to the electric ﬁeld. For charged, nonrelativistic particles the Bethe–Bloch formula for its speciﬁc energy losses in a given medium can be simpliﬁed to: −dE/dx ∝ cZ2 /E, where Z and E are the atomic number and kinetic energy of the detected particle, respectively, and c contains all relevant constants together with the quantities characterizing the detector medium. Since the energy loss per single collision is small, dE/dx increases slowly along the particle path. Only when the remaining energy is small, dE/dx increases rapidly forming the so-called Bragg peak (BP). The electrons along the track drift through the grid and are viewed as an anode current. The output signal from the anode as a function of time is proportional to the energy-loss distribution of the detected particle along its path through the detector. The atomic number of the incident detected particle is therefore related to the maximum pulse height, which corresponds to the Bragg peak and the total kinetic energy of the particle is obtained from the integration over the total output signal. The detector is ﬁlled with isobutane5) and operated at a pressure of about 300 mb. Practically, for a given gas pressure the voltages for anode and the Frish-grid shall be increased as long as the amplitude of the output signal is saturated and the signal length reaches the minimum. It indicates that the recombination of the electrons traveling through the detector is minimal, all of them are passing the Frish grid and are collected at the anode. The principle of Bragg curve spectroscopy is given in Figure 10.56 where a typical output signal of a BCD is presented. The main parameters of the BCD as being used at PISA are summarized in Table 10.19. In addition to the usual charge identiﬁcation by Bragg spectroscopy in the PISA experiment an isotope separation for almost all detected particles was achieved. The basic experimental information concerning the BCD was received from a VME-ﬂash ADC module (CAEN Mod. V729A, 40 MHz, 12 bit) allowing to perform data processing of about 1000 sample Bragg curves per second. In order to test 5) Since isobutane is characterized by 30% lower effective ionization potential compared to argon or the so-called P10 mixture (90% of

argon, 10% methane), the number of primary released electrons is increased.

359

360

10 Proton-Nucleus-Induced Secondary Particle Production Tab. 10.20 Lower (Emin ) and upper (Emax ) detection threshold for various isotopes in the PISA experiment.

Particle Emin (MeV) Emax (MeV)

p

d

t

2.0 160

2.6 215

3.0 250

3

He

2.0 580

4

He

2.5 650

6

Li

4.0

7

Be

4.5

10

B

9.0

11

C

11

14

N

14

16

O

16

the reliability of the ﬂash-ADC, the Bragg signals were also digitized with two conventional standard NIM ADC modules. Data were taken with both methods and showed agreement within less than 1%. If the particle was stopped in the active chamber volume, apart from the measured TOF, the following values were calculated from the pulse shape: the integral of the speciﬁc ionization over the track (total kinetic energy E of the particle), the maximum of the Bragg peak from the maximum of the speciﬁc ionization of the ion (BP proportional to Z), the duration R (corresponding to the range in the BCD gas volume) and a partial integral from the speciﬁc ionization at the beginning of the track (∝ E/dx ). Isotope identiﬁcation has been performed by using the correlations between the parameters R, E, E and TOF. The BCD is capable of measuring isotopic distributions of fragments ranging from Z = 2 to Si down to emission energies as low as 1 MeV/nucleon. The phoswich detectors While the energy and charge of the heavier spallation products (Z ≥ 3) will be determined using BCDs [767] combined with channel plate TOF detectors [664], light spallation products (Z = 1, 2) will be measured by employing phoswich detectors [767] placed behind the BCDs. PISA is using the phoswich scintillation detectors of conical-hexagonal shape, produced by BICRON Corporation. The face of the detector is a 1 mm thick with a slow 940 ns decay time CaF2(Eu) scintillator, acting as an energy-loss (E) detector, and a 313-mm thick fast scintillator BC-412 with a 3.3 ns decay time, acting as energy (E) detector. Particle identiﬁcation is possible via E − E technique for H, and He isotopes. The front cross section of the phoswich detector is a hexagon of 25.2 mm diameter. In these phoswich detectors 10-stage Hamamatsu HTV 2060 photomultiplier tubes are used. Due to energy losses of particles in the ‘‘thin’’ slow scintillator the energy range of correctly detected light particles is 15–150 MeV/nucleon. In summary the very low-energy thresholds and the upper detection limits for different ejectiles as measured with the PISA detectors are given in Table 10.20. Isotope separation of the ejectiles was done by combining the information from multichannel plates via TOF, silicon detector telescopes and Bragg curve spectroscopy (energy deposited inside BCDs) allowing the separation of the following isotopes: 6 Li, 7 Li, 8 Li– 7 Be, 9 Be, 10 Be– 10 B, 11 B– 11 C, 12 C, 13 C, 14 C and 13 N, 14 N [760]. In [761], the double-differential cross sections (d2 σ/ddE) were measured for the ﬁrst time with good statistics for isotopically identiﬁed intermediate mass fragments

10.3 Proton Cooler Synchrotron COSY at J¨ulich

produced by interaction of 2.5 GeV protons with a gold target. For that measurement the following individual isotopes of the elements from hydrogen to boron were resolved: 1,2,3 H, 3,4,6 He, 6,7,8,9 Li, 7,9,10 Be, 10,11,12 B, whereas for heavier ejectiles from carbon to aluminum only elemental identiﬁcation was done. Measurements of these double-differential cross sections for nine angles of 12◦ , 15◦ , 20◦ , 35◦ , 50◦ , 65◦ , 80◦ , 100◦ , and 120◦ and the investigation of the interaction of medium and high-energy protons with atomic nuclei are important for providing benchmark data in the GeV incident proton energy range, understanding the complex reaction mechanism itself and testing the reliability of physical models describing the fast intranuclear cascade INC-phase as well as the subsequent statistical decay from an equilibrated or thermalized hot nucleus. The GeV proton-induced reactions on nuclei compiled by the PISA collaboration representatively discussed further are of particular interest for developing new models for the description of highly energetic composite particles [117]. 10.3.3.2 Experimental Results of PISA As mentioned the experiments at the internal beam of COSY allow to perform the investigation of the reactions induced by protons on thin targets (of the order of 50–200 µg/cm2 ); thus they enable to get the cross sections without uncertainties (e.g., absorption and energy loss) involved by propagation of reaction products in the material of the target. The multiple circulation of the beam in the COSY ring is used to compensate for the small reaction rate of beam protons with the thin target and to allow for the measurement with optimal counting rates of the order of 1000–2000 s−1 for a total intensity of about 1010 protons in the ring. The constant reaction rate is achieved by a negative back coupling between the counting rate and degree of overlapping of the proton beam with the surface of the target via controlled shifting of the beam in respect to the axis of the COSY beam line. Thus such an internal beam experiment offers a unique possibility to measure efﬁciently and precisely the cross sections on thin targets. As discussed in detail in Ref. [761], the energy spectra for all nuclear fragments, determined at several scattering angles representatively shown for 4 He and 7 Li fragments in 2.5 GeV proton-induced reactions on Au in Figure 10.57, appear to be of Maxwellian shape with an exponential high-energy tail. The low-energy part of the distribution is almost independent of the angle, but the slope of high-energy tail of the spectrum increases monotonically with the angle.The contribution strongly varying with angle is present at higher energy in all experimental spectra. The slope of this anisotropic energy contribution increases with the angle, which can be interpreted as an effect of fast motion of an emitting source in the forward direction. The shape of the angle-independent part of spectra can be reproduced by the twostage model of the reaction, e.g., an intranuclear cascade of the nucleon–nucleon and meson–nucleon collisions followed by statistical emission from an equilibrated residual nucleus. However, the absolute magnitude of the spectra predicted by two-stage model, using Boltzmann–Uehling–Uhlenbeck model for the intranuclear cascade and the generalized evaporation model (GEM) of [254] for statistical emission of fragments,

361

10 Proton-Nucleus-Induced Secondary Particle Production

100

100 Au (p, 4He)

10

Au (p, 7Li) 10−1

1000

1000

1 10−2 0.1 10−3

0.01

100

100 d2 s/dΩdE [mb sr −1 MeV−1]

362

650

10

650

10−1

1 10−2 0.1 10−3

0.01

100

100 160

10

160

10−1

1 10−2 0.1 10−3

0.01 0.001 0 (a)

60

120

180

240 0 30 Energy [MeV] (b)

Fig. 10.57 Energy spectra of 4 He (a) and 7 Li particles (b) for 2.5 GeV p+Au. The bullets • [233] show the NESSI results and the ◦ [761] show the results of the PISA experiment for the corresponding emission angles.

60

90

120

150

10−4 180

The lines show the prediction by evaporation of 4 He and 7 Li evaluated by means of GEM program [254] from excited residual nuclei of the ﬁrst stage of the reaction with properties extracted from BUU calculations.

is in agreement with the experimental data only for the light charged particles the H and He ions. Furthermore, the theoretical cross sections underestimate signiﬁcantly the yield of heavier fragments at high kinetic energies for all ejectiles. This indicates that another mechanism plays an important role besides the standard two-stage mechanism. The nice agreement shown in Figure 10.57 of the NESSI data [233] confronted with the PISA data [761] on an absolute normalization scale(!)

10.3 Proton Cooler Synchrotron COSY at J¨ulich 10

1 3H

Cross section d2s/dEdΩ [mb MeV−1 sr−1]

1 0.1

0.01

0.01

0.001

100

100 2H

10

4He

10

1

1

0.1

0.1

100

10

10

6He

0.1

1H

3He

1

1

0.1

0.1

0.01

0.01

0.001 0 (a)

50

100 150 200 250 300

0

30

60

90

120

150

Particle energy [MeV] (b)

Fig. 10.58 Energy spectra of 1,2,3 H (a) and 3,4,6 He particles (b) for 2.5 GeV p+Au. The ◦ are results of PISA experiment [761] for the corresponding emission angles. Dashed lines show the prediction of evaporation of H and He isotopes evaluated by means of GEM

model [254] from excited residual nuclei of the ﬁrst stage of the reaction with properties extracted from BUU calculations. The full lines correspond to phenomenological model of two emitting sources as described in [761] (after Bubak et al. [761]).

clearly give conﬁdence to the completely independently analyzed experimental data. In Figure 10.58, the open circles represent typical spectra of protons, deuterons and tritons measured in the PISA experiment [761] by telescopes consisted of silicon semiconductor detectors and 7.5 cm thick scintillating detector of CsI placed at scattering angle of 65◦ with respect to the proton beam. The dashed lines show evaporation contribution evaluated by means of the BUU and GEM evaporation model, whereas the full lines correspond to phenomenological model of two emitting sources described in detail in [761]. Note the change of the scale for the triton spectrum. The right panel of Figure 10.58 shows typical energy spectra of helium ions 3,4,6 He measured by the telescopes of PISA consisted of silicon semiconductor detectors placed at scattering angle of 35◦ with respect to the proton beam – open circles. Note different vertical scales for each spectrum. The lines have the same meaning as for the H isotopes in Figure 10.58(a). Figure 10.59 shows the typical spectra of lithium ions 6,7,8,9 Li and 7,9.10 Be particles and Figure 10.59 for 2.5 GeV p+Au measured in the PISA experiment. The lines have the same meaning

363

10 Proton-Nucleus-Induced Secondary Particle Production 0.1

0.1

0.01

9

Li

10

Be

1E-3

0.01

1E-4 1E-3

0.1 8

1E-3

Li

ds/dΩdE [mb/sr*Mev]

ds/dΩdE [mb/sr*Mev]

0.01

1E-4 1 7

0.1

Li

0.01 1E-3

0.1 9

0.01

Be

1E-3 0.1 7

1

Be

0.01

0.1

6

Li

0.01

1E-3

1E-3 1E-4

1E-4 0

50

100

150

200

250

0

30

60

E [MeV]

90

120 150 180

E [MeV]

Energy spectra of 6,7,8,9Li

(a)

Energy spectra of 7,9,10Be

(b) 0.1

0.1 B

0.01

O

0.01

12

1E-3 1E-3

1E-4

0.1 11

B

0.01 1E-3

ds/dΩdE [mb/sr*Mev]

ds/dΩdE [mb/sr*Mev]

364

0.1 10

0.01

N

1E-3 1E-4 1 C

0.1

B

0.01

0.1

0.01 1E-3

1E-3 1E-4

1E-4 0

30

60

90

120 150 180

0

30

E [MeV] (c)

Energy spectra of 10,11,12B

60

90

120 150 180

E [MeV] (d)

Energy spectra of C,O,N

Fig. 10.59 Energy spectra of 6,7,8,9 Li, 7,9.10 Be, 10,11,12 B, and C, O, N particles for 2.5 GeV p+Au. The ◦ are measured results of PISA [761] for 35◦ with respect to proton beam. The dashed and full lines have the same meaning as in Figure 10.58.

10.3 Proton Cooler Synchrotron COSY at J¨ulich

4He

d2s/ dEdΩ [mb sr−1 MeV−1]

101

7Li

10−1

100

10−2

10−1

10−3

9Be

10−1

11B

10−2

10−2 10−3

10−3

0

50

100 0 50 Energy [Mev]

100 150

Fig. 10.60 Typical spectra of 4 He, 7 Li, 9 Be, and 11 B ejectiles measured at 35◦ with respect to incident beam for three proton energies of protons, 1.2 GeV (open circles), 1.9 GeV (full squares), and 2.5 GeV(open triangles) incident on Au targets. The cross sections at 2.5 GeV proton beam energy were published in Ref. [761] and the data at 1.2 and 1.9 GeV are taken from Ref. [762].

as those of Figure 10.58. Finally, Figure 10.59 exhibits the spectra of boron ions 10,11,12 B and spectra of carbon, nitrogen, and oxygen ions and Figure 10.59 without isotopic separation measured in the PISA experiment [761] for 2.5 GeV p+Au at 35◦ with respect to the incident proton beam. Double-differential cross sections d2σ/ddE as a function of scattering angle and energy of ejectiles were also measured as a function of incident kinetic energy of the protons. This allows to study the incident particle energy dependence of the light charged particles production. A detailed analysis of the energy dependence of intermediate mass fragments will be published in a forthcoming thesis by PiskorIgnatowicz [769]. Typical spectra of isotopically identiﬁed ejectiles obtained in the PISA experiment as a function of bombarding energy are shown in Figure 10.60. As can be seen in the ﬁgure, the shape of spectra does not vary signiﬁcantly with beam energy. The main effect present for all products is monotonic increase of the absolute value of the cross sections with beam energy. Furthermore, all the spectra for all bombarding energies are bell shaped with two components as described earlier. The low-energy component of the Gaussian shape is attributed to evaporation from an equilibrated, excited nucleus, and the high-energy exponential component my be interpreted as a contribution of a nonequilibrium mechanism. The data for the LCPs represented in Figure 10.60 for alpha-particles have similar character and energy dependence as those for IMFs; however, the nonequilibrium component is more pronounced. The ﬁnal PISA double-differential cross section

365

10 Proton-Nucleus-Induced Secondary Particle Production 175 MeV p + Ni 100 deg

175 MeV p + Ni

101

0.1 20 deg × 1

10−1 20 deg × 0.5 10−2

0.01 ds/dΩdE [mb/sr∗MeV]

100 ds/dΩdE [mb/sr MeV]

366

100 deg × 0.25

10−3

2H

1E-3 H×1

3

1E-4

3He

1E-5

6Li

× 0.1 7Li

1E-6 1E-7

7

10−4 0 (a)

40

80 120 E [Mev]

0

160

Energy spectra for protons

×1

(b)

20

× 0.1

4He

× 0.01

80

100

× 0.01

Be × 0.001 40 60 E [MeV]

Energy spectra for d, t, 3He, 4He, 6,7Li, 7Be

Fig. 10.61 Kinetic energy spectra for protons at 20◦ , 65◦ , and 100◦ following 175 MeV p+Ni. Symbols are data of the PISA experiment, and lines are from Ref. [770]. The PISA data of d, t, 3 He, 4 He, 6,7 Li, 7 Be spectra for 175 MeV p+Ni and ejectiles measured at 100◦ with respect to incident beam.

experimental data ﬁles including ejectiles up to Z = 13 for 1.2 and 2.5 GeV p+Au will be made accessible in electronic form (see also Section 10.3.3.3). A detailed analysis and interpretation of the 2.5 GeV p+Au data can be found in Ref. [761]. The 1.2, 1.9, and 2.5 GeV p+Au data and explanations are of Ref. [762]. The PISA experimental data for 175 MeV proton-induced reactions on Ni target are shown in Figure 10.61. Absolute normalization of the data was done by comparing double-differential cross section of protons measured by PISA experiment with the cross sections published by Foertsch at al. [770]. In this paper the energy spectra of protons were determined for many angles, i.e., from 15◦ to 70◦ in 5◦ steps and for 80◦ , 90◦ , 100◦ , and 120◦ , thus it was possible to compare the PISA data at several angles of 15◦ , 20◦ , 65◦ , and 100◦ with those of Ref. [770]. It was found that the shapes of all compared spectra agree very well and, moreover, the ratio of the data of PISA to those of [770] is the same for all angles. Therefore, the normalized cross sections for all products observed in the 175 MeV p+Ni experiment rely on the absolute normalization of proton data found in [770]. The normalization factor was found using the method of weighted least squares for each angle separately and then mean value of four angles were used as normalization factor. The statistical error of normalization factor was found to be close to 3%. Additionally, systematic

10.3 Proton Cooler Synchrotron COSY at J¨ulich

error of data of Foertsch (as authors claimed it is close to 10%) should be taken into consideration. The second method of normalization for the 175 MeV p+Ni reaction was performed independently. It consisted in comparing the experimental total cross section for emission of 7 Be with results of parameterization of 7 Be data published in the literature [760]. This method is less accurate as comparing proton spectra with results of [770] because of two reasons: • statistics of 7 Be spectra in reaction Ni(p,7 Be) is much poorer than statistics of proton spectra, • the experimental total cross sections should be derived from the spectra by integration over angle and energy, which is biased with virtually large error because the experimental spectra are not measured at very low 7 Be energies, where the cross sections are relatively large. Nevertheless, both methods gave normalization factors, which agreed with accuracy of about 20% what are quite good results taking into account the fact of a 10% error of normalization, quoted in [770], inaccuracy of total 7 Be cross sections extracted from the spectra, and the error of parameterization of Bubak et al. [760]. The good agreement gives additional conﬁdence in the absolute normalization. As a function of incident proton beam energy, the He-production cross sections on Fe measured by the NESSI group [228], Hannover group [740], SPALADIN group [771], and PISA group [769] are compiled in Figure 10.62. The latest data points of SPALADIN at 1 GeV and PISA at 175 MeV are also included. The SPALADIN result obtained in inverse kinematics of Fe on protons at GSI shows a value slightly above the NESSI data, but is deﬁnitely still smaller than the

Helium production cross section [mb]

103

102

Hannover-group NESSI-group SPALADIN-group PISA-group (proton + Ni) INCL4-ABLA INCL4-GEMINI INCL-CLUSTER-GEMINI

101 0

500

1000 1500 2000 Incident proton energy [MeV]

Fig. 10.62 Production cross section of 3,4,6 He isotopes as a function of incident proton beam energy. The symbols: NESSI [228], Hannover [740], SPALADIN [771], PISA [769] data, curves: calculation by INCL4.3+ GEMINI/ABLA.

2500

3000

367

368

10 Proton-Nucleus-Induced Secondary Particle Production

systematics of Michel et al. [740]. The data shown here for PISA are for Ni reaction, but a comparison should be legitimate, because Fe and Ni are very close in terms of atomic number. Note that for the PISA data [769] the cross sections for the individual of 3,4,6 He isotopes are given at 175 MeV. The Monte Carlo calculation getting closest to the available experimental He data is the INCL4-Clus-GEMINI version (dashed line in Figure 10.62), which accounts by using a coalescence approach for cluster (here composite He particles) emitted in the ﬁrst fast phase of the reaction. The two solid lines in Figure 10.62 take into account only the He particles being emitted during the slow evaporation phase and therefore as expected the abundance of production cross sections is underestimated in INCL4/ABLA or INCL4/GEMINI. In conclusion the two experiments, NESSI and PISA, have been consulted to validate models with regard to reaction cross sections or reaction probabilities, neutron-, and charged particle production cross sections and angular-, and energy distributions for GeV proton-induced reactions on various thin targets. PISA experiment e.g., has shown to be able to measure the products of pA collisions with Z-identiﬁcation up to at least Z = 16 and isotope identiﬁcation to masses up to 13–14% with a particularly low-energy threshold of less than 1 MeV/A. In brief summary the two experiments PISA and NESSI contribute the following information: • NESSI: – 4π detection system for LCPs and neutrons, and neutron multiplicity spectra, – double-differential cross sections for p,d,t, 3,4,6 He, 6,7,8,9 Li, – targets of Al to U with emphasis on Au, – incident proton beam energies 0.8, 1.2, and 2.5 GeV – Refs. [228, 233, 622, 656, 664, 735, 736, 750] • PISA: – no neutron detection, but due to internal beam operation high statistics, very good Z and A identiﬁcation of reaction products, – double-differential cross sections for p, d, t, 3,4,6 He, 6,7,8,9 Li, 7,9,10 Be, 9,10,11,12 B, 11,12,13,14 C, N, O,... – targets of Al, Ni, Nb, Ag, and Au – incident proton beam energies of 175 MeV on Ni, and 1.2, 1.9, 2.5 GeV on all targets. – Refs. [664, 760–762] The completely independently performed and analyzed experiments NESSI/PISA are in good agreement. A set of experimental benchmark data is provided for the development and test of models capable of describing among other features the emission of the high-energy component of composite particles When however comparing the NESSI and PISA data to the measurements performed by mass spectrometry [740, 741], the measured He production cross sections do not coincide in particular for light targets. The discrepancies between the two experimental methods for light targets are not yet understood. The huge amount of data collected for proton-induced reactions here and elsewhere by

10.4 Production of Residual Nuclides at Various Proton Energies

Michel et al. [740, 741] will be valuable for the identiﬁcation of deﬁciencies of existing INC/evaporation codes. 10.3.3.3 Data Library of H and He in Proton-Induced Reactions At the beginning of 2001 the creation of a database [772] for hydrogen and helium production cross sections in a wide energy range up to several GeV on thin targets has been initiated in the framework of the HINDAS project (High and Intermediate Energy Nuclear Data for Accelerator-Driven Systems). The motivation was essentially driven by the lack of cross sections for production of the lightest isotopes. The database is a compilation of experimental cross sections for proton-induced isotope production at energies from a few MeV to 10 GeV. There are also some data for energies up to 30 GeV. Presently, for proton-induced reactions this compilation contains about 15000 data points for 38 targets and 50 elements. All data are derived from available literature and private communications. Each record of the database contains the following information: atomic mass A and atomic mass number Z of the target, incident energy of the projectile in (MeV), type (A, Z) of ejectile, total production cross section in (mb), error of the production cross section in (mb), angle, references, and certain comments. The whole database was written in ‘‘Excel format,’’ in ASCII format, and is also available for users through the Internet (cf. Ref. [773]).

10.4 Production of Residual Nuclides at Various Proton Energies

The production of residual nuclei and the formation of integral reaction cross sections for nuclide production by medium- and high-energy protons are basic data for a large number of applications in science and technology [774]. These applications range from the production of cosmogenic nuclides in extraterrestrial matter by galactic cosmic and solar ray protons over space and environmental sciences, accelerators and high-intensity spallation neutron sources (activation of components, radiation protection, and safety), medicine (radionuclide production and radiation therapy), and at least to the technology of accelerator-based nuclear waste transmutation and energy amplifying (cf. Chapters 20 on page 593 and 21 on page 613). In the recent years, the main goal of the experiments in this ﬁeld was to characterize the reaction mechanisms of proton-induced collisions in matter [775, 776] and to provide a database for applications in astro and cosmic ray physics [34–38], whereas nowadays experiments are considering target materials in applications for high-intensity accelerator technology, for MW spallation neutron sources, and for ADS research [133, 543]. During the recent years, several comprehensive experimental projects were undertaken to complete the existing database. An extensive database is now available on excitation functions published by Michel et al. [340, 740], Schiekel et al. [777], Gloris et al. [778], Leya et al. [741, 779], Ammon et al. [780], and

369

370

10 Proton-Nucleus-Induced Secondary Particle Production

Titarenko et al. [781] in the energy range from 0.2 to 2.6 GeV. Other extensive experimental programs aimed to measure a complete isotopic production cross sections and mass yields of spallation residues, e.g., isotopic and mass yield distributions, ﬁssion and evaporation residues, by inverse kinetic methods and proton irradiated thin targets up to proton energies of 2.6 GeV. The data are published by Enquist et al. [68, 782], Ta¨ıeb et al. [783], Bernas et al. [784, 785], Ricciardi et al. [350], Villagrasa-Conton [786], and by Titarenko et al. [787, 788]. Because of the large amount of existing data only some examples for structure and important target materials will be demonstrated in the following subsections. 10.4.1 Excitation Functions and Production Cross Sections

The term excitation function is used in nuclear physics to describe a graphical plot of the yield of a radionuclide as a function of the bombarding projectile energy or the calculated excitation energy of the compound nucleus. The characteristic shape of the excitation function can often be related to the nuclear reaction formalism. The special features as the effective energy threshold, the slope of the function, and if there is a maximum at a certain energy are all important and signiﬁcant to compare different nuclides and their similarities and differences between their reaction mechanisms. For spallation reactions of high-energy protons with matter one may distinguish, e.g., between the processes as spallation, ﬁssion, and fragmentation which are characterized by their typical excitation functions [775, 789]. A nuclear reaction should be described then by a complete study of the exit channels (e.g., 1n, 2n, 3n, etc.). The experiments to measure excitation functions are usually performed in the so-called stacked-foil technique [778], where the foils are arranged in small stacks with thin Al foils in front of the stack to determine via the monitor reaction 27 Al(p, 3p3n)22 Na the proton ﬂux. Al foils inside the stack are used to avoid crosscontamination and recoil effects. A sketch of a typical foil stack is depicted in Figure 10.63. For the experiments exclusively high purity materials must be used. Typical weights of individual targets with diameters of 15.0 mm are 55 or 125 mg/cm2 for lead foils (with a purity of 99.99%+) and for Al foils 10 or 33 mg/cm2 (99.999% purity) [778]. In the experiments performed by Titarenko et al. [781], thin 208,207,206,nat Pb and 209 Bi were used having 10.5 mm diameter with 127–358 mg/cm2 together with Al foil monitors with the same diameter and a thickness of 127–254 mg/cm2 . The proton ﬂuences sufﬁcient for excitation function measurements are usually in the order between 1013 and 1016 per cm2 . The most comprehensive and complete database of excitation functions for many different applications were generated by Michel, Gloris and co-workers at incident proton energy ranges up to 2.6 GeV. Most of these experimental data can be retrieved from the EXFOR database [709] a joint effort of the IAEA-NDS, Vienna and The NNDC, Brookhaven. This database contains more than 15000 individual

10.4 Production of Residual Nuclides at Various Proton Energies

Saturne II Saclay

TSL Uppsala

15 mm

15 mm

Bi Al

Pb

Au W Ta Bi Pb Au W Ta

2–5cm

10 mm

5 – 10cm

Al

Al

Proton beam Fig. 10.63 A schematic view of foil stacks used at irradiation experiments at the SATURNEII, Saclay and at the TSL, Uppsala, accelerators for lead targets (after Gloris et al. [778]).

cross sections with more than 550 reactions. Exclusively for lead 2000 individual cross sections with about 127 reactions are available. The used target materials cover almost the whole range of elements ranging from carbon up to lead [340, 740]. Various excitation functions especially for lead as target material are published by Gloris et al. [778] and by Titarenko et al. [781]. From the measurements, the phenomenology of the excitation functions exhibits several reaction modes like multifragmentation, shallow spallation products, ‘‘deep’’ spallation products, and different types of ﬁssion reactions. Comparison of the measured data with intranuclear-cascade-evaporation models and codes demonstrates the weakness of the predictive power of the models although the models were permanently improved during the last years [778, 780]. As for example the models cannot accomplish the precise distribution in A and Z of the ejectiles. The ‘‘near’’ target products, the shallow spallation products, and the ﬁssion products are predicted mostly fairly well for heavy targets, whereas the quality of the prediction of the ‘‘deep’’ spallation products, mass products far away from the target mass, decreases. Fragmentation products are much underestimated by all the theoretical models [781]. Figures 10.64(a)–(d) illustrate examples of measured excitation functions for Al and Fe targets, usually used as structure materials, and for W and Pb targets as examples for materials for spallation neutron production. The data are based on retrieved data ﬁles from EXFOR [709]. The experiments were performed at many different accelerator facilities, e.g., at SATURNEII, Saclay (France), which was shut down in 1997, at TSL, Uppsala (Sweden), at PSI, Villigen (Switzerland), at LAMPF, Los Alamos (USA), CERN, Geneve (Switzerland), and at ITEP, Moscow (Russia). Although the presented excitation functions in Figure 10.64 are only a small sample of the large amount of measured data, it is already clearly seen that proton-induced excitation functions may have a complicated structure and are functions of a multiparameter space in energy, matter, and produced individual

371

10 Proton-Nucleus-Induced Secondary Particle Production 102

5×102 102

101

101

Cross section [mb]

Cross section [mb]

Al-target

100

10−1

W-target

100

10−1 13 2 27Al(p,x)4He

−2

10

- (ley98, mic97)

13 11 27Al(p,x)22 Na - (glo01) 4 13 Al(p,x) 27 7Be - (mic95, mic97)

10−3 10

10−2 300

100 1000 3000 Incident proton energy [MeV]

11 (a) Al(p,x)23He, - 22 Na, - 47Be, (data from mic95, glo01, mic97, ley98 [340, 740, 778, 790]

- (mic02)

500 1000 2000 3000 Incident proton energy [MeV]

3×103 103 2He 4

Pb-target

102

10−1

- (mic02)

74 W(p,x)27 Co 60 0

2He 4

102 25Mn 54

4Be 7

27 Co 58

Cross section [mb]

100

- (mic02)

27

Fe-target

101

74 W(p,x)63 Eu 149 0 74 W(p,x)63 145Eu 0

63 63 (b) W(p,x)149 Eu, - 145 Eu, - 60 Co, (data from mic02 [791]

103

Cross section [mb]

372

82 Pb 204

101 80Hg 193

100 80 Ag 110

10−1

52Te 121

10−2 54Xe 134

10−2

10−3 5 10 100 1000 3000 Incident proton energy [MeV]

25 (c) Reactions Fe(p,x)42He, - 47Be, 54 Mn, 27Co - 58

10

100 1000 3000 Incident proton energy [MeV]

47 Ag, - 52 Te, - 54 (d) Reactions Pb(p,x)24He, - 110 121 134 80 Hg, - 82 Pb Xe, - 193 204

Fig. 10.64 Excitation functions of residual isotope production of protons on Al, Fe, W, and Pb targets. The crosssection data of the lower panels are from: (c) for ( 24 He) 27 from [780], for ( 47 Be) from [791], and for (25 54 Mn, 58 Co) from [340, 740, 777], and (d) from ( 24 He, 54 134 Xe) from [741], for 52 80 82 ( 47 110 Ag, 121 Te, 193 Hg) from [778], and for (204 Pb) from [781].

10.4 Production of Residual Nuclides at Various Proton Energies

nuclei. It seems not very surprising that many of the theoretical models based on statistical methods fail to predict residual mass production with a required accuracy needed to estimate, e.g., induced radioactivity or isotope production for spallation relevant technologies. Therefore, experiments will remain indispensable for certain applications in spallation research in future. 10.4.2 Isotopic and Mass Distributions of Residual Nuclides

As described in Section 10.4.1 conventional experiments on residual-nuclide production in proton- and neutron-induced reactions are performed by bombarding various target materials with protons or neutrons of the energy of interest and by analyzing the produced species after irradiation, e.g., by their radioactive decay or by off-line and on-line mass spectrometry [340, 740, 778]. These methods can only give a limited insight into the reaction mechanism, because short-lived products, which form the dominant production in most cases, cannot be observed due to the time delay between the irradiation and the measurement. Information on the reaction kinematics is also not easily accessible. In addition, stable nuclides could only be detected with much effort, e.g., by off-line mass spectrometry. As documented in a comprehensive intercomparison [340] the experimental information was insufﬁcient to develop reliable models. In the course of the concerted action ‘‘Lead for ATD’’ [133] a new experimental method has been developed at GSI based on the bombardment of an hydrogen target with heavy projectiles mainly with Fe-, Pb-, and U-ions. These experiments are known as measurements of spallation reactions in reverse or inverse kinematics methods. The spallation reaction products are identiﬁed in-ﬂight by mass and atomic number in a high-resolution spectrometer and with information on the reaction kinematics. Most of the results have been published in Refs. [68, 783–786, 792] or may be retrieved from the EXFOR database [709]. 10.4.2.1 Inverse Kinematics Measurements at GSI The employed experimental apparatus at the fragment separator (FRS) [793] at GSI, Darmstadt, Germany, is illustrated in Figure 10.65. A primary beam of, e.g., from 1 A GeV 56 Fe, 208 Pb, 238 U ions incident on a liquid H2 is delivered by the heavyion synchrotron SIS at GSI. The synchrotron produces, e.g., a 500 A MeV 208 Pb pulsed beam with a pulse duration of 4 s and a repetition time of 8 s. The proton target was composed of 87.3 mg/cm2 liquid hydrogen and enclosed between thin titanium foils of total thickness of 36 mg/cm2 . The heavy residues produced in the target were all strongly forward focused due to the inverse kinematics. They were identiﬁed using the Fragment Separator and the associated detector equipment shown in the ﬁgure. The FRS is a two-stage magnetic spectrometer (cf. Figure 10.65) with a dispersive intermediate image plane (S2) and an achromatic ﬁnal image plane (S4) with a momentum acceptance of 3% and an angular acceptance of about 15 mrad around the beam axis. Two position-sensitive plastic scintillators placed at S2

373

374

10 Proton-Nucleus-Induced Secondary Particle Production

Beam monitor

Dispersive mid/plane Scintillators ToF (BQ)1 L = 36 m

Ionization chamber music ∆E

Incident beam of 56 Fe, 208Pb, 238U Liquid H2 target

(BQ)2 S4 S2 Degrader

Fig. 10.65 Schematic representation of the fragment separator FRS at GSI with the detector equipment (after VillagrasaCanton et al. [786]).

and S4 provided the magnetic rigidity (B ) and TOF measurements, respectively, which allowed determining the mass-over-charge ratio of the particles. For an unambiguous isotopic identiﬁcation of the reaction products, the analysis was restricted to ions, which passed both stages of the fragment separator fully stripped. To identify all residues in the whole nuclear-charge range up to the projectile, it was necessary to use two independent methods in the analysis. The nuclear charges of the lighter elements, mainly produced by ﬁssion, were deduced from the energy loss in an ionization chamber (MUSIC) with a resolution Z/Z = 170 obtained for the primary beam. Combining this information with the mass-overcharge ratio, a complete isotopic identiﬁcation was performed. A mass resolution of A/A = 480 was achieved. Since part of the heavier reaction products was not completely stripped, the MUSIC signal was not sufﬁcient for an unambiguous Z identiﬁcation. Degrader thicknesses of about 5 g/cm2 of aluminum were used. The nuclear charge of the products was deduced from the reduction in magnetic rigidity by the slowing down in the energy degrader. The velocity of the identiﬁed residue was determined at S2 from the B value and transformed into the frame of the beam in the middle of the target, taking into account the appropriate energy loss. More than 100 different values of the magnetic ﬁelds were used in steps of about 2% in order to cover all the produced residues and construct the full-velocity distribution of each residue in one projectile–target combination. The reconstruction of the full-velocity distribution allows to measure reaction products formed in fragmentation and ﬁssion reactions due to their different kinematic properties. A detailed description of the experiment and the analysis procedure can be ﬁnd in [543, 784, 786]. The measured cross sections The production of residual nuclides was investigated for several systems which are particularly relevant for spallation sources and for ADS. The production rates were measured for the reactions 56 Fe,208 Pb,238 U+1 H. Some measurements were also performed with deuterium as the target material [543]. A large amount of cross sections could be measured using different incident

10.4 Production of Residual Nuclides at Various Proton Energies 208 Pb

82

+ 1H (1 A GeV) 126

Z 50

28

30 mb 10 mb 3 mb 1 mb 100 µb 10 µb 1 µb

82

20 8 2

28 20

50 N

Fig. 10.66 Residual nuclide cross sections for the reaction 208 Pb + p on a chart of the nuclides. Primordial nuclei are marked by open squares, the outer line gives the range of known nuclides, and the shell closures are indicated by double lines (by Leray et al. in [543]).

ion beam energies, e.g., for the reaction 56 Fe+p these were 300, 500, 750, 1000, and 1500 A MeV [786, 795], for 208 Pb+p these were 500, and 1000 A MeV [68, 794], and for 238 U+p for 1000 A MeV [350, 783–785], respectively. In average more than 1000 nuclides could be measured and identiﬁed per ion and ion energy. These data can be visualized on a chart of the nuclides given as an example for the 208 Pb +1 H (1 A GeV) case in Figure 10.66. The different regions on the chart of the nuclides, produced by spallation-evaporation and by spallation-ﬁssion reactions, respectively, can clearly be distinguished. In Figure 10.67, two experimental samples of results using the inverse kinematics technique are given. In Figure 10.67(a), isotopic cross sections of spallation residues are given for the reaction 56 Fe + p at 0.3 A GeV [786], and in Figure 10.67(b) for the reaction 208 Pb + p at 0.5 A GeV [794]. To visualize in the color plots the dependence of the A, Z-distribution as a function of the production cross section low-incident ion energies 0.3 and 0.5 A GeV are chosen. The isotopic cross sections of 56 Fe are shown for elements from Z = 27 down to Z = 10 with uncertainties around 10% for most of the fragments. For the lightest ones, the uncertainty could reach 20% due to the larger applied transmission correction of the target system of residual nuclei. The evaporation residues produced in spallation by the reaction 2086 Pb + p at 0.5 A GeV are depicted for elements from of Z = 69 up to Z = 83 in Figure 10.67(b). Figure 10.68 illustrates the element distribution of all reaction products from the reaction 208 Pb (1 A GeV) + 1 H. The total cross sections from spallation–evaporation and spallation–ﬁssion as a function of the charge number from Z = 22 to 82 are given, whereas Figure 10.69 shows the mass distribution of all reactions products, respectively. The total cross sections from spallation-evaporation

375

10 Proton-Nucleus-Induced Secondary Particle Production

101

40

100

30 10−1 20 56

Fe + p at 0.3 A GeV

10−2

10

0

0

5

10

15

Cross section [mb]

Atomic mass A

50

20

25

10−3

Charge Z

(a)

210

208

Pb + p at 0.5 A GeV

101

100

190

180 10−1

Cross section [mb]

200

Atomic mass A

376

170 10−2 160 (b)

68 70 72 74 76 78 80 82 84 Charge Z

Fig. 10.67 Isotopic cross section in A, Z-projection of spallation residues production for the reactions 56 Fe + p at 0.3 A GeV (a), and 208 Pb + p at 0.5 A GeV (b). Data are from [786, 794] and from the EXFOR database [709].

and spallation-ﬁssion are given as a function of the atomic mass number A = 44–207. A large amount of individual nuclide production cross sections and velocity distributions in the reactions of Fe, Pb, and U ions with hydrogen and also with deuterium have been studied in the inverse-kinetic experiments at GSI, covering most elements between oxygen and uranium. The reaction products were fully identiﬁed in atomic number Z and mass number A using the magnetic

10.4 Production of Residual Nuclides at Various Proton Energies

Total prodcution cross section [mb]

5 × 102 10

Total element production cross section of the reaction 208 Pb (1 A) + 1H

2

101

100

10−1 10

20

30

40 50 60 70 Charge number Z

80

90

100

Fig. 10.68 Spallation evaporation and ﬁssion isotope production for the reaction 208 Pb(1AGeV) + 1 H as a function of the element number Z. Data are from Enquist at al. [68].

Total production cross section [mb]

102

101

100

10

Total mass production cross section of the reaction 208 Pb (1 A GeV) + 1H

−1

10−2 1

50

100

150

200

250

Atomic mass number A Fig. 10.69 Spallation evaporation and ﬁssion isotope production for the reaction 208 Pb (1 A GeV) + 1 H as a function of the atomic mass number A (lower panel). Data are from Enquist at al. [68].

spectrometer FRS. With the measured production cross sections combined with the known decay properties it is possible to estimate the short- and long-term radioactive inventories induced in high-power spallation targets.

377

379

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments 11.1 Introduction

While the ‘‘thin’’ target experiments discussed in Chapter 10 are basically useful to validate and scrutinize the nuclear models in spallation physics, ‘‘thick’’ target experiments are mainly performed as integral experiments. These integral experiments employ extended targets with dimensions large enough to generate an internuclear cascade (INC) inside the material and aim at the study particle leakage distributions, particle yields including secondary particle production, energy deposition, and induced radioactivity. Experimentally, the ﬁrst studies of neutron yields for spallation neutron targets were carried out by Bercovitch et al. [626] using cosmic ray radiation as a proton source between 250 and 900 MeV and by Fraser et al. [59] at the Brookhaven Cosmotron accelerator in connection with the proposed Canadian ING concept [58] (cf. Section 1.3 on page 12). The Cosmotron measurements were performed as ‘‘thick’’ target experiments measuring the total neutron production yield, e.g., the number of neutrons per incident beam proton emitted from the target surface. Measurements were made for Be, Sn, Pb, and Udepleted at proton beam energies between 500 MeV and 1500 MeV. The neutron yield was determined by measuring the activation of Au foils placed at various positions within a large H2 O moderator surrounding the targets, spatially integrated to obtain the total thermal neutron captures in the moderator, and then applying a ‘‘correction” to account for neutron absorptions inside the targets. The Cosmotron data, although taken some 30 years ago, represented the most comprehensive set of measured data available in terms of beam energies and target materials covered for many years. Recently these measurements were re-evaluated by Zucker et al. [796, 797] and compared with new measurements at the alternating gradient synchrotron (AGS) of the Brookhaven National Laboratory (BNL), USA. A joint Canadian–US experimental program, called FERFICON [385, 798–802], Fertile-to-Fissile Material Conversion was initiated during the 1980s. These measurements are being made at the TRIUMPF facility, Canada, with 480 MeV protons and at the LAMPF accelerator, USA, with 800 MeV protons. These

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

380

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

extended target measurements have been studied total neutron yields, angular dependent neutron production cross sections, and fertile-to-ﬁssion conversion yields inside thorium and depleted uranium targets. Yield measurements are also reported by Lone et al. [803], Becker et al. [804], and Vassil’kov and Yurevich [617] for various targets. In addition, high-energy neutron leakage spectra emitted from thick targets were measured using the time-of-ﬂight (TOF) method at the 184inch cyclotron at Berkley, USA, by Madey and Waterman [125] with 740 MeV protons during the 1970s and by Meier et al. [696, 698] by the TOF method at the LAMPF-WNR facility, USA, applying 116 and 256 MeV protons during the 1980s. With the advent of high-intensity spallation sources and with ADS projects (see comments in Section 10.1 on page 287), more detailed studies on ‘‘thick’’ targets were investigated using a variety of target materials, target geometries and proton beams up to 2.5 GeV. A group of LANL, USA, considered thick target studies at the LAMPF-WNR facility on neutron production devoted to acceleratordriven targets by Morgan et al. [557], referred to as ‘‘Sunnyside’’ experiments. During the 1990s at the SATURNE accelerator measurements of differential neutron production cross sections and multiplicity distributions of thick targets using the experimental apparatus as described in Figure 10.15 on page 306 are given by Leray et al. [543] and by Fr´ehaut [805] up to proton energies of 1.5 GeV. More details are given in [806, 807]. At the 12 GeV proton synchrotron at KEK, Japan, neutron leakage spectra of thick lead targets up to proton energies of 1.5 GeV were also studied by Meigo et al. [808]. More systematically the NESSI1) collaboration measured neutron multiplicity distributions and energy deposition of thick targets from tungsten, mercury, and lead with various geometries up to incident proton energies of 2.5 GeV (e.g., Hilscher et al. [631], Letourneau et al. [115], Filges et al. [622, 809]). These neutron multiplicity experiments were performed using a 4π liquid scintillator detector at the cooler synchrotron (COSY) at the Forschungszentrum J¨ulich, Germany. The ASTE2) collaboration investigated measurements of spatial neutron leakage ﬂuxes and energy deposition of a thick mercury target with incident proton beam energies between 1.6 and 24 GeV at the Alternating Gradient Synchrotron (AGS) at the Brookhaven National Laboratory, USA [810–812]. Experiments on waste transmutation, e.g., the CERN-TOF [685] investigations should also be mentioned in this context. The experiments discussed in this chapter are certainly only a selection of the various efforts done worldwide, and the scope of this book cannot be a detailed comprehensive description of all measurements. In the following in order to get an idea of the ‘‘thick target’’ experiments a representative selection of investigations at various laboratories is presented.

1) NEutron Scintillator and SIlicon Detector. 2) AGS Spallation Target Experiment.

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV 11.2.1 Experiments to Measure the Neutron Yield of ‘‘Thick’’ Targets

As already discussed in Section 8.2.4 on page 263, the total neutron production or the neutron yield is an integral parameter which may be used to characterize appropriate target materials for spallation sources. Over the years many experiments were performed applying e.g simple water-bath experiments by Fraser et al. [59], Russell et al. [799], Fraser, Garvey and Milton [798, 813], and by van der Meer et al. [814]. Instead of applying H2 O as neutron moderator, West and Wood [815] used polythene blocks [815] to measure neutron yields. The ‘‘Sunnyside’’ experiment collaboration of LANL (USA), the Uppsala university (Sweden), the university of Michigan (USA), and the CEA (France) used a method named manganesebath technique, a concentration of 1% MnSO4 in H2 O [557]. The most advanced experimental determination of neutron yields and neutron leakage spectra emitted from the target surface of thick targets are the event-by-event measurements of the neutron multiplicity with 4π detector systems by Hilscher et al. [631] and Letourneau et al. [115] and the TOF methods considered by Meier et al. [696, 698], Meigo et al. [808], and by Leray et al. [543]. A compilation of available thick target (n/p)-ratios is summarized in Section 11.2.2.2 on page 402. 11.2.1.1 The Brookhaven Cosmotron Experiments The ﬁrst experiments investigated to measure neutron yields from thick targets are the experiments by Fraser et al. [59, 813] were carried out at the external proton beam of the Brookhaven Cosmotron accelerator with targets of Be, Sn, Pb, and depleted U bombarded by protons having energies from 0.5 to 2.0 GeV. These measurements were considered to provide information for the ﬁrst high-intensity spallation source project, the intense neutron generator (ING) by Bartholomew et al. [58]. Six different targets were originally studied: cylindrical targets of Sn, Pb, and depleted U of diameter 10.16 cm and length 60.96 cm, one Pb target with diameter 20.32 cm and length 60.96 cm, and a rectangular Be target square-shaped 10.16 × 10.16 cm2 with length 91.44 cm. The targets were inserted in a large cylindrical vessel with a diameter of 182.88 cm and height 182.88 cm ﬁlled with H2 O. A sketch of the experimental apparatus, the so-called water-bath experiment is illustrated in Figure 11.1. Figure 11.1 also shows the lucide frame for about 55 detector foils to measure the absolute neutron density distributions inside the H2 O moderator, which surrounds the target. For most of the experiments foils of Cu with a thickness of 0.03 and 0.0175 mm, Au foils with thickness of 0.05 mm, and also Mn foils with a 10% Ni content with a thickness of 0.0175 mm were used. The foils are Al and Cd covered and were 1 cm2 area. The values obtained by the foil activation method are believed to have an accuracy of about ±5% [58]. A series of experiments with Pb targets

381

382

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments Lucite frame with positions for detector foils

12C monitor foil

Proton beam from BNL cosmotron

Vessel filled with H2O

Targets of Be, Sn, Pb, U

1.83 m

Fig. 11.1 The BNL Cosmotron experiment with H2 O vessel, target assembly, and Lucite frame to position the foil and vanadium β-current detectors (after [813]).

of a diameter 10.16 cm were done using measurements with vanadium β-current detectors. The beam current was determined by the 12 C(p,pn)11 C reaction [59]. The logarithms of the measured ﬂuxes were ﬁtted by least squares to polynomials. Integrating the resulting distributions gives the total number of neutrons captured per second in the H2 O volume. This capture rate in a water-bath experiment is then the number of neutrons per incident proton including a correction for the neutron absorption in the target. The method to evaluate thermal neutron ﬂuxes via reaction rate measurements is well known in classical reactor physics. Details are described in standard textbooks, e.g., [63]. The values of neutron capture rates or the neutron production per incident proton for the Cosmotron experiments are shown in Figure 11.2. A summary of experiments of neutron yield production at thick targets is given in Section 11.2.2.2 on page 402 with a summary comparing different thick target experimental results for thick lead targets. The data were used to estimate the neutron source strength of the Canadian ING project [58], e.g., by bombardment of a 20.4 cm diameter × 61 cm long target of Pb by 65 mA of 1 GeV, one yields about 20 × 65 × 6.28 × 1015 ∼ 8.2 × 1018 neutrons s−1 . 11.2.1.2 The Fertile-to-Fissile Conversion Experiments The Fertile-to-Fissile Conversion (FERFICON) experiments were a collaborative effort between the Chalk River Nuclear Laboratory, Canada, and the Los Alamos National Laboratory, USA, either to measure the total neutron yield from stopping

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

Number of neutron per incident proton

60

50

- U - 10.2 × 61 cm2 - Pb - 20.4 × 61 cm2 - Pb - 10.2 × 61 cm2

40

- Sn - 10.2 × 61 cm2 - Be - 10.2 × 61 cm2

30

20

10

0 0.25

0.5

1.0 Incident proton energy [GeV]

1.5

Fig. 11.2 The measured neutron production yield as a function of the incident proton energy for various thick targets. The lines are a linear ﬁt of the data. Data are the BNL Cosmotron neutron capture rates measured in a water bath from [58].

length targets and the fertile-to-ﬁssile conversion inside stopping length targets at the LAMPF-WNR in Los Alamos by incident protons of 800 MeV and at the TRIUMF cyclotron in Vancouver by incident protons of 350 and 480 MeV [385, 798–801, 813]. Besides the measurement of the neutron yield per incident proton, the main aim of the FERFICON program was to investigate the production of ﬁssile material for use in power reactors by accelerator breeder systems capable of extending the nuclear resources for an expanding nuclear industry [813]. Several target dimensions and materials were used. Examples are given in Table 11.1 and in more detail in [799, 801, 813]. Neutron yields were measured for single solid targets of W, Pb, Th, and depleted U and for targets composed of Th √ and U rods, where the effective diameter D is calculated by D = d n, with d is the rod diameter and n is the number of rods. The fertile-to-ﬁssion conversion yields were measured inside the Th and the depleted U targets inserting Th and U foils into the targets (cf. Figure 11.3) and determining the 233 U and the 239 Pu content by measuring the 233 Pa and the 239 Np formation inside the foils. The thick targets used for the FERFICON experiment at the TRIUMF facility at an incident proton energy of 0.48 GeV have slightly different dimensions [813] compared to the targets used at the LAMPF-WNR experiment. • Pb target: diameter = 10.16 cm, length = 30.48, • Th target, 19 rod array: diameter = 18.272 cm, length = 30.48 with a rod diameter d = 4.192 cm [813], • U target, 37 rod array: diameter = 19.782 cm, length = 30.48 with a rod diameter d = 3.252 cm [813].

383

384

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments Tab. 11.1 Target characteristics of FERFICON targets used at the LAMPF-WNR facility with incident proton energy of 0.8 GeV as given in [799, 801].

Target material

Density (g/cm3 )

Diameter (cm)

Length (cm)

Wa Pb Ub Th Ud

18.26 11.31 18.4 11.38 19.04

4.45 9.85 10.01 18.28c 19.704e

24.13 40.45 40.45 36.31 30.46

U enrichment (wt%) – – 0.19802 – 0.25051

a

With a 5-cm deep reentry hole, diameter 2.54–1.42 cm. Depleted U with 0.198% 235 U. c 19 rod array, rod diameter = 4.194 cm. d Depleted U with 0.251% 235 U. e 37 rod array, rod diameter = 3.239 cm. b

Thorium target 19 rods ∅rod = 3.2393 cm

Central rod of the array

Uranium target 37 rods ∅rod = 4.194 cm

Segmented rods to insert foils

Th or foils inserted in rod Proton beam Th or U rod segmented Fig. 11.3 Illustration showing the 19-rod thorium and the 37-rod depleted uranium targets, the foil location in the arrays, and their position in a rod (after Gilmore et al. [801]).

The FERFICON experiment at the TRIUMF accelerator with 0.48 GeV incident protons were basically performed with the same method used for the Cosmotron experiments. The proton beam intensity was monitored by the 27 Al(p,3pn)24 Na reaction by determining the 24 Na activity produced in the Al foils. The axial and radial neutron ﬂux distributions were measured using bare and cadmium covered Au foils. The array of the foil distribution was somewhat larger than that in the Cosmotron experiments [813].

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

The FERFICON experiments at the LAMPF-WNR facility with 0.8 GeV incident protons were also performed using the water-bath method by placing the targets inside a cylindrical vessel with a diameter of 2 m and height 2 m, which was located inside the beam channel of the WNR [800]. The proton beam current was estimated by a three-foil aluminum packet counting the 0.025 cm thick foils with a Ge–Li detector system to determine the number of 27 Al(p, x)7 Be, 27 Al(p, x)22 Na, and 27 Al(p, 3pn)24 Na reactions. For a typical experimental run [801] the measured number of beam protons for the three reactions are ranging from 4.25 × 1015 to 1.91 × 1016 total protons for the depleted uranium target and the thorium target. The most useful quantity is the number of neutrons from the target per incident beam proton – the n/p-ratio, and not the total neutron captures in the water bath per proton. Therefore it should be noted how the water-bath experiment affects the total neutron yield. (1) High-energy neutrons above a certain energy, above several 100 MeV, are lost from the water bath. (2) Spallation reactions with the oxygen nuclei by high-energy neutrons and protons emitted from the target into the water bath may produce a secondary neutron source. (3) The neutrons may be reﬂected back into the target and will be captured. The target can work as a neutron sink. (4) The neutrons that are reﬂected into the target, if not captured, may produce secondary neutrons via (n, f ) and (n, xn) reactions. The points (1) and (2) may compensate each other and are not very dependent on the target material and the target dimensions. The effects described by points (3) and (4) may compensate, but are also dependent on the target material and the target dimensions. This is especially important for target materials with high absorption and ﬁssion cross sections in the thermal, epithermal, and the MeV energy region. For lead the water-bath effects may be minimal. For other target materials as mercury, tantalum, tungsten, thorium and uranium the measured neutron captures in H2 O has to be corrected by simulations to convert the experimental data to neutron yield data. Table 11.2 summarizes some measured H2 O neutron capture rates per beam proton of the TRIUMF at 0.48 GeV proton energy and LANL–WNR water-bath experiments at 0.8 GeV proton energy. More recently measured neutron yields, multiplicities and multiplicity distributions of extended thick targets with a 4π neutron detector by the NESSI collaboration avoid sophisticated corrections by simulations. These measurements are described in Section 11.2.2 on page 390. For both FERFICON targets, the 19-rods thorium and the 37-depleted uranium array target, spatial – radial and axial – distributions of the fertile-to-ﬁssile conversion were measured by bombarded the targets with 0.8 GeV protons. The target rods were loaded with the Th and U foils as indicated in Figure 11.3. The spatial distributions were integrated to determine the total conversion and the total ﬁssions. The amount of 239 Pu and 233 U are determined by measuring the production yield of 239 Np and 233 Pa, respectively. The analysis procedure

385

386

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments Measured H2 O neutron captures per proton for FERFICON experiments (details of the rod array targets are shown in Figure 11.3 and partly given in Table 11.1).

Tab. 11.2

TRIUMF FERFICON results at 0.48 GeV incident proton energy. Data are from [813]. Target material

Pb Pb, 7-array Th Th, 19-array Ua U, 37-array

Target density (g/cm3 )

Diameter (cm)

11.34

10.16 10.15 4.192 18.272 3.252 19.782

11.38 18.94

Target dimensions rod diameter (cm)

3.836 4.192 3.252

Length (cm)

30.48 30.48 30.48 30.48 30.48 30.48

Measured H2 O neutron capture rate per proton

8.3 ± 0.5 8.0 ± 0.4 8.1 ± 0.6 9.6 ± 0.7 9.6 ± 0.7 17.1 ± 1.0

LANL-WNR FERFICON resultsb at 0.8 GeV incident proton energy. Data are from [799, 816]. W Pb Th, 19-array U U, 37-array

18.26 11.31 11.38 18.4 19.04

4.45 9.85 18.28 10.1 19.7

4.194 3.239

24.13 40.65 40.65 40.65 40.65

10.3 (11.3)c 13.1 (13.1) 17.2 (16.5) 25.8 (24.4) 29.3 (26.5)

a

Depleted U with 0.22% 235 U. A detailed analysis of the measured captures per proton indicated an overall uncertainty ±1σ of 6.8% for the solid uranium target and 5% for the remaining targets [816]. c Values in brackets calculated with LAHET–LCS Monte Carlo system [110, 193]. b

Tab. 11.3 Number of ﬁssions and measured production yields of 239 Np, and 237 U of the conversion of 238 U produced by the bombardment by 0.8 GeV protons [801].

Quantity

U-target experiment

Calculation

Number of ﬁssions (ﬁssions/proton) 239 Np production (atoms/proton) 237 U production (atoms/proton)

5.90 ± 2.5 × 10−1 3.81 ± 8.0 × 10−2 0.95 ± 2.0 × 10−2

6.14 ± 3.7 × 10−1 3.875 ± 3.1 × 10−1 –

and further experimental details are described in [385, 799–801]. Tables 11.3 and 11.4 summarize the measured ﬁssion and conversion rates together with corresponding calculational results which are useful to estimate the production of 239 Pu and 233 U (see Eq. (11.2)). The calculations were done by using LAHET–LCS particle transport system with the Rutherford ﬁssion model [110, 193] (cf. Section 3.7 on page 165), including a

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV Number of ﬁssions and measured production yields of 233 Pa, 95 Nb, 205 Bi and 227 Th of the conversion of 232 Th produced by the bombardment by 0.8 GeV protons [801].

Tab. 11.4

Quantity

Th target experiment

Calculation

Number of ﬁssions [ﬁssions/proton] 233 Pa production (atoms/proton) 95 Nb production (atoms/proton) 205 Bi production (atoms/proton) 227 Th production (atoms/proton)

1.56 ± 2.5 × 10−1 1.251 ± 3.0 × 10−2 0.068 ± 3.0 × 10−3 0.0056 ± 3.0 × 10−4 0.046 ± 3.0 × 10−3

1.543 ± 6 × 10−3 1.267 ± 7 × 10−3 0.0553 ± 9 × 10−4 0.0077 ± 4 × 10−4 0.0221 ± 7 × 10−4

Production yield [atoms g−1 proton−1]

10−4 239Np,

U-target

237U, U-target 233Pa, Th-target 227Th,

Th-target

10−5

10−6

10−7

−5

0

5

10

15

20

25

30

35

40

Target depth [cm] Fig. 11.4 Axial distributions of 239 Np and 237 U in the depleted uranium target, and 233 Pa and 227 Th in the thorium targets, respectively (data are from Gilmore et al. [801]).

precise three-dimensional geometry description of the experiment. The measured axial conversion distributions are shown in Figure 11.4. For the analysis of the measurements the monitor foils and the dissolved uranium and thorium foils were counted with a Ge(Li) detector system. The axial distributions of the measured reaction products were used to determine the total production per incident beam proton inside the targets. The total number for each reaction is given by Eq. (11.1)

reactiontotal (i) =

M · L · numberproton

L Ni (z)dz, 0

(11.1)

387

388

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

with M is the mass of the target in gram, L the length of the target in cm, numberproton is the number of incident protons, Ni number of atoms produced per gram of target material, and z is position of foils into the target. The amount of the produced 239 Pu and 233 U is given by the decay of the produced 239 Np and 233 Pa β− 26.967 d β− 233 91 Pa −→ 2.355 d

239 93 Np

−→

239 94 Pu 233 92 U.

(11.2)

11.2.1.3 The PSI Thick Target Lead/Bismuth Experiments Spallation neutron production yields have been measured for protons of 420 and 590 MeV on thick Pb/Bi targets at the cyclotron of the Paul Scherrer Institut (PSI) Switzerland. The measurements of the thick target yields were investigated by using the water-bath method by means of thin 25 µm Au – with and without Cd cover – and 100 µm Mn activation foils placed at certain axial and radial positions within the water bath [814] (cf. see also the Sections 11.2.1.1 and 11.2.1.2 about the Cosmotron and FERFICON experiments). A schematic presentation of the experimental apparatus is shown in Figure 11.5. The water bath is a plexiglass vessel with the dimensions 1000 × 750 × 900 mm3 . A water tight beam line is inserted into the water bath to house the target. The Pb/Bi target consists of Pb and Bi disks each 10 mm thick and 100 mm in diameter. For different incident proton energies 300, 420, and 590 MeV up to 30 disks were used corresponding to the proton ranges (Table 11.5). As indicted in Figure 11.5, a number of plexiglass guide tubes is inserted into the water bath for positioning the Au and Mn foils at well-deﬁned axial – in Z – and radial locations. The following 1000 mm Water bath with plexiglass vessel

Pb disk

Proton beam

Bi disk

100 mm

Al foil

900 mm

Z

Plexiglass guide tubes for foil measurements in Z and radial positions

Fig. 11.5 Sketch – not to scale – of the water-bath experiment to measure H2 O capture rates of Pb/Bi targets at the PSI cyclotron at incident proton energies of 300, 420, and 590 MeV. The different target lengths are given in Table 11.5.

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV Tab. 11.5

Characteristics of the Pb/Bi targets for the PSI thick target experiments.

Incident proton energy (MeV) 300 420 590

Proton range (cm)

Number of target disks

∼9.5 ∼16.0 ∼27.5

16 18 30

Target lengths (cm) 16 18 30

positions were possible: In axial direction at Z = 25, 55, 85, 125, 155, 175, 205, 235, 265, and 295 mm and in radial direction, measured from the target axis, at R = 76, 126, 176, and 226 mm. The total number of protons was determined by the well-established method irradiating a 0.28-mm thick Al foil placed in front of the target with the same diameter of 100 mm as the target. The activation cross section induced by the beam protons is given by 27 Al(p,3n3p)22 Na. The following cross sections for the reaction 27 Al(p,3n3p)22 Na at different incident beam energies were adopted [814] σ = 14.6 ± 0.6 mb at 300 MeV, σ = 14.8 ± 0.6 mb at 420 MeV, σ = 14.9 ± 0.6 mb at 590 MeV.

(11.3)

The total number of protons for the higher bombarding energies could be determined as numberproton = (6–10 ± 0.3) × 1013 at 300 MeV, numberproton = (3.8 ± 0.2) × 1013 at 420 MeV, numberproton = (7.1 ± 0.3) × 1013 at 590 MeV.

(11.4)

The novel approach analyzing the water-bath experiment at PSI consists in scaling Monte Carlo calculated (n/p)calc -ratios by means of the average ratio measured to Monte Carlo calculated 198 Au foil activities [814]. The total number of neutrons emitted per incident proton usually called the neutron yield per incident proton n/p is determined from the spatially measured distribution of the 198 Au-speciﬁc activity. Conventionally the spatial neutron ﬂuence distribution is experimentally integrated over 4π to determine with some corrections the total measured thick target yield (n/p)meas . The procedure adopted by van der Meer et al. [814] circumvents potentially the inaccurate 4π integration of an extended source in the water bath sampled over a relatively small set of measured spatial points via activation foils to estimate the integral quantity n/p. The following steps are considered by the PSI experiment: • The 198 Au measured speciﬁc activities are normalized per incident beam proton Eqs. (11.3), (11.4), and (11.6) to receive a measured spatially sampled distribution of measured speciﬁc activities per incident beam proton.

389

390

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

• The Monte Carlo particle transport system MCNPX (cf. Section 5.2.1 on page 209) is then used to calculate the 198 Au-speciﬁc activities per incident proton A(ri , Zi )calc and the neutron yield (n/p)calc . • The measured 198 Au-speciﬁc foil activities A(ri , Zi )meas per incident proton at each location (ri , Zi ) are divided by the calculated ones. Thus giving a normalized spatial dependent activity Ameas/calc (ri , Zi ). • A weighted average of the values Ameas/calc (ri , Zi ) is then taken over the spatial points (ri , Zi ) on the spatially sampled distribution. • The ﬁnal experimental (n/p)meas ratio is determined by the following equation (n/p)meas = (n/p)calc · Ameas/calc (ri , Zi ).

(11.5)

It should be noted [814] that the above-described procedure is insensitive to the value of (n/p)calc and to its error, since the product of the two right terms in Eq. (11.5) effectively cancels out the dependence of (n/p)calc . This is only true if the MCNPX Monte Carlo estimation reproduces well the shape and the magnitude of the neutron ﬂux distribution. Also the procedure is free from systematic errors only if the Monte Carlo simulation reliable predicts the principal nuclear reactions, primarily, (1) spectral and angular distributions of the fast neutrons produced and emitted in the spallation process that occur inside the thick target, and (2) the moderating process by such neutrons in the H2 O surrounding the target. A detailed analysis by van der Meer et al. [814] concluded that the conditions to estimate the value of (n/p)meas adopting Eq. (11.5) are indeed fulﬁlled for both incident proton energies of the PSI experiment, 420 and 590 MeV. The 300 MeV incident proton data were not assigned to an accurate n/pmeas value because the number of protons in the irradiation was determined imperfect. The resulting values (n/p)meas of the PSI experiment following the procedure given by van der Meer et al. [814] are determined including a detailed error estimation as (n/p)meas = 6.0 ± 0.3 at 420 MeV, target length = 18 cm, (n/p)meas = 9.6 ± 0.4 at 590 MeV, target length = 30 cm,

(11.6)

where the uncertainty is given as ±1σ . A comparison with n/p ratios and neutron multiplicity data published in the literature for thick Pb targets showed that the PSI data fall well within the range of former experimental systematics. 11.2.2 Neutron Multiplicities Measured with a 4π Detector at the COSY Accelerator at J¨ulich

The aim of the thick target neutron multiplicity experiments of the NESSI collaboration at the cooler synchrotron (COSY) at J¨ulich, Germany, was to enrich the previously obtained data with the use of primary proton beams with energies

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

Beam pipe with vacuum Proton beam from COSY

S3,S5-S8

Ne343 NESSI liquid scintillator 4Π detector gadolinium loaded S10

To beam dump

S1 S11-S14

Air 60 cm

Thick target 153 cm

480 cm

713 cm

Fig. 11.6 The setup of the NESSI experiment for neutron multiplicity measurements on thick targets.

of 0.4 up to 2.5 GeV bracketing more closely the energy envisioned for future spallation sources and ADS projects. Three materials were studied – W, Pb, and Hg – as thick targets, whereas Hg is the best choice at present for the commissioned high-intensity MW spallation neutron sources SNS, USA, JPARC, Japan, and the future ESS. A large number of cylindrical target sizes have been explored, both in length and diameter. In thick targets the development of the INC depends strongly upon the size of the target and this justiﬁes many different geometries to be explored. Altogether about 300 measurements have been performed, for thick targets providing a wealth of experimental data to be confronted with high-energy transport code systems, which are used as standard tools in ADS and spallation source design [622]. The experimental equipment, a 4π detector, namely a large spherical vessel (BNB3) ), ﬁlled with a liquid scintillator loaded with gadolinium, which is described in detail already in Section 10.3.2.1 on page 10.3.2.1, is set up for the thick target measurements without the inner silicon ball detector. The available space is used for the mounting of cylindrical thick targets with diameters and lengths up to 15 and 35 cm. Figure 11.6 illustrates the experimental arrangement installed at an external proton beam line of the COSY accelerator at J¨ulich showing the neutron ball with auxiliary plastic scintillators to control the experiment. The neutrons produced in the target and emitted from the target surface are slowed down in the liquid scintillator by elastic scattering with the H and C atoms and are eventually captured at different instants with high cross section by the Gd nuclei when reaching thermal energy. The detector is thus used, ﬁrst, as a nuclear reaction trigger and then as a neutron multiplicity meter. The detector response consisting of γ -rays resulting from the neutron capture in Gd is delayed by about 1 to 50 µs (about 16 µs on the average) with respect to the spallation reaction. This is mainly due to the low Gd concentration imposing an appreciable diffusion time for the thermal neutron before being captured by a Gd nucleus. As a consequence, the neutron signals have been selected within a time gate opened 0.7 µs after the 3) Berlin Neutron Ball (BNB).

391

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments p + Pb 0.8 GeV

60

2 cm Neutron multiplicity (not corrected for efficiency)

392

10 cm

35 cm

2 cm

10 cm

35 cm

2.5 GeV 2 cm

10 cm

35 cm

40 20 0 1.2 GeV

60 40 20 0 60 40 20 0

0

500

0

500

0

500

Light yield [MeVee]

Fig. 11.7 Neutron multiplicity Mn versus the prompt light Esum of the NESSI detector in MeVee (the electron equivalent) for proton-induced reactions on Pb targets of thicknesses of 2, 10, and 35 cm and a diameter of 15 cm bombarded with energies

of 0.8, 1.2, and 2.5 MeV. The color code is normalized to the same intensity for all distributions (in au) in order to directly compare the yield (after [115, 664]).

reaction takes place and closed after 45 µs when the probability to capture a neutron is reduced to 2%. As described in Section 10.3.2.1, the prompt light signal Esum preceding the delayed neutron capture arises from the sum of kinetic energies of all kind of reaction products entering the neutron ball detector, in addition to the neutrons charged particles and γ quanta contribute. Since the threshold for detecting the prompt light ﬂash is as low as 2 MeVee, the electron equivalent, a nuclear reaction is characterized by the occurrence of a prompt light signal larger than this threshold, even if there are no neutrons released in the reaction at all. The complex measured correlation between the neutron multiplicity Mn and the prompt light signal Esum in the NESSI detector is shown for 0.8, 1.2, and, 2.5 GeV for proton-induced reactions on Pb targets of different thicknesses or length in Figure 11.7. For a ﬁxed target thickness and incident proton energy the larger the Esum will be, the smaller the measured multiplicity Mn results. This is due to the high-energy particles generally producing more light in the scintillator than evaporative neutrons or γ -particles. The less energy these ‘‘fast’’ particles deposit in the target, the less effective the nuclei are heated during the intra- and internuclear cascade and the less neutrons

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

are ﬁnally evaporated. On the expense of the prompt light signal for ﬁxed incident energy of the proton Mn increases with increasing target thickness. Consequently for thick targets the major contribution of the prompt light signal rises from evaporative neutrons and γ -particles. Thereby quenching factors for low-energy neutrons scale the light signal down. In other words the originally available energy is converted quite efﬁciently into the production of neutrons in thick targets of several nuclear interaction lengths. The scintillator light is registered by 24 fast photo tubes distributed evenly at the surface of the vessel. In contrast to measurements implying liquid scintillator detectors for TOF information, the present measurements have been performed without low-energy threshold, since the neutron needs to be thermalized down to 0.025 eV in order to be captured. The efﬁciency of the BNB detector, already discussed in Section 10.3.2.1 on page 10.3.2.1, is about 55% for neutron energies at 20 MeV and decreases to about 15% at an energy of 100 MeV (cf. Figure 10.42 on page 10.42). For thick targets, an overall efﬁciency can be taken into account for each experimental condition. The overall detection efﬁciency increases with the target lengths or thicknesses and material density as depicted in Figure 11.8. The efﬁciency is excellent in all experimental cases. Therefore, the 4π detector NESSI is a unique system for these thick target experiments. The detection efﬁciency increases with increasing target thickness, since the leaking neutrons out of the target surface become less and less energetic due to

Overall neutron detection efficiency [%]

0.78

0.76

0.74

0.72

0.4 Gev 1.2 Gev 2.5 Gev

0.7 Pb 0.68

0

20

Hg 0

20

W 0

20

Target length [cm] Fig. 11.8 The simulated overall neutron detection efﬁciency of the NESSI detector for thick W, Hg, and W targets of 15 cm diameter bombarded by proton energies of 0.4, 1.2, and 2.5 GeV (after Letourneau et al. [115]). Not the offset of the ordinate.

393

394

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments Tab. 11.6

Combinations of target materials, target sizes explored at various energies.

Energy (GeV) Target W

Hg

Pb

0.4

0.8

Diameter (cm)

1.2

1.8

2.5

Thickness (cm)

2 8 12 15

1–34.75 34.75 10–34.75

0.112 0.5–34.75 34.75 2–34.75

0.112 5–34.75 5–34.75 1–34.75

0.112 0.5–34.49 20–34.49 1–34.49

0.112 0.5–34.75 2–34.75 1–34.75

2 15

33.7

2–33.7

0.5 2–30.45

0.5 2–33.7

0.5 5–33.7

2 8 12 15

0.5 1–35 35 5–35

0.2 1–40 1–35 1–35

0.2 35 35 1–35

0.2 0.5–40 15–39 1–35

0.2 2–35 35 2–35

their slowing down within the target. For the thick measurements the experiment has been run with the target in the air (cf. Figure 11.6). The beam pipe was closed by a thin capton foil located about 60 cm downstream from S1 scintillator. The thick targets For thick targets, three materials, mercury as target material for high-intensity spallation neutron sources, lead, and tungsten have been chosen which are representative of the target and core materials of high intensity ADS. Systematic studies of a large variety of different cylindrical geometries and incident energies as summarized in Table 11.6 have been studied. All target pieces were made from chemically pure (≥ 99.98%) material of W, W, Hg, and Pb. Figure 11.9 illustrates how the different target pieces are assembled. The large possible variation of target geometries and materials make the thick target experiment NESSI to an important benchmark for obtaining key parameters necessary to design and construct neutron-producing targets via spallation. The mercury was ﬁlled in cylindrical stainless steel containers with a wall thickness of 1 mm, a diameter of 15 cm and different lengths. As indicated in Figure 11.9, the tungsten target was constructed as a ‘‘LEGO’’ design of different hollow and full cylinders. 11.2.2.1 Thick Target Results of the NESSI Experiment at the COSY Accelerator The study on thick target measurements considers data on reaction probabilities Preac , hadronic interaction lengths, average neutron multiplicities Mn with reference either to the number of neutrons generated per reaction or per incident proton Mn /p, and in particular neutron multiplicity distributions dPreac /dMn as obtained with different diameters and lengths of W, Hg, and Pb targets bombarded with 0.4, 0.8, 1.2, 1.8, and 2.5 GeV protons. Due to the multitude of measurements and particle transport simulations investigated by the NESSI only a representative

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

Tungsten targets diameters = 150, 120, 80 mm

150 mm

120 mm 80 mm

150 mm

10 mm

20 50 mm mm

100 mm

Lead targets diameters = 150, 120, 80 mm

120 mm 80 mm

Mercury targets diameters = 150, 120 mm Fig. 11.9 The dimensions – not to scale – of target geometries for mercury, tungsten, and lead target studied at the NESSI experiment.

selection is given. The interesting reader should refer the secondary literature published recently by the NESSI collaboration [114, 115, 133, 379, 543, 621, 622, 631, 664, 735, 736, 817]. Reaction cross sections and hadronic interaction lengths The key observables of thick target measurements with the 4π neutron ball detector are the neutron multiplicity Mn , measured event-by-event, and the reaction probability Preac . The reaction probability Preac is deduced from the ratio of the number of triggered events (cf. Section 10.3.2.1) divided by the number of incident protons counted by detector S1 (cf. Figure 11.6 on page 391). Moreover, since the incident protons were individually counted and the detector has a very low detection threshold of about 2 MeVee, the neutron multiplicity could be related to both, to the reaction events and to the incident proton events. Figure 11.10 illustrates the dependence of the proton survival probability (1 − Preac ) on target thickness. The data are for 1.2 and 2.5 GeV incident protons and for W, Hg, and Pb target cylinders of 15 cm diameter and a W target of a diameter 8.0 cm. As seen in Figure 11.10 as a function of the target thickness, the experimental data are well ﬁtted by a constant logarithmic representation of the survival probability for all three target materials at 2.5 GeV bombarding proton energy. This indicates a constant reaction cross section. The constant logarithmic behavior is also seen at 1.2 GeV for the Pb target but for the Hg and the W targets with a diameter of 15 cm there is a deviation from the linearity. This effect is caused by the strong absorption of particles, mainly by incident protons, loosing its energy via electronic stopping before undergoing a nuclear reaction. Therefore, the survival probability

395

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

1.0

Survival probability (1-Preac)

396

1.2 GeV p on Pb 2.5 GeV p on Pb

0.1

1.2 GeV p on Hg 2.5 GeV p on Hg 1.2 GeV p on W 1.2 GeV p on W, Ø = 8 cm 2.5 GeV p on W 0

5

10

15 20 25 Target length [cm]

Fig. 11.10 Survival probabilities (1 − Preac ) of incident protons as a function of cylindrical target lengths for 1.2 and 2.5 GeV protons on Pb, Hg, and W targets of 15 cm diameter and on a W target of 8 cm diameter with 1.2 GeV incident protons. The

30

35

40

straight lines give the best ﬁt of the data for all targets, except the W targets at 1.2 GeV incident protons and of diameters of 8.0 and 15.0 cm. Data are from Letourneau et al. [115].

looks ‘‘artiﬁcially’’ too high. This absorption decreases the light yield of the detector and therefore the multiplicity. The effect is partly recovered by reducing the radius thickness as seen in Figure 11.10 for the W target with a radius of 8 cm. The survival probability follows quite accurately the exponential law 1 − Preac = exp (−L/Lint ),

(11.7)

where L is the target length and Lint the interaction length. Measured and calculated interaction lengths are given in Table 11.7. The calculated hadronic interaction lengths resulting from the Monte Carlo calculations agree very well with published experimental values [115]. As a consequence of the constancy of the nucleon–nucleus cross section above some 100 MeV, the gradient of the exponentials does not depend on the incident kinetic energy of the projectile. The difference in the gradient for the three different materials originates mostly from their difference in density and much less from different reaction cross sections.

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV Comparison of experimental and calculated interaction lengths and reaction cross sections for W, Hg, and Pb targets (data are from [115, 817]).

Tab. 11.7

Material

L int (cm)

W Hg Pb

Experiment 10.84±0.2 15.06±0.4 18.00±0.3

σ reac (b) Calculation 10.05 13.91 17.66

Experiment 1.46±0.03 1.64±0.05 1.69±0.03

Calculation 1.62 1.71 1.73

For a 35-cm length target, the term (1 − Preac ) approaches the 10% level in Pb and 1% level in W, while the range due to electronic interaction is as large as 170 and 97 cm for 2.5 GeV protons in Pb and W, respectively. The reaction probability Preac is used to determine the reaction cross sections σreac σreac =

ln(1 − Preac ) · A (LAv · ρ · d)

(11.8)

with, A, ρ, d and L being the mass, density and thickness of the target and LAv the Avogadro number, respectively. The experimental reaction cross sections deduced from the measured Preac are also given in Table 11.7 of the three target materials W, Hg, and Pb. These values are slightly smaller than the results of the Monte Carlo calculation with the HERMES systems calculations. An agreement of the same order of magnitude is found when the MCNPX code system is used instead of the HERMES code, demonstrating that the description of the observable σreac is well predicted by theoretical models. This analysis is reﬂected also for the examples in Table 11.8 for different target lengths or thicknesses and the incident proton energies of 1.2 and 2.5 GeV. Neutron multiplicities and neutron multiplicity distributions Here the term ‘‘neutron multiplicity’’ comprises all neutrons originating from primary and succeeding secondary reactions within the target material. In the thick target measurements only neutron leakages can be observed. The neutron yield is not accessible in any experiment since it reﬂects the neutron production at the point of origin when the neutrons are created, whereas the leakage spectrum can be measured as a source of neutrons leaking from the target surface after they have left the target material. The originality of the NESSI experiment compared with the previous ones lies in the possibility to measure neutron multiplicity distributions and not only their average values. There are essentially two observables measured at thick targets by the NESSI detector [621, 631]: (1) the reaction probability Preac , and (2) the neutron multiplicity distribution dPreac /dMn . In order to compare the measured observables of the NESSI experiment with previous experiments the mean multiplicity Mn must be derived from the

397

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments Pb Average neutron multiplicity per incident proton

398

Hg

W

50 20 10 5

1

2.5 GeV 1.8 GeV 1.2 GeV 0.8 GeV 0.4 GeV

0

20

0

20

0

20

Target lenght [cm]

Fig. 11.11 The average neutron multiplicity per incident proton Mn /proton as a function of the target lengths and thicknesses. Targets are thick W, Pb, and W targets with a diameter of 15 cm bombarded by protons of energies of 0.4, 0.8, 1.2, 1.8, and 2.5 GeV. The measurements are corrected to background and detection efﬁciency (after Letourneau et al. [115]).

multiplicity distribution dPreac /dMn . From the reaction probability Preac and mean multiplicity Mn , the mean number of neutrons per incident protons is estimated as Mn /p = Mn · Preac .

(11.9)

The integral value Mn /p is of particular importance for the design of spallation sources whereas the experimentally measured neutron multiplicity distribution dPreac /dMn is one of the most sensitive test of intra- and internuclear cascade evaporation models and particle transport codes. In Figure 11.11 experimental results of Mn /p are plotted vs. the lengths of the lead, mercury, and tungsten cylindrical targets, and for the ﬁve incident proton energies of 0.4, 0.8, 1.2 1.8, and 2.5 GeV, as obtained in the NESSI experiments. As expected, for every target, the mean multiplicity increases with increasing target length, albeit in a nonlinear fashion. It should be noted that the measured Mn /p is corrected by the efﬁciency of the detector. A comparison of average multiplicities with theoretical predictions using standard Monte Carlo models HERMES and MCNPX (cf. Section 5.1 on page 207) is given with complete experimental and model average neutron multiplicities Mn and reaction probabilities Preac for different energies and target materials in [622, 664, 817] and it is partly summarized in Table 11.8. This table includes the simulated mean neutron multiplicities Mn , corrected for the NESSI detector neutron detection efﬁciency and Monte Carlo calculated MnC before taking the detector efﬁciency into account. All calculations account for the fact that neutrons are slowed down in the target material. Both ﬁssion and elastic scattering were included. All other options have been chosen according to the standard set of parameters used in spallation intra–inter nuclear cascade evaporation models. The agreement between calculation and experiment for the second moment of the

Average neutron multiplicity per reaction (<Mn>)

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

45

Pb-target d = 15cm

Hg-target d = 15 cm

W-target d = 15 cm

40 35 30 25 20 15 1.2 GeV NESSI 1.2 GeV HERMES 1.8 GeV NESSI 1.8 GeV HERMES 2.5 GeV NESSI 2.5 GeV HERMES

10 5 0

0

20

0 20 0 Target length [cm]

20

Fig. 11.12 Average multiplicities per reaction Mn/Preac as a function of the target length of Pb, Hg, and W targets of diameter = 15 cm at incident proton energies 1.2, 1.8, and 2.5 GeV compared with efﬁciency corrected Monte Carlo model predictions.

distributions within a few percent gives additional conﬁdence to the spallation physics models under consideration, at least as far as the description of neutrons is concerned. Figure 11.12 shows average neutron multiplicities per hadronic interaction Mn /Preac produced as a function of target thickness (diameter 15 cm) for 1.2, 1.8, and 2.5 GeV protons on Hg, Pb, and W targets compared with Monte Carlo model predictions. As seen in Figure 11.12, the model predictions with HERMES code agree very well with the experimental observations, over a wide range of target geometries and target materials. The observed increase in the neutron multiplicity with increasing target length is due to an increase in the reaction probability, Preac and, to a lesser extent, to an increase in secondary reactions with the target length. Some of these data are also given in Table 11.8. For the full set of data the reader may refer to [115]. Hg targets: As far as average values and Hg targets (Table 11.8, Figure 11.12) are concerned, for all Monte Carlo codes considered here, one observes good agreement with the experimental results. Discrepancies between model calculations and experimental data are generally less than 5% for both, Preac and Mn , and a broad range of energies. The maximum discrepancy is 7.4% in the case of the 5 cm Hg target bombarded with 2.5 GeV protons. Pb targets: For the Pb targets, the deviation of theoretical predictions with respect to experimental data decrease with increasing target thickness, while with increasing incident energy divergences increase. The maximum discrepancies are found for thick target bombarded with 2.5 GeV. Note that the divergences for even higher incident proton energies (4.15 GeV) [730] still increase.

399

400

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

Tab. 11.8 Examples of average neutron multiplicities Mn and reaction probabilities Preac for cylindrical tungsten, mercury, lead targets of 15 cm diameter bombarded with protons of 1.2 and 2.5 GeV energies.a

Target length (cm)

Experiment Mn

Preac

Monte Carlo calculation HERMES C Mn Mn

Preac

MCNPX Mn

MMC n

Preac

Incident proton energy 1.2 GeV – tungsten target with diameter = 15 cm 15 35

21.6 ± 3.2 22.6 ± 3.0

0.729 0.902

20.9 ± 3.2 21.6 ± 3.1

26.9 ± 3.6 27.6 ± 3.4

0.784 0.971

22.5 ± 3.3 23.4 ± 3.1

28.9 ± 3.7 29.8 ± 3.5

0.781 0.964

40.7 ± 4.4 47.3 ± 4.0

52.7 ± 5.0 60.6 ± 4.5

0.781 0.973

21.2 ± 3.3 22.5 ± 3.2

27.7 ± 3.6 29.1 ± 3.6

0.660 0.885

35.0 ± 4.3 40.1 ± 4.1

45.7 ± 4.8 51.6 ± 4.6

0.655 0.884

20.5 ± 3.2 22.1 ± 3.2

27.1 ± 3.6 28.8 ± 3.5

0.567 0.859

33.9 ± 4.2 40.4 ± 4.1

44.7 ± 4.8 52.2 ± 4.6

0.575 0.861

Incident proton energy 2.5 GeV – tungsten target with diameter 15 cm 15 35

36.6 ± 4.1 41.6 ± 3.8

0.758 0.952

36.7 ± 4.2 42.3 ± 3.9

47.6 ± 4.8 54.4 ± 4.4

0.782 0.973

Incident proton energy 1.2 GeV – mercury target with diameter = 15 cm 15 30

20.5 ± 3.1 21.9 ± 3.1

0.645 0.847

19.9 ± 3.2 21.2 ± 3.1

26.1 ± 3.6 27.5 ± 3.5

0.660 0.889

Incident proton energy 2.5 GeV – mercury target with diameter = 15 cm 15 30

33.7 ± 4.0 38.7 ± 3.9

0.647 0.866

33.2 ± 4.2 38.5 ± 4.1

43.9 ± 4.8 50.3 ± 4.6

0.663 0.887

Incident proton energy 1.2 GeV – lead target with diameter = 15 cm 15 35

20.2 ± 3.2 22.2 ± 3.1

0.571 0.848

19.6 ± 3.2 21.4 ± 3.1

25.9 ± 3.6 27.9 ± 3.5

0.579 0.867

Incident proton energy 2.5 GeV – lead target with diameter = 15 cm 15 35

32.3 ± 4.0 38.4 ± 3.9

0.577 0.848

31.7 ± 4.1 37.7 ± 4.0

42.5 ± 4.7 49.7 ± 4.6

0.580 0.865

a The values of M C are Monte Carlo calculated average neutron multiplicities before having taken detector efﬁciency n into account. The square root of the RMS (root mean square) is also given for all measured and calculated average multiplicities. The experimental data are from [115] and the calculational values are from [622, 664, 817].

W targets: Observations similar to those for mercury and lead were made for the tungsten targets. At 1.2 GeV, agreement with experimental data is very good for the HERMES calculations, while it is still quite satisfactory for the MCNPX calculations. However, for higher incident energies, the data clearly favor HERMES over other Monte Carlo predictions. As mentioned earlier, the originality of the NESSI experiments lies in the possibility to measure neutron multiplicity distributions and not only their average values. In the following some examples of such neutron multiplicity distributions

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV 1.2 GeV protons on Hg 0.04

5 cm

15 cm

30 cm

0.035

dPreac / dMn

0.03 0.025 0.02 0.015 0.01 0.005 0

0

20

40

0

20

40

0

25

50

Neutron multiplicity Mn

Fig. 11.13 Neutron multiplicity distributions dPreac /dMn as a function of the neutron multiplicity Mn of Hg targets with diameters = 15 cm and lengths = 5, 15, and 30 cm bombarded with protons of 1.2 GeV. The black symbols are the measurements and the thin lines are HERMES computer simulations. 2.5 GeV protons on Hg 0.03 2 cm

15 cm

35 cm

0.025

dPreac /dMn

0.02 0.015 0.01 0.005 0

0

20

40

0 50 0 Neutron multiplicity Mn

50

Fig. 11.14 The same as in Figure 11.13 but with W targets with diameters of 15 cm and lengths 2, 15, and 35 cm bombarded with protons of 2.5 GeV.

given as dPreac /dMn as a function of the neutron multiplicity Mn for W, Hg, and Pb targets are illustrated and compared with Monte Carlo predictions. As seen from Figures 11.13–11.15, the general shapes of the experimental distributions are well represented by simulation calculations obtained with the HERMES Monte Carlo. More details of comparisons between experimental and

401

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

(a)

1.2 GeV protons on Pb and W targets 0.04 2 cm

15 cm

35 cm

0.035 Pb-target

0.03 0.025 0.02 0.015 0.01 dPreac / dMn

402

0.005 0 0.04

2 cm

35 cm

15 cm

0.035 W-target

0.03 0.025 0.02 0.015 0.01 0.005 0 (b)

0

20

40

0

20

40

0

25

50

Neutron multiplicity Mn

Fig. 11.15 The same as in Figure 11.13 but with Pb targets (a), and W targets (b) with diameters of 15 cm and lengths 2, 15, and 35 cm bombarded with protons of 1.2 GeV.

theoretical evaluated multiplicity distributions of thick targets are given and discussed in [622, 664]. The discrepancies seem to become slightly larger for higher energies [730]. Note in the ﬁgures that the enhancement at Mn = 0 includes reactions where a nuclear reaction takes place, however the nucleus de-excited without the emission of a neutron. 11.2.2.2 A Summary of Neutron Yield Experimental Data Tables 11.9 and 11.10 summarize most of the experiments on neutron production measurements on thick targets by incident protons with respect to the time of their publication. Given are the incident proton beam energies, the investigated target materials and their dimensions, the measured quantities, and methods. The different methods for the neutron measurements are also indicated. It is seen from Tables 11.9 and 11.10 that most of the thick target measurements are related to lead targets investigating average multiplicities per incident beam proton. Some of these experiments consider only one target geometry, one or

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV Summary(I) of published thick target experiments with respect to the time of publication, incident proton energy, target material, and target dimensions.a

Tab. 11.9

Time of publ.

Incident proton energies (GeV)

Targets and dimensions ∅, L (cm)

Measured quantity

Method

1965

0.47/0.54/ 0.72/0.96/ 1.47

Be 10.2 × 10.2 × 91.6 Sn, Pb, U ∅ = 10.2, L = 61 Pb,∅ = 20.4

Mn /p

MOD Au-foils

[59]

1968

0.4/0.5/0.66

Pb,∅ = 10 − 26 L = 55

Mn /p

Fission chambers

[818]

1971

various 0.316 − 0.998

Pb,∅ = 10 L = 60

Mn /p

MOD BF3

[815]

1973

0.73

238 U

d2 σ/dEd

TOF NE202/228

[125]

∅ = 15, L = 60

References

1979

0.26

Fe, 238 U

Mn /p

TOF LQ − SCIN

[804]

1983

0.1

Pb, 7 Li,∅ = 6.2/5.7 L = 1.6/17.4

Mn /p

MOD, Au-foils

[819]

1983

0.25

Pb,∅ = 5 L = 10

Mn /p

235 U,238 U SDTR

[820]

1987

0.1

Fe, Cu, Th,∅ = 6 L = 1.6

MOD Au-foils

[803]

1989

0.113

Be, C, Al, Fe, ∅ = 3.65 L = 5.70/5.83/ 4.03/1.57 238 U,∅ = 4, L = 3

TOF BC418

[697]

d2 σ/dEd

a The measured quantities are given (1) d2 σ/dEd (the angular distribution of the leakage neutron spectra), (2) Mn /p (mean number of leakage neutrons per incident beam proton, and the employed methods are (1) TOF), MOD (moderation in H2 O and polyethylene). The neutron distributions and spectra are measured with Au foils, BF3 counters, plastic and liquid (LQ-SCIN) scintillators, and solid track (SDTR) detectors.

two incident proton energies and are using the water-bath method. In contrary the recent investigations on thick targets of the NESSI collaboration cover a large range of incident proton energies from 0.4 to 2.5 GeV, a large variation in target dimensions on diameter and length, and studied important target materials as W,

403

404

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments Summary(II) the same as in Table 11.9 but recently some additional methods are employed with the n-ball experiment to measure neutron multiplicity distributions dPreac /dMn are indicted (see Table 11.8) (also threshold detectors and 3 H counters are used).

Tab. 11.10

Time of Incident published proton energies (GeV)

Targets and dimensions ∅, L (cm)

Measured quantity

Method

References

1990

0.256

C, Al, Fe, ∅ = 8 L =(C)17.45/30 (Al)12.15/20 (Fe)4.7/8 238 U,∅ = 4 L = 3.5

d2 σ/dEd

TOF BC418

[696, 698]

1991

0.99–8.1

Pb ∅ = 20, L = 60

Mn /p

MOD BF3

[617]

TOF,NE213

[808, 821]

MOD He

[796, 797]

3 He,

1995

0.5/1.5

Pb,15 × 15 × 20 cm3

d2 σ/dEd

1996

0.8/1.0/1.2/1.4

Pb, W, ∅ = 10.2 L = 61/40

Mn /p

3

1997

0.895/1.21

W ∅ = 20, L = 60

Leakage spectra

Threshold detectors

[822]

1998

0.197

Pb,∅ = 12 L = 2 − 25

dPreac /dMn

n-ball,NE343 +0.3%wt Gd

[632]

1998

1–5

Pb,U,∅ = 15/8 L = 5/35/20/40

dPreac /dMn

n-ball,NE343 +0.4%wt Gd

[631]

1999

0.5/1.5

Pb,15 × 15 × 60 cm3

d2 σ/dEd

TOF,NE213

[808]

2000

0.4/0.8/1.2 1.8/2.5

W, Hg, Pb

dPreac /dMn

n-ball,NE343 +0.4%wt Gd

[115]

2001

0.8/1.2/1.6

Pb,∅ = 20 L = 105

d2 σ/dEd

TOF NE213

[133]

2004

0.42/0.59

Pb, Bi,∅ = 10 L = 16/18/30

Mn /p

MOD Au-foils

[814]

Hg, and Pb used at the current spallation neutron sources and foreseen for ADS applications. As already mentioned the measured neutron multiplicity distributions are a sensitive test for particle transport simulations. Some experiments consider neutron leakage spectra measured either as d2 σ/dEd or as surface reaction rates with

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV A compilation of neutron multiplicity data per incident proton of thick Pb targets.a

Tab. 11.11

Incident proton energy (GeV)

Pb-target diameter (cm)

Length (cm)

0.47/0.72/0.96/1.47

10.2

61

0.47/0.72/0.96/1.47

20.4

61

0.4//0.5/0.66 0.99/1.47/2.0/2.56/ 3.17/3.65/4.45

16 20

0.316/0.66/0.997 0.1 0.25 0.8/1.0/1.2/1.4 0.197 1.22/2.2/3.17/4.15 0.4/0.8/1.2/1.8/2.5 0.42/0.59

10 6.2 5 10.2 12 15 15 10

Mn /p

References

7.96/11.76/ 16.64/26.40 8.67/13.94/ 20.29/31.47

[59]

55 60

6.0/8.2/12.5 21.3/31.4/40.2/51.3/ 61.5/68.1/81.1

[818] [617]

60 1.6 10 61 25 35 35 30

3.13/10.61/17.1 0.343 2.64 13.6/17.38/22.31/26.21 1.44 26.7/42.2/53.77/63.85 6.34/17.22/24.97/35.1/43.44 6.0/9.6

[815] [819] [820] [797] [632] [631] [115] [814]

a

The ﬁrst column gives the incident proton energies, the second and third column the target dimensions, the fourth the multiplicities related to the energies in the ﬁrst column, and the last column gives the references for the data plotted in Figures 11.16 and 11.17.

threshold detectors positioned on the targets. Table 11.11 summarizes measured Mn /p values of thick Pb targets for incident protons with energies from 0.1 to 5.0 GeV where a large variety of measured data exists. The different experimental Mn /p values are plotted as a function of the incident proton energy in Figures 11.16 and 11.17 for incident proton energy ranges 0.1 GeV ≤ Eproton (incident) ≤ 5.0 GeV and 0.1 GeV ≤ Eproton (incident) ≤ 2.5 GeV, respectively. The data of the NESSI collaboration [115, 631] and the data of Vassil’kov et al. [617] are ﬁtted by a second order polynomial function. As shown in Figure 11.16 up to an incident proton energy of about 2.0–2.5 GeV the neutron multiplicity Mn /p is almost linearly dependent on the incident proton energy. Above a certain energy, other particle production channels as, e.g., π ± , π 0 , and kaon production will be opened, thus the incident proton energy is dissipated. The difference between the NESSI data [115, 631] and the data of Vassil’kov et al. [617] is related to larger target dimensions, diameter of 20 cm and length of 60 cm, compared to the NESSI experiment with a diameter of 15 cm and a length of 35 cm. The neutron multiplicity is still increasing with diameter at higher energies, whereas at lower energies the effect of the target geometry is much smaller as seen in Figure 11.17.

405

Average neutron multiplicity per proton Mn /p

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments 100 Yn = 0.99401+21.52163 Ep-0.80341 Ep2

90 80

Yn = 1.13423+23.70098 Ep-1.97546 Ep2

70 60 50

d=10.2, I = 61cm (Fa65) d=20.2, I = 61cm (Fa65) d=16.0, I = 55cm (Vas68) d= 20.0, I= 60cm (Vas91) d= 10.0, I= 60cm (Wes71) d= 6.2, I= 1.6cm (Lon83) d= 5.0, I= 10cm (Rya83) d= 10.2, I=61cm (Zuc97, Zuc98) d= 12, I= 25cm (Lot98) d=15.0, I =35cm (Hil98, Let00) d =10.0, I =30cm (Mee04)

40 30 20 10 0 −10 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Incident proton energy [GeV]

Fig. 11.16 Measured neutron multiplicities Mn /p of Pb targets in the energy range 0.1 GeV ≤ Eproton (incident) ≤ 5.0 GeV. Complied data are given in Table 11.11 with the references indicated in the ﬁgure.

Average neutron multiplicity per proton Mn / p

406

50 40 30 d =10.2, I =61cm (Fra65) d= 20.2, I =61cm (Fra65) d= 16, I =55cm (Vas68) d =20, I =60cm (Vas91) d =10, I= 60cm (Wes71) d= 6.2, I= 1.6cm (Lon83) d =5, I =10cm (Rya83) d =10.2, I =61cm (Zuc97, Zuc98) d = 12, I= 25cm (Lot98) d =15, I =35cm (Hil98, Let00) d= 10, I = 30cm (Mee04)

20 10 0 −10 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Incident proton energy [GeV]

Fig. 11.17 Same as in Figure 11.16 but Mn /p of Pb targets in the energy range 0.1 GeV ≤ Eproton (incident) ≤ 2.5 GeV. Complied data are given in Table 11.11 with the references indicated in the ﬁgure.

The difference of the values Mn /p at the same incident proton energies are mainly caused by different target dimensions or by the absolute accuracy, which for the water experiments is believed to be accurate within ±5% to ±10%, whereas the NESSI data are estimated to be accurate within ≤ ±5%.

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

11.2.3 Neutron Leakage Spectra Distributions of Thick Targets

As already mentioned, the TOF method was considered for thick target experiments to measure the neutron leakage yield spectra at the LANL-WNR, Los Alamos, USA, on stopping-length and near-stopping-length target materials with incident proton beams of 113 and 256 MeV energy by Meier et al. [696–698]. At the synchrotron at KEK, Japan, thick Pb target leakage neutron spectra were measured by Shin et al. [823] and Meigo et al. [808] applying 0.5 and 1.5 GeV proton beams. At the SATURNE accelerator, France, experimental investigations on emitted neutron spectra distributions from thick cylindrical Fe and Pb targets with various lengths and diameters were undertaken with 0.8, 1.2, and 1.6 GeV proton energies by Leray et al. [133, 543]. 11.2.3.1 The LANL-WNR Thick Target Experiments Stopping-length and near-stopping-length target materials (9 Be, C, O, 27Al, Fe, Pb, 238 U) are used at 113 and 256 MeV proton beam experiments by Meier et al. [696–698, 824] to measure the absolute differential neutron yield leakage spectra emitted at scattering angles of 7.5◦ , 30◦ , 60◦ , 120◦ , and 150◦ . The LANLWNR facility and its speciﬁc properties of the TOF experiment were already discussed in detail in Section 10.2.1 on page 289. The experiments were conducted

Absolute neutron yield [n sr−1 MeV−1]

101 100

26

10−1

Fe(p,xn) - 256 MeV stopping target

10−2 10−3 10−4 10−5 10−6

7.5°

10−7

30° × 10−1 60° × 10−2

10−8

150° × 10−3

−9

10

10−1

100

101 Neutron energy [MeV]

Fig. 11.18 Experimental 256 MeV proton-induced absolute differential neutron yields for the reaction 26 Fe(p, xn) for a stopping-length Fe target. Each successive curve, starting from the smallest angle 7.5◦ , is scaled by a multiplication factor of 10−1 , e.g., 30◦ × 10−1 , 60◦ × 10−2 , and 150◦ × 10−3 .

102

5×102

407

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

101 Absolute neutron yield [n sr−1 MeV−1]

408

100

238U(p,xn)

- 256 MeV stopping target

10−1 10−2 10−3 10−4 10−5 10−6

7.5° 30° × 10−1

−7

10

60° × 10−2

10−8

150° × 10−3

10−9 10−1

100

101

102

5×102

Neutron energy [MeV] Fig. 11.19 Same as in Figure 11.18 but for the reaction 238 U(p, xn) and a stopping-length U target.

with incident proton beam energies of 116 and 256 MeV. The target characteristics of stopping-length and near-stopping length targets are summarized in Table 11.12. In Figures 11.18 and 11.19 the absolute differential neutron yields for the scattering angles 7.5◦ , 30◦ , 60◦ , and 150◦ for an incident proton energy 256 MeV on stopping-lengths Fe and U targets are plotted [696, 698]. The target dimensions are given in Table 11.12. Both measurements show at an emission angle of 7.5◦ and a neutron energy of about 200 MeV the quasielastic peak in the neutron yield production, which vanishes at higher emission angles. This effect is also observed in the ‘‘thin’’ target data. All the data are retrieved from NNDC experimental nuclear reaction database (EXFOR/CSISRS) [709]. 11.2.3.2 The KEK Time-of-Flight Thick Pb Target Experiments The TOF experiment at the KEK facility and its speciﬁc properties were already discussed in Section 10.2.3 on page 312. The intensity of the proton beam was very weak, ≤ 105 particles per pulse therefore the incident protons on the target could be counted one-by-one. The size of the beam was 2.0 cm in the vertical plane and 1.6 cm in the horizontal one in FWHM, respectively [823]. The used Pb target in natural abundance was of rectangular shape 15 × 15 × 20 cm3 . Protons of an energy of 0.5 GeV were stopped completely, whereas protons of 1.5 GeV caused an average energy loss of about 0.26 GeV. The detector efﬁciencies were estimated as described in Section 10.2.3 on page 312 and more in detail in [808]. The results of the experiment together with Monte Carlo particle production and particle transport simulations are illustrated in Figures 11.20 and 11.21. The estimated uncertainties of the neutron yield are energy dependent and are given

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV Stopping-length and near stopping-length target materials used at the 113 and 256 MeV proton beam experiments by Meier et al. [696–698, 824].

Tab. 11.12

Stopping length targets at 113 MeV incident protons Element Be C Al Fe 238 U

Radius (cm)

Length (cm)

3.65 3.65 3.65 3.65 4.00

5.70 5.83 4.03 1.57 3.00

Target mass (g) 434.2 394.8 455.2 517.1 2819.9

Stopping length targets at 256 MeV incident protons Be C Al Fe 238 U

6.60 8.00 8.00 8.00 4.00

27.86 30.00 20.00 8.00 5.00

7048 9928 10918 12644 4770

Near stopping length targets at 256 MeV incident protons Be C Al Fe 238 U

6.60 8.00 8.00 8.00 4.00

17.86 17.45 12.15 4.70 3.00

4517 5775 6632 7429 2863

for neutrons with energies ≤ 20 MeV of about ±1σ = 9–12% and increases up to ±1σ = 19–25% for neutron energies of about 200 MeV [808]. As seen from the ﬁgures the measured data were compared with Monte Carlo results using the NMTC/JAERI-MCNP-4A system [808]. In general, the agreement is fairly well in the low-energy regime ≤ 10 MeV whereas in the energy range between 20 and 80 MeV the calculated values are about 50% lower. Also at backward angles, the simulations underestimate the measured results. 11.2.4 The LANL SUNNYSIDE Experiments

The aim of the LANL SUNNYSIDE experiment [557, 825] was to measure the neutron production for prototyping targets for accelerator driven systems ADS and speciﬁcally for APT1) applications for incident protons in the energy range from 0.4 to 2.0 GeV. Most of the experiments were investigated at the SATURNE accelerator at CEA-Saclay, France, at incident proton energies of 0.4, 1.6, and 2.0 GeV. Some

409

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

102 101 100 Neutron yield [n sr −1 MeV −1 p−1]

410

NMTC/JAERI-MCNP-4A Cugnon NN NMTC/JAERI-MCNP-4A Free NN

15° ×102 30°× 10 60°

10−1 90°× 0.1

10−2 10−3 10−4

120° −2 ×10 150° −3 ×10

10−5 10−6 10−7 10−8 100

Proton energy 0.5 GeV

101

102

103

Neutron energy [MeV] Fig. 11.20 Neutron yield spectra for 0.5 GeV protons incident on a thick Pb target measured at scattering angles of 15◦ , 30◦ , 60◦ , 90◦ , 120◦ , and 150◦ . The symbols represent the different angle-dependent measured yield spectra. The dashed and solid lines are results of Monte Carlo simulations with NMTC/JAERI coupled with MCNP-4A (after Shin et al. [823]).

of the experiments were carried out at the experimental LANL-WNR area using a 0.8-GeV proton beam already described in Section 10.2.1.1 on page 290. A sketch of the experimental setup is given in Figure 11.22. A target and a lead blanket assembly of 60 cm outer diameter, a thickness of 16.51 cm, and a length of 200 cm is embedded into a water moderator vessel of 2.5 m in diameter and 3.0 m in length. The neutron multiplicity per incident beam proton Mn /p is determined considering the manganese water-bath technique. The neutrons leaking out of the target are captured in the manganese producing 56 Mn, which has a half-life of 2.6 h and emits gamma rays of 0.846 MeV energy. The upper vessel section contained only water whereas the lower two sections contain a 1–2% MnSO4 solution varying during the experiment. The total volume of H2 O in the upper vessel was 5.047 m3 and the volume of the MnSO4 solution in the two lower vessels was 9.245 m3 . Since most of the 56 Mn is produced near the target a mixing of the manganese solution is accomplished by pumping system before extracting a sample to determine the total 56 Mn production. Details are given in [386].

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

102 15°×102

101

30°×10

Neutron yield [n sr−1 MeV−1 p−1]

100 10−1

60° 90°×0.1

10−2

120° ×10−2

10−3

150° ×10−3

10−4 10−5 10−6 NMTC/JAERI-MCNP-4A Cugnon NN NMTC/JAERI-MCNP-4A free NN Proton energy 1.5 GeV

10−7 10−8 100 Fig. 11.21

101 102 Neutron energy [MeV]

103

Same as in Figure 11.20 but for an incident proton energy of 1.5 GeV.

Four types of targets were chosen which are relevant for various ADS systems. • cylindrical Pb target with diameter of 25 cm and length 120 cm, stopping length for 0.8 GeV protons is about 40 cm, • cylindrical target of 7 Li diameter of 25 cm and length of 170 cm made of seven steel container sections containing the 7 Li metal, the length of the target is only sufﬁcient to stop protons with an energy of 0.4 GeV, • cylindrical target as a mixture of Th in molten salts with Li and ﬂorine – ThO2 /Li2 CO3 /teﬂon, the average density of this target is to low to stop 0.8 GeV protons therefore a teﬂon plug was added downstream of the target, • cylindrical W target diameter of 15.24 cm and length 81.27 cm, the target was backed by a Pb beam stop with diameter of 25 cm and length of 37.38 cm. The results of the experiment are the total numbers of 56 Mn atoms and the total number of protons, which were determined by the Al foil activation method and by an integrating current transformer measuring the total proton beam charge [557]. A comparison of the beam charge measurements with the transformer and the Al foil activation method agreed in average to 2%. The number of 56 Mn per beam proton is the measured quantity, which must be compared with spallation reaction transport simulations to calculate at least the neutron yield or multiplicity Mn /p.

411

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11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

Moderator vessel: Ø = 250 cm, length = 300 cm volume: about 14 m3 circulation 12× 103 cm3/s

0.4-2.0 GeV

Lead blanket Ø = 60 cm, length = 200 cm Foil insertion pipe Lead target Ø= 25, length =120 cm Polyethylene plug

Proton beam

1–2% MnSO4 solution Legend Lead Polyethylene H2O/1–2% MnSO4

Fig. 11.22 A schematic sketch SUNNYSIDE experiment with the target holder, the lead blanket, and the water vessel containing the MnSO4 solution (after Morgan et al. [386, 557]).

As discussed in [825], the total systematic uncertainties in the measurements were generally in the range of 3–4%. Some systematic uncertainties are caused from the calibration of the counters to measure the 56 Mn and the determination of the number of beam protons considering the reactions 27 Al(p,3pn)24 Na and Tab. 11.13 Experimentally measured 56 Mn-production rates per proton at different incident beam energies for a Pb and a W target and comparison with MCNPX Monte Carlo calculations given as the ratio exp/calc.

Target

Proton energy (GeV)

MnSO4 (wt%)

Solid Pb ∅ = 25 cm

0.4 0.8 0.8 0.8a 1.6 2.0

0.833 0.833 0.994 1.647 1.647 0.833

0.050 0.171 0.205 0.335 0.855 0.576

3.8 3.3 4.3 3.7 3.1 3.3

0.96 0.97 0.97 0.97 1.01 1.05

Solid W ∅ = 15 cm

0.4 0.8 1.6 2.0

1.647 1.647 1.647 1.647

0.059 0.202 0.519 0.669

3.9 2.8 2.7 3.2

0.89 0.92 0.97 0.98

a

See Morgan et al. [557].

Exp. 56 Mn/proton

Uncertainty (%)

Exp./calc.

average

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV 27 Al(p,x)22 Na by the Al foil activation, and the total volume of water in the system, the MnSO4 concentration. In Table 11.13 some results for solid Pb and W targets of the SUNNYSIDE experiment are summarized and compared with the calculated values using the MCNPX particle transport system [194]. The data are from Morgan et al. [825]. The examples of the comparison between the experimental and the calculated results, given as the ratio exp/calc, for thick Pb and W targets surrounded by a 60 cm thick Pb blanket (cf. Figure 11.22) show a good agreement. The MCNPX calculations are used with the default parameters, the BERTINI–ISABEL model with pre-equilibrium [825].

11.2.5 Energy Deposition Experiments with Thick Mercury Targets

As already mentioned the spallation neutron sources (SNS) [681] at Oak Ridge, USA, and J-PARC [629] at KEK, Japan, are operated at a proton beam power of about 1 MW, whereas future sources are envisioned to be operated with 5 MW proton beam power and beyond. Liquid mercury has been selected as ﬁrst priority material for the high power spallation targets originally proposed for the European Spallation Neutron Source (ESS) [551]. Operated in a 1 µs pulsed mode up to 100 kJ per pulse will be deposited into the target systems of such spallation sources. The container material for the liquid mercury will be subject of high radiation damage, high thermal mechanical load and corrosion by the liquid metal. Computer calculations show that because of the high thermal mechanical load, tensile stresses may occur in the container. Therefore, it is essential to understand the energy deposition mechanisms of high-intensity proton pulses incident on thick targets. The experimental collaborations of the NESSI [809] and ASTE [812]2) performed therefore several experiments to measure the thick target energy deposition during the proton pulse train on mercury targets. The NESSI collaboration applied the proton beam of the COSY accelerator at J¨ulich with 0.8 and 1.2 GeV energy protons for mercury and lead targets of 15 cm diameter and 35 cm length, whereas the ASTE collaboration used the proton beam of the AGS at the BNL, Brookhaven, to measure the energy deposition and the temperature rise in a thick mercury target of diameter 20 cm and length 130 cm during a proton pulse train of 24 GeV incident energy and a deposition power of 30 kJ per pulse. Due to the extremely short proton pulse of 1 µs applied at high-intensity spallation neutron sources, a pressure wave might be induced in the liquid metal. That means the dynamic behavior of the liquid metal and the impulse transfer to the target container must be additionally considered for the design of high-power targets. The alternating stress and pressure make high demands against the fatigue strength of the container material. Since the spatial distribution and intensity of the energy deposition are initial values for the thermodynamic calculations, it has also inﬂuences on (1) the design of the target container, like mechanical 1) APT, Accelerator Production of Tritium.

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11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

stability, ﬂow dynamics of the liquid metal and optimization of the cooling, (2) the request at structure materials, like a behavior in relation to strong temperature gradients, fatigue strength, corrosion resistance, (3) and the life time of the target. A reliable prediction of the distribution and intensity of the energy deposition in the target presuppose an accurate simulation of particle production, particle transport and energy deposition mechanisms. Since the rise in temperature produced in the target is caused mainly as a consequence of ionization processes of charged particles the power density in the target can be determined via the measurement of these processes. 11.2.5.1 The Energy Deposition Thick Mercury Target Experiment at COSY J¨ulich For the proton energies and the intensities available at the COSY accelerator the method of thermoluminescence detectors (TLD)s seems to be suitable for the measurement of the energy deposition in a spallation target. This method is well known from dose measurement in radiation protection and have been successfully employed in J¨ulich to measure dose distributions and even the Braggpeak in high resolution in phantom irradiation experiments in the incident proton energy range up to 0.3 GeV [826]. Measurements were investigated with incident proton beam energies of 0.8 and 1.2 GeV on lead and mercury targets of 15 cm diameter and 35-cm length which were equipped with 200 TLD detectors. For the measurements thulium doped calcium ﬂuoride thermoluminescence detectors were utilized. For the measurements detectors from Harshaw were used with a chip size of 0.3 × 0.3 × 0.1 mm3 . The dose response of the used TLD is linear in proton – He2+ , Ne10+ – and in π − -ﬁelds up to a linear energy transfer (yD ) smaller than 30 keV or 70 keV µm−1 [827]. The detectors are not sensitive to neutrons. More details of the analysis procedure and the Monte Carlo simulations is given in Ref. [828] Figure 11.23 shows the setup of the mercury target and the position of the detectors. The Hg target with a diameter of 15 cm and a length of 35 cm was assembled in stainless container segments of different thicknesses ﬁlled with Hg (cf. Section 11.6 on page 11.6). The detectors were positioned between the target segments by a positioning disk of 1 mm thick stainless steel. The ﬁrst disk was equipped with 73, all following with 33 TLD detectors. TLD detectors and the stopping power Charged particles lose their energy during the passage through matt mainly by the inelastic scattering and by ionizing. The Bethe–Bloch formula (cf. Section 1.3.6.1 on page 33) describes the mean energy loss dE/dx of a charged particle by ionization. To draw conclusions from a dose measured by the TLD material to the energy deposition in a spallation target, the different stopping power values of a charged particle related to the material must be known. The ratio of the stopping power Starget in the target material to the stopping power Sdetector in the detector material converts the dose in TLD CaF2 to the dose deposited in the target material. Figure 11.24 shows the stopping power for protons in the target material Hg and in the TLD detector material as a function

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV TLD detectors Ø 6 mm

Detector discs

15 cm

Ø 5 mm

35.7 cm

Fig. 11.23 The geometry of the mercury target assembly. Indicated are the stainless steel disks equipped with TLD detectors.

CaF2 Stopping power S [MeV cm2 g−1]

102

Hg S(Hg) / S(CaF2)

101

100

10−1

10−2 1

10 102 Proton energy [MeV]

103

Fig. 11.24 Proton energy dependent stopping power S in the TLD of CaF2 , the Hg target material, and their stopping power ratio.

of the proton energy. The ratio of the stopping power in the target material Hg and in the TLD CaF2 approaches in the area relevant for the measurements above 20 MeV kinetic energy of the particles against a constant value. Due to this behavior of the ratio, the measured dose in CaF2 can be transferred to the target material [828].

415

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

0.6

0.6

xsr = −0.1 cm sx = 0.56 cm

0.5

Energy deposition [J kg−1]

Energy deposition [J kg−1]

416

0.4 0.3 0.2 0.1 0

−5

0 2.5 −2.5 x – axis [cm]

5

ysr = −0.03 cm sy = 1.16 cm

0.5 0.4 0.3 0.2 0.1 0

−5

0 2.5 −2.5 y – axis [cm]

5

Fig. 11.25 Gaussian-ﬁtted measured distributions of the horizontal and vertical energy deposition in front of the Hg irradiated with 1.2 GeV protons. σx and σy are the standard deviations of the Gaussian ﬁt and the values xsr and ysr indicate the shift of the maximum in the x- or y-direction.

Proton beam intensity distribution The proton beam intensity distribution was measured with a TLD disk in front of the mercury target at an incident proton energy of 1.2 GeV (cf. Figure 11.23) and is used for the Monte Carlo simulations of the energy deposition inside the thick Hg and Pb targets. The TLD disk in front of the target was equipped with 33 TLD chip detectors along the vertical, y-axis, the horizontal, x-axis, and the 45◦ -axis. The discrete measured values on the x- and y-axis were ﬁtted with a Gaussian function to obtain the intensity distribution. The distributions are given in Figure 11.25, a standard deviation of ± 1σ in the x-direction σx =0.56 cm, and in the y-direction σy =1.16 cm for the y-axis (cf. Figure 11.25) has been found. The zero point of the coordinate system corresponds to the center of the target. It was further assumed that a superposition of the two gaussian distributions in the x- and y-direction represent the distribution of intensity in the xy-plane in the form

f(x,y) = af(x) f(y) +∞ +∞ and f(x,y) dxdy = 1.

(11.10)

−∞ −∞

Figure 11.26 shows the comparison of the measured values to the 45◦ -axis and the corresponding Gaussian ﬁt. The deviation of the measured points x = −0.8, y = 0.8 from the assumed Gaussian ﬁt is shown in Figure 11.26 for example. Related to the measured value the assumed function f(x,y=x) (dashed line) indicates an error of 63%. The deviation of the measured values in relation to the assumed function f(x,y=x) is caused mainly by a shift of the maximum by 0.4 cm. This deviation is situated however in the context of the measurement inaccuracy, which results from the position of the TLDs

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV 0.6

0.5 0.4

(−0.8; 0.8)

0.3

FHg

0.2 0.1 0

(a)

+x −y

−2

0

2

[cm]

Energy deposition [J kg−1]

Energy deposition [J kg−1]

0.6

0.5 0.4 0.3 0.2 0.1 0

−x +y

(b)

−x −y

−2

0 [cm]

2

+x +y

Fig. 11.26 Comparison of the measured values (indicated as triangles) on the 45◦ -axis with the Gaussian ﬁt for Hg target with 1.2 GeV protons. For further explanations, see the text further. Comparison of measurements (exp.) and Monte Carlo simulations (calc.) of the energy deposition along the z-axis of Hg and Pb targets with diameters of 15 cm and lengths of 35 cm.

Tab. 11.14

Incident proton energy 1.2 GeV Position on z-axis (cm)

0.05a 0.05b 1.50 3.70 9.15 14.35 19.55 24.75 a b

exp.

Calc. (J cm−3 p−1 ) × 10−12

Hg 0.436 0.751 0.940 0.732 0.512 0.268 0.146 0.070

Pb 1.29 1.86 2.00 2.06 1.72 1.00 0.49 −

Hg 0.438 0.754 0.857 0.784 0.522 0.368 0.224 0.114

Calc./Exp.

Pb 1.24 1.79 1.91 1.78 1.54 1.03 0.67 −

Hg 1.00 1.00 0.91 1.07 1.02 1.37 1.53 1.64

Pb 0.96 0.96 0.96 0.87 0.90 1.02 1.36 −

Normalized to stainless steel. Normalized to Hg/Pb material.

in the measurement. Taking this into account the above Gaussian approximation of the beam intensity distribution is used for the Monte Carlo simulations of the energy deposition. The results are compared with the measurements and given in Table 11.14. In additional irradiation experiments using a Pb target a higher spatial resolution of the distribution of intensity of the proton beam could be obtained, because of a new position disk. The distribution of intensity of the proton beam could be mapped completely by the TLDs, which cover an area of 2.8 × 2.8 cm2 . The measured and

417

12 10 8 6 4 2 0

−2

−1

0

1

x – axis [cm]

2

Energy deposition in arbitary units

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

Energy deposition in arbitary units

418

12 10 8 6 4 2 0

−2

−1

0

1

2

y – axis [cm]

Fig. 11.27 Measured (triangle) and simulated (lines) intensity distribution of the proton beam for the irradiation of the Pb target with 1.2 GeV protons.

Monte Carlo simulated response is shown in Figure 11.27. The triangles indicate the measured distribution of intensity and the solid lines of the simulated ones. Results and conclusions The axial energy deposition can be described by the following features: • The energy deposition in the target window, which produces thermal load must be considered for the design of the containment. • Value and position of the peak-energy deposition and the shape of energy deposition along the z-axis in the target determine the pressure gradient in a liquid target material.

Figure 11.28 shows the measured and simulated distribution of the energy deposition along the z-axis of the Hg and Pb target irradiated with 1.2 GeV protons. The triangles indicate the measured values and the circles the Monte Carlo simulated results. The energy deposition at the position z = 0 indicates the energy deposition produced in the stainless window of the target. All other values are the deposition results inside the target material. For the Monte Carlo simulations the contributions of protons, deuterons, tritons, helium, pions, muons, and recoil products from the intra–inter nuclear cascade evaporation process to the energy deposition were taken into account. The agreement between measurements and simulations is fairly well. Underestimated is the maximum of the energy deposition in the target by the simulations, whereas with increasing depth the energy deposition is slightly overestimated. The measured values, the results of the simulation calculations, and the ratio of the calculated results to measured ones are summarized in Table 11.14. The energy deposition calculations were performed by the HERMES code system [88]. The absolute agreement between simulation and experimental results is fairly well. For the Hg target the peak deposition on the z-axis is slightly underestimated by the simulation whereas the tails of the distribution along the z-axis are slightly

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

Energy deposition [j cm−3 p−1 × 10−12]

1

Experiment MC calculation

0.8 0.6 0.4 0.2 0

0

2.5

5

7.5

10 12.5 15 Target depth [cm]

17.5

20

22.5

25

2.5 Energy deposition [j cm−3 p−1 × 10−12]

Experiment 2

MC calculation

1.5 1 0.5 0

0

2

4

6

8 10 12 Target depth [cm]

14

16

18

Fig. 11.28 Distribution of the energy deposition in J cm−3 per incident proton along the z-axis for the irradiation of an Hg target (a) and a Pb target (b) with 1.2 GeV protons.

overestimated. The accuracy between simulation and experiment is in the order of 5–10%. It was concluded from the results of the validation of the experiments that the predictive power simulating energy deposition in mercury and lead spallation targets is sufﬁcient and accurate to supply reliable parameters for the engineering layout. 11.2.5.2 The Thick Mercury Target Experiment ASTE at the AGS Accelerator at BNL The purpose of the ASTE collaboration was to perform experiments to verify experimentally a number of predictions from theoretical calculations on the neutron and thermodynamical behavior of spallation targets with mercury designed for pulsed operation in the megawatt power regime [812, 829]. The experiments started in 1997 with a ﬁrst test run with a bare cylindrical (diameter 20 cm, length 130 cm) mercury target and were continued with reﬂected target systems (cf. Section 13.3.3.3 on page 466 and Figure 13.29 on page 466). The main goals of the experiment were to verify experimentally a number of theoretical predictions: • energy deposition distribution at GeV incident proton beam energy measured as a temperature jump during the pulse tain [810, 830]; • distribution of neutron leakage reaction rates;

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11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

Bars for activation foils

Connection for thermocouples Fig. 11.29 The ASTE stainless steel target container ﬁlled with mercury of diameter of 20 cm and length of 130 cm. Also shown are the bars for the activation foil measurements and the connection lines to the thermocouples inside the mercury.

• pressure waves in mercury and stress wave monitoring of the target container [829, 831]; • spallation product measurements, reaction rate distributions in reﬂected target systems and neutron spectra time-of-ﬂight measurements [812]. The ASTE target, a 20 cm diameter and 130 cm long cylindrical stainless steel container with a hemispherical front ﬁlled with mercury, is shown in Figure 11.29. Of major interest of the experiment was the estimation of the energy deposition distribution in the target at short pulsed incident proton beams, which was at the ASTE experiment accomplished by measuring the temperature jump. The temperature jump measurements were carried out by mounting thermocouples at axial positions inside the Hg target medium. Figure 11.30 shows a sketch with the positions of the 32 thermocouples inside the mercury placed in the lower half midplane of the target cylinder. The 1.5 mm thick encapsulated Chromel-Alumel thermocouples (type K) [830] were thinned down to a thickness of 0.5 mm over the last 15 mm in the radial direction in order to improve their time response. The distributions of the thermocouples in radial direction were chosen on the basis of an assumed parabolic radial power distribution. The noise of the system was about 0.5 K dependent from the cable lengths to data acquisition system which was about 50 m. The beam intensity and its proﬁle was measured by an Al foil, 20 × 20 cm2 , 25 µm thick, by the Japanese group of the ASTE-collaboration. The radioactivity of the proton-induced production of 22 Na and 7 Be was determined by placing the Al foil on an image plate and integrating the measured radioactivity over pixel sizes of 2 × 2 mm2 . The resulting beam proﬁle is shown in Figure 11.31. The beam center is not located in the target coordinate center. The distribution is slightly elliptical. The measured proﬁle in the xy-direction was used to compare the experimental results with Monte Carlo calculations given in Figures 11.32 and 11.33.

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV

1300 mm 980 680 480 380

2. 3. 4. 5. 6.

1.

Proton beam Fig. 11.30

7. 12 . 8. 13. 9. 10. 14. 11.

15. 20. 16. 17. 21. 18. 19. 22.

23 . 24. 25. 26. 27.

28 .

31.

32.

200

20 40 60 80

280 230 180 130 80 30

29. 30.

The positions of the 32 thermocouples inside the mercury of the Aste.

24 GeV proton beam profile on the ASTE target Beam intensity

100

3.00 × 10−4 1.82 ×10−4

x [mm]

50

1.14 ×10−4 6.70 ×10−5

0

3.41 ×10−5 −50

4.20 ×10−6 0.0

−100 −100

−50

0 y [mm]

50

100

Fig. 11.31 Measured beam intensity and density proﬁle of the proton beam at an energy of 24 GeV incident on the ASTE mercury target.

Measurements were performed at three different proton energies: 1.5, 7, and 24 GeV. The 1.5 and 7 GeV incident proton pulses incident on the target delivered not enough energy to produce a measurable temperature jump of more than 0.1 K at any thermocouple position in the target. Only a pulse with all protons of the AGS in two bunches, 2 × 4.0 × 1012 protons of 24 GeV in less than 30 ms introduced a maximum temperature jump of 3.4 K in the target (cf. Figure 11.32). A comparison of the axial distribution of a measured and a simulated temperature jump is given in Figure 11.32. The calculations were performed using the measured incident proton beam density proﬁle. The maximum measured temperature jump of 3.4 K shown in Figure 11.32 corresponds to peak power density of about 6.4 J cm−3 using the values of 0.139 J

421

11 Proton-Matter-Induced Secondary Particle Production – The ‘‘Thick’’ Target Experiments

Temperature jump [K]

4.0 ASTE experiment HERMES calculation 0 (inclusive Π -decay deposition)

3.0 2.0 1.0 0.0 −10.0

10.0

30.0 50.0 70.0 Target depth [cm]

90.0

110.0

Fig. 11.32 Measured and Monte Carlo simulated temperature jump produced inside the mercury target during a 25 kJ incident proton pulse of 24 GeV energy. The simulation is predicted by the HERMES Monte Carlo code [88].

1015 Energy integrated neutron surface flux [n cm−2 s−1]

422

Monte carlo simulations

1014

1013

Indium reaction rates of ln(n,n′)115mln

115

1.5 GeV 7.0 GeV 24.0 GeV

1012 0.0

25.0

50.0 75.0 Target length [cm]

100.0

125.0

Fig. 11.33 Comparison of simulated and experimental results of the neutron leakage ﬂux with incident protons of 1.5, 7, 24 GeV measured with indium threshold foil detectors on the surface of the ASTE mercury target. The leakage ﬂuxes are normalized at an incident proton beam power of 5 MW.

g−1 K−1 for the speciﬁc heat capacity and 13.52 g cm3 for the density of the mercury. A numerical integration over the measured axial and transversal temperature proﬁles over the whole target was used to determine the total power deposition per proton in the target during the pulse train [830]. These values are summarized in Table 11.15. A series of experiments on the bare ASTE mercury target were investigated at incident proton of 1.5, 1.6, 7, 12, and 24 GeV on spatial and spectral distributions of the fast neutron leakage using various activation detectors with different threshold energies, e.g., activation foils of In, Nb, Al, Bi, Co, Tm, Y, Ni, and Ti. Details are

11.2 Proton-Induced Thick Target Experiments in the Energy Range 0.1–2.5 GeV Total energy deposition per pulse, total energy deposition per proton, and percentage of energy deposition of the beam power in the ASTE mercury for incident proton of an energy of 24 GeV (data are from Ref. [830]).

Tab. 11.15

Radial extrapolation

Linear Parabolic

Total energy deposited per proton pulse (kJ)

Total energy deposited per proton (GeV)

16.7 18.7

13 14.6

Deposited energy in percent of beam power 54.2 61.0

given by Takada et al. [832]. The 115 In(n, n )115m reaction was selected as the baseline reaction detector because of its low-energy threshold energy of 0.34 MeV compared to the other detectors. Therefore, the reaction rate distributions of 115 In(n, n )115m were measured, most extensively of all detector foils, along the beam axis on the cylindrical surface of the target. The comparison of measured and simulated results gives an agreement of about 12% for the FWHM of the measured and calculated distributions. For all incident proton beam energies there is a tendency of the estimated neutron leakage after the peak position to underestimate by about 3–10% of the measured distribution.

423

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12 Neutron Production by Proton, Antiproton, Deuteron, Pion, and Kaon Projectiles As discussed for the economy of neutron production in Sections 8.2.2, 8.2.4 and shown in Figure 8.5, there is not much advantage for incident proton beam energies beyond 1–2 GeV. Since at energies well above 1 GeV pion production becomes a dominating process [633] the question arises how efﬁcient pions are for neutron production. Is there a considerable fraction of the initial available energy lost via decay channels like π 0 → 2γ or π + → µ+ + νµ ? To what extent is this loss compensated for by lower electronic energy loss of charged pions prior to nuclear reactions? Pions approach their minimum ionization power at considerably lower energies (0.3 GeV) than protons (2 GeV). To study these questions the comparison of proton- and antiproton-induced neutron production in thick targets is an ideal method, since in the case of p the neutron production is mediated essentially via pions originating from p-nucleon annihilation production on average 5 pions (3π ± + 2π 0 ). That is why in the following more generally hadron (π, K, p, p, d)-induced neutron production in thick Pb targets will be compared up to 5 GeV/c [664, 730]. It might be advantageous for the operation of the accelerator and target assembly of spallation neutron sources to employ at a given beam power considerably higher beam energies than 1 GeV. But since at increasing energy meson production (mainly πs) is increasing, an increasing part of neutron production is due to secondary-meson-induced reactions. How efﬁcient are these pions in producing neutrons? In order to answer this question hadron-induced neutron production as a function of particle energy has been investigated by the NESSI collaboration [664, 730]. In particular neutron production for proton-, antiproton-, and pioninduced reactions has been compared. In the latter reaction neutron production is predominantly induced by π ± and π 0 . No data exist at all for pion-induced reactions which are of importance to account for the yield of secondary reactions, with the pions being produced in a primary (anti-)proton nucleus interaction. In addition, in the framework of the nuclear physics driven motivation described in Section 9.4 especially antiproton-induced reactions in ﬂight and at rest are capable of exciting nuclear matter without disturbing dynamical effects generally induced in heavy ion reactions. Complementary to heavy ion reactions, antiproton-induced reactions represent an alternative method for producing highly excited nuclear matter and enable probing the nuclear equation of state at high temperatures. The Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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12 Neutron Production by Proton, Antiproton, Deuteron, Pion, and Kaon Projectiles

rather high energy transfer is due to the phase-time-structure of the elementary NN-annihilation with a radius of interaction of ≈ 1.8 fm and a coherence length of cτ ∼ 1.5 fm. In case of antiproton annihilation at rest, the keV-antiprotons are captured by the nucleus like ‘‘heavy electrons.’’ They cascade down to lower energy levels emitting Auger-electrons and annihilate with a nucleon of the nucleus at the periphery of the nucleus. On the average 5 pions, as well as strange particles K, , , are produced by partly heating the nucleus in a radiation-like way [671]. Much more thermal excitation energy can be transferred to the nucleus using energetic GeV-antiprotons, because the annihilation takes place much closer to or even inside the nucleus. Increasing the p-energy does not a priori implicit high E ∗ , because at the same time the average kinetic energy of annihilation pions is also increased and the pion absorption via the -resonance becomes less effective. INC model calculations [676] show the spin in p reactions to remain small (≤ 25) and the equilibration time (30 fm/c or 10−22 s) [169] to be much smaller than the dynamical periods in heavy ion reactions [677]. The latter effect is of extremely high importance when for high temperatures (T ≈ 6 MeV) the characteristic evaporation times are less than 10−22 s. The physical picture of annihilation in ﬂight and at rest for pA reactions is drawn in Refs. [379, 663, 664, 673]. The secondary beam facility at the Proton Synchrotron (PS) at CERN, Geneva, enabled the measurement of Mn simultaneously for p, p, d, K, and π ± at the same incident momentum and charge. Details on this experiment can be found in Refs. [219, 631, 664, 730]. For protons, antiprotons, positive and negative pions Table 12.1 gives the ﬁrst moment Mn of dσ/dNexp as well as the most probable neutron number Mnmax and its standard deviation σ as derived from a Gaussian ﬁt to the multiplicity distribution dσ/dNexp at the position of the maximum. From the measured reaction probability Preac and Mn the mean number of neutrons per incident proton Nn /p = Mn × Preac was deduced. For protons, the NESSI collaboration observed with increasing target thickness an increase of both the mean neutron multiplicity Mn as well as the most probable neutron multiplicity Mnmax with the relation Mn ≤ Mnmax . For the thickest targets of 35 cm Pb Mn has almost attained the value of Mnmax (Table 12.1) simply due to the fact that the intensity of low neutron multiplicity events has become very small due to secondary reactions. For 35 cm Pb as well as 40 cm U, the intensity of the measured distribution which cannot be described by a Gaussian is smaller than 5% while for thin targets it amounts to 20–30%. For target thicknesses higher than 35 for Pb or 40 cm for U any further increase in the neutron yield per incident proton Nn /p is essentially due only to further increase of the reaction probability. The observed steep increase in the number of neutrons per incident proton Nn /p for target thicknesses up to about 10 cm, instead, is due to the combined increase in the reaction probability Preac and the mean neutron multiplicity Mn with target thickness. Contrary to other methods these two quantities are measured independently in the NESSI experiment and not as a product. The observed larger neutron multiplicity for U compared to Pb can be ascribed in the case of thin targets (cf. Table 12.1) to a higher probability for energy absorption in the bigger

12 Neutron Production by Proton, Antiproton, Deuteron, Pion, and Kaon Projectiles

427

target nucleus, to the lower neutron binding energies of U spallation products, and eventually to one or more extra neutrons from ﬁssion of the residual nucleus (ν = 1.92 for spontaneous ﬁssion of 238 U). In a thick target of U ﬁssion can be induced by many secondary particles and become a dominating process. It multiplies the number of neutrons to the extent that the neutron yield in a 40-cmlong U-target is nearly doubled as compared to Pb: MnU /MnPb = 1.5 and 1.7 at Ep = 1.22 and 4.15 GeV, respectively. The mean neutron multiplicities Mn for π ± , K+ , p, p, and d+ on a thick Pb-target (35 cm length, 15 cm diameter) is presented in Figure 12.1 at incident momenta 2, 3, 4, and 5 GeV/c, respectively. These momenta are corresponding to somewhat higher kinetic energies for πs than the respective proton energies. Since for such a thick target Preac 1, the given values can be considered also as mean numbers of neutrons per incident particle.

Tab. 12.1 Results for thin and thick Pb and depleted U targets: the mean neutron multiplicity Mn , the number of neutrons per incident particle Nn /p, and Nn /π ± ,the most probable neutron number Mmax n , and its standard deviation σ , the latter two are obtained from a Gaussian ﬁt to the distributions of Mn .a

Incident particles protons/antiprotons Moment Target l inc. part. (cm) (GeV/c)

d (cm)

1.94 1.94 1.94 −1.94 2.00 3.00 4.00 −4.00 5.00 −5.00 1.94 1.94 4.00 5.00 5.00

15 18.0 15 21.3 15 26.0 15 − 15 26.7 15 42.2 15 53.9 15 − 15 63.8 15 − 5 × 5 23.3 8 38.0 8(15) 90.1 5 × 5 35.6 8(15) 112.2

a

Pb Pb Pb Pb Pb Pb Pb Pb Pb Pb U U U U U

0.2 5.0 35 35 35 35 35 35 35 35 0.3 40 40 0.9 40

Mmax n

σ

Mn

7.4 14.5 10.7 19.4 11.5 25.4 − 52.5 13.0 26.7 16.5 41.1 20.4 51.7 − 72.2 24.5 60.8 − 79.5 8.8 19.9 19.4 38.8 28.6 87.6 21.8 28.5 30.5 106.0

Nn /p

Pions π ± Mmax n

0.16 − 4.8 − 20.5 − 35.3 − 22.6 35.5 34.9 48.0 44.0 57.5 65.6 − 51.0 66.0 71.2 − 0.53 − 35.3 − 84.1 99.3 2.56 36.7 101.0 115.3

σ

Mn

− − − − − − − − 16.5 32.5 20.1 46.2 22.9 55.1 − 60.5 27.8 63.3 − 68.6 − − − − 33.1 93.5 24.5 30.5 36.1 107.5

Nn /π ±

− − − − 20.5 34.6 38.7 47.0 50.1 − − − 69.3 1.74 72.4

These values have been multiplied by the factor 1/0.85 in order to account for an assumed mean detection efﬁciency of 85%. Errors are in the order of 1–5%. Negative momenta in the ﬁrst column of the table correspond to antiprotons or negative pions (π − ), l and d indicate the target length and diameter, respectively.

12 Neutron Production by Proton, Antiproton, Deuteron, Pion, and Kaon Projectiles p+ p+ thin p+ K+ d+ p− p−

80 70 Mean neutron multiplicity 〈Mn 〉

428

60 50 40 30 20 10 0

0

1

2

3

4

5

6

Incident (available) energy [GeV]

Fig. 12.1 Average neutron multiplicity Mn for incident protons p+ , antiprotons p− , pions π ± , kaons K+ , and deuterons d+ as a function of incident kinetic energy on 35cm-long, 15-cm-diameter Pb target. Mn has been corrected for a mean efﬁciency of

εn = 0.85 (cf. Eq. (10.3) and Figure 10.42). For p− the small ﬁlled squares indicate Mn also at the available incident energy, see text. The ﬁlled and open triangles display Mn for thin Pb targets. The curves are and Mmax n to guide the eye.

If Mn induced by p and p is compared at the same incident energy the neutron numbers in case of p are up to a factor of two higher. If however the p-nucleon annihilation energy of 2mp · c2 is taken into account, the ‘‘available energy’’ results p to Einc + 2mp · c2 = 1.22 + 1.88 = 3.1 GeV. Thus, for instance, the comparison with 1.22 GeV p should be rather made at an incident proton energy of 3.1 GeV. Mn is indeed very similar for p and p-induced reactions when compared at the same available incident energy. Proton and π ± -induced reactions should also be compared at the same incident kinetic energy. The multiplicities are somewhat smaller for pions than for protons if compared at the same incident energy1) (cf. Figure 12.1). In the case of π − one might argue that the capture of a π − in a nucleus at the end of the INC converts the rest energy of the pion (138 MeV) to nuclear excitation [775]. This would favor a comparison at an available energy of π− Einc + mπ c2 . In any case the value Mn has been measured at the same momenta and consequently the best approach to the same incident kinetic energy is the comparison p π of Einc = 4.15 GeV and Einc = 3.86 GeV as shown in Figure 12.1. However, the neutron multiplicity distributions and the corresponding average values Mn , as shown here, are relatively independent of the primary hadron species. For π ± and p the total reaction cross section is about 13% smaller [583] and 20% larger [662, 663] 1) While they are slightly larger when compared at the same momenta

12 Neutron Production by Proton, Antiproton, Deuteron, Pion, and Kaon Projectiles

than that for protons, resulting in correspondingly lower and higher neutron production per unit length along the trajectory of the beam particles in the target, which is a measure of the produced neutron density. Since the reaction cross section is also somewhat larger for deuterons than for protons this ﬁnding implies for the neutron yield per incident deuteron Nn /d = Preac × Mn even larger values, which qualitatively agree with the ﬁndings of Vassilkov et al. [617]. However, the uncertainty for deuterons in the present experiment is considerably larger since the secondary beam of the CERN-PS contains much less deuterons than protons (2 and 8) × 10−3 at 5 and 3 GeV/c, respectively. In summary, Mn of the considered hadrons are very similar within 10% if compared at the same incident available energy in the energy range of 1–6 GeV [662, 663, 730]. These ﬁndings indicate that neutron production mediated by mesons, which is increasing for proton-induced reactions with bombarding energy, is similarly efﬁcient as spallation reactions without mesons being involved.

429

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13 Experiments to Study the Performance of Spallation Neutron Sources 13.1 Introduction

To study the performance of spallation sources in terms of neutron ﬂux and neutron spectra output, complex target–moderator–reﬂector (TMR) experiments were investigated since 25 years. The most common use of spallation produced neutrons is to provide a ‘‘thermal,’’ a ‘‘cold’’ or ‘‘hot’’ neutron source for condensed matter studies, but as already discussed, spallation neutrons are also considered in tritium breeding, as neutron sources for material damage studies, in fertile to ﬁssile breeding and for transmutation of radioactive waste from nuclear power plants. Despite different goals, the same physical processes are involved in all of them and basically they only differ in the selection of materials and geometric conﬁguration that enhances the planned use and the relative importance of the nuclear physics processes. Compared to ﬁssion neutrons, neutrons produced by the spallation process have a much broader energy range from 2 to 3 MeV up to several GeV, the energy of the incident protons. The ﬁrst stages of TMR experiments are facility speciﬁc, may demonstrate feasibility, and will then be the choice of materials and geometry that enhance the particular nuclear aspects veriﬁed by large-scale experiments. Examples are the the German SNQ study experiments [833], the various examples of TMR experiments conducted by groups from Europe, Japan, and USA at accelerators ANL, BNL, J¨ulich, LANL, LNS, and PSI published, e.g., at conferences of the ‘‘International Collaboration of Advanced Neutron Sources’’ (ICANS-IV to XVII during 1981–2005 [834]).

13.2 The Target–Moderator–Reﬂector Issue

An optimal neutron producing system for an ideal neutron spallation source for neutron scattering experiments may be described by a statement of Gary I. Russell of LANL, USA, ‘‘A useful neutron is a neutron with the right energy, at the right time, at the right place.’’ Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

432

13 Experiments to Study the Performance of Spallation Neutron Sources Tab. 13.1

Moderator classiﬁcation for spallation neutron sources.

Moderator classiﬁcation

Neutron energy (meV)

Neutron wavelength ˚ (A)

Moderator temperature (K)

Ultra colda Cold Thermal Hot

≈ 2.5 × 10−4 0.1–10 10–100 100–1000

≈ 500 10–3 4–1 1–0.2

5–8 10–120 120–1000 1000–6000

a Data are based on the SUNS ultracold neutron source at PSI, Switzerland.

The purpose of moderators and reﬂectors surrounding a spallation target is to convert leakage neutrons from the target to low-energy neutrons to an energy spectrum with continuous or pulse characteristics with the possible highest intensity. A comprehensive description and discussion of the various aspects concerning the TMR systems needed for the utilizing spallation neutron sources in neutron scattering research is given by Carpenter [56], Ikeda and Carpenter [835], Bauer [57], Watanabe [635], and in Refs. [834, 836, 837]. Basic examples of target–moderator conﬁgurations are already given in Figure 8.12 on page 271. The process of reducing the energy of the neutrons produced in the spallation target to the thermal or subthermal energy region by elastic scattering is referred to as thermalization, slowing down, or moderation. The material used for the purpose of thermalizing or slowing down neutrons is called a moderator. Table 13.1 shows a classiﬁcation of moderators with a range of neutron parameters, e.g., energy range, wavelengths, and temperatures suitable for spallation neutron sources. An efﬁcient moderator reduces the velocity of neutrons in a small number of collisions, but does not ideally absorb them to any great extent. Slowing down the energy of the neutrons in as few collisions as possible is desirable in order to produce a large amount of thermal neutrons and also to reduce the number of resonance absorptions in the structure materials, which are contained in the TMR unit. The slowing-down process of neutrons in matter is well known from reactor physics and is published in detail in, e.g., the book of Beckurts and Wirtz [63]. An ideal moderating material used for spallation neutron sources should have the following nuclear properties: • large scattering cross section • small absorption cross section • large energy, loss per collision. A convenient measure of energy loss per collision is the logarithmic energy decrement also known as lethargy:

13.2 The Target–Moderator–Reﬂector Issue

ξ = ln(Eint ) − ln(Eﬁnal ) = 1 − (α/(1 − α)) Eint ξ = ln Eﬁnal ξ = 1 forA = 1 and ≈ 2/(A + 2/3) for A > 1,

(13.1)

with = ln(1/α), α = (A − 1)2 /(A + 1)2 as auxiliary quantities, which are used to describe the details of the scattering process in the laboratory system [63]. The parameters are, ξ = average logarithmic energy decrement, Eint = average initial neutron energy, Eﬁnal = average ﬁnal neutron energy, and A = the atomic mass number of the moderator atom. The symbol ξ is commonly called the average logarithmic energy decrement because of the fact that a neutron loses, on the average, a ﬁxed fraction of its energy per scattering collision. Since the fraction of energy retained by a neutron in a single elastic collision is a constant for a given material, ξ is also a constant. Because it is a constant for each type of material and does not depend on the initial neutron energy, ξ is a convenient quantity for assessing the moderating power of a certain material. For hydrogen ξ = 1, and for large atomic masses A, ξ can be very well approximated by ξ ≈ 2/(A + 2/3). Since the quantity ξ is the average logarithmic energy loss per collision, the total number of collisions n necessary to moderate a neutron with an initial energy Eint to a certain energy Ei is given by Eint . n · ξ = ln Ei ln(Eint /Ei ) . (13.2) n= ξ As for example about 22 collisions are needed to slow down a neutron from 20 MeV to a thermal energy of 0.025 eV scattered in a water moderator with a ξ = 0.926 using Eq. (13.2). Sometimes it is convenient to work with an average fractional energy loss per collision as opposed to an average logarithmic fraction. If the initial neutron energy level and the average fractional energy loss per collision are known, the ﬁnal energy level for a given number of collisions may be calculated using the following formula: Eﬁnal = Eint · (1 − frac)n ,

(13.3)

where Eint is the initial neutron energy, Eﬁnal is the neutron energy after n collisions, n is number of collisions, and frac is the average fractional energy loss per collision. Although the logarithmic energy decrement ξ is a convenient measure of the ability of a material to slow down neutrons, it does not measure all necessary properties of a moderator. The other important parameters of the slowing-down process, the slowing-down power (sdp) and the moderating ratio, are a better measure of the capabilities of a moderating material. The sdp is the product of the logarithmic energy decrement ξ and the macroscopic cross section for scattering s in the

433

434

13 Experiments to Study the Performance of Spallation Neutron Sources Tab. 13.2 Logarithmic energy decrement, slowing-down power, and moderating ratio of common moderator materials (data are from [57, 63]).

Moderator material

Density (g cm−3 )

Logarithmic energy decrement ξ

Slowing down power sdp (cm−1 )

H (liquid) H2 O D2 O Be C

0.07 1.00 1.10 1.85 2.23

1.0 0.926 0.510 0.207 0.158

0.86 1.39 0.179 0.157 0.087

s is the free scattering cross b abs is for thermal neutrons. a

Moderating ratio (mr)

61 66 5406 167 215

Scattering/absorption cross section Σs a Σabs b (cm−1 ) 0.86 1.5 0.35 0.76 0.55

1.4 ×10−2 2.1 ×10−2 3.3 ×10−5 9.4 ×10−4 4.0 ×10−5

section.

material. The most complete measure of the effectiveness of a moderator is the moderating ratio (mr). The moderating ratio is the ratio of the sdp to the macroscopic cross section for absorption a . That means a good moderator should capture only weakly. The higher the moderating ratio, the more effectively the material performs as a moderator. The relations of sdp and mr are given by Eq. (13.4). Table 13.2 shows the slowing-down power and the moderating ratio for different common moderator materials. sdp = ξ · s [cm−1 ] s , mr = ξ · a

(13.4)

with s is the macroscopic scattering cross section and a is the macroscopic absorption cross section in cm−1 . The moderating ratio is usually determined with the average absorption cross section at room temperature. The time dependence of the moderation process can be introduced by the time Ti between the collisions of the neutrons with the moderator atoms which is a function of the mean free path λ of the neutrons in the moderator material given by the inverse macroscopic free scattering cross section of the moderator free in cm−1 . This means the frequency of collisions experienced by a neutron of a certain velocity vi is given by vi free , thus the time between collisions is given as Ti = 1/vi free or Ti · vi = λ ≈constant. This expression means that the total time it takes to slow a neutron down to a ﬁnal velocity v is inversely proportional to v. Based on superthermal transport theory [838] for slowing-down process of neutrons in a proton gas (hydrogen), Carpenter and Yelon [839] suggested for the time dependence of the slowing-down neutron ﬂux (v, t) after a short source pulse a relation for the product of v · t a functional dependence given by (v, t) ∼ (ξ · free · v · t/γ )2/γ · exp(−ξ · free · v · t),

(13.5)

13.2 The Target–Moderator–Reﬂector Issue

with γ = 1, for A = 1 and ≈ 4/(3A) for A > 1. The average slowing-down time ts , its standard deviation ts , and the FWHM t1/2 are given by Bauer [57] as 1 v 1 ts = v 1 t1/2 = v ts =

· (1 + 2/γ )γ /(ξ free ), · (1 + 2/γ )1/2 γ /(ξ free ), ·

3 . ξ free

(13.6)

As shown in the appendix on page 687, hydrogen is by far the best moderator. In order to have a high enough density, it must be either in a liquid or super critical state, or a compound with high hydrogen content must be used for which the value v · ts is ≈ 1 cm [57]. In the slowing-down region, the neutron spectrum inside a moderator is approximately proportional to 1/E or more exactly, (1/E)1−α , where E is the neutron energy and α is a number between 0.1 and 0.2 considering the neutron leakage from the moderator during the slowing-down phase [635]. In the thermal equilibrium region, the neutron spectrum represents a Maxwellian distribution due to the balance between the moderator atoms and the neutrons as given in Eq. (13.7). (E)Max =

th · E · exp(−E/(kB · Teff )), (kB · Teff )2

(13.7)

where th is thermal neutron ﬂux, kB = 0.08866165 meV/K , and Teff is the effective moderator temperature. By changing the moderator temperature, Teff , one can shift the thermal equilibrium Maxwellian spectrum to higher or lower energies. This is very nicely demonstrated in Figure 13.1 for H2 O moderators at 20, 70, and 293 K. The example shows the Maxwellian part in the spectrum is shifted to lower energies as the temperature of the moderator decreases. The neutron ﬂux in the slowing-down energy range above 1 eV is independent of the moderator temperature and proportional to 1/E. The deviation from the 1/E behavior below 1 eV for low temperatures is mainly a result of the increase in the scattering cross section and hence a shorter lifetime of the neutrons. The utilization of cryogenic moderators at research neutron spallation is therefore of great importance and are reviewed recently [840]. At energies lower than about 1 eV the time distribution and the pulse shape of a neutron pulse from moderators is determined by the fundamental mode decay time 1/α, which could be evaluated by the time-dependent diffusion theory [63]. The neutron ﬂux I(t) in the moderator after the pulse peak I0 (t) can be written as I(t) = I0 (t) · exp(−α · t) with α = a · v + DB2 − CB4 . . . ,

(13.8)

435

13 Experiments to Study the Performance of Spallation Neutron Sources

Neutrons per incident proton [cm−2 eV−1]

436

10 −6

Ice T-20 K Ice T-70 K Water T-293 K

10 −7

10 −8

10 −9 −4 10

1 10 −3 10 −2 10 −1 Neutron energy [eV]

10

Fig. 13.1 Measured energy spectra from H2 O ice moderator at T = 20 and 70 K and from a H2 O moderator of a temperature at 293 K. The measurements are performed at the JESSICA facility (cf. Section 13.3.3.2[611]).

where a is macroscopic absorption cross section of the moderator material, v the neutron velocity, D is the diffusion coefﬁcient, C the cooling coefﬁcient, and B2 is the geometrical buckling of the moderator for the fundamental mode. Since a · v is constant for a 1/v absorber and the third term in Eq. (13.8) is usually small, the second term in Eq. (13.8) becomes dominant for a small hydrogenous moderator. For a thin moderator the geometrical buckling B2 is mainly determined by the moderator thickness, therefore the decay constant α increases with decreasing thickness of the moderator resulting in a faster decay. The pulse width of the neutron distribution at FWHM, t1/2 , of the exponential decay is given by t1/2 = ln 2/α. For a short incident proton pulse of about several µs the pulse rise-up time is usually much shorter than t1/2 (cf. Figure 13.7). Therefore, the pulse width is mainly determined by t1/2 . But to obtain a very narrow pulse, a very thin moderator is essential which yields to a decrease in the time-integrated neutron ﬂux and also in peak intensity [635]. The other important component, the reﬂector, of a TMR system should enhance the neutron intensity of the low-energy neutrons by partly reﬂecting the leakage neutrons from the target, which do not directly enter the moderator. Reﬂector materials should have a large macroscopic scattering cross section. Common reﬂector materials are, e.g., D2 O, Be, C, Ni, W, and Pb. Data characterizing reﬂector materials for spallation sources together with absorption and scattering cross sections are given in tables in the appendix on page 687. For pulsed spallation neutron sources different TMR systems with ambient temperature, cold and ultracold moderators and different reﬂector materials are used to utilize the different applications. Decoupling and poisoning the reﬂectors and moderators with neutron absorbing material (B4 C, Cd, Gd, etc.) are applied methods to provide a useful neutron pulse shaping.

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

• applications with high neutron peak ﬂux using high-intensity moderators with a tolerable pulse width, • applications with high neutron peak ﬂux using high-resolution moderators, where absorbing materials as decoupler surrounds the moderator or decouple the reﬂector to prevent slow neutrons being returned from the reﬂector, or absorbing material (poisoning) is placed inside the moderator or the premoderator to limit the time slow neutrons spend diffusing out of the moderator (decoupling and poisoning determine the neutron pulse shape), • applications with high neutron average ﬂux using moderators large enough to achieve complete thermalization. Such applications are mostly used by continuous spallation sources. During the 1980s with the startup of several spallation neutron sources, the WNR at LANL, USA, IPNS at ANL, USA, KENS at KEK, Japan, and the construction of the Rutherford source SNS (now ISIS), the planned neutron spallation sources SIN (now SINQ) at PSI, Switzerland, and the high-intensity German SNQ source triggered an intensiﬁed research program on TMR and moderator concepts was initiated [834]. This worldwide research is still continued with the emphasis to utilize cold and ultracold moderators to increase the neutron ﬂux at high-intensity MW spallation neutron sources [635, 836, 841, 842]. Some of the experimental investigations on TMR experiments are discussed in Section 13.3.

13.3 Target–Moderator–Reﬂector Experiments with Complex Geometries and Realistic Material Compositions 13.3.1 The Early Experiments

Thermal neutron ﬂux generation by high-energy protons was experimentally studied during the ING project [58] by Fraser et al. [59]. These test measurements were investigated using the same experiment in measuring H2 O capture rates to determine neutron multiplicities of thick targets discussed in Section 11.2.1.1 on page 381. From these measurements the thermal neutron ﬂux distributions inside a large H2 O water vessel in radial and axial direction were measured estimated for Be, Sn, Pb, and U targets at different incident proton beam energies. The measurements were validated by Coleman and Alsmiller [639] and by Armstrong et al. [338]. With the advent of the ICANS conferences at end of 70s, more realistic TMR experiments were planned and investigated [843]. Measurements are reported for a continuous source system with large H2 O and D2 O moderators, with neutron beam tubes, and using a Pb target with diameter of 13 cm by Thorson [844] at the TRIUMF accelerator. With an incident proton beam of 500 MeV and an average current of 100 µA thermal neutron peak ﬂuxes of about ∼ 5.5 × 1012 cm−2 s−1

437

438

13 Experiments to Study the Performance of Spallation Neutron Sources

for a H2 O moderator and about ∼ 3.3 × 1012 cm−2 s−1 for a D2 O moderator were achieved. 13.3.2 Neutron Performance Studies at Reﬂected Target–Moderator Systems 13.3.2.1 Neutron Studies of a Reﬂected ‘‘T’’-Shape Moderator at LANL-WNR During the years 1980–1982 in LANL, USA, the high current target at the WNR facility was developed. For this purpose, various TMR experiments were performed to measure spectra and neutron beam ﬂuxes of neutrons ≤ 10 eV and at neutron pulse widths of ≤ 0.2 eV. All these measurements were accomplished at the low current time-of-ﬂight (TOF) facility (cf. Section 10.2.1.1 on page 290 and [800, 845, 846]). A sketch of the reﬂected ‘‘T’’-shape premoderator–moderator system is shown in Figure 13.2. Different targets were used of Pb, W, and U all 24.13 cm long and with a diameter of 4.45 cm. Each of the targets had at the ﬁrst a 5 cm re-entrant hole with 2.54–1.42 cm diameter. The proton beam had a 1.5-cm diameter beam spot of the targets with an incident energy of 800 MeV. Cadmium with a thickness of 0.076 cm was used as the neutron decoupler of the surrounding Be reﬂector formed a 46 cm cube (cf. Figure 13.2). The polyethylene thickness of the moderator was measured with thicknesses of 0.64, 1.27, 1.91, and 2.54 cm. This yields an increase Neutron beams from moderator surface

Shadow bar Poison

Decoupler

Reflector

W target Decoupler Proton beam

Neutron beam

Premoderator Moderator

Fig. 13.2 Sketch of the reﬂected ‘‘T’’-shape premoderator/ moderator experimental model of the LANL-WNR (after [800]).

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Neutron flux φ(E) [arbitary units]

104

103

Be reflector Pb/Be reflector CH2 reflector

102

101

100 0.001

0.01

0.1

1.0

10.0

100.0

Neutron energy [eV]

Fig. 13.3 Comparison of measured thermal neutron spectra of the experimental model of Figure 13.2 using Be, polyethylene, and Be/Pb reﬂectors (after [800]).

in thermal leakage ﬂux from about 0.5 to 1.5 [800]. Beryllium as a moderating reﬂector was traditionally the standard reﬂector for spallation neutron sources. Other moderating reﬂectors, so-called slow reﬂectors, compound materials with hydrogen as H2 O, D2 O, or instead polyethylene as substitute were investigated and compared with so-called fast reﬂectors, which could be Pb, iron (steel), Cu, etc. Figure 13.3 shows a measured neutron spectral comparison of a moderator conﬁguration surrounded by decoupled Be, an uncoupled polyethylene, and a decoupled Pb/Be reﬂector. As shown in Figure 13.3, the Be reﬂector produces a slowing-down ﬂux about 2.5 times higher than that of a polyethylene reﬂector. The difference between Be and Pb/Be is only marginal. It has been shown that the time structure of neutron pulses with a Pb reﬂector may be also marginally superior to other reﬂector materials [833]. Further studies at the end of the 1980s were continued on the development of the LANSCE system [847] performing measurements of neutron beam ﬂuxes on high-intensity H2 O moderators and high-resolution cold moderators of liquid hydrogen. 13.3.2.2 The SNQ Target–Moderator–Reﬂector Experiments at the PSI Accelerator (1) Thermal neutron experiments:

During the SNQ study phase from 1980–1985, a large variety of TMR experiments were performed at the accelerator facilities of PSI, Switzerland, CERN, Switzerland, and SATURNE, France, which are mainly investigated by the SNQ teams of the Forschungszentrum J¨ulich [619, 833, 848–853]. The quantities which were measured were mainly the integrated thermal neutron leakage, the thermal neutron ﬂux distribution, and the time structure of the neutron ﬁeld for various conﬁgurations of target, moderator, and reﬂector. Among them were a cylindrical Pb–Bi target in a D2 O vessel and a slab target with a hybrid moderator conﬁguration (cf. Figure 13.4) [848]. It should be mentioned that in the SNQ project, the

439

13 Experiments to Study the Performance of Spallation Neutron Sources

Modenator Reflector

D20-Level Target p Neutrons

p

Al-Table

Neutrons

(a)

Target

D20-Level 85 cm

(b)

170 cm Al-tube 150 f

50

60

10

D20-Level

250 cm

Neutrons

60

110

440

p

Pb-Bi Target 150 f

Grooved moderator

m

0c

17

(c)

170 cm

Fig. 13.4 Schematic illustration of the TMR experiments at PSI, Switzerland with an incident proton beam of 590 MeV. (a) Pb slab target inside D2 O vessel; (b) Pb slab target with hybrid moderator conﬁguration (D2 O below target, and polyethylene (‘‘H2 O’’) moderator with polyethylene reﬂector above the target), (c) cylindrical Pb–Bi target inside D2 O vessel (after Bauer et al. [848, 850]).

proton beam shall hit the target with pulses of a duration of 0.5 ms once every 10 ms. Therefore, it was essential to study the time structure of the resultant thermal neutron ﬁeld in different concepts which were considered. The results were used to predict the performance data for a 5-MW spallation neutron source with 500 µs long proton pulses. The targets were mounted inside a vessel of stainless steel 170 × 170 × 250 cm3 ﬁlled with D2 O, which could be ﬁlled up to a level of 170 cm. Because the SNQ target was designed as a spinning wheel target [142] most of the experiments were investigated with a slab target. The slab target was composed of 27 Pb bricks 50 × 50 × 200 mm3 separated by 6 mm thick polyethylene sheets to simulate the water cooling of the target placed on a Al-table (cf. Figure 13.4). The polyethylene moderator, a so-called grooved type moderator, in the conﬁguration (b)

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions Neutron energy [meV] 100 50 20

10 7

5 4

3

Size: height =15 cm Depth =10 cm Width =15 cm Groove depth = 5 cm Groove width =1.6 cm

10000

2

1

GROOVED Neutrons

COUNTER TARGET

Counts

1000

FLAT 15 cm

Neutrons

100 15 cm 5 cm

10

0

COUNTER TARGET

50

100

150

200

250

Channel number [40 µs/ch]

Fig. 13.5 Comparison of TOF spectra measurements from grooved and ﬂat cold (20 K) methane moderators (after Inoue et al. [857] and Ishikawa et al. [858]).

was a 50 mm thick polyethylene slab at the center with 60 mm long and 10 mm thick ﬁns on both sides. This principle of increasing the neutron intensity of a pulsed neutron source was reported by Bauer et al. [848, 849, 854, 855] and by Carpenter et al. [856] for polyethylene moderators and by Inoue et al. [857, 858] for cold 20 K methane moderators. Detailed optimization studies were also investigated by Kiyanagi et al. [859] on grooved thermal moderators for pulsed neutron sources. As seen from Figure 13.5, a grooved moderator produces considerably a higher neutron intensity than a ﬂat moderator, but resulting in broadening of the pulse shape. Therefore, these moderators could only be used effectively in neutron scattering experiments where the resolution is not very sensitive to the pulse width. Experiments show that the intensity gain depends on the reﬂector material as well as on the coupling among the reﬂector, the moderator, and the target [854, 859]. It is likely that in small hydrogenous moderators as the used polyethylene moderators in these experiments (cf. Figure 13.4(b)), one decay constant α is usually sufﬁcient to describe the time dependence of the neutron ﬁeld [848]. This view is supported by the slope of the trailing edge of the neutron pulses measured for the polyethylene moderator as shown in Figure 13.7. It should be mentioned that the decay constants from these slopes are not the true constants due to the contribution of the ﬁnite resolution of the proton pulse to the pulse width of the neutron pulse width. A correction may be determined by evaluating the second moment of the proton pulse width distribution. For the proton pulse width distribution of the experiment a value of σproton = 160.3 µs could be determined which yields an

441

13 Experiments to Study the Performance of Spallation Neutron Sources 2500 Pb slab target hybrid moderator Counts/channel [arbitrary units]

442

2000

Measured values Calculated (a = 0.5×10−2 [µs−1)

1500

1000

500

0

0

1

2 Time [ms]

3

4

Fig. 13.6 Time structure of the neutron ﬁeld as a linear plot in the polyethylene moderator of the hybrid conﬁguration with a Pb slab target. Solid curve is a guide to eye through the measured data given as crosses, the open circles are calculated values with α = 0.5 × 10−2 µs−1 [848]. 2 exponential decay derived by the second moment as σexp = 2 · τ 2 [848]. The ‘‘true’’ decay time τtrue is then determined by

τtrue =

2 τ 2 − σproton /2,

(13.9)

which leads to a ‘‘true’’ decay time of τtrue ≈ 207 µs, which is the case given in Figure 13.6. In Figure 13.6 the open circles represent a calculation performed by Bauer et al. [848] and a decay time of 200 µs using the measured proton pulse. The results agrees fairly well with the measured data. Figure 13.7 shows the measured neutron pulse in linear-log scale with the two decay constants α1 = 0.423 × 10−2 µs−1 and α2 = 0.1205 × 10−3 µs−1 . Although the polyethylene moderator is not really thin, it is clearly seen that α1 dominates the decay process as discussed by Eq. (13.8). In Table 13.3 some ‘‘best’’ values of corresponding equivalent thermal neutron ﬂuxes for Pb ﬂat targets in a large D2 O moderator (cf. Figure 13.4(a)) and for a hybrid moderator (Figure 13.4(b)) are given for an incident proton energy of 590 MeV and an average beam power of 10 mA roughly equivalent to the SNQ values of 1100 MeV protons and 5 mA beam power [848]. The ratio of the peak ﬂux to the corresponding equivalent neutron ﬂux is also given in the table.

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Counts/channel [arbitrary units]

104

Pb slab target hybrid moderator 103

a1 = 4.23×10−3 [µs−1]

102 a2 = 1.205×10−4 [µs−1]

101

0

1

2

3

4

5

Time [ms] Fig. 13.7 Same as Figure 13.6 but plotted logarithmic scale. The plot shows that the neutron pulse decay is dominated by one single decay constant [848]. Tab. 13.3 Some ‘‘best’’ values of corresponding equivalent thermal neutron ﬂux for an incident proton energy of 590 MeV and an average beam power of 10 mA neutron leakage of experimental arrangement given in Figure 13.4 (data are from Bauer et al. [848]).

Conﬁguration

Moderator

Pb-ﬂat target (see (a) Figure 13.4) Pb-ﬂat target hybrid version (see (b) Figure 13.4)

D2 O

8.0

D2 O H2 O a

5.6 6.8

a

Neutron equivalent thermal ﬂux Φ(equ) (1014 × cm−2 s−1 )

Peak ﬂux Φ/Φ(equ)

7.9 18.4

Reﬂected H2 O moderator with grooves (cf. [848] on page 417).

(2) Cold neutron experiments: The experimental setup shown in Figure 13.4(b) was slightly changed, but uses the same large rectangular vessel into which the targets of Pb and U, moderators, and reﬂectors of D2 O, C plus premoderator, and Pb plus premoderator were installed. The details are given in Figure 13.8. Different cold moderators, grooved and ﬂat moderators of varying size, were used to measure the leakage ﬂux, the neutron life time and neutron spectra distributions with reﬂectors of heavy water D2 O, graphite

443

444

13 Experiments to Study the Performance of Spallation Neutron Sources C-reflector 3 120×120×80 cm or Pb-reflector 3 70×60×60 cm (L×B×H) H2-moderator

Diaphragm f1 (f50) BF3 - counter Diaphragm f2 (50×25.4)

2350

1550

450

H2O-premoderator (20 mm)

300

90

n 20 Al 5 PE

D2O level

100

Vessel filled with D 2O

850 800

1Cd 10Al 30×30Al

Protons 590 MeV

Fig. 13.8 Schematic sketch of the SNQ experimental setup for cold neutron measurements using a H2 -moderator at the PSI accelerator. Dimensions of the experiment are in [mm]. (In the ﬁgure both reﬂectors – of C and Pb – are indicated, although they are not used in the same experiment.) [851].

C, and lead Pb, respectively. In summary, four pairs of moderator vessels for the cold H2 in normal- and in para-status are investigated (para–ortho ratio of cold H2 see page 450). Each pair consisted of a ﬂat and a grooved vessel with a constant ﬁn width of 1.3 cm for all vessels. Both moderators have the same volume and the same dimensions in direction to the neutron beam. Thus, the moderators differed in an ‘‘effective thickness along the neutron beam direction being equal to 25, 36, 56, and 78 mm. Details of the construction of the cold H2 moderator and its operation are described in [851]. The neutron life time in the cold moderator was measured with a small boron 10 B depleted BF3 counter shielded against thermal neutrons from the reﬂector by a cadmium cover. The ﬂight path used was a 2.35-m neutron beam channel depicted in Figure 13.8. Tables 13.4 and 13.5 show a selection of the measured results of average-, and peak ﬂuxes, neutron life times, and pulse widths on different moderator sizes and reﬂector materials. As discussed in Ref. [851], there was apparently no gain factor obtained for cold grooved moderators as it was measured with ambient temperature moderators with grooves (cf. Table 13.3). The determined neutron temperature from the experiments was found to be about 80 K for almost all experimental cases and is therefore much higher than the thermodynamic value. This high neutron temperature is due to a spectral hardening via absorption or by an insufﬁcient moderation. As noted in Ref. [851], an important result is that the combination of Pb reﬂector with a cold H2 moderator gave highest peak ﬂux and shortest neutron life time.

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

445

Measured time averaged cold neutron ﬂuxes for cold H2 -moderators and Pb slab targets with different reﬂector materials.a

Tab. 13.4

Target

Effective moderator thickness (mm)

Φthermal (1014 × cm−2 s−1 )

Time-averaged cold neutron ﬂux

Reﬂector system

Pb Pb Pb Pb a

D2 O 3.2 3.1 2.7 3.0

25 36 78 96

C + premoderator – 3.0 – 2.5

Pb + premoderator – – 2.2

Given are the measured data from ﬂat vessel moderators. Data are from Bauer et al. [851].

Tab. 13.5 Experimental results for various neutron ﬂux parameters for a liquid grooved H2 -source of a dimension 11 × 11 × 3.5 cm3 as a function of the used reﬂector material with 238 U ﬂat target (data are from Bauer et al. [851]).

Reﬂector material and dimensions (cm3 ) D2 O 170×170 × 85 C (cooled) 120 × 120 × 80 Pb 60×60 × 60

Average cold ﬂux Φth (1014 × cm−2 s−1 )

Peak cold ﬂux th Φ

Φ/Φ

Neutron life-time (10−6 s)

(1014 × cm−2 s−1 )

6.6±0.4

79

12

710

620

5.4±0.4

108

20

350

390

4.3±0.3

116

27

230

320

Neutron pulse-width (10−6 s)

13.3.3 Experiments of Short-Pulsed Target–Moderator–Reﬂector Systems

With the development, the design and the construction of high-power short-pulse spallation neutron sources high-efﬁciency moderator systems at cryogenic and ambient temperatures became an important area in the last decade. As mentioned earlier, moderators are one of the important devices of a pulsed neutron source, which determine the quality of the experiments performed at these sources. After a long experience on cold and thermal sources at research reactors [653, 860, 861] and at low-intensity spallation sources [641, 643, 679], several groups from Japan, USA, and Europe have performed and initiated research programs on cold and ambient moderator physics [611, 862–869] and theoretical ground-work [870–872]

446

13 Experiments to Study the Performance of Spallation Neutron Sources

on neutron scattering and other applications of high-intensity pulsed neutron sources [551, 627, 629, 681, 836, 842, 873] during the recent years. Early ideas in this ﬁeld of research were published by Whittemore and McReynolds [874, 875]. Further basic research studies are undertaken by Carpenter et al. [56, 641] at the IPNS, ANL, USA, by Inoue et al. [876, 877] at the Hokkaido University, Japan, and by Ikeda, Inoue and Watanabe et al. [858, 878, 879] at the KENS facility, Japan. The essentials of these experimental investigations will be described and discussed in the following sections. 13.3.3.1 Target–Moderator–Reﬂector Experiments at the Hokkaido Electron Linear Accelerator A large variety of TMR experiments was performed at the electron linear accelerator facility at the Hokkaido University, Japan, by Inoue et al. [857, 876, 877, 879–881] and Kiyanagi et al. [859, 865, 866, 868, 882–885]. This electron LINAC facility with an electron energy of 45 MeV (beam power up to 5 KW, electron beam peak current of about 100 mA, pulse rate of 200 Hz, and a duty factor of 0.06%) is mainly used for neutron performance test experiments and detector development. The facility is able to generate about 2.5 × 1012 neutrons s−1 per kW beam power of fast neutrons for this electron energy with a nonﬁssionable target, e.g., lead [886]. About 1% of this fast neutron source can be converted to thermal or cold neutrons with a proper TMR system. Basic experiments investigated by Inoue et al. [857, 877, 880, 881] were mainly concerned with studies and tests on a variety of cold moderator materials, moderator chambers, and on tests of suitable refrigerators. Among these experiments are the measurements of the cold neutron gain factors [877] of neutrons at 10 A˚ wavelength and the study of different moderator materials of cylindrical moderators with diameter of 20 cm and height 20 cm and ﬂat moderators with width of 25 cm, height 25 cm, and thickness of 5 cm at different temperatures [881]. The moderator materials and moderator temperature used were the following: (1) H2 O at temperatures of 293, 230, 180, 112, 77, 20, and 10 K, (2) H2 at 18 K, (3) CH4 (methane) at 112, 77, 57, 31, and 20 K, (4) C2 H6 (ethane) at 182, 120, 77, 20, and 16 K. From these measurements it was concluded that a moderator with cold methane should be a suitable cold moderator material obtaining a cold neutron gain factor of about 40 at 20 K for long neutron wavelengths. Some of the experiments were performed with BeO, graphite, and parafﬁn reﬂectors and a Cd decoupler between moderator and reﬂector for pulse shaping [881]. Figure 13.9 shows typical TOF neutron spectra from a ﬂat 20 K methane moderator compared with spectra of 300 K ambient- and 22 K ice H2 O moderators. Based on the former experiments of Inoue et al., the group of Kiyangi et al. continued the moderator experiments at the Hokkaido electron linac facility during the 1990s up to 2006. These investigations are mainly performed to optimize the utilization of the planned TMR system of the high-intensity short-pulsed Japanese spallation neutron source, which have been started its operation in 2008 [629]. As mentioned above, these experiments cover a broad range of different moderator conﬁgurations and materials. Most of the experiments were performed on different liquid H2 moderator conﬁgurations since liquid hydrogen may be from

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions Neutron energy [MeV] 500

50 20

10

5

3

2

1.5

3

10

Neutron flux spectrum [arbitrary units]

H2O (300 K) H2O (22 K) CH4 (22 K)

102

5 cm

101

25 cm 25 cm Neutrons 0

4 8 Time-of-flight [ms]

12

Fig. 13.9 Comparison of TOF spectra measurements of a 20 K methane moderator, a 22 K ice moderator , and an ambient temperature H2 O moderator (after Inoue et al. [881]).

certain technology reasons the best choice to utilize high-intensity spallation neutron sources. Also experiments with different moderator materials as methane CH4 , methane hydrate H2 O–CH4 , mesitylene, methanol, ethanol, benzene methanol, and benzine were conducted. Most of these experiments were also validated by particle transport simulations to test the scattering kernels of different moderator materials [865]. Some of the main issues and experimental examples are as follows: • experiments with liquid H2 moderators: coupled, decoupled, with and without premoderators, and poisoned premoderators, [882, 883, 887, 888], • experimental studies of the neutron performance of a hydrogen moderator on para-hydrogen concentrations [889–892], • experiments of tailoring neutron pulse shapes from coupled liquid H2 [885], • experiments on neutron performance with various moderator materials [865, 866, 868], • mockup experiments on ﬂux–trap moderator conﬁgurations [884] to enhance the slow neutron intensity. The experimental apparatus The principle experimental arrangement used for the moderator experiments at the Hokkaido electron linac facility is shown in Figure 13.10. The left panel in the ﬁgure shows the arrangement for coupled moderator experiments, whereas the right panel shows the principle arrangement for decoupled moderator experiments. The incident electron beam energy was

447

448

13 Experiments to Study the Performance of Spallation Neutron Sources

Liquid N2

Premoderator (polyethylene 15 mm thick)

Decoupler (Cd or B4C)

Heat exchanger

Neutrons

Moderator 5×12×12 cm3 Reflector (graphite) (a)

Rectangular Pb target 7×8×15 cm3 (b)

Neutron collimator (boric/acid-resin)

Fig. 13.10 The principle experimental TMR assemblies performed for moderator experiments at the Hokkaido electron linac facility. The left panel (A) shows the arrangement for coupled moderator experiments, whereas the right panel (B) shows the principle arrangement for a decoupled moderator experiment (after Kiyanagi [868]).

35 MeV on a lead target. The material composition of the experimental arrangement could easily be changed, e.g., instead of a polyethylene, H2 O or ZrH2 could be used as premoderators in the case of coupled moderator experiments [883]. It was also possible to ‘‘poisoning’’ the premoderator with a 0.5 mm thick Cd sheet [887] for pulse shaping the neutron pulse. The Cd is also used to decouple the moderator from the reﬂector (cf. Figure 13.10(B)). The reﬂector was, for all experiments, of graphite with a size of 80 × 80 × 80 cm3 . The viewed surface area of the moderator was 12 × 12 cm2 . The thickness of the moderator could be varied from 2.5 to 5 cm [868, 882]. A mica crystal positioned of about 7 m from the moderator surface was used as an energy analyzer for the pulse shape measurements. For the spectrum measurements 3 He detectors were applied positioned at a distance of 6 m to the moderator surface. The temperatures of the moderators were about 20–30 K [868]. Experimental results (1) Premoderator studies and improved pulse shapes for liquid H2 , CH4 , and mesitylene moderator

Two general methods may be used to improve pulse shapes of cold neutrons from coupled liquid hydrogen moderators with a premoderator. One is to decouple a premoderator from the reﬂector and the other is to use a poisoned premoderator as given and described in Figure 13.10. Figure 13.11 gives an overview about the pulse shaping of cold neutrons measured on different moderator geometries.

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

3.94 Å : Coupled (3 cm) : CH4 decoupled : H2 decoupled

Intensity [arbitrary units]

1.0

: Decoupled premoderator (1 cm) : Poisoned premoderator (inner 0.5 cm outer bottom 1.0 cm) 0.5

0.0

0

500 Emission time [µs]

1000

Fig. 13.11 Comparison of cold neutron pulse shapes from ﬁve moderator systems: (1) a coupled 5 cm thick liquid H2 moderator with a 3 cm thick premoderator, (2) a decoupled solid CH4 moderator, (3) a decoupled liquid H2 moderator, (4) a a decoupled liquid H2 moderator with a 1 cm thick premoderator, and (5) a coupled liquid H2 moderator with a poisoned premoderator (after Kiyanagi et al. [887]).

Figure 13.11 compares the pulse shapes of cold neutrons at a wavelength of 3.94 A˚ with a premoderator thickness of 3 cm with and without decoupling from the reﬂector. Liquid H2 and solid methane CH4 at 20 K in the decoupled case were also compared. In the case of a poisoned premoderator the Cd poison sheet of 0.5 mm separates the premoderator of H2 O in an inner part with a thickness of 0.5 cm and an outer part of about 2.5 cm. Comparing the pulse shapes from the various composite moderators with 5 cm thick CH4 at a neutron wavelength of ˚ the solid CH4 is superior to the other systems (cf. Figure 13.11). This about 4 A, advantage vanishes at longer neutron wavelengths where a composite moderator with liquid H2 and poisoned premoderators were close to the results of a decoupled solid CH4 moderator [887]. Measurements on the intensity gain as a function of the premoderator thickness, the moderator thickness, and the moderator material indicate that the spectral intensity in the range from 4 to 10 A˚ does not depend on the moderator thickness, whereas the optimal thickness of the premoderator is about 2 cm in the case of mesitylene as given in Figure 13.12 [868]. This thickness of 2 cm is almost the same as in the case of H2 O and CH4 moderators [868]. Therefore, it may

449

13 Experiments to Study the Performance of Spallation Neutron Sources

1.0 Reletive intensity

450

Wavelengths from 4 to 10 Å

0.5

Moderator thickness – 2.5 cm Moderator thickness – 4.0 cm

0.0

0

1 2 Premoderator thickness [cm]

3

Fig. 13.12 Premoderator thickness for two mesitylene moderators, 2.5 and 4.0 cm thick, plotted as a function of the relative intensity gain of a neutron wavelength range of 4–10 A˚ (after Kiyanagi [868]).

be considered that the optimal premoderator thickness is not so different for the common materials as H2 O, CH4 , etc. (2) The ortho–para issue of cold liquid H2 moderators Knowing the ortho to para-hydrogen ratio in a liquid hydrogen moderator at a highintensity pulsed spallation neutron source is important when optimizing the design of liquid hydrogen moderators in the energy range below about 50 meV [893]. The equilibrium concentration at T = 20 K of para hydrogen is 99.8%, whereas at T = 300 K the equilibrium is at 25% para-hydrogen. The naturally ortho–para conversion is very slow, which takes about 43000 h from 25% to 99%. Figure 13.13 shows evaluated scattering cross sections for para-hydrogen and a mixture of para and ortho hydrogen [871, 894] which were evaluated for Monte Carlo simulations in MCNPX format. For both there exists an excellent agreement between the calculated and measured cross sections. The sharp drop in the para H2 curve below 50 meV is due to spin coherence and the second drop below 5 meV is due to intermolecular interference [893]. As shown in Figure 13.13 there exists a difference in the para to the mixture of para–ortho cross sections below an energy of some meV. As the para-hydrogen concentration increases with time by natural conversion even without a catalyst [893]. It also increases by neutron- and γ -irradiation. It is therefore essential to understand the inﬂuence of the ortho-para ratio on the neutron performance of liquid H2 moderators. More details about scattering models and laws may be found in Refs. [872, 895]. At present liquid hydrogen is the most important cold moderator for the highpower spallation sources J-PARC and SNS. Measurements were performed to

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions 100 Para-hydrogen at T = 14 K

10

Total cross section [b per molecule]

IKE SCATHD Seiffert (1970)

1 1.E−05

1.E−04

1.E−03

1.E−02 Energy [eV]

1.E−01

1.E+00

1.E+01

250 Normal hydrogen at T = 14 K 200 IKE SCATHD Seiffert (1970) 150

100

50

0 1.E−04

1.E−03

1.E−02 Energy [eV]

1.E−01

1.E+00

Fig. 13.13 Total neutron scattering cross section for paraH2 (upper panel) and for ‘‘natural’’-H2 , a mixture of orthoand para-H2 (ratio 3:1). Note the different scale at the ordinate in the ﬁgure. Data are from Seiffert(1970) [896], calculations are from IKE SCATHD [894]. (after Keinert et al. [894]).

determine the neutronic performance of liquid hydrogen moderators at various para to ortho hydrogen ratios. For this purpose, an ortho–para conversion system was applied using a Fe(OH)3 catalyst to accelerate and control the para-hydrogen concentration [890]. Several experiments were performed at the Hokkaido accelerator and at the Manuel Lujan Neutron Scattering Center at LANL to measure the change of the neutronic performance due to the ortho–para ratio of liquid hydrogen moderators [889–892]. Figure 13.14 shows pulse shapes measured for the coupled and decoupled liquid hydrogen moderators for para concentrations of 35% and 99%

451

13 Experiments to Study the Performance of Spallation Neutron Sources 3×106 16.8 meV 6

2.5×10 Intensity [arbitrary units]

452

Moderator liquid H2 thickness 5 cm

2×106 Coupled para 35 Coupled para 99 Decoupled para 35 Decoupled para 99

1.5×106 1×106 5×105

0

100

200 300 400 Emission time [µs]

500

Fig. 13.14 Comparison of pulse shapes in linear plot as a function of different para-hydrogen ratios of 5 cm thick liquid H2 moderators in a coupled and a decoupled arrangement at a neutron energy of 16.8 meV (after Ooi et al. [891]).

investigated at the Hakkaido electron accelerator. The neutron intensity in arbitrary units is given as a function of the emission time in microsecond. The experimental conditions for the coupled moderator measurements with a 1.5 cm thick polyethylene premoderator are given in Figure 13.10 in the left panel, whereas the decoupled experimental arrangement with decoupler and liner is shown in the right panel of the ﬁgure. The para-hydrogen fraction was determined by measuring the change of the thermal conductivity due to the para concentration [891]. It is seen in Figure 13.14 that the pulse peak intensities increase with the para-hydrogen concentration for both moderator systems. In the coupled case the decay of the neutron pulse is very similar, whereas in the decoupled case the neutron pulse decay is much faster for a higher para concentration. This tendency was observed for all neutron energies below 25 meV [891]. The pulse width decreases with increasing para concentration for both moderators. (3) Neutron performance of methane hydrate, mesitylene and other nonexplosive moderator materials. In Figure 13.15, spectral intensities are compared to a mesitylene moderator with those of solid CH4 and liquid cold H2 [868] at temperatures around T = 20–30 K. The moderator of H2 had a para-hydrogen concentration of about 35%. All moderators are measured in the coupled case as indicated in Figure 13.10 in the left panel. The spectra of CH4 and H2 are almost the same [885]. The spectral intensity of the mesitylene moderator is much lower than that for the CH4 and H2 moderators in the cold low-energy region at about ≤ 0.01 eV. The reason of this low spectral intensity is that mesitylene in the cold neutron energy region is effected by

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Intensity [arbitrary units]

109

108

107

106

105 0.0001

Mesitylene [coupled] Liquid H2 [coupled] Solid CH4 [coupled] 0.001 0.01 0.1 Neutron energy [MeV]

1

Fig. 13.15 Comparison of measured neutron energy spectra of cold coupled moderators of mesitylene, liquid H2 , and solid CH4 at temperatures around T = 20–30 K. The experimental arrangement is given in the left panel of Figure 13.10 (data are from Kiyanagi et al. [868]).

higher rotational levels of the mesitylene [897, 898]. It should be noted that from the radiation damage point of view, hydrogen and molecules having benzene rings are better moderator materials for high-intensity spallation neutron sources [899]. Mesitylene, methanol, ethanol are such materials. The results shown in Figure 13.15 may indicate that a coupled liquid H2 moderator will be superior to CH4 or mesitylene by using a para-hydrogen moderator with a larger thickness of about ∼ 15 cm [868]. The spectral intensities for other ‘‘nonexplosive’’ moderator materials were measured also to compare them with the nonexplosive mesitylene [868]. The experiments were performed in the coupled case with moderator thicknesses of 4 cm and with a premoderator of 2 cm (cf. Figure 13.10(A)). These moderator materials can be divided into two groups: (1) methanol and mesitylene, and (2) ethanol, benzene, and benzene methanol. The ﬁrst group, e.g., methanol and mesitylene gives much high intensities for cold neutrons as the moderator materials in the second group indicated in the measurements shown in Figure 13.16. The reason for the higher intensities of methanol and mesitylene are due to the fact that the molecules have methyl groups and the hydrogen atomic number density in these materials is higher than that of ethanol. The spectra intensity of mesitylene and methanol is almost the same, although the intensity of the mesitylene moderator is somewhat higher compared to the methanol moderator above the peak energy (cf. Figure 13.16). From these results it was concluded that the mesitylene moderator material would be best among the nonexplosive materials. The neutron performance of para-rich hydrogen moderators is approaching to that of a methane moderator. Therefore, mesitylene should be used in the case where ‘‘safe’’ materials are required, and

453

13 Experiments to Study the Performance of Spallation Neutron Sources

1010 Intensity [arbitrary units]

454

109 Mesitylene Methanol Ethanol Benzene methanol Benzene 108

0.001 0.01 Neutron energy [eV]

0.1

Fig. 13.16 Comparison of measured neutron energy spectra for different ‘‘nonexplosive’’ moderator materials (after Kiyanagi et al. [868]).

para-hydrogen moderators should be used at high-intensity spallation neutron facilities where more severe safety regulations are considered [868]. 13.3.3.2 Target–Moderator–Reﬂector Experiments at the J¨ulich Proton Synchrotron COSY The JESSICA experiment (Juelich Experimental Spallation Target Set-up In COSY Area) was a full-scale TMR experiment at the COSY cooler synchrotron [725, 726] at the Forschungszentrum J¨ulich, Germany. The aim of the experiment was to investigate the advanced cold moderators for the upcoming next generation neutron sources like ESS (European Spallation Neutron Source) [551, 873, 900], SNS (Spallation Neutron Source at ORNL, USA) [681], or JSNS (Japanese Spallation Neutron Source) [629] at J-PARC, Japan. The JESSICA assembly JESSICA was an 1:1 mock up of the TMR assembly of a target station of the planned 5 MW source ESS. The data obtained at JESSICA are used to ﬁnd the best-suited moderator material for the next-generation neutron sources. The main topic of the experimental investigations was the study of the neutron behavior of advanced cold moderators and the validation of Monte Carlo simulation codes as well. Especially, new neutron scattering kernels, which were developed during the course of the JESSICA project by Bernnat et al. [871, 894] could be validated and checked against the measured data. The investigated moderator materials were H2 O at ambient temperature, ice at T = 20 and 70 K, CH4 , methane hydrate, and mesitylene at T = 20 K. The target containing 3500 cm3 of mercury is located in the center of a Pb reﬂector with a diameter of 1.3 m and height of 1.3 m surrounding the Hg target. The moderators were mounted in the so-called wing geometry. This means two moderators are placed above and below the target to prevent fast neutrons from the target directly leaking out of the system. This

Incident proton beam

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Hg target

N eu tro n

be am

Moderator

Reflector of Pb

Fig. 13.17 Schematic drawing of the JESSICA TMR assembly with Hg target, the reﬂector vessel with the Pb rods, the test moderator, and the neutron beam hole arrangement.

reduces the fast neutron background considerably. Whereas three moderators are ﬁlled with water the lower upstream moderator position is used to study various cold moderator materials as shown in Figure 13.17. This moderator can be ﬁlled with different moderator materials and could be operated at any temperature between 10 and 300 K. Two different moderator geometries were used: (1) a moderator with a rectangular shape with a height of 12 cm, a width of 15 cm, and a thickness of 5 cm due to the ESS design [551], and (2) a cylindrical moderator with a diameter of 9.5 cm and height of 11 cm with a reentrant hole (diameter = 3.6 cm). Figures 13.18 and 13.19 give a vertical cut through the target–moderator assembly and a photograph of the JESSICA facility installed at an external proton beam area of the COSY accelerator. Because of the low proton beam intensity COSY is particularly suitable for studying the neutron performance of advanced moderators, because radiolysis and activation levels are negligible. Not only can the proton beam energy be tuned from 0.8 to 2.5 GeV, the negligible activation rate permits one to easily modify the geometry, construction details, and the materials involved. Furthermore, the neutron performance can be studied and the gathered data can be linearly scaled to higher beam intensities as they will be available in high-power spallation neutron sources. Figure 13.20 shows the whole experimental setup through a schematic diagram, already depicted Figure 13.19. The neutron ﬂight path as well as the detectors are shielded in order to reduce the background, which is caused by high-energy neutrons leaving the reﬂector and being reﬂected at the concrete walls of the experiment hall. These high-energy neutrons are thermalized within a 22.5 cm thick polyethylene layer (42.5 cm in

455

13 Experiments to Study the Performance of Spallation Neutron Sources

∅ 1300 mm Reflector

Pb

Proton beam 0.8 – 2.5 GeV

1800 mm

1200 mm

Hg target

Beam height over floor

456

Hg storage

Test moderator

Fig. 13.18 Vertical cut through the JESSICA TMR facility with Hg target, moderators and Pb reﬂector as shown in Figure 13.19.

Neutron detectors

WCM

ICT Reflector JESSICA ess

Graphite crystal

Fig. 13.19

Target

The JESSICA experimental apparatus at the COSY proton synchrotron at Julich. ¨

case of the detector housing) surrounding the neutron ﬂight path (cf. Figures 13.19 and 13.20). The thermalized neutrons are prevented from reaching the detector by being captured inside a boric acid layer with an average thickness of 2 cm. JESSICA was operated with a beam intensity of 4 × 108 up to 4 × 109 protons per pulse incident on the Hg target. The repetition rate was 1/30 Hz with a pulse length of approximately 0.5 µs. The applied fast kicker extraction and the beam instrumentation especially investigated for the JESSICA experiment are given

15

0

cm

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Graphite crystal

38

7

cm

Neutron detectors

15 0 cm

Shielding

Moderator

Target Reflector

Start counter

ICT

WCM

Protons

Fig. 13.20 Schematic drawing of the JESSICA experimental setup with the proton beam line, the proton beam monitors ICT and WCM, start counter, neutron detector, crystal analyzer, and a cut through the TMR arrangement (after Nunighoff ¨ et al. [611]).

in [728, 901]. To determine the number of protons per pulse, two proton beam monitors with different working principles are installed in the proton beam line (cf. Figure 13.20). A Wall Current Monitor (WCM) [902] measuring the mirror current in the wall of the beam tube and an Integrating Current Transformer (ICT) [903] measuring the current induced in a coil when the proton beam passes through are used. It has been shown [611] that these monitors agree within about 10% and allow an absolute normalization of the neutron spectra measurements. The number of protons per pulse is indispensable to determine the neutron-to-proton ratio in order to compare the experimental data with Monte Carlo simulations on an absolute scale. The characteristics of the moderators to be investigated are studied by TOF measurements of the neutrons coming out of the moderator surface. Therefore, a 5.37 m long neutron ﬂight path was constructed. At the end a neutron detector is placed to measure the TOF spectra, from which the energy spectra can be deduced. To obtain detailed information of the time structure and wavelength dependency of the neutron pulses, a graphite crystal can be moved into the neutron ﬂight path. Neutrons fulﬁlling the Bragg condition are reﬂected by the crystal and can be detected with a second neutron detector viewing the crystal (cf. Figure 13.20). Neutron time-of-ﬂight measurements At the TOF measurements the moderator surface is perpendicular to the neutron ﬂight path. The viewed surface is limited by the cross section of the neutron beam tube with an inner diameter d = 10 cm. The neutron spectra are measured at the end of the neutron ﬂight path by a LiGdBOscintillator detector [611]. This detector has an active area of A = 16.6 cm2 , but to avoid dead time effects the active area was reduced by an aperture to A = 4.5 cm2 of a 1 mm thick cadmium layer and a 1 cm thick B4 C layer. The detector

457

458

13 Experiments to Study the Performance of Spallation Neutron Sources Tab. 13.6 Neutron temperatures compared with moderator temperatures (cf. Figures 13.21 and 13.1 on page 436).

Moderator material Ice Ice Water

Moderator temperature (K) 20 70 300

Neutron temperature (K) 71±4 110± 2 343± 15

efﬁciency was calculated by Monte Carlo methods for mono-energetic and folding the obtained ﬂux with the neutron absorption cross section for 6 Li [611, 904]. The measurement starts when the proton beam passes through a plastic scintillator, the start counter, in Figure 13.20 in front of the target. In this way the neutron TOF spectrum could be measured for each single proton pulse. The TOFt spectrum of the thermal neutrons were performed by a difference measurement taken with and without a 1 mm thick sheet of Cd in front of the ﬂight path. The difference spectrum is used for the determination of the neutron temperature. An example of ice and H2 O is given in Table 13.6. For measurements within the slowing-down neutron energy region the Cd was replaced by boron carbide (B4 C), because the former is increasingly transparent for neutrons with energies higher than about 0.4 eV. The storage time of the thermalized neutrons within the moderator was determined by measuring the wavelength-dependent TOF spectrum. This is done by placing the above-mentioned graphite mono crystal into the neutron ﬂight path (Figure 13.20), which selects speciﬁc wavelengths fulﬁlling the Bragg condition for the chosen Bragg angle of = 45◦ according to n · λ = 2 · d · sin ,

(13.10)

˚ d is the lattice spacing, is the Bragg angle, and where λ is the wavelength in A, n is the order of the reﬂection. From the resulting TOF spectrum the pulse width at FWHM and the decay constant is determined assuming an exponential decay of the pulse. With a lattice spacing of d = 3.35 A˚ and a Bragg angle of =45◦ we ˚ Higher are able to analyze the wavelengths λ = 4.74, 2.37, 1.58, 1.19, and 0.95 A. orders can not be resolved and vanish in the high-energy background. Experimental results of JESSICA (1) Time-of-ﬂight neutron spectra of ice and ambient water

In Figure 13.21 the TOF spectra for ice at T = 20 and 70 K are compared to the spectrum of an ambient temperature water moderator. The corresponding energy spectra are already shown in Figure 13.1 on page 436. The spectra have been normalized to the number of incident protons, the active detector area, and per time bin width. Further corrections have been performed for

Neutron TOF spectra [neutrons × 10−10 cm−2 s−1 per proton]

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

T= 20 K T= 70 K T= 293 K

0

1000 2000 3000 4000 5000 6000 7000 8000 Time [µs]

Fig. 13.21 Neutron TOF spectra of ice moderators at T = 20 and 70 K compared to the spectrum of a H2 O moderator of T = 300 K temperature. The spectra are compared on an absolute scale (after Nunighoff ¨ et al. [611]).

the dead time. As expected, a spectrum shift toward longer ﬂight times – i.e., lower kinetic energy of the neutrons – is observed for lower moderator temperatures. The small peak at about 800 µs is an effect caused by the decreasing absorption cross section of the cadmium layer. In this region, the Cd is partially transparent for thermal and epithermal neutrons but the peak is independent of the moderator material and moderator temperature. Assuming a Maxwellian distribution of the velocity of the neutrons, we are able to determine the neutron temperature. Transforming the time-dependent ﬂux (t) into the velocity-dependent ﬂux (v), the neutron temperature can be determined by the slope of the straight line in a semilogarithmic plot based on Eq.(13.11). (v) mn 2 · 0 ln = ln − · v2 . (13.11) 4 3 v 2 · kB · T vT In Eq. (13.11), v denotes the velocity of the neutrons, mn the neutron mass, kB the Boltzmann constant, vT velocity of the neutron at temperature T, and T the neutron temperature. The neutron temperatures obtained from Eq. (13.11) for two ice moderators and an ambient temperature water moderator are listed in Table 13.6 and compared with the real moderator temperatures. The neutron temperatures are higher than the moderator temperatures. The reason for this discrepancy is that the neutron distribution has a slowing-down source of epithermal neutrons and a loss of 1/v absorption compared to the moderator molecular energy distribution. In general this results in a hardening of the Maxwell–Boltzmann distribution of the neutrons, if the absorption is not too strong and has no resonance structure. (2) Wavelength-dependent TOF neutron spectra of ice and ambient water As described in Section 13.3.3.2, a detailed view on the time behavior of the neutron pulses can be obtained by measuring the wavelength-dependent TOF spectra. In

459

0.16

2.37 Å

1.19 Å

0.18

1.58 Å

13 Experiments to Study the Performance of Spallation Neutron Sources

Water at T= 293 K Ice at T= 20 K

0.14 0.12 0.95 Å

Neutron TOF spectra [neutrons × 10−11 cm−2 s−1 per proton]

460

0.1 0.08 0.06 0.04 0.02 0

1000

2000

3000

4000

5000

6000

7000

Time [µs] Fig. 13.22 Wavelength-dependent TOF neutron spectra on an ice moderator of a temperature T = 20 K (dotted line) compared with an ambient temperature water moderator at T = 293 K (solid line) (after Nunighoff ¨ et al. [611]).

Figure 13.22, the wavelength-dependent TOF spectra for water at T = 300 K and ice at T = 20 K are shown. From Figure 13.22, a relative shift of the abundance of the spectrum toward lower kinetic energies, e.g., for longer ﬂight times and for lower moderator temperatures can be seen. The neutron intensity of the water moderator at λ = 1.19 A˚ is much higher than for ice, whereas the opposite results for the wavelengths of λ = 2.37 A˚ ˚ At longer wavelengths, the colder moderator shows more intensity. The or 4.74 A. pulse widths in FWHM and decay constants for two moderator temperatures, 20 ˚ and 300 K, have been determined at wavelengths of 1.19, 1.58, 2.36, and 4.74 Aare given together with MCNPX Monte Carlo simulations as shown in Table 13.7. Tab. 13.7 Comparison of measured pulse widths and decay times for several wavelengths (cf. Figure 13.22) for a water moderator at 293 K temperature and an ice moderator at 20 Ka .

˚ Wavelengths (A)

1.19

1.58

2.37

4.74

92.1(73.4±14) 0.014

96.9(87.4±14) 0.015

– –

56(46.2±14) 0.039

101(86.7±14) 0.019

286(280±60) –

293 K water Pulse width FWHM in µs 58.7(59.2±14) 0.016 Decay constant in µs−1 20 K ice Pulse width FWHM in µs Decay constant in µs−1 a

36(40±14) 0.057

The results of the Monte Carlo simulations are given in parenthesis (data are from Pohl [904]).

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Such data are important for the design of new neutron scattering instruments at spallation neutron sources. It can be seen that the cold ice moderator reduces the pulse width by about 39% ˚ and agrees within 4% for 2.37 A˚ compared for wavelengths of 1.19 A˚ and 1.58 A, to an ambient temperature water moderator. Furthermore, the decay constant is higher in the case of an ice moderator than in a water moderator at 293 K resulting in a faster decay of the pulse. This will allow a higher time resolution in a real neutron spallation source. (3) Time-of-ﬂight neutron spectra and time structure measurements of methane hydrate and mesitylene moderators. From measurements reported in [611, 867, 875, 877, 879–881, 887] and discussed in Sections 13.3.3.1 and 13.3.3.2 the energy spectra from ice and solid methane at T = 20 K are well known. The ice moderator under consideration [611] has a maximum of the neutron spectrum at an energy of ≈5–6 meV and solid methane have the highest intensity at ≈1–2 meV [868]. The idea was to combine both materials into a new moderator material which should exhibit the maximum neutron ﬂux of solid methane and ice over a broader energy range. Methanehydrate has been sought to be such moderator material. The structure may be described in the following way: a single methane molecule CH4 is encaged in an ice cage formed by approximately six water molecules (CH4 + 5.75 × H2 O). It is further assumed that the methane molecule inside the ice cage behaves like a single methane molecule and is not inﬂuenced by the surrounding ice cage. This assumption was conﬁrmed by various inelastic neutron scattering experiments on methane hydrate [842, 905–909]. Especially, the behavior of the trapped methane molecule was intensively investigated. Because ice is one of the main components of methane hydrate more systematic measurements at different ice moderator temperatures were investigated. Figure 13.23 illustrates these neutron spectra measurements. At a temperature T = 248 K close to the freezing point, the neutron spectrum is very similar to the spectrum of a H2 O moderator at room temperature T = 293 K. For the ﬁrst time a realistic methane-hydrate moderator was investigated with the JESSICA experiment. The rectangular moderator vessel was ﬁlled with methane hydrate. The density was estimated to be in the range from 0.44 to 0.77 g/cm3 . In Figure 13.24, the measured energy spectra of methane and ice are compared with the spectrum of methane hydrate at T = 20 K. It can be seen that methane hydrate does not show the expected superposition of the ice and methane spectra. The position of the maxima are the same for methane and methane hydrate. In the energy range below 7 meV the spectrum of methane hydrate has the same shape like solid methane; however the intensity is reduced by a factor three compared to the solid methane. This is due to the lower hydrogen density in methane hydrate–about 5.98 × 10−22 atoms cm−3 – compared to solid methane with 7.958 × 10−22 atoms cm−3 . For higher neutron energies – between 20 and 100 meV – the methane-hydrate moderator shows a slightly higher neutron ﬂux than the methane moderator. However, the ﬂux of the ice moderator is superior

461

13 Experiments to Study the Performance of Spallation Neutron Sources

10–7 Neutron spectrum [n cm–2 eV–1 per proton]

462

T=20K T=70K T=165K T=248K T=293K

10–8

10–9

10–10

10–11

10–4

10–3

10–2

10–1

1

10

102

Neutron energy [eV] Fig. 13.23 Comparison of measured neutron spectra of ice moderators as a function of the moderator temperature. A water moderator at T = 293 K is shown for comparison also (after Nunighoff ¨ et al. [867]).

to the methane-hydrate moderator as well as the methane moderator in the energy range between 5 and 100 meV. This already indicates that the energy spectrum of a methane-hydrate moderator is not a superposition of the energy spectra of each single material. Especially in the energy region, where ice should be dominant, the intensity is reduced. The intensity of the cold neutrons is reduced by a factor of three comparing a methane-hydrate moderator to a solid methane moderator. Mesitylene is also a potential moderator material as discussed in Section 13.3.3.1 on page 448 and shown by the measurements of Kiyanagi et al. [868]. Compared to methane the low damage effects from induced radiation make mesitylene a potential candidate as a moderator material in high-intense radiation ﬁelds of high-power spallation sources [899]. Especially, the rotational modes in the low-frequency range make mesitylene a promising material for cold moderators. Detailed investigations considered that mesitylene has three different crystallographic phases the so-called phase I, phase II, and phase III [910]. The existence of a speciﬁc phase or their mixtures depends strongly on the actual freezing conditions. At the JESSICA facility mesitylene cold neutron spectra were measured and compared with spectra of solid methane, liquid hydrogen, and ice at a temperature of T = 20 K. In contrast to other measurements all these spectra could be compared on an absolute level – normalized per incident beam proton – and were measured in a neutron ﬁeld similar to a neutron spallation source in the GeV energy range. With a new S(α, β) scattering law data ﬁle for mesitylene, it is possible to compare the measurements with MCNPX simulations [869].

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Neutron TOF spectra [neutrons cm–2 s–1 per proton]

10–5

10–6

CH4 Methane hydrate Ice

10–8

10–10 –4 10

10–2 100 Neutron energy [eV]

101

Fig. 13.24 Comparison of measured neutron spectra of ice, solid methane, and solid methane-hydrate moderators at a moderator temperature of T = 20 K. The measured data are normalized to the number of incident protons and background and detector efﬁciency corrected (after Nunighoff ¨ et al. [867, 869]).

Figure 13.25 shows a comparison of the measured energy spectrum of mesitylene compared with solid methane, liquid hydrogen, and ice at a temperature of T = 20 K measured with the JESSICA facility. It can be seen that mesitylene shows a very similar spectrum like liquid hydrogen. In the energy range between 20 meV and 1 eV mesitylene is superior to liquid hydrogen. As mentioned above, in the described experiments phase III of mesitylene was used. Maybe an increase in the cold energy range could be achieved by annealing the frozen mesitylene close below the melting point to transform phase III into phase I, as described in [897, 910]. This will open more low-lying energy modes, which could be exited by incoming neutrons and thus resulting in colder energy spectra. A comparison of measured and simulated energy spectra with MCNPX from a mesitylene moderator at T = 20 K using the new developed S(α, β) scattering law data ﬁle [870, 911] for mesitylene is shown in Figure 13.26. As seen in Figure 13.26, the agreement between the measured neutron production and the simulated one is very good. For the energy range between 1 and 7 meV the simulation determines a higher neutron ﬂux than measured, while for energies ≥ 7 meV the calculation is below the experimental measurements. The maximum of the neutron spectrum is slightly shifted toward lower energies for the simulated curve. As already discussed, investigations of the time structure of neutron pulses emitted from moderators are of particular concern for the performance of a

463

13 Experiments to Study the Performance of Spallation Neutron Sources

Neutron TOF spectra [neutrons cm–2 s–1 per proton]

10–5 Ice CH4 Mesitylene H2

10–6

10–7

10–8

10–9 –4 10

10–3

10–2 10–1 100 Neutron energy [eV]

101

Fig. 13.25 Comparison of measured energy spectra for ice, methane, and mesitylene, and liquid H2 normalized to the number of beam protons and corrected to background and detector efﬁciency. In the experiment, mesitylene in the phase III status was used (after Nunighoff ¨ et al. [869]).

MCNPX phase II MCNPX phase III JESSICA exp.

Neutron spectra [neutrons cm–2 s–1 per proton]

464

10–6

10–7

10–3

10–2

10–1

Neutron energy [eV]

Fig. 13.26 Comparison of measured (phase III) and with MCNPX Monte Carlo simulated cold neutron spectra (phase II and phase III) produced from a mesitylene moderator at T = 20 K (after Nunighoff ¨ et al. [869]).

moderator at a pulsed spallation source. A small pulse width and a fast decay time of the pulse is desired. The measured wavelength-dependent neutron spectra of ice, methane hydrate, mesitylene, and methane were analyzed with a lattice spacing of

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Neutron pulse width FWHM [µs]

300

Ice Methane-hydrate Methane Mesitylene 200

100

0.5

0 0.5

1.5

2.5

3.5

4.5

5.0

Neutron wavelength l [Å]

Fig. 13.27 Comparison of neutron pulse widths in FWHM of measured neutron wavelength dependent TOF spectra at JESSICA for ice, methane hydrate, methane, and mesitylene (after Nunighoff ¨ et al. [869]).

3.35 A˚ and a Bragg angle of = 45◦ . Neutrons with wavelengths of λ = 4.74, 2.37, 1.59, 1.19, and 0.95 A˚ could be distinguished. For higher orders of n, even smaller wavelengths cannot be resolved and vanish in the high-energy background. The pulse widths in FWHM and the decay times of the pulses were determined from the measured spectra. Comparisons of ice, methane hydrate, methane, and mesitylene moderators materials of neutron wavelength dependent TOF spectra at JESSICA are shown in Figure 13.27 for the pulse widths and in Figure 13.28 for the decay times. The decay times of the neutron pulses were determined by exponential ﬁtting. 250

Decay time t [µs]

200

Ice Methane-hydrate Methane Mesitylene

150 100 50 0 0.5

1.5

2.5 3.5 Neutron wavelength l [Å]

4.5

5.0

Fig. 13.28 Comparison of the decay time τ determined from measured neutron wavelength dependent TOF spectra at JESSICA of ice, methane hydrate, methane, and mesitylene (after Nunighoff ¨ et al. [869]).

465

466

13 Experiments to Study the Performance of Spallation Neutron Sources

The ice moderator shows the broadest pulses; the peaks are narrower in case of methane and methane hydrate. It can be concluded that solid methane is a very fast moderator material compared to normal ice. Methane-hydrate lies in between for longer wavelengths and is comparable with methane at shorter wavelengths. From these results, it can be concluded that methane hydrate beneﬁts from the encaged methane molecules as compared to normal ice. The intensity in the lower energy range as well as the time behavior is dominated by the methane molecules of the methane hydrate. 13.3.3.3 Target–Moderator–Reﬂector Experiments at the Brookhaven Alternating Gradient Synchrotron AGS As mentioned in Section 11.2.5.2 on page 419, the bare thick target experiments of the AGS–ASTE collaboration [812, 829] using the mercury target were continued with a water moderator and a lead reﬂector [912, 913]. The mercury target (∅ 20 cm × length 130 cm) was surrounded by a lead reﬂector (1 × 1 × 1 m3 ) and was irradiated by 1.94, 12, and 24 GeV protons. A vertical cut through the TMR ASTE assembly is given in Figure 13.29. The spectral intensities of thermal neutrons from the moderator were measured by the current-mode time-of-ﬂight (CTOF) technique, which is discussed in detail in [914], using enriched 6 Li and 7 Li glass scintillators. With this technique only several incident proton pulses from the accelerator are needed to obtain sufﬁcient statistics for each incident proton beam energy. The results have shown that the neutron spectral intensity per incident beam proton integrated over the Maxwellian energy region of the measured neutron spectrum was almost proportional to the proton energy of the incident beam on the Hg target. The arrangement of different components of the experimental setup is given in Figure 13.30. The ambient water (H2 O) moderator with dimensions of

Hg safety container

Mercury target

1.016 m Lead reflector

Proton beam from BNL-AGS

1.110 m H2O moderator

1.257 m

Fig. 13.29 A schematic view of the ASTE experiment with mercury target, lead reﬂector and water moderator (after Nakashima et al. [912]).

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

18 m

Pb reflector Shielding

Hg target

TOF detector

B4C glass scintillator 6Li

Proton beam height H2O moderator

Fe collimator

Fig. 13.30 A perpendicular view of the arrangement of different components of the ASTE experiment as installed at the AGS accelerator proton beam line (after Meigo et al. [913]).

10 × 10 × 5 cm3 was placed at 3 cm below the target container (cf. Figure 13.30). The slow neutrons were extracted from the moderator surface 10 × 10 cm2 and were transported through an iron collimator and an evacuated tube having mylar foil windows with a thickness of 0.23 mm at the entrance and the exit. The neutron detectors of 6 Li and 7 Li glass scintillators with a neutron absorber of B4 C in front were placed at a distance of 18 m from the moderator surface (cf. Figure 13.30) in a shielded detector house. The pulse height distribution of the system was calibrated with an Am–Be source. Neutron detectors in the current-mode time-of-ﬂight technique The applied neutron detectors are an enriched 6 Li glass scintillator with a low γ sensitivity (GS20), and an enriched 7 Li glass scintillator with minimal neutron but high γ sensitivity (GS30). Both detectors have dimensions of 50.8 mm in diameter and 6.4 mm in thickness. The speciﬁcations are given in Table 13.8. The scintillation light is produced by 4 He and 3 H nuclei via the reaction 6 Li(n, α)3 H in the 6 Li glass scintillator. To subtract the contribution of γ -rays the enriched 7 Li glass scintillator, GS30, was used. The resulting net signal for neutrons can be obtained by subtracting the GS30 result from the GS20 results. With this technique, common noises, e.g., Tab. 13.8

Speciﬁcations of the Li-glass scintillator detectors (data are from [913]).

Parameter Li content wt (%) 6 Li enrichment (%) Density (g cm−3 ) Wavelength (nm) Decay time for γ -rays (ns)

6 Li-enriched

glass (GS20)

7.2 96 2.5 395 100

7 Li

glass, 6 Li depleted (GS30) 8.0 0.1 2.5 395 100

467

13 Experiments to Study the Performance of Spallation Neutron Sources

from background induced by spikes of the kicker magnets or dark current of the photomultiplier tubes, PMT, could be eliminated [913].

Experimental results Protons with energies of 1.94, 12, and 24 GeV with intensities of about 1012 protons per pulse were injected on the Hg target. The time width of pulses was about ∼100 ns.

Neutron spectrum [n/Lethargy/sr per proton]

10−8

10−9

10−10 1.94 GeV -Z = 11 cm 12 GeV -Z = 16 cm 24 GeV -Z = 20 cm

10−11

10−1 10−2 Neutron energy [eV]

100

10−8 Incident protons 24 GeV Neutron spectrum [n/Lethargy/sr per proton]

468

Exp. Calc.

10−9

10−10

10−2 10−1 Neutron energy [eV]

Fig. 13.31 Normalized thermal neutron spectra measured at the ASTE TOF experiment for beam energies of 1.94, 12, and 24 GeV (upper panel). Thermal neutron spectrum per incident proton with beam energy of 24 GeV compared with Monte Carlo simulations of NMTC-JAM [917] (lower panel) (after Meigo et al. [913]).

100

13.3 Reﬂector Experiments with Complex Geometries and Realistic Material Compositions

Several proton beam diagnostics devices were applied: (1) An integrating current transformer, ICT (210-20:1), from Bergoz [903], which could be operated for a pulse width ranging from picoseconds to several microseconds, (2) a foil activation method with Cu foils placed in front of the Hg target vessel, where the protons were determined by the γ -rays of 24 Na produced by the Cu(p,24 Na)-reaction, (3) the beam proﬁle was measured by a segmented parallel-plate ion chamber, and alternatively by an image plate technique with Al activation foils. The image of the image-plate represents the intensity distribution of the radioactivities induced in the Al foil corresponding to the incident proton beam intensity proﬁle. The relative exposure doses of each pixel with a size of 200 µm2 could be analyzed by an imaging plate reader [913]. Measured neutron spectra After subtraction of the signals of the 7 Li glass scintillator from the 6 Li glass scintillator, the thermal TOF neutron spectra measured by the CTOF method was obtained. The detection efﬁciency of the scintillators were calculated with the MCNP-4A code [915] using an evaluated neutron cross section library [916]. It was found that the detection efﬁciency of the enriched 6 Li detector was 100% for thermal neutrons. The measured neutron spectra obtained are shown in Figure 13.31. The broad Maxwellian thermal peak distribution is clearly visualized. A comparison [912] of the spectrum measured at 24 GeV with Monte Carlo simulations is given on absolute scale in Figure 13.31 using the NMTC-JAM/PHITS code [917]. The comparison shows an excellent agreement. Thus the NMTC/JAM system for neutron ﬂux calculations could be validated on measurements for a TMR system from a few tens of GeV down to the meV neutron energy region [912].

Maxwellian intensity ×106 [neutrons cm–2 sr–1 W–1]

1.5

1.0

0.5 0

5

10

15

20

Proton energy [GeV] Fig. 13.32 Dependence of the maximum neutron intensity over the Maxwellian peak region normalized to the incident power of protons as a function of the incident proton beam energy (data are from [913]).

25

469

470

13 Experiments to Study the Performance of Spallation Neutron Sources

By integration of the neutron spectra of Figure 13.31 in the Maxwellian peak region, a value for the neutron intensity as a function of the incident proton beam energy could be determined (cf. Figure 13.32). It can be recognized from the experimental values that the neutron intensity per proton power in Watt decreases as the proton beam energy increases and is almost proportional to the incident proton energies, which is shown in Figure 13.32. Measurements on neutron intensity changes by moving the target along the beam direction within a range of 15 cm resulted only in a difference in thermal peak intensity within 10%. This insensitivity is mainly caused by the broad maximum in the Maxwellian energy range of the thermal neutron ﬂux from the H2 O moderator.

471

14 Experiments on Radiation Damage in a Spallation Environment 14.1 Introduction

Till now there is very scarce experimental information available on the lifetime of structural components in the radiation environment of spallation targets and components. Therefore the lifetime, e.g., for the proton beam window material, the target material if it is solid material (Pb, W, Ta, or U, etc.), the structure material inside the target (Al, Zr, different steel alloys, etc.), the material of the return hull, if a liquid metal target is used, and at last the structure materials of components as moderators, reﬂectors, neutron beam pipes, etc., is desirably needed. The best way to overcome this lack of knowledge is to investigate irradiation experiments on special material specimens at operating spallation sources [918, 919], at particularly suitable irradiation facilities, or to investigate specimens obtained from spent targets and components of already operating spallation sources, as e.g., LANSCE [630], ISIS [643], and SINQ [627]. Because there are no facilities particularly dedicated for irradiation purposes, generally measured results of a postirradiation examination of spent targets and components are the best way to accumulate experimental data on the irradiation-induced changes of the mechanical properties of these materials. Concerning radiation damage, the most critical region in high-power targets of spallation sources is in the center of the target window which typically accumulates a proton ﬂuence of, e.g., 1.6 × 1026 protons/m2 within one year of full power operation of the ESS [551, 873] with 5 MW beam power. In steels this leads to a displacement dose of about 60 displacements per atom, dpa, and a helium concentration of almost 1 at.%. Based on the experience of ﬁssion and fusion materials it is expected that hardening and low-temperature embrittlement is responsible for the main changes in the mechanical properties of the materials due to the considered temperature range of 100–250◦ C. Since 1996, spent target components from LANSCE (Los Alamos Neutron Science Center) and from the ISIS (Spallation Neutron Source at Rutherford and Appleton Laboratory) were became available for postirradiation investigations. The available materials included four different alloys: an austenitic stainless steel (AISI 304L), a nickel-base alloy (IN 718), a martensitic stainless steel (DIN 1.4926), and a refractory metal, tantalum (used as the target material for the ISIS target). The specimen preparation and the measurements were mainly performed in the hot cells of Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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14 Experiments on Radiation Damage in a Spallation Environment

the Forschungszentrum J¨ulich, Germany. Several mechanical tests, including the Vickers hardness test [920], a three-point bending and tensile tests were conducted. The fracture surfaces were observed by scanning electron microscopy (SEM) after bending and tensile tests. The changes of the microstructures after irradiation were investigated by transmission electron microscopy (TEM). 14.1.1 Irradiation Conditions and Studied Materials

The investigated spent targets and components are a LANSCE Water-Degrader and a LANSCE Beam-Window, a beam window from the Paul-Scherrer-Institut irradiated in LANSCE, and an ISIS tantalum target with structure materials. The ISIS target consisted of a target container with a proton beam window made of AISI 304L stainless steel and 23 D2 O cooled Ta plates as target material. The details of the materials, dimensions and the operation conditions can be found in Refs. [921–924]. The irradiation conditions and other relevant parameters are summarized in Table 14.1, which is adopted from [924]. The material properties of some common target and structure materials are given in the appendix in the tables on page 683. The proﬁles of the incident proton beam on the spent components were measured by γ -scans in the hot cells at J¨ulich. It was found that the positron decay of 22 Na, 44 Ti, and 57 Co was mainly caused by the proton beam in the Ni- and Fe-based alloys. Therefore, the integrated positron decay distributions were used. As a result the intensity distribution of the proton beam at all components could be approximated Tab. 14.1

Materials and irradiation conditions (data are given by Chen et al. in [924]).

Materials Protons in (A h) Beam proﬁle σx /σy (mm) Peak ﬂuence (protons/m2 ) Maximum irradiation temperature (◦ C)a Maximum dpa Maximum He (appm) Maximum H (appm)b a

LANSCE water degrader

LANSCE window

PSI window

ISIS target

IN 718 5.29 −

AISI 304L 5.29 22.6/28.8

IN 718 3.41 −

DIN 1.4926 2.83 16.3/23.6

Pure Ta 1.74 17.0/20.7

2.9 × 1025

2.9 × 1025

6.4 × 1025

2.6 × 1025

1.7 × 1025

250

250

400

250

200

8.5 1510 5890

8.5 1680 5270

20 3330 13000

6.8 1510 4720

11 580 −

The maximum irradiation temperature refers to maximum temperature in the beam center at maximum operating power of the spallation source. b The values represent the hydrogen concentration produced in the material, neglecting energetic or diffusion losses, etc.

14.1 Introduction

by a two-dimensional Gaussian shape with variances σx and σy , respectively (cf. Table 14.1). 14.1.2 Experimental Results

Vickers microhardness HV0.2

14.1.2.1 Microhardness and Three-Point Bending Tests The microhardness was investigated applying the Vickers hardness test method [920]. The Vickers number (HV) is calculated by HV = 1.854(F/A), where F is the applied load force in kgf, A is the area of the indentation in mm2 . The applied load is usually speciﬁed when HV is cited. It should be noted that the data determined by hardness tests can not be directly used for any engineering purpose. But microhardness tests are easy to perform and provide a quick qualitative information on changes of the mechanical properties. The hardness tests were made on samples which were cut from different components (cf. Table 14.1) to receive specimens with a perfect ﬂat surface for the measurements. To deal with a high-dose gradient, microhardness tests were performed with a load L = 2 N(HV 0.2). The results on each position have been averaged over several indentations along the thickness. In Figure 14.1 the hardness data of the four different materials given in Table 14.1 are shown and compared. 450

550

400

500

350

450 400

300

IN 718

AISI 304L 250

350

(a)

(b)

300 400 250 350 200 300 150 Ta (99.99%)

DIN 1.4926

250 0 (c)

5

10

100

0 (d)

Displacement [dpa] Fig. 14.1 Dependence of Vickers microhardness HV0.2 at room temperature (RT) on displacement dose for (a) AISI 304L, (b) IN 718, (c) DIN 1.4926, and (d) Ta (after Chen et al. [924]).

5

10

473

14 Experiments on Radiation Damage in a Spallation Environment

Attention should be drawn to the IN 718 material, which is the material that, after hardening up to about 1–2 dpa, shows a softening at even higher doses. The hardness level of IN 718 after about 8 dpa is still comparable with that one of DIN 1.4926 (about 400 HV 0.2), but the trend of the two materials is rather different. All the other three materials, i.e., AISI 304L, DIN 1.4926 and Ta, show continuous hardening after irradiation. Both steels reach a level of 400 HV 0.2 at about 7 dpa, while the pure Ta reaches only a hardness of about 250 HV 0.2 at 11 dpa. In addition to the microhardness measurements three-point bending test were investigated on the irradiated materials with samples of 15 × 2 × 3 mm3 in size with an unusual ratio of length to cross section [921]. This technique was preferred to the more standard four-point bending in order to keep the sample as small as possible. The high gradient of the irradiation dose would prevent a constant level of irradiation inside a larger specimen. Figure 14.2 shows a schematic drawing of the three-point bending device used for the bending tests. This system was installed in a standard tensile testing machine equipped with a 5000 N load cell [921]. The tests were performed with a 5 KN load cell and with a crosshead speed of 0.2 mm/min. The experimental setup allowed a maximum deﬂection of about 2 mm. In order to study possible inﬂuences of specimens’ shape and geometry, extensive tests were made on unirradiated specimens before investigating irradiated material. Details are described in Ref. [921]. One of the major problems in these investigations was related to the reference on unirradiated materials. The spent components, from which the specimens were prepared, were operated for several years in spallation environments, but no archive material was left for comparison. Therefore, Inconel 718 was chosen as reference material for studying the size dependence of the bending results. The results of the three-point bending tests are qualitatively similar to the results found in the microhardness tests. The data for all materials are shown in Figure 14.3. The IN 718 specimens did show a trend for softening at an irradiation dose of about 2.1 dpa as already shown in Figure 14.1(b) by microhardness test. In this

.1 m m

Load L

h=2

474

+ I = 10 mm s

Fig. 14.2 A schematic drawing of the three-point bending device with load L and deﬂection s (after Carsughi et al. [921]).

14.1 Introduction 1000

3500

8.3 4.4

800

0 dpa

3000

2.8 0.3 dpa

7.4

2500

600

2000

400

1500

2.8

5.7

8.5

1000 Load [N]

200 0

500

AISI 304L

0

(a)

(b)

800

1400 1200 1000 800 600 400 200 0 0.0 (c)

IN 718

6 3.4 0.2

11 9 4

600

0 dpa

400

0 dpa

200 DIN 1.4926 0.5

1.0

1.5

2.0

Pure Ta 2.5

0 0.0 (d)

0.5

1.0

1.5

2.0

2.5

Deflection [mm]

Fig. 14.3 Three-point curves of (a) AISI 304L, (b) IN 718, (c) DIN 1.4926, and (d) pure Ta (after Chen et al. [924]).

case a reduction of ductility1) could also be observed. All the other materials, i.e., AISI 304L, DIN 1.4926, and pure Ta, did show a hardening with a reduction of ductility. Among the steels, the austenitic one, AISI 304L, showed a large reduction in ductility, which was clearly visible during the bending test, e.g., the sample irradiated up to about 8.3 dpa broke already after 0.5 mm of deﬂection. On the opposite, the martensitic steel, DIN 1.4926, irradiated up to about 6.8 dpa did not break within the maximum attainable deﬂection of about 2 mm. The results for pure Ta were very surprising. A highly brittle material was expected, but the results show instead an irradiation hardening but no reduction in ductility under the given experimental condition. Even the Ta sample irradiated up to 10 dpa did not break during the three-point bending test but showed an extreme ductile behavior and could be bent end to end without failure (cf. Figure 14.4). The Ni-base superalloy, IN 718, showed a trend for softening also, but the values of the failure loads were still much higher than the other materials, although the reduction in ductility was rather strong at 8.5 dpa (Figure 14.3). 14.1.2.2 Tensile Strength, Scanning- and Transmission Electron Microscopy Tensile strength is the stress at which a material breaks or deforms in an unstable manner. The quantitative information of the strength and ductility of irradiated 1) Ductility is a mechanical property used to describe the extent to which materials can be deformed plastically without fracture.

475

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14 Experiments on Radiation Damage in a Spallation Environment

Ta 10 dpa

2 mm

Fig. 14.4 Optical micrograph of a Ta specimen from the ISIS plate target irradiated to 10 dpa after bending end to end, The given scale in the ﬁgure gives a measure of 2 mm (after Chen et al. [923]).

materials will be achieved with tensile tests performed in hot cells. A tensile test is the most fundamental type of mechanical test which can be performed on materials. Tensile tests are relatively simple and fully standardized. Usually a standard test piece or specially formed specimen is gripped at either end by a suitable apparatus in a testing machine, which slowly exerts an axial pull so that the specimen is stretched until it breaks. The test provides information on proof stress, yield point, tensile strength, elongation, and reduction of area. Considering the high spatial gradient of the proton beam distribution in the window and target components, miniature-type tensile samples were machined from the spent components. The specimens used here had a thickness of about 0.5 mm, length of 5 mm, and width in the gauge region of 1.2 mm. All tensile tests were performed at room temperature 25◦ C and 250◦ C in air. For the tests a 2 kN MTS tensile machine was applied which was equipped with a video-extensometer to measure the elongation directly in the gauge area. The strain2) rate was about 10−3 s−1 . Typical stress–strain curves are given in Figures 14.5 and 14.6 for the PSI window material DIN 1.4926 at T = 25◦ C and 250◦ C compared with the material Mod9Cr1Mo at T = 164◦ C from the APT irradiation program [925, 926], and stress–stain curves of the Ta specimens from the ISIS target at temperatures of T = 25◦ and 250◦ C with a strain rate of 10−3 s−1 . The tensile properties of DIN 1.4926 before and after irradiation is depicted in Figures 14.5(a) and (b) for the temperatures 25◦ C and 250◦ C. For comparison a tensile test result is shown in the ﬁgure, panel (b), of a quite similar material Mo9Cr1Mo from a previous irradiation program for the Accelerator Production of Tritium (APT) project [926]. From Figure 14.5, it is seen that the strength of the ferritic steels increased with the irradiation dose. All materials begin necking after a relative small strain of about <1% at a very low irradiation dose. The total elongation remains almost constant after a ﬁrst large drop at the beginning of the irradiation. 2) Strain is the deformation per unit length caused by the applied stress, i.e., force per unit area of the specimen.

14.1 Introduction 1400

Ttest = 25°C

250°C

164°C

1200

Stress [MPa]

8.8 1000

6.6

800

5.6 3.3

6.2 2.9 4.2 0 dpa

1.2 0.3

600

1.5

0 dpa

0 dpa

400 DIN 1.4926

200 0

0 (a)

5

10

DIN 1.4926

Mod9Cr1Mo

15

20

0 (b)

5

10 15 Strain [%]

0 (c)

5

10

15

20

Fig. 14.5 Stress–strain curves of DIN 1.4926 specimens of the PSI-window. (a) tensile tested at 25◦ C (left panel) and (c) tensile at 250◦ C, respectively (right panel). The dashed curves in (b) show for comparison a tensile test at 146◦ C of a material from the APT irradiation program [925] (after Chen et al. [924]).

Ttest = 25°C

Stress [MPa]

600

250°C

11 dpa 11 dpa

400

0.6 dpa 0.6 dpa

unirr.

200

unirr. 0

0 (a)

10

20

30

40 0

10

20

30

40

(b)

Strain [%] Fig. 14.6 Stress–strain curves of Ta specimens of the ISIS target, (a) tensile tested at 25◦ C (left panel) and (b) at 250◦ C, respectively, with a strain rate of 10−3 s−1 (after Chen et al. [923]).

The behavior of pure Ta before and after irradiation in the ISIS target environment shown in Figure 14.6 is similar compared with the DIN 1.4926 material, the total elongation of Ta drops at a dose below 0.6 dpa, but up to the maximum available dose of 11 dpa the retained ductility has a much higher value (strain to necking of

477

478

14 Experiments on Radiation Damage in a Spallation Environment

8–10%), whereas the DIN 1.4926 material shows only 1–2% strain to necking at a dose of about 7 dpa. Two other methods which were applied to inspect irradiated specimens are, (1) SEM that images the sample surface by scanning it with an electron beam in a raster pattern and yields information about the topography of the specimen’s surface, (2) TEM, where a beam of electrons is transmitted through ultrathin specimens. The ﬁrst TEM system was built by Ruska and Knoll in 1931 [927]. More details of SEM and TEM investigations of the specimens of the spent components may be found in [921–924]. An example of typical microstructures observed by the TEM method after 800 MeV proton irradiation is shown in Figure 14.7 given in Ref. [924]. The alteration of the microstructure with displacement dose for the considered materials is also discussed for 304L in [926], for IN 718 [925], and for DIN 1.4926 in [919]. The analysis of different TEM graphs of irradiated materials shown in Figure 14.7 adds up to the following results: (a) for AISI In 304L, the dominant microstructure is a high density of small ‘‘black dot’’ defect clusters and faulted Frank dislocation loops. The densities of small clusters and loops were saturated at a dose of around 1 dpa. The cluster size remains constant at an average of 2 nm, but the loops continue to grow by net absorption of self-interstitials up to 23 nm at a dose of 8.5 dpa, (b) for IN 718 irradiated to 8.5 dpa a remarkable change is observed by the disappearance of γ and γ phases. The γ and γ superlattice diffraction spots, clearly evident for unirradiated samples, were absent after irradiation [924]. As in IN 718 8.5 dpa

AISI 304L 8.5 dpa

(a)

(b) Pure Ta 11 dpa

DIN 1.4926 6.6 dpa

(c)

(d) Fig. 14.7 TEM graphs showing examples of the microstructure in the analyzed samples. (a) AISI 304L with 8.5 dpa, (b) IN 718 from LANL water degrader with 8.5 dpa, (c) DIN 1.4926 with 6.6 dpa, and (d) pure Ta

with 11 dpa. (a) and (b) are bright ﬁeld images with z = 011, g = 002, (c) and (d) are weak beam dark ﬁeld images (g, 4g) with z = 001, g = 110. The resolution limit was 1 nm (after Chen et al. [924]).

14.1 Introduction

the case of 304L, a dense population of Frank-loops with an average diameter of 15 nm were formed on (1 1 1) habit planes (cf. Figures 14.7(b)–(d)) for DIN 1.4926 and pure Ta, on the contrary, the evolution of small clusters and loops is much slower in the bcc materials DIN 1.4926 and pure Ta than in the fcc materials 304L and IN 718. The density of defects in DIN 1.4926 is one order of magnitude lower than that in 304L. The sizes of the defects were 5 and 3 nm in DIN 1.4926 and pure Ta, respectively, which is ﬁve times smaller than that in 304L and IN718. No bubbles or voids were observed in all investigated irradiated materials down to the TEM resolution limit of 1 nm. Remarks on damage cross section calculations As already mentioned in Chapter 6 on page 215, irradiation experiments are supported in some sense by theoretical work to calculate displacement cross sections to estimate the dpa’s from protoninduced spallation products in structure materials. In addition experiments on recoiling light and heavy residues (HR) and the production of H and He assist in the selection of suitable materials (cf. Chapter 10.3 on page 327). In Figure 14.8 displacement cross sections σd obtained with INCL2.0+GEMINI and LAHET (RAL, ORNL) are compared [544]. Both codes result in almost the same and constant damage cross section σd as a function of the incident proton beam energy. This constant σd above about 1 GeV implies that the proton-induced damage decreases with increasing incident energy p(GeV)+Fe

p(GeV)+Ta

104 HR

sd (b)

INCL

LAHET(RAL,ORNL)

103

RAL

102

H RAL

sHe/sd (ppm)

He 400 300 200 100 0

L

RN

L

ORN

O

RAL

RAL

NL OR

1

2

L ORN

3

1 4 Ep (GeV)

2

3

Fig. 14.8 Radiation damage cross sections σd induced by H, He, and HR as calculated by INCL2.0/GEMINI (thick lines) and LAHET(RAL,ORNL) (thin lines); He/dpa ratio σHe /σd for beam exposed 2 mm windows Fe (left) and Ta (right) (after Hilscher et al. [544]).

4

479

480

14 Experiments on Radiation Damage in a Spallation Environment

when normalized to the same number of neutrons produced in thick targets. The ratio of He production to displacement per atom (He/dpa=σHe /σd ) is strongly increasing with proton energy in the case of the two versions of the LAHET code (RAL and ORNL), while it is almost constant for the INCL2.0/GEMINI code. For more details refer to [544]. Radiation damage and effects from gas production are not the only criterion for the selection of materials. There are other effects, e.g., in the window region or the container of liquid metal targets where the material must be able to withstand the high mechanical stresses generated by the pressure waves from the target liquid (Hg) or local erosion damage in steel in contact with a heavy liquid metal in which pressure waves are induced by pulsed beams with high-intensity peaks [829, 928]. Finally it should be noted that it is a practice to select materials of construction that will not seriously degrade during their exposure to sustained operation. Therefore material degradation, which is not speciﬁc for spallation applications, is an accepted fact and will also occur in a spallation radiation environment. This material degradation concerns, e.g., cables and electrical isolations, moderator materials and components, measuring equipment (semiconductors, radiation monitors), gaskets made of plastic and ceramic materials, cooling liquids, etc.

481

15 Experiments to Shield High-Energy Neutrons of Spallation Sources As discussed recently by Nakamura et al. [582] in a review article and in Refs. [559, 929, 930], shielding experiments are important to investigate the accuracy of shielding calculations (see also Chapter 7 on page 233). Such studies are indispensable for the radiation protection of accelerators and target stations of high-intensity spallation neutron sources and ADS systems. As pointed out by Nakamura et al. [582] several shielding experiments have been performed at energies below 100 MeV; however, in the high-energy region above several 100 MeV up to several GeV shielding experiments are very scarce. In this energy region deep penetration experiments with neutrons are quite desirable to study the neutron dose attenuation lengths. In addition even the existing data are very limited and moreover disputed. Several deep penetration experiments on neutrons between 230 and 2700 MeV at different facilities were performed in the past years: • at the Loma Linda University Medical Center, USA, with 230 MeV protons of Siebers et al. [931], • at the TRIUMF facility, Canada, with 500 MeV protons by Moritz et al. [932], • at KENS at KEK, Japan, with 500 MeV protons by Nakao et al. [933], • at the WNR at LANL, Los Alamos, USA, with 800 MeV protons by Amian et al. [934] and Bull et al. [935], • at ISIS at the Rutherford and Appleton Laboratory, UK, with 800 MeV protons by Nunomiya et al. [936], • at the SATURNE accelerator at Saclay, France, with 2700 MeV protons by Bourgois et al. [937], • At the AGS accelerator at BNL, Brookhaven, USA, with protons from 1.6 to 24 GeV energy by Nakashima et al. [812, 912] From the above-mentioned experiments three are selected and described below. These experiments cover most of the issues of the shielding requirements of high-intensity spallation neutron sources.

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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15 Experiments to Shield High-Energy Neutrons of Spallation Sources

15.1 Shielding Experiments at the Los Alamos WNR Facility’s Spallation Target

The deep penetration experiment conducted at the Los Alamos WNR facility’s spallation neutron target [938, 939] was one of the ﬁrst shielding experiments at a spallation neutron producing target station driven by medium energy protons of 800 MeV energy [934, 940]. Spectrum averaged attenuation lengths for high-energy neutrons in iron were measured utilizing multireaction spallation detectors and threshold detector foils [941]. The high-energy neutrons were produced at the Los Alamos WNR LANSCE facility in a tungsten spallation target [939] hit by 800 MeV protons with an average beam current of about 4 µA ≡ protons per second. The detectors were embedded into the bulk shield of the facility. Spallation products from foils of aluminum, copper, cobalt, and nickel were used having threshold energies between 0.5 and 400 MeV. In addition, results for peripheral threshold reactions of iron, indium, zirconium, and niobium with threshold energies below 14 MeV were also investigated. For the energy range between 0.5 and 400 MeV, spectrum averaged attenuation lengths were determined. The information of these experimental results were used to benchmark computational models and radiation transport computer codes applied on shielding problems of the 5 MW German SNQ spallation neutron source [142, 552, 595]. The most reasonable technique to detect neutrons inside a shield is by counting decaying residual nuclei of high-energy interactions with suitable target materials. Especially for accelerator environments, spallation reactions on copper have been proposed by Routti [942, 943] as a means to extend the known threshold-foil technique to higher hadron energies. The yield cross sections for many spallation products have a threshold type energy dependence with threshold energies of tens or hundreds of MeV. The advantage of these spallation detectors is that several gamma-active products with different threshold energies can be obtained from only one measurement. An example of these production cross sections for nat Cu by Routti [942] is illustrated in Figure 15.1. The threshold reaction technique was also applied at the ASTE shielding experiment given in Section 15.3 on page 491. The problem with these reactions, however, is that the spallation yield cross sections are uncertain above 20 MeV. While the experiments can reveal clearly the exponential decrease of reaction rates with shielding thickness without any prior knowledge of cross sections to determine the attenuation lengths, a quantitative comparison between experiment and calculation suffers from the lack of reliable cross-section data for these spallation yield cross sections. The accuracy of calculated reaction cross sections is generally around 20–50% as compared to measured values of these reaction cross sections. Today the knowledge of reliable cross-section data when applied for calculations is much more improved by extensive databases evaluated and measured, e.g., by Michel et al. [543] (cf. Section 10.4.1 on page 370). A horizontal cut of the LANSCE-WNR target station with tungsten target (diameter of 4.45 cm) and moderator–reﬂector assembly placed in a cavity with a diameter of about 206 cm, the shield with neutron ﬂight paths, and the stringer for

15.1 Shielding Experiments at the Los Alamos WNR Facility’s Spallation Target

Reaction cross section [mb]

103 Curve

102

1 2 3 4 5 6 7 8 9 10

101 100 10−1 10−2

Spallation cross sections for Cu 2 3 6 9 7 5 4 10 1 8

59Fe 58

Co

57Co 56

Co Mn 48 V 46 Sc 48 Cr 44 Sc 24Na 52

10−3

2 3

10−4 100

1

4

5

6 7 9 8

101

10

102

103

104

Energy [MeV] Fig. 15.1

Calculated reaction cross sections for Cu (after Routti and Sandberg [943]).

the insertion of foils are illustrated schematically in Figure 15.2. The individual foil containers and the foil positions in the stringer are indicated. The stringer system consists of outer massive iron rings, a vacuum pipe, a central iron tube – the socalled stringer – and 10-cm long massive iron cylinders and the foil containers. The stringer loaded with iron plugs and foil containers could be removed from ﬂight path 5 after irradiation for loading and unloading foils. A 3 He counter indicated on the left side of the stringer in the lower panel of Figure 15.2 serves as neutron ﬂux monitor and was positioned in a polyethylene cylinder at the ﬂight path’s end. During irradiation, the 3 He detector counts were recorded to correct for time variations of the incident proton beam intensity and the resulting neutron ﬂux intensity. This position was chosen to prevent interference from neighboring experiments. Most irradiations were performed with a tungsten target of 4.45 cm diameter, 24 cm length, and a beryllium reﬂected water moderator assembly in place. About seven runs with total irradiation times between 116 and 260 h were performed with an average beam current on the target of about 4 µA. After irradiations, the reaction products in the foils were determined directly by counting in Ge(Li) gamma-ray spectrometers. All foil activities were corrected for self-absorption in the foils, for decay during counting, and for the time elapsed at the end of irradiation. The number of reactions per incident proton and per nucleon follows from the measured data and are determined with the following formula: R=

A0 , (1 − e−λ·T )Np · N

(15.1)

with A0 is the corrected activity at the end of irradiation (s−1 ), (1 − e−λ·T ) is the factor to correct the decay during irradiation, Np is the number of protons per second (s−1 ), N = ρ · m is number of foil nuclei, ρ = NA /W is number of atoms

483

484

15 Experiments to Shield High-Energy Neutrons of Spallation Sources Outer vacuum pipe PE rings Fp5 Inner vacuum pipe Target

Iron rings Fp4

Fp3

364 cm Concrete

(a)

Steel 103 cm

Moderator reflector assembly

Foil container

PE 3

He monitor PE

Fe Fe Foil positions

(b)

Fig. 15.2 Schematic horizontal cut of the LANSCE-WNR target station and the bulk shield (a). The stringer for the foils (b) was inserted into neutron ﬂight path 5 for the irradiations. Details of the target–moderator–reﬂector assembly are described in more detail in [938, 939] (after Amian et al. [934, 941]).

per gram (g−1 ), m the mass of the foil (g), W atomic weight of foil (g/mole−1 ), NA the Avogadro number (6.022 × 1023 mole−1 ), T the total irradiation time (s), and λ is the decay constant (s−1 ). Note that Eq. (15.1) is only valid for irradiation runs with stable proton beam intensity, therefore the decay during irradiation must be approximated by a sum of expressions characterizing time bins of almost constant beam intensity [941]. The following foil materials of natural isotopic composition of 30 mm diameter and 1 mm thickness were inserted into the stringer (cf. Figure 15.2) and given with their reactions in Table 15.1. Details about their threshold energies and the effective cross section are described in [941]. Figures 15.3 and 15.4 show measured depth-dependent reaction rates for some reactions of irradiated nat Cu foils and of nat Ni foils, respectively. The reaction rates have been multiplied by the distance d to the tungsten target squared (cf. Figure 15.2) and are plotted against the depth in the shield. Results for other reactions are given in [934, 941]. The 3 He monitor normalization turned out to be within less than 8–10%. Spectrum-averaged attenuation length For all reactions given in [934] the attenuation lengths λatt were determined. As discussed in Chapter 7 on page 233 the

15.1 Shielding Experiments at the Los Alamos WNR Facility’s Spallation Target Tab. 15.1

Properties of the used detector foils and and their reaction products.

Foil material

Decay product

Al Cu

24 Na, 22 Na, 7 Be 59 Fe, 58 Co, 57 Co, 56 Co, 52 Mn, 54

Mn, 48 V, 46 Sc, 24 Na

58 Co, 57 Co, 56 Co, 55 Co

Co Zr Ni

88 Zr, 88 Y 57 Co, 57 Ni, 56 Co, 56 Ni, 55 Co

10−26

d2 × reactions/proton/neutron

10−27 −28

10

10−29

Cu

58

Co

Cu

57

Co

Cu

59

Fe

Cu

52

Mn

Cu

48

V

10−30 10−31 10−32 10−33 0

50

100

150

200

Depth d in shield [cm] Fig. 15.3 Measured depth-dependent reaction rates for some reactions on nat Cu. To eliminate the solid angle dependence, the reaction rates have been multiplied by the distance to the target center squared (cf. Figure 15.2) (after Amian et al. [934]).

attenuation length describes the 1/e attenuation of high-energy hadrons, mainly neutrons, at deep penetrations, e.g., several mean paths in the shielding material where the neutron ﬂux is assumed to be in equilibrium. The simple model expression, which may be used to ﬁt the experimental reaction includes the geometry term (1/d2 ) and the exponential attenuation (e−d · ρ/λatt ): R(d) =

A1 · e−d · ρ/λatt , (d + 103)2 + 7.62

(15.2)

where R(d) is reaction per proton and per nucleon at distance d in the shield, d is the depth in the shield (cm), ρ the density of the shielding material (g/cm2 ), parameter

485

15 Experiments to Shield High-Energy Neutrons of Spallation Sources 10−25 10−26 d2 × reactions/proton/neutron

486

10−27 10−28

Ni

58

Co

Ni

57

Co

Ni

56

Ni

Ni

56

Co

Ni

56

Ni

Ni

55

Co

10−29 10−30 10−31 10−32 10−33 0

Fig. 15.4

50

100 150 Depth d in shield [cm]

Same as Figure 15.3 but for reactions on

nat Ni

(after Amian et al. [934]).

A1 = (R(d = 0) = 1.06662 × 104 ) estimated from Eq. (15.2) with the reaction R(d) at d = 0, and λatt is the = attenuation length (g/cm2 ). The denominator in Eq. (15.2) represents the actual distance to the neutron-producing target (cf. Figure 15.2). It should be noted that energy-dependent attenuation lengths could not directly be derived from the measured reaction rates. The attenuation lengths represent some sort of an average over the energy range of the respective reaction given by the energy dependent reaction cross section. A least-squares ﬁt procedure was applied in a logarithmic scale corresponding to the way the data are plotted, e.g., in Figures 15.3 and 15.4. To ensure to obtain data only from the exponential attenuation region all experimental data points up to 15 cm were ignored in the least-square procedure [941]. Table 15.2, e.g., summarizes the nat Cu and nat Ni foil reactions as of Figures 15.3 and 15.4; the spectrum-averaged attenuation lengths. In summary, more than 30 reactions were investigated [941] in this high-energy spallation shielding environment at 90◦ to the beam axis. A simple analysis of the measured reaction rates assuming a 1/r 2 geometrical attenuation gives a spectrum-averaged attenuation length for the LANSCE-WNR bulk shielding of (153 ± 9) g/cm2 or (19.6 ± 1.2) cm, largely independent of the threshold energies of the reactions.

15.2 Shielding Experiments at the ISIS Spallation Source

A further important shielding experiment at a currently operating spallation neutron source is the experiment performed at the short-pulsed spallation neutron

15.2 Shielding Experiments at the ISIS Spallation Source Examples of determined attenuation lengths λatt (data are from [941]).

Tab. 15.2

Target foil

Reaction product

nat Cu

Attenuation length (cm)

58 Co

19.72 19.73 19.31 21.09 22.85

57 Co 59

Fe

52 Mn 48 V nat

58

Ni

Co

19.48 19.29 19.72 20.35 20.05 19.56

57 Co 57 Ni 56

Co

56 Ni 55 Co

Top center of shielding plug

6 cm-thick steel plate

520

460

Shield top level 81 439 42.5

147

97

220

He duct

123

284

130 98 265

511 470

124

130

85 Ta target

190 Target vessel

H + 800 MeV 170 µA 50 Hz

Building floor level Concrete Steel

Unit : cm

Fig. 15.5 Vertical cut through the ISIS spallation neutron source target station (after Nunomiya et al. [936]).

source ISIS [643] with incident protons of 800 MeV on a tantalum target surrounded by a moderator with a reﬂector of beryllium and a bulk shield of steel and concrete. Details of this experimental studies are given in Refs. [936, 944–947]. A vertical cut of the ISIS target station is shown in Figure 15.5. The ﬁgure shows a cross-sectional view along the beam direction of the proton beam, the target vessel in which the D2 O-cooled tantalum disk target (length = 296.5 mm, diameter = 90 mm) and the moderator–reﬂector system are mounted. The dimensions of the bulk shield built

487

15 Experiments to Shield High-Energy Neutrons of Spallation Sources

120 196

Shield blocks of iron/concrete Iron igloo wall thickness 60 cm

Steel plate Concrete Vertical shield plug

528

488

Steel 90° Tantalum target D2O cooled

Protons 800 MeV 170 µA, 50Hz

Fig. 15.6 Vertical cut through the iron ‘‘igloo’’ with the additional blocks of shielding material of iron or concrete (Refs. [936, 946]).

of steel and concrete are also depicted with a vertical shielding plug constructed of about 284 cm steel and 97 cm concrete in 90◦ direction. The shielding experiment was performed at the top center of the shielding plug indicated in Figure 15.5 with an iron ‘‘igloo’’ (on the top center) as shown in Figure 15.6. This igloo reduces the background for the measurements caused by neutron leakage from the ISIS bulk shield. The iron ‘‘igloo’’ has an inner diameter of 120 cm, a wall thickness of 60 cm and height of 196 cm. As indicated in Figure 15.6, the inner part of the igloo could be ﬁlled with additional shield blocks with a diameter of 119 cm either with iron (density = 7.8 g/cm2 ) of thicknesses 10, 20, 30, 40, 50, and 60 cm or with concrete (density = 2.36 g/cm2 ) blocks of thicknesses 20, 40, 60, 80, 100, and 120 cm. The different thicknesses of the shielding blocks provide the spatial mesh for the measurements. At a proton beam energy of 800 MeV, the neutrons were produced as pulses to 50 Hz synchrotron operation from the tantalum target, and were measured with different activation detectors. The γ -rays from the activation detectors were analyzed with standard equipment of high impurity germanium (HPGE) detectors [947]. The applied activation detectors are summarized in Table 15.3. The cross-section data of 12 C(n,2n)11 C are given in [948, 949] and the 209 Bi(n,xn) activation data are given in [948], and calculated by Fukahori [950]. The 27 Al(n,α)24 Na data are from ENDF/B-VI [464], whereas the data for the reaction 155 In(n,γ )116m In are from ENDF/B-VI [464] and from evaluations given in the Los Alamos LA-150 data library [951]. For the 155 In(n,γ )116m In measurement a multimoderator spectrometer was used ﬁlled with 2.875 g In2 O3 powder in a spherical cavity of 0.735 cm radius in a acryl cylinder [952] which is placed in a spherical polyethylene moderator. Five different types of moderator detectors

15.2 Shielding Experiments at the ISIS Spallation Source

489

Applied activation detectors with their reaction processes applied at the ISIS shielding experiment (data are given by [947]).

Tab. 15.3

Reaction

Detector type/size diameter/thickness (mm)

Average mass (g)

Half-life

Threshold energy (MeV)

12 C(n,2n)11 C

Disk 80 / 30 Marnelli (Figure 15.7) Marinelli (Figure 15.7) Disk 80/11 Disk 80/11 Disk 80/11 Disk 80/11 Disk 80/11 Moderator sphere

265.6 901.7 1425 529.6 529.6 529.6 529.6 529.6 2.875

20.4 min 20.4 min 11.8 min 36.4 min 1.77 h 1.67 h 11.76 h 11.22 h 54.1 min

20.4 20.4 3.247 70.89 61.69 54.24 45.37 38.13 Thermal

27

Al(n,α)24 Na

209 Bi(n,10n)200 Bi 209 Bi(n,9n)201 Bi 209

Bi(n,8n)202 Bi

209 Bi(n,7n)203 Bi 209 Bi(n,6n)204 Bi 155 In(n,γ )116m In

77 mm

30 mm

110 mm

∅ 80 mm

50 mm

80 mm Fig. 15.7 Typical geometry of the activation detectors. The left panel of the ﬁgure shows the disk type detector, whereas the right panel shows the Marinelli-type geometry (after Nakao et al. [946]).

were applied with 9.8, 5.5, 3.3, and 2.0 cm radius, and one without moderator. The neutron spectra were determined by unfolding technique by the SAND-II procedure [953]. The response functions for the detector were calculated with the MCNPX code [194]. More details about the multimoderator spectrometer may be seen in Refs. [936, 946, 947, 952]. As described and discussed in [936] the activation detectors were located at various positions on the additional shield surface inside the igloo for several thicknesses of the iron and concrete blocks (see Figure 15.6). The graphite reaction detectors 12 C(n,2n)11 C were used to get the attenuation length of the neutrons above 20 MeV. Figure 15.8 shows the attenuation proﬁles of the graphite reactions as a function of the iron and concrete shield thicknesses. The upper curve in the ﬁgure gives the results without additional shielding along the center axis as shown in Figure 15.6.

15 Experiments to Shield High-Energy Neutrons of Spallation Sources

Reaction rate [atom−1 coulomb−1]

490

12

10−20

C(n,2n)11C

10−21

Cal. Exp. Air Concrete Iron 10−22 0

20

40 60 80 100 Additional shield thickness [cm]

120

Fig. 15.8 The measured (ﬁlled symbols) and calculated (open symbols) 12 C(n,2n)11 C reaction rates as a function of the additional shield thickness (iron and concrete) at center position (cf. Figure 15.6). The results indicated as ‘‘air’’ are results without additional shielding material (after Nakamura et al. [582], Nakashima et al. [912]). Tab. 15.4 Comparison of the measured and calculated attenuation lengths derived from the 12 C(n,2n)11 C reaction rates (data are from [582, 936]).

Shielding material

Iron (7.8 g/cm2 ) Concrete (2.36 g/cm2 )

Attenuation length (g/cm2 ) Exp. 161.1 ± 2.1 125.4 ± 5.1

Calc. 150.3 ± 5.8 116.7 ± 3.8

Calc./Exp. 0.93 0.93

The three curves represent the reaction values of the additional shield thicknesses on the center of the vertical axis (depicted in Figure 15.6). The error bars are the statistical errors. The determined attenuation lengths of the measurement are given together with calculated values in Table 15.4. In Table 15.5 the measured attenuation lengths of the ISIS experiment are compared with other experiments of 800 MeV incident protons. In addition measured data are included for 0.5, 12, and 25 GeV incident protons. The neutron energy spectra were also measured at the top of the bulk shield in vertical direction with the 155 In(n,γ )116m In loaded multimoderator detector sphere. The measurements were investigated at three positions of the detector: (1) directly on the ﬂoor at central position without additional shielding, (2) with 60 cm concrete shielding, and (3) with 30 cm iron shielding. In Figure 15.9 the measured neutron

15.3 Shielding Experiments at the ASTE–AGS Target–Moderator–Reﬂector Assembly Comparison of attenuation lengths λ of various shielding experiments on iron and concretea .

Tab. 15.5

Shielding material

Facility

Proton energy (GeV)

Attenuation length λ (g/cm2 )

Density (g/cm3 )

Detector

References

Iron

KEK ISIS LANSCE-1 LANSCE-2

0.5 p 0.8 0.8 0.8

116 161.1 ± 2.1 148.0 ± 2 153.9 ± 9

7.01/7.15 7.8 7.18 7.8

[954] [936] [935] [934, 941]

KEK CERN

12 25

188 ± 12 147 ± 10

7.01/7.15

C, Al C Cherenkov Al, Fe, Co, Cu, Ni, Zr, In C, Al C, Al

KEK ISIS KEK CERN

p 0.5 0.8 12 25

123 125.4 ± 5.1 143 120

2.35 2.36 2.35

C, Al C C, Al C, Al

[954] [936] [955] [569]

Concrete

[955] [569]

a All measurements are investigated at 90◦ direction in respect to the incident proton beam. The references of the data are indicated in the table.

energy spectra for these three detector positions compared with simulations are shown. The calculations were performed with the three-dimensional Monte Carlo particle transport code MARS [608, 956]. The neutron energy spectrum (1) at the shield top has two components, a peak at about 100 MeV with neutrons as a direct component in 90◦ from the tantalum target and a broad maximum at about 1 MeV from neutrons slowed down in the shield. The neutron spectrum (2) has still the peak at 100 MeV but has a rather ﬂat distribution below 1 MeV caused by elastic scattering from light elements like hydrogen in the concrete. The neutron spectrum (3) behind the 30-cm-thick iron shield is a typical spectrum where higher energy neutrons are slowed down by inelastic collisions and is characterized by a broad peak in the 10–500 keV region caused by the relatively low inelastic cross sections in this energy region.

15.3 Shielding Experiments at the ASTE–AGS Target–Moderator–Reﬂector Assembly

The ASTE collaboration [812, 832, 957] carried out a shielding experiment [912] using 2.83 and 24 GeV proton beams incident on the ASTE bare mercury target with steel and ordinary concrete shields placed at lateral and at forward positions to the bare mercury target. The purpose of the ASTE experiment and the issues of the ASTE bare mercury target- and the mercury target–moderator–reﬂector experiment with ambient water moderator and Pb reﬂector are already described in Section 11.2.5.2 on page 419 and in Section 13.3.3.3 on page 466. Figure 15.10

491

15 Experiments to Shield High-Energy Neutrons of Spallation Sources

107 Cal. Exp.

106

(1)

105 Neutron flux [n cm−2 coulomb−1 lethargy−1]

492

Top floor 528 cm above the target

104 103 (2) 2

10

+ Concrete 60 cm

1

10

(588 cm above the target) × 10−3

100 10−1 (3)

10−2

+ Iron 30 cm (558 cm above the taret) × 10−6

10−3 10−4 10−5 10−9

10−7

10−3 10−5 10−1 Neutron energy [MeV]

101

103

Fig. 15.9 Comparison between measured and calculated energy spectra at three different positions at the vertical shield of the ISIS facility (after Nakamura et al. [582]).

shows the arrangement of the steel and ordinary concrete shielding surrounding the mercury target. The mercury target was placed inside a cave area of the AGS accelerator of concrete with the dimensions of 2 m in width and 2.7 m in height. The lateral shields of ordinary concrete of 5.0 m thickness and steel of 3.3 m thickness were placed at a distance of 1 m from the mercury target, whereas the forward steel shield of 3.7 m thickness are mounted at 3.5 m from the far end of the mercury target (cf. Figure 15.10). All shields had cross sections of more than 2 × 2 m2 with densities of steel and concrete of 7.74 g/cm2 and 2.45 g/cm2 , respectively. The spatial neutron ﬂux attenuation inside the shielding were determined by reaction rate distributions of activation samples of 27 Al(n, α)24 Na, 115 In(n, n )115m In, 197 Au(n, γ )198 Au, and 209 Bi(n, xn) reactions. This procedure is similar as applied at the ISIS shielding experiment already described in the last section.

15.3 Shielding Experiments at the ASTE–AGS Target–Moderator–Reﬂector Assembly

493

Concrete 5.0 m

Proton

Hg target

3.5 m

Steel

2.0 m

3.3 m

3.7 m

Steel

Reaction rate p−1 (target nucleus)−1

Fig. 15.10 Horizontal cut through the shielding arrangement of iron and concrete shields around the thick mercury target (diameter = 200 mm, length = 1300 mm) of the ASTE experiment at the AGS accelerator at BNL (after Nakashima et al. [812, 912]).

10−28 Exp. NMTC/JAM (free) NMTC/JAM (In-medium) MCNPX

10−29 10−30 10−31

209

Bi(n,6n) 204Bi

10

10−30

10−32

10−31

10−33

10−32

10−34

10−33

24 GeV Iron lateral

10−35 0

50

100

150

Exp. NMTC/JAM (free) NMTC/JAM (In-medium) MCNPX

−29

209

Bi(n,6n) 204Bi

24 GeV Concrete lateral

10−34 200 250 0 50 100 150 200 250 300 350 400 Shield thickness [cm]

Fig. 15.11 Measurements of space dependent 209 Bi(n, 6n)204 Bi reaction rate distributions in iron and concrete shields and comparisons with NMTC/JAM and MCNPX simulations (after Nakashima et al. [912]).

A beam intensity of about 1012 protons per pulse, in total up to 3 × 1016 protons, were needed to measure with reasonable statistics data up to a depth of about 2.5 m inside the lateral steel shield and up to about 4 m inside the lateral concrete shield. Figure 15.11 illustrates as an example the measured spatial distributions of neutron reaction rates of the 209 Bi(n, 6n)204 Bi reaction with 24 GeV protons incident on the Hg target. The threshold energy of this reaction is about 38 MeV.

494

15 Experiments to Shield High-Energy Neutrons of Spallation Sources

The comparison with the NMTC/JAM and the MCNPX particle transport simulations at 24 GeV protons of the 209 Bi(n, 6n)204 Bi reaction shown in Figure 15.11 agrees with the measurements within a factor of 2–3 for the reaction attenuation at all positions except at distances lower than 25 cm inside the shield. This differences are supposed to be due to the fact that the actual geometry around the target was too complicated to make an exact geometry model for the simulations [912]. The measured reaction with 209 Bi(n, 6n)204 Bi at proton energies of 2.83 GeV not shown here, shows the same reaction attenuation compared to the 24 GeV proton measurements [812]. Additional calculations [812] for the neutron reaction rate attenuation (1/proton/target nucleus×d2 ) or for the neutron dose rate attenuation (Sv/s/proton×d2 ) were investigated using the Moyer model. It could be shown that for an attenuation length estimated by Stevenson et al. [569] of λatt = 147 g/cm2 for iron, the measured neutron attenuation for both incident proton energies – 2.83 and 24 GeV – are fairly well described. As a very ‘‘clean’’ experiment, within the scope of other shielding experiments, the measurements provided various interesting results which are useful on highintensity spallation target or ADS shielding, and will be a benchmark for deep penetration particle simulations, respectively.

Part III Technology and Applications

497

16 Proton Drivers for Particle Production 16.1 An Introduction

During the recent years, extensive research work was undertaken to develop highpower proton accelerators with nominal proton beam energies in the GeV range and designed for a proton beam current of about 5–10 mA and a proton beam power of about 1–10 MW. These parameters are achieved with linear accelerator-, synchrotron-, or cyclotron-based designs. It should also be mentioned that the evolution and utilization of cyclotrons and synchrotrons in particle physics at low energy lead to ﬁrst proposals by Wilson [958] using proton beams to treat cancer more than 60 years ago. A short overview about this application is given in Section 22.1 on page 623. Although the applications vary, most projects rely on the production of spallation neutrons by high-intensity pulsed or continuous neutron sources, on applications of nuclear waste transmutation or energy production usually called energy amplifying. In addition to the application of high-intensity proton accelerators to produce spallation neutrons, proton accelerators as a highintensity proton source, a ‘‘proton driver,’’ can generate neutrino super-beams and other high-energy secondary particles as muons, kaons, pions, antiprotons etc. Such proton drivers can be used as the ﬁrst stage of a neutrino factory and a muon collider. These applications will be discussed in detail in Section 22.3 on page 638. The main difference between a proton driver and a spallation source is the proton energy and the used target material: A proton driver generally has a proton energy of about 2–4 GeV or higher. The used material of the particle production targets may be different from those applied for spallation neutron source targets where usually heavy metal targets are applied. For spallation neutron sources mainly two proton driver approaches are commonly employed. To achieve higher energies, e.g., above ≥ 1 GeV synchrotronbased designs are considered. The energy range covers from as low as 3 GeV to 1 MW beam power, e.g., the J-PARC spallation neutron source [629]. Much higher energies as high as 120 GeV and 2 MW as discussed for the Fermilab main injector upgrade are possible. The linac-based design for high energy and high power is certainly limited in energy by the cost. The existing linear accelerators are LANSCE with 0.8 GeV [630] and SNS with 1 GeV [681] proton energy. There were proposals Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

498

16 Proton Drivers for Particle Production

for proton linear accelerators, e.g., with proton energies of 2.2 GeV/3.5 GeV at CERN [959] and with 8 GeV energy at the Fermilab [960]. For more details see also the ‘‘Scoping studies’’ of the ISS Accelerator Working Group [961, 962].

16.2 Proton Drivers for Spallation Neutron Sources and Secondary Particle Production

Table 16.1 summarizes the existing low- and high-energy proton drivers for secondary particle production and examples for their proposed upgrades. More details and present proposals in this ﬁeld are given in Refs. [963, 964]. Figure 16.1 shows the different classes of existing spallation neutron facilities, continuous wave (CW), long pulse (LP) and short pulse (SP), and examples of high energy and proposed high-intensity proton drivers. A short description of the three classes of high-power spallation neutron sources are given below. More details as the description, the performance parameter and the working scheme are given in Chapter 17 on page 505. The three classes of spallation neutron sources are as follows: • The existing CW facilities are driven by high-energy, high-intensity cyclotrons, e.g., the TRIUMF cyclotron [966] at 0.5 GeV and 0.15 mA proton current and the SINQ isochronous-cyclotron at PSI [627] with a beam power of about 1.2 MW at 0.59 GeV and 2 mA proton current. An upgrade programm for SINQ is underway to raise the beam power up to 1.8 GeV [967]. Cyclotrons are operated essentially in CW mode. A proton current of 5–10 mA seems possible. They could be also an option for ADS applications. Compared to other proton drivers, they could be built at a relatively low cost. • A linac alone could be operated in CW or in LP mode. A high beam power is possible but the construction costs are generally rather high. An example of an LP facility is the LAMPF high-energy, high-intensity linear accelerator with a beam power of 1 MW at 0.8 GeV with proton pulse lengths in the millisecond range. • SP facilities with proton pulses in the microsecond range are usually driven by (a) a combination of a full power linear accelerator with an accumulator or storage ring or (b) by a combination of a partial-energy linear accelerator followed by a rapid cycling synchrotron. Examples for (a) are the LANSCE facility with the LAMPF linear accelerator and the PSR compressor ring of about 80 kW beam power at 0.8 GeV [630], the SNS spallation source [681] with a 1 GeV full power 1.4 MW RF superconducting linear accelerator (SC) and an accumulator. Examples for (b) are the ISIS facility in the UK with a beam power of 160 kW with a 70 MeV linac and a 0.8 GeV synchrotron [643], and the J-PARC spallation source in Japan with a 0.4 GeV linac followed by a 3 GeV synchrotron with a beam power of 1 MW [629]. The combination of a full power linac and a compressor ring allows high intensity due to full energy injection into the compressor ring. The construction costs are relatively high. But with a higher repetition rate multiple target stations are possible. A combination of a

16.2 Proton Drivers for Spallation Neutron Sources and Secondary Particle Production Existing low- and high-intensity proton sources and their proposed upgrades. Data are based on the Snowmass 2001 survey [964, 965] and on various references of the ‘‘Joint Accelerator Conferences Website’’ [963].

Tab. 16.1

Facility

System

KENS-KEK

40 MeV linac and synchrotron 50 MeV linac and synchrotron Linac and one storage ring 70 MeV linac and synchrotron SC linac one storage ring Cyclotron Cyclotron

IPNS-ANL LAMPF-LANL LANSCE-PSR ISIS-RALa SNS-ORNLb SINQ-PSIc TRIUMF -Vancouverd JHF-3GeV JHF-50GeV AGS-BNLe SPS-CERN ESS-Europe SPL I -CERNf SPL II -CERNg

400 MeV linac and synchrotron synchrotron 200 MeV linac and synchrotron synchrotron SC linac and two storage rings Linac Linac

Energy (GeV)

Beam power (MW)

Protons per pulse (×1013 )

0.023

0.15

20

15

0.068

0.3

30

0.8 0.8 0.8

1000 70 200

0.8 0.056 0.160

2.5 2.5

20 50

1.0

1400

1.4

0.59 0.5

1500 250

0.885 0.125

0.5 0.45

Beam current (µA)

4.6

15 940 156

Rep. rate (Hz)

60 cont. cont.

3

333

1.0

8

50 24

15 6

0.75 0.14

32 7.5

0.3 0.5

1.25 3750 3750 1800 1400

0.5 5 5 4 5

4.8

0.17

400 1.334 1.334 2.2 3.5

47 15 17

25

50 75 50

a

Upgrade to a second target station. Proposed upgrade to a proton energy of 1.3 GeV, a beam power of 3.0 MW, and two storage rings. c Proposed upgrade to 1.8 MW beam power. d Proposed upgrade to a 450 µA beam energy. e Proposed upgrade to a proton energy of 28 GeV and beam power 1.0 MW. f Proposal under consideration. g Proposal under consideration. b

partial-energy linac and a synchrotron is a good solution to obtain a high proton energy at relatively low cost. Such a system is naturally appropriate to yield short pulses. But the intensity is limited by the injection energy of the linac into the synchrotron. • An often proposed proton driver is the Fixed Field Alternating Gradient Synchrotron (FFAG) which was intensively studied during the 1950s and 1960s. The FFAG concept have had a rebirth in the year 2000. During the recent years

499

16 Proton Drivers for Particle Production

104 ESS SPL I

Proton beam current [µA]

500

SINQ

103

LAMPF

TRIUMF

102

5 MW beam power

SNS 1 MW beam power

ISIS JHF 30 GeV

PSR-LANSCE

101

IPNS

0.1 MW beam power

KENS

AGS

JHF 50 GeV

100

SPS-CERN

10−1 10−1

100

101

102

103

Proton energy [GeV] Fig. 16.1 Existing proton drivers of spallation neutron sources and examples of high-energy and high-intensity proton drivers for particle physics application.

several workshops at CERN, KEK, BNL, TRIUMF, etc., emphasized the advantage of FFAGs with their high repetition rate and their large momentum acceptance over synchrotrons. Moreover the FFAG is a ring accelerator that has the functions both of acceleration and storage. The ﬁrst ever FFAG for 150 MeV protons was recently built by Mori and co-workers [968] at KEK. Several FFAG applications in the energy range between 0.1 up to several GeV are envisaged and proposed, e.g., for medical applications, for ADS, and for secondary particle production of neutrons or muons [969, 970]. 16.2.1 Synchrotron-Based vs. Linear-Accelerator-Based Spallation Neutron Source

An accelerator-based spallation neutron source is built in general of four parts: (1) accelerator, (2) target, (3) neutron beam line, and (4) experiments and detectors. With these parts one may built SP sources, LP sources, or continuous or steadystate sources (CW). The different realized concepts are described in Chapter 17 on page 505. The trade-off of pulsed sources compared to continuous sources is a high neutron ﬂux versus a certain time structure of the neutron beam. Typical parameters of modern high-power pulsed spallation neutron sources are: • beam power Pproton ∼ 1–5 MW • proton energy Eproton ∼ 0.5–3 GeV • repetition rate f ∼ 10–60 Hz • number of protons per pulse Nproton ∼ 1013 − 4 × 1014 .

16.2 Proton Drivers for Spallation Neutron Sources and Secondary Particle Production

The beam power Pproton (MW) is given as Pproton (MW) = 1.6 × 1016 × Eproton (GeV) × Nproton × f (Hz)

(16.1)

The different proton drivers for spallation neutron sources (1) Synchrotron-based spallation neutron source:

The synchrotron-based source consists of a lower energy proton linac with proton energies between 70–400 MeV, depending on the concept, and a rapid cycling synchrotron. It works in the following way: • An ion source generates high-intensity H− beams. • A low-energy linac accelerates H− pulses of about ∼ 1 ms length to 70 and 00 MeV, depending on the concept. • The H− particles are injected into the synchrotron via charge exchange processes, in which the electrons are stripped by a foil, e.g., made of carbon. The electrons are dumped and the H+ particles, the protons, are accelerated in the ring of the synchrotron up to several GeV. • The accelerated protons can be extracted in a single turn onto a spallation target with pulse lengths of about 1 µs or less. • The process of injection and extraction is repeated typically 10–60 times every second. (2) Linear-accelerator-based spallation neutron source: The linear-accelerator-based spallation neutron consists of a full-energy linac and an accumulator ring also named compressor- or storage ring. It works in the following way: • An ion source generates high-intensity H− beams. • A linac accelerates H− pulses of about ∼ 1ms length to ∼ 1–1.5 GeV, depending on the concept. • The H− particles are injected into the accumulator ring via charge exchange processes, in which the electrons are stripped by a foil, e.g., made of carbon. The H+ particles, the protons, are accumulated in the ring. The injection process usually takes several hundreds to a few thousand turns. • The accumulated protons can be extracted in a single turn onto a spallation target with pulse lengths of about 1 µs. • The process of injection and extraction is repeated 10–60 times every second. Advantages and disadvantages of synchrotron and linear accelerator proton drivers for spallation neutron sources • Compared with a linac-based spallation source, a synchrotron-based one has the following advantages: (1) for the same beam power the investment is much less. A proton synchrotron is less expensive to built than a proton linac with the same proton energy. (2) For the same beam power, one could operate the synchrotron

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16 Proton Drivers for Particle Production

at lower beam intensity, because the beam energy could be higher. (3) Because the injecting linac has a lower beam power, the stripping foil technology is easier to handle, e.g., lower energy deposition, lower secondary particle production, and larger beam losses may be tolerated. (4) A high-intensity accumulator is a DC machine, which has usually a problem in the intensity limitation due to the so-called e–p instability1) . This is never been observed in synchrotron which is an AC machine. • The disadvantages of a synchrotron-based spallation source are: (1) A synchrotron, an AC machine, is more difﬁcult to built as an accumulator ring, a DC machine. The hardware consists of large aperture AC magnets, rapid cycling power supplies, eddy current effects in the coils and the beam pipe, high power tunable RF systems, etc. (2) Also AC machines are more difﬁcult to operate than DC machines. Therefore, the reliability is much lower than that for DC machines [965]. Details of the design concepts of linear accelerator and synchrotron-based spallation neutron sources are discussed in more detail in a lecture by Chou [965]. The principles and up-to-date aspects of RF linear accelerators can be found in the book by Wangler [972]. A survey of the design and the operational experience of existing and proposed proton facilities with emphasis on synchrotrons and accumulators are described in reviews of Refs. [973, 974]. The research and development of accelerators for spallation neutron sources have opened many other applications of high-intensity proton sources. Some examples will be given in the following sections. For more details, the interested reader may contact the ‘‘Joint Accelerator Conferences Website’’ [963]. 16.2.2 The Beam Loss Issue at High-Intensity Proton Accelerators

The beam loss and the beam loss control are one of the most challenging problems in high power proton accelerators. The most demanding requirement in the design of an accelerator chain is to keep the accelerator complex under hands-on maintenance [551, 873, 975]. For a 1 MW proton beam power, e.g., 1% beam loss results in a loss of 10 kW or about 6.24 × 1013 protons per second which may exceed the beam power on targets for most of the existing physics experiments. A rule of thumb, based on the experience on the LAMPF linear accelerator [976] and on simulations, is that the uncontrollable beam loss should have an upper limit of about 1–2 W/m in average which is a loss, e.g., for a 1 GeV, 1 MW machine of about 6 × 109 protons per meter on average. Such a goal is not impossible but very demanding. 1) The e–p instability is a phenomena due to electron cloud production by beam-residual gas ionization or proton beam losses in the vacuum chamber walls [971].

16.2 Proton Drivers for Spallation Neutron Sources and Secondary Particle Production

High-level losses have bad impacts, e.g., • on the accelerator reliability by out-gassing, spark down, radiation damage of cable, electronics, power supplies, etc., • on accelerator availability by structure activation, and cooling time before maintenance, • on the accelerator radiological protection cost, e.g., the shielding requirements which are based essentially on the assumed beam losses. It is distinguished between two types of beam losses: controlled and uncontrolled losses. The controlled losses are occurring at choppers, special designed collimators, and beam dumps where they are collected. These losses therefore can be localized and remote handling with special shielding can be implemented. The uncontrolled losses are spread over the entire machine and must be kept as low as possible. Many sources of these uncontrolled losses are possible by beam misalignment or mismatch, accelerator elements error, accelerator elements failures, H-stripping on residual gas or by magnetic ﬁeld, and scattering on residual of beam particles. The mentioned uncontrolled losses are very similar for all machines, linacs, synchrotrons, and accumulators. But there are minor differences: (1) an important difference is between accumulator and synchrotron. Because the injected beam power of the injection linac for a synchrotron is lower compared to the injection beam power for an accumulator ring, a higher beam loss can be tolerated. This is an advantage of a synchrotron machine with high proton beam power. (2) In circular accelerators as synchrotrons the beam stability is a more important issue compared to linacs. Any small effect which tends to ‘‘blow up’’ the beam is repeated many times and may result in a disastrous loss to the beam pipe walls.

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17 The Accelerator-Based Neutron Spallation Sources 17.1 Introduction

Since 50 years ﬁssion-based research reactors were the ultimate tool for scientists to study the structure, dynamics, and magnetic properties of matter, the effects of radiation on the properties of materials, the production of new isotopes, and the isotopic composition of elements as well as the physics of nuclei. But it was realized that the available time averaged neutron ﬂux of research reactors with the advent of the high-ﬂux reactor HFR-ILL at Grenoble, France [653], is more or less saturated. To still further increase the time averaged neutron ﬂux would be extremely difﬁcult due to the heat dissipation of almost 200 MeV per useful neutron in a ﬁssion reactor. Also the lifetime of the reactor core will be extremely shortened at higher power densities due to the fast burn-up of the fuel. Neutron production in spallation reactions induced by energetic particles in heavy targets has been observed already in the late 1940s. Considered as genesis or originator of all spallation sources are the spallation sources of KENS [679, 977] at KEK, Japan, IPNS [641, 978] at ANL, USA the TRIUMF source [979, 980], Canada, and the WNR and LANSCE spallation facility [630, 981] at LANL, USA. Earlier studies during the 1960s for a very intense source were considered at the ING project (Intense Neutron Generator) at Chalk River, Canada, based on PbBi targets with a tremendous beam power of 65 MW (1 GeV proton beam energy) [58]. However the project was terminated in 1968. A very good review of early work before 1978 can be found in Ref. [982]. It should also be mentioned here that a very ambitious project, the German high-intensity spallation neutron source SNQ [601] with 5 MW beam power and an incident proton energy of 1.1 GeV, laid the cornerstone for all future high-intensity spallation neutron sources. SNQ was a joint project between the German research centers J¨ulich and Karlsruhe during 1980–1985. As a result of a continuous progress in accelerator technology, the construction of powerful intense spallation sources became possible, providing new opportunities for solid-state physics, life and biology research, nuclear science, and material science. In fact, during the 1980s and 1990s a variety of major spallation source projects have been initiated, constructed, built, commissioned or are now even under construction: (a) the most powerful continuously running spallation source Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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17 The Accelerator-Based Neutron Spallation Sources

of 1.0 MW beam power SINQ at PSI, Switzerland [478, 627, 983, 984], (b) the shortpulsed running spallation source 0.16 MW ISIS at the Rutherford and Appleton Laboratory, UK [643, 985], (c) the short-pulsed spallation source 2 MW SNS at ORNL, USA, [681, 986] recently commissioned, (d) and the short-pulsed spallation source 1–5 MW J-PARC at KEK/JAERI, Japan [628, 629, 987]. Among the latter projects are the 5–10 MW European Spallation Neutron Source ESS in Europe still under study 1) [729, 873]. Also China is on the way to construct in Dongguan, Guandong, a pulsed spallation neutron source CSNS with a beam power of 0.12 MW and a proton energy of 1.6 GeV on a tungsten target [988]. This facility with an upgrade capability up to 0.5 MW beam power will complement the existing China Advanced Research Reactor (CARR) and the synchrotron light sources at Hefei, Beijing, at Hsinchu, and at Shanghai [988, 989]. In Russia at the INR in Moscow, a linear accelerator with 0.6 GeV proton energy and with an average proton current of 0.5 mA or 0.3 MW is operating as a multipurpose neutron complex and a beam therapy irradiation facility [990, 991]. Figure 17.1 illustrates the historic trend of the thermal neutron ﬂux intensity of research reactors and spallation sources as time averaged and peak thermal ﬂuxes. To complete the picture of neutron sources, a summary survey of existing research reactors is given in Table 17.1. The performance parameters of high-ﬂux nuclear reactors used for neutron research are given in Table 17.2 also for comparison. With intense, short-pulse or continuous neutron beams from accelerator-based sources it is possible to study a wide range of scientiﬁc and applied technical problems. Powerful neutron sources, such as subcritical spallation/ﬁssion hybrid target systems [992–995], provide in future a basis for various, potentially important applications often entitled as ‘‘accelerator-driven systems’’ (ADS). For example, such facilities may be used to achieve the incineration or transmutation of radioactive nuclear waste [682, 708, 996–999] or to effectively produce electrical energy and as a byproduct tritium [1000] for the start-up phase of future D–T fusion reactors. It is also important to note that spallation-driven neutron-producing facilities show a greater promise for future improvements in peak neutron intensities (cf. Figure 17.1) than ﬁssion reactors do. Accelerator-based spallation neutron sources present an inherently safe way to produce neutrons, because the neutron production stops when the proton beam is turned off. It also produces few hazardous materials compared to research reactors. All these factors underscore the advantage of spallation neutron sources compared to reactors. Combining all the possible applications of high-intensity spallation systems could lead to the construction and the operation of ‘‘multipurpose-facilities’’ – an example is the J-PARC project under construction in Japan [629, 987].

1) In the original ESS feasibility study of 1996 [551] the spallation source was planned to have two short-pulse target stations and 5 MW power. A further concept favors both a

so-called long pulse and a short-pulse target station with 5 MW each or a long-pulse system with a beam power of 10 MW [480].

17.2 Research Reactors or Continuous/Pulsed Spallation Sources? 1018 Thermal neutron flux [n/cm2 s]

SNS, USA

MTR NRU

1015 NRX

HFIR

HFBR

ILL KENS

X-10

1012

ESS J-PARC ISIS LANSCE FRM-II IPNS SINQ-II SINQ

Tohoku Linac

109

Berkeley 37-inch cyclotron

106

CP-2

Fission reactors Particle driven (cw)

CP-1

Particle driven (pulsed) Trendline reactors

0.35 m Ci Ra-Be source

103

Trendline pulsed sources Chadwick

100 1920

1930

1940

1950

1960

1970

1980

1990

2000

2010

2020

Year

Fig. 17.1 The development of the available thermal neutron ﬂux for reactor- and spallation-based neutron sources given as a historical trend.

17.2 Research Reactors or Continuous/Pulsed Spallation Sources?

Neutron ﬂuxes from traditional research reactors have nearly reached their limits because of heat dissipation in the reactor core of ﬁssion-driven research reactors. The precision and resolution of neutron scattering experiments depend highly on increasingly better neutron monochromatization. Better monochromatization in turn entails less intensity or lower precision. Consequently pulsed spallation neutron sources with orders of magnitude higher peak or continuous ﬂuxes were built. Examples are the spallation neutron sources in USA, the SNS with 1.4 MW beam power [681] and in Japan, the J-PARC 1.0 MW source [629], and the continuous spallation neutron source SINQ at PSI in Switzerland [627]. Others are projected and planned, e.g., ESS 5 MW pulsed spallation neutron source with an expected thermal neutron peak ﬂux of up to 2 × 1017 neutrons ×cm−2 × s−1 [551] and the European initiative for a long-pulse ESS of about 5–10 MW beam power [480, 1001]. The new generation spallation neutron sources will yield a tremendous progress. Its intensity increases by orders of magnitude will revolutionize the neutron science. To convey an impression of the potential power of an pulsed neutron spallation source, e.g., the ISIS spallation neutron source [643], produces short pulses of an even higher peak ﬂux than those provided by the world’s strongest research reactor at the Institute Laue-Langevin [653]. But the peak intensity of ISIS is only about 1/80 of that projected for ESS or about 1/35 of SNS, respectively, as shown in Table 17.17 on page 559. The need for both reactor-based continuous and accelerator-based pulsed neutron sources has long been realized by the neutron science community. Due to the dramatic improvements in accelerator technology in recent years, generally neutron

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17 The Accelerator-Based Neutron Spallation Sources Tab. 17.1 Existing research reactors in operation worldwide (data are based on [1002–1004]).

Reactor neutron sources in operation

Beam power (MWth)

Thermal neutron ﬂuxa ((n) cm−2 s−1 )

Europe: LVR-15, NPL, Prague, Czech Republic HFR ILL, Institut Laue-Langevin, Grenoble, France ORPHEE, LLB, Leon Brillouin Laboratory, Saclay, France BERII, Helmholtz-Zentrum, Berlin, Germany FRG-1, GKSS Geesthacht, Germany FRM II, Munich-Garching, Germany BRR, KFKI, Budapest, Hungary HCR, RID, Delft, The Netherlands JEEP-II, The Neutron Laboratory, Kjeller, Norway IB-2, Frank Laboratory of Neutron Physics, Dubna, Russia North America

10 58.3 14 10 5 20 10 2 2 2

5 × 1013 1.5 × 1015 3 × 1014 2.5 × 1015 1.4 × 1014 8 × 1014 2 × 1014 2 × 1013 2.3 × 1013 1 × 1013

HFIR, High Flux Isotope Reactor, Oak Ridge, USA MURR, University of Missouri Research Reactor Center NRU, Canadian Neutron Beam Centre, Chalk River, Canada Asia

85 10 125

1 × 1015 − 3 × 1014

OPAL, Bragg Institute, ANSTO, Australia HNRR, China Institute of Atomic Energy, Beijing, China Dhruva Research Reactor, BARC, Mumbai, India HANARO, KAERI, Korea JRR-3, Japan Atomic Energy Agency, Tokai, Japan KUR, Kyoto University Reactor, Kyoto, Japan

20 60 100 30 10 5

3 × 1014 8 × 1014 1.8 × 1014 1 × 1014 1 × 1014 4 × 1012

1.25

7 × 1013

0.002

8 × 107

Continuous spallation source SINQb n cm−2 s−1 , Paul Scherrer Institut (PSI), Switzerland Proton driven 9 Be(p, xn) source LENS, Indiana University Cyclotron Facility, USA a b

Typical maximum unperturbed ﬂuxes. Upgrade to 1.8 MW in progress would yield a thermal neutron ﬂux of about 1 × 1014 .

pulses can be produced with much higher intensity than that available from continuous sources. Furthermore, unlike the situation at a continuous neutron source, pulsed sources allow the determination of the kinetic energy of individual neutrons using ‘‘time-of-ﬂight’’ (TOF) methods and making ‘‘movies’’ of molecules in motion. Like a ﬂashing strobe light providing high-speed illumination of an object, the spallation neutron sources in the MW beam power range, as for example, will produce pulses of neutrons every 20 ms with 30–80 times more neutrons than are produced at the most powerful pulsed or continuous neutron sources currently available. Table 17.1 gives on overview about research reactors with their thermal

17.2 Research Reactors or Continuous/Pulsed Spallation Sources? Tab. 17.2

High-ﬂux research reactors with their main parameter regime.

Reactor type

HFR-ILL (Grenoble) HFIR (ORNL) FRM-II (Munic) a

Thermal power (MW)

Core cooling

58.5

D2 O

85.0

H2 O

20.0

H2 O

Enrichment

All highenriched 235 U

Reﬂector

Φthermal Neutron ﬂuxa (n/cm2 s)

D2 O

1.5 × 1015

Be

1.0 × 1015

D2 O

8.0 × 1014

Typical maximum unperturbed ﬂuxes.

power in MWth operated in different countries over the world, whereas Table 17.2 summarizes some detailed performance parameters of advanced neutron research reactors. For comparison the most powerful continuous spallation neutron source SINQ [627] is also mentioned in Table 17.1. With an upgrade to 1.8 MW beam power [967], the thermal neutron ﬂux is boosted to a value comparable with research reactors. Technical details and performance parameter of spallation neutron sources with proton drivers with a proton beam power ≥ 0.1 MW are given in Section 17.3. A summary is given in Table 17.17 on page 559. Many of the world’s nuclear reactors are used for research and training, materials testing, or the production of radioisotopes for medicine and industry. They are basically neutron factories. The research reactors are much smaller than power reactors, and many are even located on university campuses. There are about 280 such reactors operating in 56 countries. Their power is typically designated in megawatts thermal (MWth). Most of them have a power lower than 100 MWth, compared with 3000 MWth for a typical light water (LWR) power reactor. In fact, the sum of the total power of the world’s research reactors is little over 3000 MWth. Research reactors are simpler than power reactors and operate at lower temperatures. They need far less fuel, and far less ﬁssion products build up as the fuel is used. On the other hand to gain a high intensity, their fuel requires more highly enriched uranium, typically up to 20% 235 U, although for very high-neutron ﬂuxes, the use of high enriched fuel, e.g., 93% 235 U is recommended. One special feature of research reactors is neutron activation to produce the radioisotopes, widely used in industry and medicine, by bombarding particular elements with neutrons. For example, 90 Y microspheres to treat liver cancer are produced by bombarding 89 Y with neutrons. The most widely used isotope in nuclear medicine is 99 Tc, a decay product of 99 Mo. It is produced by irradiating a target of 235 U foil with neutrons and then separating the molybdenum from the other ﬁssion products in a hot cell. Most 99 Tc production has been using high enriched uranium targets, but increasingly low enriched uranium is favored. Research reactors can also be used for industrial processing. Neutron transmutation doping makes silicon crystals more electrically conductive for use in electronic

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17 The Accelerator-Based Neutron Spallation Sources

components. In test reactors, materials are subject to intense neutron irradiation to study changes. For instance, some steels become brittle, and alloys which resist embrittlement must be used in nuclear reactors (cf. Chapter 6 on page 215). Like power reactors, research reactors are covered by IAEA safety inspections and safeguards, because of their potential for making nuclear weapons. India’s 1974 atomic bomb explosion was the result of plutonium production in a large, but internationally unsupervised research reactor. 17.3 Spallation Neutron Sources

In the following sections, a short description will be given of operating, being in commission or planned spallation neutron sources with a proton beam power ≥0.1 MW. A summary of the design and the operational parameters of the different spallation sources is given in Table 17.17 on page 559. 17.3.1 The LANL Spallation Neutron Source MLNSC and the Los Alamos Neutron Science Center LANSCE

The spallation source concept at the Los Alamos National Laboratory (LANL), USA, is based on the Los Alamos Meson Physics Facility (LAMPF) – a three stage, high-intensity proton accelerator. The LAMPF machine was the ﬁrst truly high current medium energy proton linear accelerator, which operates at a beam power of 1 MW. This medium-energy linear accelerator was constructed with the primary aim to study the production of pions and their interaction with nuclei [680, 1005]. Since 1990 and with the closeout of the nuclear physics program in 1995, the mission of the LAMPF accelerator complex was redirected to the development and use of spallation neutron sources for research and applications [630, 1005–1007]. The accelerator complex is now called the Los Alamos Neutron Science Center (LANSCE). The LANSCE, which formerly referred to the Manuel Lujan Jr. Neutron Scattering Center (MLNSC) now named as Lujan Center, comprises the high power 1 MW and 0.8 GeV proton linear accelerator (LAMPF), a proton storage ring (PSR) with about 100 KW and 0.8 GeV proton energy, a pulsed spallation neutron source at the Lujan Center, commissioned in 1977 and the Weapons Neutron Research (WNR) experimental facility, a proton radiography facility, a large variety of spectrometers at the Lujan Center. A material test station (MTS) with fast neutron irradiation capabilities is planned. Figure 17.2 shows an artist’s view of the spallation neutron source complex. Indicated in Figure 17.2 is the PSR storage ring, the proton beam line from the PSR bombarding the spallation target from the top, the experimental area around the spallation source and the LAMPF linear accelerator, which runs parallel to the road as shown in the right of the ﬁgure. Details of the layout of the LANSCE user facility are shown in Figure 17.3. The LANSCE complex comprises the following facilities and areas:

17.3 Spallation Neutron Sources LAM

PF

2 1

3

1 Proton beam from LAMPF 2 PSR storage ring 3 Target area 4 Experimental area 5 Support building

4

5

Fig. 17.2 An artist’s view of the LANSCE/PSR facility with the pulsed spallation neutron target source as given in 1990 by Lisowski et al. [680].

Proton Linear Accelerator (LAMPF) • two ion sources producing H+ and H− beams; • a drift tube linear (DTL) accelerator with an energy range from 0.75 up to 100 MeV; • a nonsuperconducting (NC) side-coupled linear accelerator (SCL) with an energy range from 100 up to 800 MeV. Weapons Neutron Research Facility (WNR) • applying research with high-energy neutrons and protons for nuclear science and nuclear applications; • WNR accepts H− beams directly from LAMPF up to 5 µA with a pulse width of about 125 ps FWHM allowing neutron TOF measurements with a time resolution of less than 1 ns. • It is also possible to transport the proton beam of the storage ring PSR to the WNR with a repetition rate of 20 Hz, but with the current limitation of 5 µA. A ‘‘white’’ neutron source with useful neutron energies from about 100 MeV to above 600 MeV produced by protons striking a tungsten target are generated with neutron collimation for different angles relative to the proton direction for six ﬂight paths (cf. Figure 17.3). Manuel Lujan Jr. Neutron Scattering Center (Lujan Center) The spallation neutron source of the Lujan Center uses the 800 H− beam to produce thermal, epithermal, and cold neutrons in the meV–keV range for neutron scattering research. The PSR compresses the 750 µs LAMPF accelerator pulses to 125 ns (FWHM) long pulses at a rate of 20 Hz. The protons are hitting a light water cooled split-tungsten target with ﬂux-trap and backscattering moderators. The average proton beam power and

511

17 The Accelerator-Based Neutron Spallation Sources Transition and matching

+

Isotope production + facility (H )

H Source −

H Source

8.3 ms

Area B Ultracold − Neutrons (H )

Area C Proton radiography − facility (H )

0.8 GeV Drift tube linear accelerator

DTL

Area A (inactive, but proposed as advanced fuel cycle test facility, H+)

Side-copuled linear accelerator SCL

Length about 730 m Area D − (H )

Accelerator pulse rate 120 per second

Lujan center

H- Intensity

512

PSR 7 6

Time Pulses of 20 Hz to Lujan Center

Pulses of 100 Hz to WNR

ER-1

4 3 120L 5

90R

60R 90L

30R 15R

WNR

15L 30L

Fig. 17.3 The different experimental areas of the LANSCE user facility (after Lisowski et al. [1005]).

beam current are about 100 kW and 0.125 mA, respectively. The above parameters lead to an average thermal neutron ﬂux of 1 × 1012 cm−2 s−1 and a peak thermal neutron ﬂux of 2.3 × 1015 cm−2 s−1 . The instrument suite at the Lujan Center is depicted in Figure 17.4 as given in Ref. [1007]. Isotope production facility Facility comprised of a 100 MeV proton beam line from LANSCE to a target segmented in different production regions to allow optimized production of a wide range radioisotopes for medical diagnostics, treatment, and research. Proton radiography facility (dRAD) The facility provides 50 ns wide H− beam pulses with about 109 protons for the study of dynamic processes using the proton pulses and a magnetic lens image system. Because protons interact through both the strong nuclear and the electromagnetic force, transmission measurements allow simultaneous imaging and determination of material properties with very high resolution [1008]. The results of the radiography are multiframe radiographs that resolve object features with 1 mm accuracy using samples of up to 60 g/cm2 . Interested readers may refer to, e.g., [1009, 1010]. Ultracold neutron source (UCN) The UCN sources operational at LANSCE [1011] use solid deuterium at 5 K and moderate neutrons from a tungsten spallation target coupled to a set of different moderators of graphite/beryllium and cold polyethylene. With a proton beam current of about 4 µA, this will be the most

17.3 Spallation Neutron Sources High-pressure HIPPO environ. 4 High-intensity powder

Fp5

FDS 7 SCD 6

HIPD 3

SPEAR 9 LQD 10

Residual stress

Asterix 11a

SMARTS 2

Inelastic scat. Protein crystallo.

Single crystal Vibrational spectr. Hi pressure diffraction and tomography

ER-1

Pair distribution

NPDF 1

ndpg 12 PHAROS 16

PCS 15

DANCE ln500 14 13

513

Reflectometers soft matter polarized beams Small angle

Backscattering INS

Electric dipole moment of n High-resolution inelastic

Fig. 17.4 The instrument suite and ﬂight paths of the Lujan Center with a short description of the research topics (after [1005, 1007, 1012]).

intense UCN source. Fundamental physics measurements such as, e.g., the betadecay asymmetry resulting from polarized UCN decay is envisaged [1005] (see also Section 22.4 on page 642). The Lujan TOF spectrometers for neutron scattering studies of condensed-matter are located in two experimental areas, indicated with ER1 and ER2 in Figure 17.3 and are part of the Lujan Center complex. The instruments installed at the Lujan Center are characterized in the following way and illustrated in Figure 17.4: • crystallography: NPDF, HIPD, HIPPO, SCD, PCS; • engineering and strain: HIPPO, SMARTS, NPDF; • disordered materials: NPDF, HIPD, HIPPO; • large-scale structures: LQD, SPEAR, Asterix; • excitations: Pharos, IN500, FDS; • magnetism: Asterix, Pharos, HIPD, HIPPO; • biology: PCS, SPEAR, LQD. The Neutron Powder Diffractometer (NPDF), shown as one example of the many instruments in Figure 17.5, is a high-resolution total-scattering powder diffractometer located at ﬂight path 1 and 32 m from the spallation neutron target. It comprises 20 detector panels with a total of 160 position-sensitive 3 He detectors in the backscattering region of the instrument. The neutrons for the instrument are produced by a chilled water moderator of 283 K of the spallation neutron source.

514

17 The Accelerator-Based Neutron Spallation Sources 148° bank

119° bank 90° bank

Neutron beam

40° bank

Sample area Sample

−148° bank

−119° bank −90° bank

−40° bank

Fig. 17.5 The neutron powder diffractometer (NPDF) at the Lujan Center (after Proffen and Encinias [1012]).

The neutron beam size is about 5 cm high and 1 cm wide. The NPDF is designed for pair distribution function (PDF) studies of disordered and nanocrystalline materials, but it is equally well-suited for high-resolution crystallographic studies. Further information can be found in Ref. [1012]. 17.3.2 The Rutherford and Appleton Laboratory Short-Pulsed Spallation Neutron Source ISIS

The ISIS2) spallation neutron source, prior known as the SNS (Spallation Source) was approved in 1977 and produced the ﬁrst neutron beam in 1984. The original concept of the accelerator and target complex was presented by Mannig [1013] and by Carne [640, 1014] at the 3rd and 4th Meetings of the International Collaboration of Advanced Neutron Sources (ICANS-II/IV) and described also in Refs. [642, 1015, 1016]. ISIS is the major facility at the Rutherford Appleton Laboratory, UK, and has been operating for over twenty years. ISIS is currently expanding with a construction of a second target station that will lead to new opportunities in soft condensed matter, biomolecular sciences, advanced materials and nanoscale science. For further reading see Refs. [643, 1017]. The ISIS spallation neutron source complex is illustrated in Figure 17.6 and comprises the following facilities and areas: 2) ISIS is not an acronym. It refers to the ancient Egyptian goddess and the local name for the river Thames.

17.3 Spallation Neutron Sources 70 MeV H− linac 52 m

H− Ion source MICE project

First target station TS-1 Iris Osiris Crisp Surf Loq

Prisma rotax Sandals

T

Het

Maps

Emu Musr Hifi EC muon facility

Pearl

G

Extracted proton beams

Let

43 ≈1

Hrpd

rod

Nim

Engin-x

m

em

Mari

Sxd

Merlin

Vesuvio

0.8 GeV proton synchrotron

RIKEN muon facility ca Argus s o

is

ar

l Po

Wish

Second target station TS-2

Offspec Inter Polref Sans2d

≈ 150 m

Fig. 17.6 The ISIS spallation source complex with the injection linac, the synchrotron, the ﬁrst target station TS-1, the second target station TS-2, and most of the experimental facilities [643, 1017] (Courtesy of ISIS).

Proton injection linac and the rapidly cycling proton synchrotron (RCS) The ion source of the injector linac, which produces H− -ions, is fed with hydrogen gas together with hot caesium vapor. The H− -ions acquire an energy of 35 keV and then passed into the radio frequency quadrupole (RFQ) and accelerates the ions up to 665 keV. A four-tank 202.5 MHz Alvarez H− drift tube linac (DTL) accelerates the beam from 665 keV to 70 MeV. The linac pulses transported to the synchrotron are ∼200–250 µs long with a typical amplitude of 22–25 mA. Final acceleration of the beam occurs in the synchrotron. The 163-m circumference rapidly cycling proton synchrotron (RCS) was built in the early 1980s. Ten dipole bending magnets are used to keep the beam traveling around on a circular orbit of radius 26 m, while quadrupole magnets

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17 The Accelerator-Based Neutron Spallation Sources

keep the beam tightly focused. On the injection entry the H− beam is stripped off its electrons by a 0.25 µm thick aluminum oxide stripping foil. The resulting protons are accumulated in the synchrotron over approximately 130 revolutions. The advantage of this charge exchange injection scheme is that a larger number of protons ∼2.8 × 1013 can be accumulated in the synchrotron. At the end of the 10-ms long acceleration cycle the 0.8 GeV beam is extracted by six fast kicker magnets and a septum magnet as two proton pulses each ∼100 ns long and separated by ∼320 ns. The entire acceleration process is repeated 50 times per second, so a mean current of 200 µA is delivered. More details are given in [1017]. As illustrated in Figure 17.6 all protons are transported to either a 155-m long transport line to the target station TS-1 or along a 143-m long line to the target station TS-2. It should be mentioned that the proton beam injection onto the ISIS targets is horizontal. This technique minimizes the beam losses and the induced radioactivity compared to the vertical proton beam injection onto the target which is accomplished at the spallation sources of the LANSCE at Los Alamos and SINQ at PSI. Target stations TS-1 and TS-2 with their instruments The TS-1 target was originally built with depleted uranium [1018], but changed in 1990 to tantalum, and then in 2001 to tantalum-coated tungsten. The target consists of a series of plates with different thicknesses cooled by D2 O and is surrounded by a Be reﬂector with two ambient temperature H2 O moderators above the target and two cryogenic moderators below, one consists of liquid methane at 100 K and the other is liquid hydrogen at 20 K (cf. Chapter 18 on page 561). The TS-2 target, recently commissioned, is a cylindrical tantalum-coated tungsten target 68 mm in diameter and 307 mm long and cooled through the surface by D2 O. TS-2 target station is optimized for the utilization of cold neutrons. The TS-2 conﬁguration consists of two moderators in wing geometry (cf. Section 8.3 on page 269, Figure 8.12), a 25 K decoupled solid methane and a 25 K coupled liquid hydrogen moderator. The target and the moderators are surrounded by Be rod reﬂector contained in a vessel cooled by D2 O [1019]. To operate both targets simultaneously, the beam for TS-2 is obtained by deﬂecting one pair of pulses out of every ﬁve pairs of pulses from the extracted proton beam line to TS-1. This means the TS-2 will run with a repetition rate of 10 pps, whereas the original repetition rate for TS-1 is reduced from 50 to 40 pps [1017]. The TS-1 target station supports 18 neutron beam lines with the following characterized instruments: • crystallography: GEM, HRPD, PEARL, POLARIS, ROTAX, SXD; • engineering: ENGIN-X; • disordered materials: GEM, SANDALS; • large-scale structures: CRISP, LOQ, SURF; • excitations: ALF, HET, MAPS, MARI, MERLIN, PRISMA; • molecular spectroscopy: IRIS, INES, OSIRIS, TOSCA, VESUVIO; VESTA; • muons: ARGUS, DEVA, EMU, MuSR, RIKEN; • neutrinos: MICE, KARMEN.

17.3 Spallation Neutron Sources Neutron beam lines to instruments

Target remote handling cell

Target service area

Proton beam 0.8 GeV

Shielding

Tungsten target

Fig. 17.7 The ISIS TS-1 target station with the 18 neutron beam channels, the position of the neutron- producing tungsten target, the shielding, and the target remote and service cell (after [643]).

Figure 17.7 schematically shows a horizontal cut of the target station TS-1 with 18 neutron beam lines for the instruments, already illustrated in Figure 17.6, the neutron-producing tungsten target, the remote handling cell for maintenance and repair operations, and the service area containing the cooling equipment for target, moderators and reﬂector unit. More engineering details are given in Chapter 18 on page 561. The absolute neutronic performance of ISIS was determined from gold foil activation measurements [1020] during the commissioning phase for an incident proton beam of 0.55 GeV. The predicted values from the measurements were 2.3 × 1010 , 1.9 × 1010 , and 2.1 × 1010 neutrons × eV−1 sr−1 µA−1 s−1 100 cm−2 , for the ambient water moderator, the methane moderator, and the cold H2 moderator, respectively. To normalize these values at an incident proton energy of 0.8 GeV and a 200 µA proton beam current, the values has to be multiplied by a factor of 3.16 × 102 due to the higher beam energy and the higher proton beam current of 200 µA3) . The ﬁnal results were found in an excellent agreement with the design values [1016, 1020]. The TS-2 target station supports with its 19 neutron beam lines seven new instruments in surface science, disordered materials, magnetic diffraction, small angle neutron scattering, and slow dynamics. In a second phase, additional instruments will be considered. The instruments at the TS-2 target station are characterized in the following way: • reﬂectometers: Inter, OffSPEC, Polreff; • small-angle scattering: Sans2d; 3) The neutron production is known to scale as (Eproton – 120) [1016], where Eproton is the proton energy in MeV, giving a reduction of

a factor of about 1.58 for the 0.55 GeV beam used in the commissioning run.

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17 The Accelerator-Based Neutron Spallation Sources

Cryostat

6.5 m disc chopper

Neutrons from target

10.0 m disc chopper Sample can

Diffraction detectors

Mica analyzer bank Detector bank (mica-analyzed) Transmitted beam monitor

Curved glass guide Converging supermirror guide Incident beam monitor Graphite analyzer bank

Neutrons to beam

Detector bank (graphite-analyzed)

Fig. 17.8 The ‘‘high-resolution quasielastic and inelastic neutron scattering spectrometer’’ IRIS (after [1021, 1022]).

• intermediate range order: Nimrod; • high-resolution magnetic diffraction: Wish; • high-resolution spectroscopy: Let. As an example, an artist’s view of the ‘‘High Resolution Quasi-Elastic and Inelastic Neutron Scattering Spectrometer’’ IRIS with long d-spacing diffraction capabilities is shown in Figure 17.8. IRIS is a TOF inverted-geometry crystal analyzer spectrometer designed for quasielastic and low-energy high-resolution inelastic spectroscopy installed at target station TS-1. Neutrons scattered from the sample are energy-analyzed by means of Bragg reﬂection from one of two large single crystal arrays (pyrolytic graphite and muscovite mica) in close to backscattering geometry. Some important parameters concerning the instrument are moderator (hydrogen cooled to 25 K), wavelength limiting choppers disk choppers at distances of 6.3 and 10.0 m. The primary neutron ﬂight path is a curved neutron guide of 2.35 Km radius with 65 mm vertical and 43 mm horizontal cross-section feeding a 2.5 m focusing super mirror guide to the sample. Sample position is at a distance of 36.41 m from the moderator and with beam size at sample 30 mm (vertical) × 20 mm (horizontal). Intensity at sample is 5.0×107 cm−2 s−1 (white beam at full ISIS intensity). Muons are also produced at ISIS using a thin carbon target in the proton beam before the neutron target at the target station TS-1. The muons are produced by colliding the ISIS proton beam with a 10-mm thick carbon target 20 m upstream of the neutron target. The collisions of the protons with the carbon target produce pions which decay with a mean lifetime of 26 ns into muons. The muon beam is fully polarized, and this polarization is maintained as the beam is transported to the muon spectrometers. The muon target uses 2–3% of the proton beam.

17.3 Spallation Neutron Sources

Envisaged upgrade plans After the construction of the second target station TS-2 there are several upgrade plans envisaged for Rutherford and Appleton Laboratory complex, which are described in [1017, 1023–1025]. These are (1) a new 180 MeV H− linac injector, which could raise the ISIS beam power to 0.5 MW, (2) a multimegawatt upgrade, e.g., construction of a new synchrotron, operating either at 3 GeV and 50 Hz or at 8 GeV and 16.7 Hz, with injection directly from the existing ISIS 0.8 GeV beam, or to increase the beam power by taking the 300 µA current expected from the present ISIS synchrotron and increase the energy from 0.8 up to 3 GeV, which will result in a beam power of ∼1 MW, and (3) to construct a second high-energy synchrotron and stacked above the ﬁrst, with both operating at 25 Hz. An energy of 3 GeV could be used for an upgraded neutron source and the higher acceleration would be to 6 GeV for a 5 MW neutrino proton driver [1023]. The international Muon Ionization Cooling Experiment (MICE) has been proposed to demonstrate the feasibility of ionization cooling of muon beams. This can be considered as one of the major technological jump needed toward the development of a ‘‘neutrino factory’’ for the production of pions from a megawatt proton beam. The MICE muon beam line is currently under construction. The ISIS proton beam hits the removable MICE target, producing lots of pions. The pions decay in a solenoid channel and the muons with the right momentum are selected by a dipole magnet [1025, 1026] (see also Section 22.3 on page 638). ISIS supports an international community of around 1600 scientists who use neutrons and muons for research in physics, chemistry, materials science, geology, engineering, and biology. 17.3.3 The PSI Continuous Spallation Neutron Source SINQ

A general design concept of the continuous Swiss Spallation Neutron Source SINQ, formerly denoted with the acronym SIN, was ﬁrst presented by Fischer [645, 1027] and by Tschal¨ar [1028] around 1979/1981. Details of the technical concept were published several times during its construction [983, 1029]. SINQ [627] is a neutron source mainly for research with extracted beams of thermal and cold neutrons, but hosts also facilities for isotope production and neutron activation analysis. It is a spallation source which closely resembles a medium ﬂux research reactor geometry with its central core surrounded by a reﬂector (cf. Figure 17.11). The spallation source SINQ complex comprises the following facilities. The PSI proton ring cyclotron The ring cyclotron is a separated sector cyclotron with a ﬁxed proton beam energy of 590 MeV, built by PSI and commissioned in 1974. The 72 MeV beam from the injector-2 cyclotron is injected into an orbit in the center of the ring, accelerated over 186 revolutions and is extracted at the full energy of 590 MeV at a current routinely up to 2.3 mA and a total proton beam power of about 1.35 MW. The 590 MeV beam is then transported through the experimental hall in a shielded tunnel to the meson target and the SINQ target station. Figure 17.9 illustrates the

519

17 The Accelerator-Based Neutron Spallation Sources Injector-2 72 MeV

870 keV preacc.

10 m

520

10 m 590 MeV ring cyclotron

590 MeV beam to meson target and SINQ

Injector-1

Beams for low energy exp.

Fig. 17.9 The PSI accelerator facilities with: Injection Energy 72 MeV, extraction energy 590 MeV, extraction momentum 1.2 GeV/c, energy spread (FWHM) about 0.2%, beam emittance ca. 2π mm× mrad, beam current 2.3 mA DC, accelerator frequency 50.63 MHz, time between pulses 19.75 ns, bunch width about 0.3 ns, extraction losses about 0.03% (after PSI [627] and Kramer/PSI 1995).

cascade of the three accelerators, the Cockcroft-Walton pre-accelerator at an energy of 870 keV, the four-sector injector-2 with an energy of 72 MeV, and the eightsector main ring cyclotron. Figure 17.10 shows a photograph of the 590 MeV sector cyclotron. A small fraction of the beam (20 µA) is split off early to serve a proton irradiation and cancer therapy test facility4) . An upgrade program is under way to increase the beam power of the proton accelerator to 1.8 MW [967]. The SINQ target complex The proton beam to the SINQ is bent downwards through a sloping drift tube for onward transport with a vertical injection on the SINQ target. Figure 17.11 gives an impression about the principle design features of the SINQ neutron source with the vertical proton beam injection from below onto the target, the D2 O vessel, and the shielding arrangement, whereas Figure 17.12 4) A separate accelerator for the cancer therapy facility is planned in the near future.

17.3 Spallation Neutron Sources

Fig. 17.10 The PSI 590 MeV proton sector cyclotron showing the eight sectors of the ring cyclotron (after [627]).

60t crane Bulk shield

LBE target D2O tank Neutron beam

Proton beam line Liquid metal dump

10 m

Fig. 17.11 A sketch with a vertical cut of the SINQ target station with the vertical proton beam injection onto the target, the D2 O vessel, the LBE target, thermal neutron beam channels, and Fe shielding (after Tschal¨ar [1028]).

gives an impression on the whole facility with the vertical beam injection from below the target station, indicated scattering instruments, and auxiliary equipment. Figure 17.13 illustrates the target–moderator–reﬂector (TMR) system of SINQ. A vertical and horizontal cut through the D2 O moderator vessel is shown in Figure 17.13. The present target is an array of lead rods, enclosed in zircaloy clad and cooled in cross ﬂow by heavy water coolant. The target is situated in the center tube of the heavy water moderator vessel which has a diameter of about 2 m containing 6 m3 D2 O. Cold neutrons are extracted to the experiments by neutron guides from a cold moderator of about 20 l of liquid deuterium D2 at 25 K. This ‘‘cold neutron source’’ is situated in a horizontal insert inside the moderator vessel and near the target,

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17 The Accelerator-Based Neutron Spallation Sources H2O-cooled top shield

Shielding wall Target

SINQ control room

Target and moderator loop delay tanks D2O-moderator SINQ cooling plant room

Used target storage pits

Fig. 17.12

Neutron scattering instrumentation in the guide hall

Proton transport line

A schematic view of the whole SINQ facility (after Wagner [1030]).

where the thermal neutron ﬂux has its maximum. As it is seen in the horizontal cut in Figure 17.13, the vertical proton beam injection has the advantage to allow a maximum number of horizontal beam tubes and neutron guides compared to a horizontal proton beam injection. The beam loss rate in the beam bending area is about ≤ 1 nA/m. With a continuous thermal neutron ﬂux in the 1014 neutrons cm−2 s−1 range SINQ is well competitive with modern medium ﬂux research reactors [1031]. An ambitious upgrade program ultimately to a proton beam current of 3 mA of the cyclotron would lead to a further ampliﬁcation of the neutron ﬂux. Neutrons are extracted through ﬁve thermal and two cold neutron beam holes mounted inside the vessel ﬁlled with the D2 O moderator at ambient temperature. A system of seven neutron guides is directing neutrons from a 20 l liquid D2 -cold moderator. Figure 17.14 illustrates a schematic layout of the beam lines and the instruments located inside the experimental hall [1031]. The SINQ spallation neutron source facility has a broad user community. The following dedicated user instruments are investigated at the spallation neutron source SINQ: • time-of-ﬂight spectrometer FOCUS; • backscattering spectrometer MARS; • triple axis spectrometer with multianalyzer RITA II; option, • triple axis spectrometer with polarization analysis option TASP; • triple axis spectrometer EIGER. Research in various ﬁelds of condensed matter physics are done in various ﬁelds, e.g. as high-temperature superconductors, critical phenomena in ferroelectrics, low-dimensional magnetism, colossal magnetoresistance manganites and cobaltates, etc.

17.3 Spallation Neutron Sources Helium refrigerator

Helium supply

D2 System

Target cooling system

D2Condenser

Cooling plantroom

Target endosure cooling system

Moderator cooling system

Cold helium ~25K

Secondary cooling loop

Target plug

Vertical plug

H2O reflector

Target

D2O Moderator

Cold moderator Horizontal plug D2O

Beam shutter

D2 Neutrons

Neutron beam trubes

Reflector Beam window Targetblock shielding (steel & concrete)

Proton beam channel Protons 590 MeV

(a) Sector 50:

Sector 60:

Rabbit systems NAA, PNA.,

Th ne erm utr al on s

‘‘Cold’’ neutron

s

H2O Reflector Gæjet:GJA

Moderator tank Helium enclosure

Horizontal plung

Sector 70

Neutronbeam tubes

ns

tro

eu

n al

m

er

D2 O

D2

Th

Th

Target block shielding (steel & concrete)

er

Target

ma

ln

eu

tro

ns

Reflector H2OScatterer

al erm ns Th utro e n

NEUTRA

ons

Sector 30:

‘‘Cold’’ neutr

Sector 80

Sector 40: HRPT

D2O Moderator

Liquid modrator (T = 25K)

TriCS

(b)

Fig. 17.13 The SINQ TMR assembly. (a) Indicates the target position and the D2 cold source, whereas (b) shows the tangential neutron beam lines delivering the cold and thermal neutrons to the experiments (after [627] and from Heyk 1998).

POLDI

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17 The Accelerator-Based Neutron Spallation Sources 105 m POLDI TriCS

Grid scale = 7 m

NEUTRA HRPT

1.62 × 10

Funspin

2.67 × 108

7 AMOR

SANS-I MARS

ICON

RITA-II NAA/ PNA GJA

Morpheus

TASP

DMC EIGER SANS-II

D2O vessel

6.34 × 108 ~ 46.8 m

FOCUS

[m]

Fig. 17.14 The SINQ neutron beam lines and their instruments and examples of neutron ﬂux data in units of (neutrons cm−2 s−1 mA−1 × 2.2) at the neutron guide measured by Au-foil activation [1032] (after Wagner et al. [1031]).

A further large research ﬁeld is the design, build and operation of a liquid metal target on the basis of a lead–bismuth eutectic [1033–1035]. In 2006 a liquid metal target with eutectic lead–bismuth target material was tested successfully in the framework of the MEGAPIE-Project. The MEGAPIE target improved the neutron yield to about 80%, related to the beam current. This Megawatt Pilot Experiment (MEGAPIE) is a joint initiative of six European research institutes, JAERI, Japan, KAERI, Korea, and DOE, USA. Details are given in Chapter 18. 17.3.4 The European Spallation Neutron Source Project ESS

In the ‘‘Large Scale Facilities Report’’ to the Commission of the European Community (CEC) in 1990, the ‘‘Neutron Study Panel’’ recommended to carry out studies for a next generation neutron source in Europe. In 1991–1992, a joint initiative of the Forschungszentrum J¨ulich, Germany, and of the Rutherford Appleton Laboratory, UK, explored with a series of workshops the concept of a future European accelerator-based pulsed high-intensity neutron spallation source. The recommendations of these workshops formed the basis for the speciﬁcations of the ESS – the European Spallation Source: • a proton accelerator with 5 MW beam power and a proton pulse length of about 1 µs, • two target stations: 5 MW at 50 Hz, 1 MW at 10 Hz . With the start of a the multinational study with eight European countries and the CEC in 1993, the establishment of the ESS scientiﬁc council, the feasibility of the 5 MW ESS spallation neutron source was demonstrated and published in the following ﬁnal reports during 1996: • Volume I – The European Spallation Source [1036], • Volume II – The Scientiﬁc Case [1037], • Volume III – The Technical Study [551].

17.3 Spallation Neutron Sources

A comprehensive overview is given in [1038]. After a high priority R&D program, a revised concept for ESS was ﬁnalized in 2002. The results reﬂect on a revised version of the normal conducting (NC) linear accelerator design of [551] and the advance in a super conducting (SC) linear accelerator system [873, 1039, 1040]. Both systems, the NC and the SC linear accelerators, can meet the speciﬁed performance of ESS [873]. A speciﬁc SC reference design was ﬁnally selected [1039] which can serve about 10 MW operating power compared to the ESS NC linear accelerator [1040]. Also novel ideas in neutron scattering utilization [1041], and a major change in the high-power target stations concerning a short-pulse (SPTS) and a long-pulse (LPTS) target station were taken into account with the following parameters: • SPTS, 50 Hz, 1.4 µs, 5 MW • LPTS, 16 23 Hz, 2 ms, 5 MW. • • • • •

The results were published in several revised study reports: Volume I – European Source of Science [1042]; Volume II – New Science and Technology for the 21st Century [1043]; Volume III – Technical Report [873]; Volume IV – Instruments and User Support [900]; Volume III – Update, The ESS Project, Technical Report Status 2003 [1039].

In the following sections the main items of the technical design of the ESS spallation neutron source design, as given and documented in 2003, will be shortly summarized. Accelerators of the European Spallation Neutron Source ESS A schematic sketch of the anticipated facility comprising a full energy 1.334 GeV linear accelerator, two compressor rings, and the SPTS and LPTS target stations is given in Figure 17.15. This sketch is based on the ESS facility design in the year 2002/2003 [873, 1039]. As shown in Figure 17.16 the ESS spallation neutron source complex consists of a 10 MW, negatively charged hydrogen (H− ) ion, full energy 1.334 GeV SC linear accelerator capable of simultaneously delivering 5 MW, 1.4 µs pulses to a SPTS operating at 50 Hz and 5 MW, 2 ms long pulses to an LPTS (LPTS) operating at 16 2/3 Hz. The double compressor ring compresses the 50 Hz proton pulses of the linear accelerator by a factor of 800 in time before they are delivered to the SPTS. The main parameters of the ESS 1120 MHz superconducting (SC) reference linear accelerator design are summarized in Table 17.3. The main difference between the proposed ESS accelerator complex shown in Figure 17.16 and the accelerators constructed and now being commissioned for SNS-ORNL, USA [681] and for J-PARC, Japan [629] is the demand of a simultaneously delivering both short and long pulses [1044]. The SC part of the 1120 MHz ESS linac uses 43 cryomodules, each housing four elliptical bulk Nb superconducting cavities illustrated in Figure 17.17. Each cavity consists of six cells of β = 0.8 equipped with one SC main power coupler. The ESS cryomodule layout proﬁts considerably from the work of the J-PARC team on their 972 MHz SC cavities. A comparison of the cavity and cryomodule data is given

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17 The Accelerator-Based Neutron Spallation Sources

m 00 ~12

Ion source front-end

Linear accelerator

~850 m

Long pulse target-LPTS

Compressor rings Short pulse target-SPTS Fig. 17.15 ESS – a possible layout: Artist’s view of the ESS facility showing the ion source, the linac tunnel leading to the accumulator and compressor rings from where the beam is distributed to the SPTS station. The LPTS with instruments is directly connected to the linac. Some auxiliary buildings are also shown (after [664, 1039]). SPTS 2 accumalator rings radius ~35 m H− ion sources 65 mA each-

achromat 280 MHz

RFQ

2 × 57 mA

DTL

560 MHz 114 mA

SP, LP CCDTL

2.2 m SP, LP Chopper

Funnel section 100 MeV

75 keV

2.5 MeV

1120 MHz SC linac

228 mA Equivalent current 560 MHz 6 cells per CCL CCL cavity b = 0.8 b = 0.912

400 MeV

1334 MeV

20 MeV ~262 m

~308 m

LPTS

Energy ramping and bunch rotation

~78 m

Fig. 17.16 The ESS accelerator complex with the 1120 MHz superconducting (SC) reference linac, the achromat, the two compressor rings, the short pulse and LPTSs (after [1040]).

in Table 17.4. More details can be found in the Volume III – Update, The ESS Project, Technical Report Status 2003 [1039]. The guiding principle for the compressor ring design was the requirement to deliver 5 MW of beam power to the SPTS, which can be met through the use of two, 50 Hz, 1.334 GeV accumulator rings. Stacked one above the other, these are ﬁlled and emptied successively once every cycle with 2.34 × 1014 protons per ring. The particles are accumulated via a multiturn charge exchange ring injection process so as to compress the time duration of the linac pulse [1045]. In order to control beam losses, halo scraping will be applied in the transfer line from the linac to

17.3 Spallation Neutron Sources Main parameters for the ESS reference linear accelerator (after [1039] and Letchford and Bongardt [1040]).

Tab. 17.3

Parameter

SPTS target station

LPTS target station

50 1.4 µs 1.334 107 5.1

16 2/3 2.0 ms 1.334 152 5.1

Beam data Pulses (s−1 ) Pulse length Final energy (GeV) Peak beam power (MW) Mean beam power (MW) 280/560 NC-linac part Final energy (GeV) Overall length (m) Peak RF power (MW)

0.40 262 64

78

1120 MHz SC-linac part Energy range (GeV) SC-linac length (m) Acceleration gradient In SC cells (MV m−1 ) Peak RF power (MW) AC cryo power in SC part (MW) Total length from ion source to LPTS target (m)

0.4–1.334 308 10.2 75

107 4 748

the rings. The transverse and longitudinal proﬁles of the beam emerging from the H− -linac are cleaned using a number of stripping foils in a large achromatic 180◦ bending section (cf. Figure 17.16). Each ring contains a rectangular injection foil, 42.5 mm wide and 14.3 mm high, with mass per unit area of 540 µg cm−2 corresponding to a thickness of 3.5 µm for graphite. 2.34 × 1014 H− ions are stripped of two electrons over a 470 µs pulse duration (583 revolutions) at a repetition rate of 50 Hz. The injected H− ions, stripped electrons and re-circulating protons scatter in the foil and generate large temperature rises through atomic excitations and ionization. Radiation cooling reduces the temperature between pulses and a constant peak temperature is reached after the passage of approximately seven pulses. Tracking simulations suggest a foil heating with a peak temperature for graphite of 1880 K. This is well below the melting point of 3823 K for graphite. More details of the ESS compressor ring design, the achromat, and the beam transfer to the targets can be foun in Refs. [551, 873, 1039, 1045, 1046]. The ESS facility was originally designed to deliver 5 MW beam power to both the SPTS and the LPTS (cf. Figure 17.16 and [1039]), which leads to unprecedented performance with virtually no compromises for any of the scientiﬁc ﬁelds in neutron science [1040]. On the other hand, using a 16 2/3 Hz LPTS only but

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17 The Accelerator-Based Neutron Spallation Sources

Nb superconducting cells

Power

Couplers

Overall cryomodule length

Warm part: quad.-poles, pumping, diagnostics

5.27 m

1.9 m

Vacuum vessel

Fig. 17.17 A schematic drawing of a six-cell lattice period of the 1120 MHz ESS SC linear accelerator of Figure 17.16 (after [1040]). Tab. 17.4 Cavity and cryomodule data of the ESS 1120 MHz superconducting linear accelerator.

ESS 1120 MHz SC linac Cavity data

Cryomodule

β = 0.8, 6 cells 4 cm iris radius 6 cm coupler port radius Acceleration gradient 10.2 MV/m

43 cryomodules 4 cavities per module Cavity to cavity separation 0.7 m Total length 5.27 m

with 10 MW beam power at 2 ms, many of the high-priority instruments will proﬁt [1047, 1048]. Such an alternative ESS scenario would lead to substantially reduced capital and operating costs: the accumulator rings would not be needed, an H+ beam could be used instead of an H− beam. An example for a layout of a basic ESS LP linac is shown in Figure 17.18, which is very similar to the ESS SC reference linac design. Two 75 mA H+ beams are combined together at 20 MeV and accelerated by 1120 MHz SC cavities up to 3 GeV [1040]. Only one type of cryostat is required, as the SC cavity length itself is kept constant, but the number of cells per cavity is changed at 1.4 GeV in order to shorten the SC linac length. An accelerating gradient of 10 MV/m leads to 1.2 MW peak power in the SC main coupler. Studies of Letchford and Bongardt [1040] investigated the possible different options for advanced ESS long-pulse linear accelerators. A comparison of these options is summarized in Table 17.5. The target stations The target system is crucial for the feasibility and performance of a high-power spallation neutron source as ESS. The power rating of ESS

17.3 Spallation Neutron Sources H− ion sources 85 mA each

280 MHz

RFQ

2 × 75 mA

4 cavities /cryomodules

SP, LP CCDTL

2.2 m

CCL

SP, LP Chopper

Funnel section 100 MeV

75 keV

2.5 MeV

1120 MHz SC linac

560 MHz

DTL

400 MeV

6 cells per cavity b = 0.8 1.4 GeV

5 cells per cavity

LPTS

b = 0.96 3 GeV

20 MeV ~262 m

~330 m

~495 m

Fig. 17.18 The alternative ESS accelerator complex with the 1120 MHz superconducting (SC) linac serving a long-pulse target station (after [1040]). Tab. 17.5 Comparison of different ESS long-pulse linear accelerator options (data are from Letchford and Bongardt [1040]).

Parameter Average power (MW) Final energy (GeV) Pulse length (ms) SC linac length [m] power/SC coupler (kW) AC croy power (MW)

Basic linac

Extended linac

Advanced linac

10 2 2 524 (330 + 194) 46 4

10 3 1.34 825 (330 + 495) 33 6

15 3 2 825 (330 + 495) 46 6.5

exceeds both, the most ambitions pulsed spallation source under commission (SNS at ORNL, USA) and the most powerful existing target (with continuous beam operation, SINQ at PSI, CH) by factors of 5. The strongest existing pulsed source (ISIS at RAL, UK) is exceeded by as much as a factor of about 30, while the peak neutron ﬂux of ESS would have been about two orders of magnitude higher than that of the ILL reactor. The corresponding increase of the loads to the target can only be handled by employing several innovative concepts, which have been investigated and assessed during the ESS project. The target design developed in the original ESS Study from 1996 [551] involves a ﬂowing liquid mercury target in a steel container. Mercury as target material was suggested by Sigg in 1992 and proposed by Bauer [1049] for the ESS high-power target in 1995. It was chosen for ESS for its ability to cope with the high average power deposition of nearly 3 MW in the target material and its good neutron performance [636] compared with other target materials (cf. Figure 8.8 on page 266). It is expected to result in acceptable life-time under the demanding radiation and thermal loads of the 5 MW short pulsed proton beam, although some more development work is required to cope with the high-pulse power: The energy delivered by the accelerator system in one single proton pulse to the Short Pulse Target is 100 kJ, about 60 kJ of which are

529

530

17 The Accelerator-Based Neutron Spallation Sources 10 m Module storage

Hg target & reflector

Containment vessel

Storage cask 105 kg crane

Bulk shield

Proton beam

Remote handling

Beam Collimators neutron beam catcher Proton beam shutter Horizontal plugs window for moderator exchange

Shutter storage

Decontamination cell

Module storage Underground cooling circuits

Fig. 17.19 A horizontal cut of the ESS target station overall layout for the short and long-pulse utilization. LPTS (after [1050, 1051]).

deposited as heat in a volume of a few liters in the target during 1.4 µs. Due to the much longer relaxation times of the resulting thermomechanical loads, special care must be taken to avoid unacceptably large stress on the target container and possible deleterious effects of cavitation. Since the considerations that lead to the choice of a mercury target for the SPTS are also valid for the LPTS, the same target concept is foreseen for both. (Although the energy in one pulse for the LPTS is even three times higher 5) (about 300 kJ), the effects on the target structure are considered somewhat less serious due to more than 1000 times longer pulse duration.) The two target stations could be of essentially identical design, as far as the targets and their handling systems are concerned. Differences may result in the moderator layout and in the beam lines. Using largely identical target systems for both, SPTS and LPTS, will have positive economic advantages for design, licensing, operation, and handling of the targets. It also allows the same basic design for the major components of the two target stations, infrastructure, and buildings. The overall layout of the target station is shown in Figure 17.19 [1050, 1051]. The horizontal beam injection for both systems (SPTS and LPTS) and the liquid state of mercury at room temperature (melting point −38◦ C, boiling point at ambient pressure 350◦ C) also favor a design concept, where the closed mercury loops are mounted on a movable support, which can roll back from its operating position into a service hot cell for maintenance. Figure 17.20 shows the principle arrangement of the Hg target, the moderators with reﬂector, and the trolley system with the liquid mercury loops. 5) This is caused by the lower repetition rate of 16 2/3 Hz of the LPTS compared to 50 Hz of the SPTS

17.3 Spallation Neutron Sources Hg target

Proton beam

Reflector

Moderators

Target trolley with primary Hg target loop

Fig. 17.20 A schematic sketch of the target trolley with the Hg target, the moderators inside the reﬂector, the Hg drain tanks, and the primary target loop (after [551]). SPTS

Hg targets

(a)

al

tr ec

isp

De

co

up

B

ed pl ou ec D al m er th

(b)

LPTS

Moderators

led

l

co

a ctr

ld

ld

o dc

Co

le up

e isp

Co

up

led

co

B

Co

up

led

ld

al

co

ld Moderator positions and neutron beam line groups

ctr

e isp

B

Fig. 17.21 Schematic representation of the moderator concept for the short pulse (a) and the LPTS (b) as proposed by the ESS instrumentation team (after [1056]).

For both target systems, SPTS and LPTS, two moderator assemblies, each with two viewed faces, are inserted horizontally above and below the target respectively (cf. Figure 17.21). This decouples moderator maintenance from the heavy and difﬁcult to manipulate reﬂector and allows for future use of advanced cold moderators (cf. in Figure 17.19 the indicated horizontal plugs for moderator exchange). Each target station will have 22 beam channels (11 on each side) separated by 11◦ , and each ﬁtted with a rotating shutter with a replaceable beam channel of outer dimensions 2.8 m long, 23 cm wide, and 17 cm high. Guides and other optical elements can be mounted and aligned inside this channel from the top of the target station with the shutter in closed position. The closest distance between moderator and guide entrance is 1.6 m and the ﬁrst choppers can be mounted 6 m from the moderators (cf. Figure 17.19). Both target stations are ﬁtted with a

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17 The Accelerator-Based Neutron Spallation Sources

Side-by-side bispectral face

Side-by-side bispectral face

Coupled cold face

Coupled cold face

Side-by-side bispectral face

Coupled cold face

Fig. 17.22 Examples of different SPTS and LPTS moderator schematics as proposed by the ESS instrumentation team [1056].

D2 O-cooled Pb reﬂector with a diameter of about 1.2 m and surrounded by a bulk shield of iron-based material with a thickness in the direction of the incident proton beam on the mercury target of 7.75 m followed by a 0.5-m thick concrete layer. A list of overall parameters for the SPTS and the LPTS concept is given in Table 17.9. The neutronic performance of the target–moderator–reﬂector system for the shortand long-pulse target stations The neutron performance has been optimized by simulations with MCNPX [194, 509] using the latest developed scattering kernels for moderators by a group of the university of Stuttgart, Germany [894]. The following parameters were used: (1) for the SPTS a pulse frequency of 50 Hz, and a proton pulse length of 1.4 µs, (2) for the LPTS, a pulse frequency of 16 2/3 Hz, and a proton pulse length of 2 ms, and for both 5 MW proton beam power with 1.334 GeV proton energy. Details of the optimization calculations are given in Refs. [1052–1055]. A schematic sketch and plan view of the moderator conﬁguration is given in Figures 17.21 and 17.22. This moderator concept is an extension to the one discussed in Refs. [551, 873]. In the ﬁgures, the colors blue and red indicate cold and thermal neutron moderators, respectively. The reﬂector (not shown in the side view) below the target is colored in yellow and the one above the target in purple only for distinction. The viewing angle for all four moderators is 62◦ . This allows for up to 6 beam ports looking at each of the 12 × 24 cm2 moderator faces. The Monte Carlo simulations aimed at being as close to realistic geometry and construction materials as possible, i.e., taking into account technical constraints resulting from the expected engineering realization of the moderator assemblies. For both target stations various moderator–reﬂector concepts have been considered such as, for example, different geometries and material compositions. These choices show substantial inﬂuence on the neutron ﬂux- and neutron current densities. Pb, Be, C, and Hg reﬂectors as well as composite systems made from these materials have been studied. Also the effect of coupling and poisoning of moderator systems on the pulse shape and intensity of neutron spectra (see explanation Section 13.2 on page 436) have been investigated. For further reading and details see [1054]. Examples of the peak neutron current densities as a function of wavelength for the SPTS and LPTS are compared in Table 17.6 for a cold coupled H2 -moderator [1054]. Values in parenthesis note the FWHM of the peak for the SPTS. In addition, the ILL

17.3 Spallation Neutron Sources

533

˚ Peak current neutron density in (1/(cm2 s sr A)) for different neutron wavelengths from a cold coupled H2 moderator at 20 K temperature.a

Tab. 17.6

˚ Wavelength (A)

2

4

6

Short Long Ratio sh/lg ILL Ratio long/ILL

1.486 × 1015 (43) 2.05 × 1014 7 H12∗ : 3.5 × 1013 6

3.708 × 1014 (120) 9.12 × 1013 4 H1: 4 × 1012 23

1.035 × 1014 (150) 3.12 × 1013 3 H15: 6 × 1011 52

a

10 7.532 × 1012 (232) 2.95 × 1012 2.5 H17: 1011 30

For the short-pulse station the FWHM of the peak is given in parenthesis in (µs).

average ﬂuxes are given [653]. Furthermore, the ratio of the short- and long-pulse peak ﬂuxes as well as the ratio between the long-pulse peak ﬂux and the ILL ﬂux are given. Figure 17.23 illustrates neutron current density distributions with different wavelengths for a cold coupled H2 moderator for SPTS and LPTS target station, respectively. In case of the short-pulse target for long wavelength, pulses with a FWHM in the order of 200 µs evolve, while for the long-pulse saturation is observed and neutron pulses with a broad plateau length of 2 ms emerge. The peak ﬂux for cold neutrons differs by factors between 2.5 and 4 for the two target stations. In contrast to the four moderator ESS concept of 1996 [551] only two moderators in brilliant position (10 cm downstream of the target front face) in wing geometry above and below the spallation target are favored in the current concept [900, 1056]. The present design is based on the use of (a) two extended moderator assemblies in the most brilliant positions above and below the target, (b) conventional water and cryogenic hydrogen moderators only, and (c) extended water premoderators where appropriate (cf. Figures 17.21 and 17.22). Therefore on the SPTS four different types of neutron beam spectra will be available: coupled cold, decoupled cold, decoupled thermal, and bispectral (combined cold and thermal). The LPTS will only have coupled cold and bispectral beams. Simulations of these new moderator concepts with engineering details included show that the extended moderators, in general, have a lower brilliance but a larger viewable surface i.e. they are only advantageous, when the beam extraction system is designed to view the entire moderator surface and the instrument is designed to utilize the full neutron beam. Details may be found in Refs. [1039, 1054]. In contrast to the values quoted in the ESS feasibility study [551] assuming an idealized case of a simpliﬁed geometry, Tables 17.7 and 17.8 summarize for the SPTS ) and current ( J, J) densities for and LPTS the peak and average neutron ﬂux (, a perturbed realistic system, e.g., including beam holes, structure and support, etc. The simulations were performed for a cold (20 K) coupled H2 and an ambient coupled H2 O moderator and a Pb reﬂector of 180 cm diameter and height. In case

17 The Accelerator-Based Neutron Spallation Sources

Neutron current [n × cm–2 s–1 sr–1 Å–1]

(× 1015)

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

(× 1014)

2Å

0

100

200

300

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

4Å

0

1.2

6Å

1 0.8

0.4 0.2 0

0

200

400

600

(× 1013)

(× 1014)

0.6

200

400

600

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

10 Å

0

200

400

600

Time [µs] Neutron current [n × cm–2 s–1 sr–1 Å–1]

534

(× 1013)

14)

(× 10

4

4

3.5

3.5 6Å

10 Å

3 2.5

2.5

2 1.5

1.5

1 0.5

0.5 0

1000

2000

3000

4000

0

0

1000

Time [µs] Fig. 17.23 Time spectra of the neutron current density for 2, 4, 6, and 10 A˚ at the short target (upper four panels) and for 6 and 10 A˚ at the LPTS for a coupled H2 -moderator (after [1040]).

2000

3000

4000

17.3 Spallation Neutron Sources Expected peak and average thermal (E ≤ 0.431 eV) neutron ﬂux densities for a premoderated cold (20 K) coupled para-H2 and an ambient coupled H2 O moderator.a

Tab. 17.7

Moderator type

Para H2 (n/(cm2 s)) amb. water (n/(cm2 s)) a

SPTS

LPTS

Peak ﬂux

Average ﬂux

Peak ﬂux

9.0 × 1016 1.3 × 1017

3.2 × 1014 3.1 × 1014

7.0 × 1015 9.0 × 1015

Average ﬂux 2.3 × 1014 3.0 × 1014

The energy 0.431 eV is the usual upper limit for the thermal energy range.

Tab. 17.8 Same as Table 17.7, but for current densities normalized to solid angle of 4◦ opening.

Moderator type

Para H2 (n/(cm2 s sr)) Amb. water (n/(cm2 s sr))

SPTS

LPTS

Peak current

Average current

Peak current

Average current

6.8 × 1015 9.8 × 1015

2.5 × 1013 1.8 × 1013

6.3 × 1014 5.0 × 1014

2.1 × 1013 1.7 × 1013

of short-pulse spallation sources, in order to prevent already moderated neutrons from entering or returning to the moderator and deteriorating the pulse shape, a decoupling Cd layer can be placed between reﬂector and moderator. For the LPTS source, the inﬂuence of different reﬂector compositions on the neutron current densities was also investigated [1055]. Up to 35% higher current is obtained for a Be than for a Pb reﬂector. However the decay time is longer as compared to Pb. The decay constants [1055] for Pb, C, and Be are 95, 153, and 198 µs, respectively. Besides the shortest decay time, the Pb option shows a long period of constant neutron current during the pulse. Besides the ‘‘classic’’ moderator materials as cold H2 (20 K) and ambient H2 O the neutron performance of the SPTS and the LPTS was studied using more advanced moderators with pure solid methane or a mixture of methane and hydrogen [1054]. Table 17.9 summarizes the parameter set of the ESS spallation neutron source as given in 2003 [1039]. The instruments and modes of operations The proposed instrument suite (cf. Engelberg meeting [1041], Clausen et al. [900], and Bauer et al. [1039]) is an extrapolation of the ISIS spallation neutron source instrumentation for the SPTS, and for the LPTS it relies heavily on the fact that neutrons can be transmitted over large distances with very low losses, that choppers can be used for pulse shaping, repetition rate multiplication and wavelength frame multiplication. The

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17 The Accelerator-Based Neutron Spallation Sources

Tab. 17.9

The main parameters of the 10 MW ESS facility.

ESS beam parameters for the short- and long-pulse target Particles Kinetic energy Beam cross section Average beam power/current on SPTS/LPTS Pulse frequency SPTS/LPTS Pulse width SPTS/LPTS Peak current SPTS/LPTS

Protons 1.334 GeV Elliptical 6 × 20cm2 , Parabolic beam intensity distribution 5 MW/5 MW, 3.75 mA/3.75 mA 50 Hz/16 23 Hz 1.4 µs (2 ×0.6 µs + 0.2 µs gap)/2 ms 62.5 A/114 mA

ESS mercury target and target station performance parameters Beam power on targets Target material and type Target container H+ window: array of thin walled pipes H+ window: size Window current density/temperature Target mass, in/output temperature Heat deposition in target Local peak power deposition in target Energy content in pulse SPTS/LPTS induced speciﬁc radioactivity for a 15 tons Hg-system Spec. after heat of target material

5 MW at 50 Hz (SPTS), 5 MW at 16 23 Hz (LPTS) Mercury, liquid ﬂow target Martensitic steel 0.3 mm wall thickness, 3 mm outer radius 60 × 200 mm2 <100 µA cm−2 / < 400◦ C 15 × 103 Kg/100◦ C/ < 280◦ C 2.8 MW at each of the two targets 2.5 KW/cm3 (time average) 100 KJ/300 KJ 8 GBq/g at shutdown, 0.8 GBq/g after 1 week

SPTS 2 moderators[1039]

Decoupled cold/thermal Coupled bispectral/cold Coupled cold/coupled bispectral (side-by-side Lead, D2 O cooled

LPTS 2 moderators reﬂectors SPTS/LPTS

0.67 MW/g at shutdown, 0.12 MW/g after 1 day

General neutronic performance of coupled ambient H2 O-moderators and premoderated cold coupled (20 K) H2 moderators at 5-MW beam power Average thermal neutron ﬂux Density inside moderator in neutrons/(cm2 s) for (E ≤ 431 MeV)

SPTS (H2 O): 3.1 × 1014 LPTS (H2 O): 3.0 × 1014 SPTS (H2 ): 3.2 × 1014 LPTS (H2 ): 2.3 × 1014

Peak thermal neutron ﬂux inside moderator in density neutrons/(cm2 s) for (E ≤ 431 MeV)

SPTS (H2 O): 1.3 × 1017 LPTS (H2 O): 1.0 × 1016 SPTS (H2 ): 9.0 × 1016 LPTS (H2 ): 7.0 × 1015

Details are given in Refs. [551, 873, 1039–1041, 1045, 1046, 1054, 1057].

17.3 Spallation Neutron Sources

performance of the presented instrument suite has been compared to SNS at 1.4 MW and the best existing neutron facilities [1048]. Neutron channels, openings in the shielding of the target, enable the neutrons to travel to the instruments where the experiments are being carried out. The instruments, typically 24 for each target, some of them as far away as 200 m, are arranged radially around each target stations (cf. Figure 17.19). On a pulsed source, neutrons with different energy (velocity) arrive at the sample and typically only a part of the neutron spectrum can be used even if the pulse repetition rate is well matched to the experiment considered. Faster (hot and thermal) neutrons can take advantage of pulses closer to each other (5–20 ms) than slower cold neutrons, for which at least 50 ms is optimally needed between subsequent pulses. The combination of a 50 Hz short pulse and a 16 32 Hz LPTS allows ESS to cover the whole range of neutron energies for condensed matter research with an efﬁciency 2–5 times superior to the short-pulse target approach only. Outlook ESS In 2003, it became clear that the European governments, despite tremendous efforts by the ESS project, decided against a new spallation source. In the meantime, the SNS spallation neutron source [681] is expected to reach full power (1.4 MW) in 2009. An upgrade to 2.4 MW beam power and a second target station is envisioned in the 20 years DOE’s Road Map. The J-PARC spallation source [629] will be commissioned in 2009, initially operate at a lower power level, but it is also from the very beginning being constructed with an identiﬁed upgrade potential. The European Strategy Forum for Research Infrastructure (ESFRI) [480, 1048] concluded that Europe needs a major new neutron facility in the long term and hence a decision on such a facility in the medium term should be made. In 2008, meanwhile ‘‘The European Spallation Source Initiative’’ is founded, henceforth to be called ESS-I [1058], an association in which the users of neutron source facilities and regional consortia interested in hosting a new facility collaborate to prepare the physics case and the planning for a next generation neutron spallation source in Europe. The objectives of ESS-I are: (1) to gather all those interested in building at the earliest possible occasion a next generation top tier neutron source in Europe, (2) to stimulate, coordinate where necessary and possibly engage in all activities that need to be carried out before a decision to recommence baseline engineering, construction planning and detailed site assessment can be taken, (3) to act as the interlocutor to national governments and funding agencies, the EU, and the ESF in matters regarding the initiative, and (4) ﬁnally to have one European counterpart to SNS and the JSNS as part of J-PARC. An ESS Preparatory Phase project, ESS-PP, as a two-year EU funded project, was started in April 2008, to carry out preparatory work toward the start of construction of ESS. The work is site independent. Just recently the decision was taken to host ESS in Lund, Sweden. More details may be found in [1058, 1059]. The current ‘‘ESS-Preparatory Phase Project’’ takes advantage of the recent experience of the ESS technical study, e.g. [551, 873, 1039, 1040, 1057, 1060] and retains the most

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17 The Accelerator-Based Neutron Spallation Sources

innovative, cost effective and lowest technical risk aspects of the original ESS project. It should be mentioned here that many ideas performed during the ESS study phase on accelerator and high-power mercury target development were taken over and realized by the SNS [681] and the J-PARC [629] spallation neutron source concepts. 17.3.5 The ORNL Spallation Neutron Source SNS

As compared to other large basic science projects, the Spallation Neutron Source (SNS) at ORNL, USA, has had also a long history up to its construction completion in May 2006 described in Ref. [1061]. In 1977, the National Research Council of the National Academy of Sciences (NAS) in USA published a statement on ‘‘Neutron Research on Condensed Matter’’, which recommended a high-ﬂux, pulsed spallation source. In 1984, the NAS reviewed the needs for major facilities and in the report on ‘‘Major Facilities for Materials Research and Related Disciplines’’ (SeitzEastman Committee) it was recommended (1) the construction of a new high-ﬂux, steady-state neutron source, called Advanced Neutron Source (ANS reactor) and (2) the development of a plan leading to a high-intensity pulsed neutron facility. After the cancellation of the proposed Advanced Neutron Source (ANS) reactor project another panel reevaluated the need for neutron facilities in the United States and strongly recommended that a 1 MW pulsed spallation source should be given the highest construction priority. Conceptual design and R&D started in October 1995, the construction of SNS at ORNL, USA, started during November 1999 and was completed in May 2006. The spallation neutron source (SNS) is a Department of Energy (DOE) major system project that is carried out as a partnership among six DOE national laboratories and is led by the SNS Project Ofﬁce in Oak Ridge, Tennessee. The national laboratories in the SNS partnership are Oak Ridge (ORNL), Argonne (ANL), Brookhaven (BNL), Lawrence Berkeley (LBNL), Los Alamos (LANL), and Thomas Jefferson National Accelerator Facility (JLab). This partnership approach was used to efﬁciently take advantage of each laboratory’s speciﬁc technical expertise, frontend systems (LBNL), LINAC (LANL, JLab), accumulator ring (BNL), target station (ORNL), and experiments and instruments (ANL, ORNL) [1061]. Figure 17.24 shows an artist’s view of the SNS spallation neutron source complex, as now commissioned at ORNL, USA. As written in the so-called Spallation Neutron Source Project Completion Report [1061] the goal of the SNS project at ORNL, USA, was to design, construct, and commission an accelerator-based, pulsed neutron research facility for studies of the structure and dynamics of materials that is substantially better than any other facility in the world. Integrated performance tests have demonstrated proton beam delivery to an operating target and the neutron conversion efﬁciency of the target system.

17.3 Spallation Neutron Sources

Front-end building Klystron building Linac tunnel

Ring Target Future target building

Central helium liquefaction building Radiofrequency facility

Center for nanophase materials sciences

Support buildings

Joint institute for neutron sciences

Central laboratory and office complex

User housing facility

06-G01707/arm

Fig. 17.24 An artist’s view of the spallation neutron source SNS at the Oak Ridge National Laboratory, ORNL, Tennessee, USA (after [681]) (courtesy SNS-ORNL). To accumulator ring 402.5 MHz REQ

Injector

MEBT

2.5 MeV

HEBT

805 MHz

DTL

CCL

86.8 MeV

SCRF, ß= 0.61

186 MeV b = 0.55

SCRF, ß= 0.81

391 MeV b = 0.71

1 GeV b = 0.87

Linac beam dump

Total length ~340 m

Fig. 17.25 A schematic sketch of the SNS linear accelerator divided into several subsystems. Speciﬁcations are based on the SNS parameter list [1062], the SNS project completion report [1061], and on Ref. [1063].

In the following sections, the main items of the technical design of the SNS spallation neutron source, as given and documented in several reports and publications [249, 479, 681, 1061–1063], will be shortly summarized. The spallation neutron source (SNS) complex A schematic sketch of the SNS facility comprising a full energy 1.0 GeV linear accelerator, high-energy beam transport line (HEBT), one accumulator ring, a ring-to-target beam transport line (RTBT), and the SPTS is depicted in Figures 17.25 and 17.26.

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17 The Accelerator-Based Neutron Spallation Sources

Ring circumference ~250 m Ring-to-target Accumulator beam transport ring (RTBT)

Ion source

~150 m

DTL CCL Front end

Spare

SCL

Section

Linear accelerator system (linac) total length ~340 m Fig. 17.26

High-energy Target beam transport building HEBT length ~170 m Target

The layout of the SNS spallation neutron source complex (after [1065]).

The SNS complex currently comprises the linear accelerator, the HEBT, the accumulator ring, the ring-to-target-transport (RTBT), and the target station. The linac generates negative H− ions and accelerates them to an energy of 1 GeV. The total length of the linac is about 340 m. The current pulse in the linac consists of a series of equally spaced mini pulses with a 402.5 Hz structure with a macro-pulse length of 1 ms. The linac pulse is guided through the HEBT to the accumulator ring. The H− pulses are injected in micropackets into the ring, overlaying the micropackets to a pulse of less than 1 µs length. In this process the H− are stripped by a 2 µm thick carbon foil to bare protons. After a full accumulation cycle in the ring with a circumference of about 250 m the intensity of the pulse is increased 103 times, shrinking the pulse length to a little less than 1 µs before being extracted and sent to the target. During normal operation, 60 pulses per second are generated with an energy of 1 GeV and an average beam power on the liquid Hg target of 1.4 MW of the target station (cf. Figure 17.26). The linac itself is divided into six subsystems (cf. Figure 17.25): the ion source, the radio-frequency quadrupole (RFQ), the drift-tube linac (DTL), the coupled-cavity linac (CCL), and two superconducting linac sections (SCRF) consisting of mediumand high-beta cryomodules. Although the linear accelerator systems starts with H ions out in the ion source as a pulsed dc beam, the RFQ system accelerates and bunches the beam at its operating frequency of 402.5 MHz. From there on, different types of accelerating structures are used to subsequently increase the kinetic energy of the ions through a series of gaps that have a voltage across them. The voltage is generated by radiofrequency (RF) waves coming from RF power sources, which are fed into the cavity structures. The superconducting RF linac (SCRF) consists of 11 medium-beta cryo modules (β = 0.61) and 12 high-beta modules (β = 0.81). The average H− ion current accelerated in the linac is about 1.4 mA. The SNS target station The SNS target station has the basic function of converting the short pulses of 1 GeV energy, 1.4 MW beam power, 60 Hz repetition rate, and a

17.3 Spallation Neutron Sources

TMR region with core vessel

Concrete roof shield

Outer boron concrete layer Shutter

Inner plug Outer plug

Neutron beam line

Outer boron concrete layer ~1.25 m

Bulk steel shielding

l

m ~6

stee

Concrete foundation Target and moderator area

Fig. 17.27 The SNS target station monolith is cylindrical in shape with an outer diameter and outer height of about 12 and 9 m, respectively (after [1064]).

695 ns proton pulse length, produced in the accumulator and delivered through the RTBT beam line on the Hg target (cf. Figure 17.26) into 18 lower energy (<1 eV), short-pulsed (tens of ms) neutron beams optimized for use by neutron scattering instruments. The heart of SNS target station for the neutron production and for the utilization of neutron scattering research is the target monolith, with a weight of over 7000 t that contains the Hg target, the Hg target moderators, reﬂector plug assemblies surrounding the target and the neutron beam line shutters as shown in Figure 17.27. The target monolith is cylindrical in shape with an outer diameter and outer height of about 12 and 9 m, respectively, with the mercury target located at the center of the monolith at about 2 m distance from the base. The TMR vessel, the neutron beam lines, and the conﬁguration of the bulk shield of steel with the outer concrete layer have also been shown in Figure 17.27. As shown in Figure 17.28 the proton beam line enters the target monolith horizontally. Eighteen neutron beam lines penetrate radially outward from the target in two 110◦ arcs on either side of the incident proton beam direction. The shutters are positioned on each neutron beam line about 2.5 m out from the mercury target in the solid-steel region and stand parallel to the axis of the target monolith. The shutters move in the axial direction to open and close the neutron beam lines (cf. Figure 17.27). The SNS incorporates mercury as its target material, which ﬂows through a stainless steel container. This kind of target for high-power applications was ﬁrst investigated for the ESS project by Bauer [1049]. A heavy liquid metal target has

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17 The Accelerator-Based Neutron Spallation Sources

15

14

13 12

16

11

17

10

18

Shutters Target moderators

Proton beam

Core vessel inserts

Plug

1

9 2

8 3 4

7 5

6

Fig. 17.28 A horizontal cut through the SNS target monolith depicting the schematics of the 18 neutron beam lines for the experiments (after Gallmeier et al. [1065]).

some advantages over a water-cooled solid target, because (1) increased power handling capability is possible with a liquid target, (2) the liquid target material lasts for the entire lifetime of the facility, and (3) the radiation damage lifetime of a liquid target system, including its solid material container, should be considerably longer (see also the next section on target engineering). The mercury target design conﬁguration, shown inside the target vessel in Figure 17.29, has a width of 400 mm, a height of 100 mm, and a length of 650 mm. The mercury is contained within a structure made from 316-type stainless steel. Mercury enters from the back side of the target, ﬂows along the two side walls to the front surface (proton beam window), and returns through a 224 × 80 mm2 rectangular passage in the middle of the target. The target window, i.e., portion of the target structure in the direct path of the proton beam is cooled by mercury which ﬂows through the passage formed between two walls of a duplex structure of the target container. A safety container is provided around the mercury target to guide the mercury to a dump tank in the unlikely event of a failure of the target container structure. The target and integrated inner plug with the moderators are exposed to a serious radiation environment and have a limited lifetime due to radiation damage effects

17.3 Spallation Neutron Sources

Shielding plugs H2 moderators Outer shielding plug Mercury target

To the trolley system

Neutron beam guide channels Neutron beam ports Proton beam

Lower target vessel H2O / H2 moderators

Fig. 17.29

The SNS Hg TMR assembly (after [1066, 1067]).

and for the moderators of cadmium/gadolinium poison burn-up, respectively. The moderator vessels are integrated with the lower inner reﬂector plug. The inner reﬂector plug will be replaced periodically as a unit, including the moderator vessels, coolant lines, and cryogenic transfer lines. Also the target module is designed for periodic remote replacement. For this purpose, the target is mounted on a 5 m long steel plug on a carriage, which can be retracted on rails into the hot cell adjacent to the target monolith inside the target building (details are given in [1061]). This very useful procedure is routinely used at the ISIS spallation neutron source facility [643] and was also foreseen for the ESS spallation source [873, 1050, 1051]. The TMR system of SNS applies one ambient H2 O moderator and three cryogenic supercritical H2 moderators grouped around the target, two cryogenic H2 on the top and two at the bottom of the target one ambient H2 and one cryogenic H2 , respectively. A heavy water-cooled inner beryllium and outer stainless steel reﬂector region surrounds the moderators and target (cf. Figure 17.30). Cadmium and gadolinium is provided as decoupling and poison material for neutron ﬂux pulse shaping. Detailed performance simulations were undertaken to predict for different moderator conﬁgurations of the neutron ﬂux and neutron current characteristics by SNS neutronics group by Iverson et al. [1068–1073]. Although detailed experimental data on the moderator performance of SNS are not yet available, one can assume that the predictions given in [1072] by using the state-of-the-art of Monte

543

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17 The Accelerator-Based Neutron Spallation Sources Supercritical H2 moderator coupled

Supercritical H2 moderator decoupled/poisoned

Be inner reflector

Stainless steel outer reflector

Hg target

Proton beam Ambient H2O moderator decoupled/poisoned

Fig. 17.30

Supercritical H2 moderator coupled

The TMR system of the SNS (after [681, 1061]).

The SNS moderator conﬁgurations [1072].The poison depth is the position in respect to the vertical location of the poison plate inside the moderator (see also Figure 17.37 on page 552).

Tab. 17.10

Moderator location

Top upstream Top downstream Bottom downstream Bottom upstream

Moderator material

Moderator temperature (K)

Decoupling material

Poison material

Poison depth (mm)

H2 H2 H2 H2 O

20 20 20 300

Cd

Gd

29.6

Cd

Gd

14.75/24.75

Carlo simulation tools and scattering kernels Carlo have an absolute accuracy of 20–30%. Table 17.10 summarizes the latest moderator systems applied at SNS. The moderator arrangement is given in Figure 17.30. Figure 17.31 shows some examples of the total neutron current per unit energy and the coherent root-mean-square (RMS) as a function of the neutron energy viewed from the moderator surfaces in normal direction at a distance of 10 m. The dimensions of the viewed moderator surfaces are 100 mm in horizontal and 120 mm in vertical direction. The top upstream moderator is cadmium-decoupled, 100% parahydrogen system at 20 K and has curved viewed surfaces. The parahydrogen material has a maximum thickness of 60 mm, an average thickness of about 55 mm, is poisoned at the centerline with gadolinium 0.8 mm thick, and is viewed from both sides. The top downstream moderator is a coupled unpoisoned parahydrogen at 20 K, and is viewed from one side only with same dimensions as the top upstream moderator, but with 20 mm thick light water as premoderator. The bottom downstream moderator is identical to the top downstream moderator. The bottom upstream moderator is cadmium-decoupled H2 O at 300 K with ﬂat viewed surfaces. The

17.3 Spallation Neutron Sources

Neutron wavelength [Å] 1

1015

10

100

545

Neutron wavelength [Å]

10−1

103

1

10

100

10−1

102 RMS emission time [µs]

Neutron current [n /sr/eV/pulse]

1014

1013

1012

1011

101

100 1010

(A) H2O Cd/Gd 300 K (B) Para H2 Cd/Gd 20 K (C) Para H2 coupled 20 K

109 10−5 10−4 10−3 10−2 10−1 100 101 102 Neutron energy [eV]

(A) H2O Cd/Gd 300 K (B) Para H2 Cd/Gd 20 K (C) Para H2 coupled 20 K

10−1 10−4 10−3 10−2 10−1 100 101 Neutron energy [eV]

Fig. 17.31 Comparison of neutron current leakage spectra and the RMS neutron emission time of SNS moderators, e.g., of (A) an ambient H2 O moderator with Cd decoupler and Gd poisoning at a depth of 15 mm, (B) an H2 moderator at 20 K with Cd decoupler and Gd poisoning at a depth of 27 mm, and (C) a coupled H2 moderator at 20 K, respectively. Data are from Ref. [1072].

moderator material is 40.5 mm thick, and is asymmetric poisoned with gadolinium 1 mm thick and is viewed from both sides. The SNS instruments The SNS instrument hall will eventually contain 24 instruments on 18 beam lines (cf. Figure 17.28). Each SNS instrument is designed to be the best in its class and to complement the other instruments in the suite. Each instrument is expected to serve several areas of science. The following ﬁrst initial state-of-the-art instruments have been provided so far: • backscattering spectrometer (BASIS), • spallation neutrons and pressure diffractometer (SNAP), • magnetism reﬂectometer (MR), • liquids reﬂectometer (LR), • cold neutron chopper spectrometer (CNCS), • wide angular-range chopper spectrometer (ARCS).

The instrument fact sheets are provided at the instrument’s web pages [1074] and give a brief overview of each neutron scattering instrument currently installed at the

102

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17 The Accelerator-Based Neutron Spallation Sources Nanoscale-ordered materials diffractometer

Wide-angular-range chopper spectrometer

Backscattering spectrometer

Ultra-small-angle neutron scattering instrument

Spallation neutrons and pressure

BL-1C

Fine-resolution fermi chopper spectrometer

Chemical spectrometer BL-16A Neutron spin echo spectrometer

Magnetism reflectometer liquids reflectometer

Cold neutron chopper spectrometer

BL-14A Fundamental neutron physics beam line Macro Single-crystal molecular diffractometer neutron diffractometer

BL-8A BL-8B

Elastic diffuse scattering spectrometer Engineering materials diffractometer Installed, commissioned, or operating In design or construction Under consideration

Extended Q-range small-angle neutron scattering diffractometer

Hybrid spectrometer

BL-10

Powder diffractometer

Target and service bay

Fig. 17.32 A view of the SNS experimental area with the target station, maintenance and hot cell, and examples of potential instruments. The majority of the target building of about 70 × 90 m2 is reserved to scattering instruments located at the neutron beam lines (after [681]).

spallation neutron source SNS. Details of different instruments are there visualized. The instrument’s web pages are updated frequently depending on the science program and the status of their commissioning. There are shared support groups for the users such as, sample environment, detectors, data acquisition, choppers, software, shielding, and an ISSC (Instrument Systems Safety Committee). Figure 17.32 gives an artist’s impression of the SNS experimental hall with the target station, the maintenance and hot cells, and indicated instruments at several beam lines. SNS power upgrade The need for a beam power upgrade or for a beam energy to the SNS was early envisioned for the baseline design of 1 GeV, 1.4 mA and 1.4 MW to 1.3 GeV, 2.3 mA, and 3 MW. Most of the components and accelerator subsystems are capable to support higher beam intensities and higher beam energy [1075–1077]. Since many of the neutron scattering measurements are intensity limited, higher neutron ﬂuxes are desired to extend the capability of the SNS experimental program. The upgrade makes a second target station feasible. In January 2009, the upgrade for the accelerator system and the construction for a second long wavelength target station (LWTS) was approved [249, 681, 1078, 1079]. The second target station (STS) will be optimized for nanoscale and biological sciences with an emphasis on novel materials for energy production, storage and use. It is planned to commission the new system during the year 2012. Table 17.11 summarizes the SNS primary parameters.

17.3 Spallation Neutron Sources

The main parameters of the 1 GeV proton energy and 1.4 MW beam power SNS facility.a

Tab. 17.11

SNS beam parameters for the short-pulse target Particles Kinetic energy Beam cross section Average beam power/current on target Average number of protons on target Pulse frequency Pulse width on target Protons per pulse on target Energy per pulse on target Peak current on target

Protons 1.0 GeV 7 × 20 cm2 (elliptical), 1.4 MW/1.4 mA 8.74 × 1015 protons/s 60 Hz 0.695 µs 1.45 × 1014 24 kJ 33.5 A

SNS mercury target and target station performance parameters Beam power on targets Target material and type Target container Front cross section size of the target Average window current density/temperature Target mass, in/output temperature Percentage heat deposition in target Energy deposited in mercury Maximum local peak power deposition in target induced radioactivity of mercury after 30 years continuous operation

1.4 MW at 60 Hz mercury, liquid ﬂow target Stainless steel 316 SS LN 10.4 × 39.9 cm2 <10 µA cm−2 /<200◦ C <27 × 103 Kg/80◦ C/<110◦ C ∼60% ∼12 kJ 9.2 J/cm3 ∼3.4 × 1016 Bq (initial) ∼2.7 × 1015 Bq (after 1 year)

Four moderators [986]

1 H2 O decoupled/poisoned/thermal 1 supercritical H2 coupled/20 K 2 supercritical H2 decoupled/poisoned/20 K inner part Be/outer part steel, D2 O cooled

Reﬂector

General neutronic performance of ambient H2 O-moderators and cold H2 (20 K) moderators at 1.4-MW beam powerb Average thermal neutron current neutrons/(cm2 s)

Peak thermal neutron current neutrons/(cm2 s)

a

Coupled (H2 O): 1.1 × 1014 Decoupled/poisoned (H2 O): 2.8 × 1013 Coupled (H2 ): 8.8 × 1013 Decoupled/poisoned (H2 ): 1.5 × 1013 Coupled (H2 O): 2.9 × 1016 Decoupled/poisoned (H2 O): 2.5 × 1016 Coupled (H2 ): 1.7 × 1016 Decoupled/poisoned (H2 ): 1.3 × 1016

The detailed reference parameter of the SC linac and accumulator ring are summarized in Ref. [1062] (for more details see also Refs. [681, 1061, 1067, 1072]). b After Gabriel et al. [1067].

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17 The Accelerator-Based Neutron Spallation Sources

17.3.6 The Japanese Spallation Source and the Accelerator Complex J-PARC

The planning and construction of J-PARC (Japan-Proton-Accelerator-ResearchComplex) dates back on the long-lasting experience on accelerator-based neutron sources in Japan in the mid-1960s [1080]. The electron linear accelerator at the Tohoku University in Sendai in the mid-1960s was dedicated for nuclear study and neutron production of metal targets. After the KENS spallation neutron source [878] was built at KEK in Tsukuba in 1980, it was successfully used as a pulsed neutron source for neutron diffraction experiments and for spallation source moderator experiments (see Section 13.3.3.1 on page 446 and Refs. [876, 885, 886]). KENS was the ﬁrst dedicated pulse neutron facility in the world and it has been operated at its proton beam power of 3 kW for 17 instruments and a cold source. Soon after KENS several more powerful sources were built successively abroad such as IPNS of Argonne National Laboratory (6kW, 1981, USA), LANSCE of Los Alamos National Laboratory (80 kW, 1985, USA), and ISIS of Rutherford Appleton Laboratory (160 kW, 1985, UK) (cf. Table 17.17 on page 559). Later on the Japanese neutron scattering community demanded a much stronger pulsed neutron source as a post-KENS source for a long time. The most striking impact on the KENS facility results from the construction of a MW-class pulsed SNS, the JSNS (Japan Spallation Neutron Source), based on a 3 GeV proton accelerator of the J-PARC project started in 2000. The J-PARC project is jointly promoted by JAERI and KEK [1081, 1082] and is under construction and commissioning at the Tokai Research Establishment of JAERI [629]. The purpose of the joint project is to pursue frontier science in particle and nuclear physics, material and life science, and nuclear technology [145] . The accelerators of the J-PARC complex The accelerator systems within the J-PARC complex are the following (cf. Figure 17.33): (1) A 0.4 GeV normal conducting proton linac (NCL) to inject beams to the 3 GeV synchrotron, (2) a superconducting linac (SCL) to accelerate protons from 0.4 to 0.6 GeV primarily used for experiments on nuclear transmutation, (3) a 3 GeV synchrotron with 1 MW beam power primarily used for life and material sciences with neutrons and muons, and (4) a 50 GeV proton synchrotron with 15 µA proton current. The 50 GeV hadron facility can produce kaon, pion and neutrino beams. The whole complex with its intense particle beams provides a large variety of science capabilities in materials and life sciences, accelerator-driven nuclear transmutation of long-lived nuclides in nuclear waste (cf. Chapter 20 on page 593), and neutrino oscillations (using Super Kamiokande) and CP violation (cf. Section 22.3 on page 638). Details of the very ambitious scientiﬁc program are described at the J-PARC web pages [629] and publications therein. A schematic layout of the major facilities of the complex is illustrated in Figure 17.33. The schematics of the two linear accelerators, the NC and SC conducting systems including the dimensions and energies obtained, are given in Figure 17.34. Table 17.12 summarizes the main beam parameter of the linear accelerator, the 3 GeV rapid-cycling synchrotron (RCS), and the 50 GeV proton synchrotron.

17.3 Spallation Neutron Sources 50 GeV experimental area (particle & nuclear physics) 3 GeV synchrotron 333 mA, 25 Hz

50 GeV synchrotron 15 mA 3 GeV spallation source

Waste transmutation with 0.6 GeV protons 0.4 GeV NC linac

0.4– 0.6 GeV SC linac Neutrinos to superkamiokande

Experimental area materials & life science (neutrons, muon)

Fig. 17.33 A schematic view of the Joint Project Accelerator Complex (J-PARC) at the Tokai Research Establishment of JAERI in Japan (after Ikeda and Yamazaki [1083, 1084]).

3m 3.1 m 27.1 m

Ion source

RFQ

DTL

~249 m 91.2 m

50 KeV 3 MeV 50.1 MeV

108.3 m To 3 GeV RCS

ACS

SDTL

MEBT (324 MHz)

Fig. 17.34

15.9 m

MEBT2 (972 MHz)

190.8 MeV

400 MeV

SCC

To ADS

600 MeV

The principle proton linear accelerator scheme (after [1084, 1085]).

The J-PARC spallation source for materials and life science The ‘‘Materials and Life Science Facility’’ (MLF) of J-PARC is aimed at promoting materials science and life science using high-intensity pulsed neutron and muon beams. The main part of the MLF facility is the 1 MW spallation source JSNS and a muon production target of graphite, which share the proton beam from the RCS in tandem fashion [987, 1086]. The MLF facility was commissioned in 2008 and will start the user operation during the year 2009. The spallation neutron source (JSNS) consists of a mercury target [1087] driven by a high-intensity proton pulse beam (3 GeV energy, 0.33 mA current, 25 Hz repetition rate, 1 µs pulse width). Mercury, ﬁrst discussed as target material for high-intensity spallation sources by Bauer [1049], is currently also favored by ESSEurope and SNS-USA as the spallation target material because of a lot of excellent features for a MW-class source in terms of high Z, liquid at room temperature, and long lifetime (see also Sections 17.3.4 and 17.3.5). Three supercritical hydrogen cold moderators systems, two above and one below the Hg target, are applied

549

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17 The Accelerator-Based Neutron Spallation Sources Tab. 17.12

The main parameter of the J-PARC accelerator systems.

NC and SC linac parameter Protons Energy for RCS injection for the ADS (SCL) Peak current Macro pulse duration Repetition rate for the 3 GeV RCS for the ADS Ring injection pulse length SCL 2 cavities Total length NCL/SCL

Rapid cycling synchrotron (RCS) H− 0.4 GeV 0.6 GeV 50 mA 500 µs 50 Hz 25 Hz 25 Hz 455 ns β = 0.73/0.77 249 m/110 m

Injection energy Extraction energy Repetition rate Average beam current Particles per pulse Circumference 50 GeV MR synchrotron Injection energy Extraction energy Repetition rate Particles per pulse Circumference

0.181/0.4 GeV 3 GeV 25 Hz 333 µA 8.3 × 1013 348.333 m 3 GeV 50 GeV 0.3 Hz 3.3 × 1014 1567.5 m

(cf. Figure 17.36). Beryllium has been considered as the reﬂector material. Along with the neutron source, the JSNS target station, the MLF building construction involves the proton beam transport line, the mercury target system devices on the target trolley, the muon target station, which is placed just up-stream of the neutron source, the users experimental instrumentation, the hot cell and auxiliary systems. The general construction is very similar in design as the construction of the spallation sources ISIS, ESS, and SNS. The MLF building has the dimensions 150 × 70 m2 with a height of about 28 m. There are 23 neutron beam lines for the pulsed SNS and four muon extraction channels for the muon target at MLF [629], respectively. Figure 17.35 shows a vertical cross-sectional view of the target station which gives the principal structure of the neutron source target station with the horizontal proton beam, the Hg TMR vessel and the bulk shielding. Some major dimensions of the target station are also indicated. Figure 17.36 illustrates the TMR arrangement of the three supercritical 20 K cold H2 moderators. Taking into account that the lifetime of the three moderators will be different, an independent removal scheme for each moderator is considered in the design. Each moderator and its reﬂector part is replaceable by remote control via vertical access for the moderator maintenance. This is accomplished by the removable reﬂector plug depicted in Figure 17.35. The Hg target maintenance is done via a horizontal access with a target trolley system inside the MFL building, where the target vessel, the surge tank, the Hg heat exchanger, the Hg piping, and pumping systems for liquid mercury are installed [1087]. The principle layout of the decoupled or decoupled asymmetric poisoned supercritical 20 K H2 moderators are illustrated in Figure 17.37. Both decoupled moderators will be used at JSNS for high-resolution instruments. The coupled moderator below the target has a different shape compared to the decoupled moderators shown in Figure 17.36. It is a cylindrical system 20 K H2 moderator with a diameter of 14 cm and height 10 cm system premoderated with H2 O.

17.3 Spallation Neutron Sources

551

2.4 m

Magnetite concrete

Steel shielding

Helium vessel

Moderator reflector

1.6 m

Steel shielding

Steel shielding

Proton beam Proton beam window

Hg target

Ø5m Ø 9.54 m Fig. 17.35

The JSNS target station of the MLF facility (after [629, 1086]).

Table 17.13 summarizes expected neutron ﬂuxes and pulse widths for the 23 neutron beam lines of the 1 MW pulsed spallation neutron JSNS inside the MLF area. All moderator systems were carefully optimized on instruments utilization [1088, 1089], on moderator–reﬂector performance and engineering [1090], on moderator vessel materials, on thermal-hydraulics and mechanical strength issues [1091], on the cryogenic systems needs [1092], and on the neutronic moderator performance [893, 1093]. Many neutronic performance details of the applied moderators for JSNS were investigated also by experiments (cf. Section 13.3.3.1 on page 446). The instruments at the MLF facility There are 23 neutron beam extraction ports for the pulsed spallation neutron source JSNS and four muon extraction channels at the muon target of 2 cm thick graphite inside the MLF experimental area. The following ﬁrst initial state-of-the-art instruments suite have been provided so far: • space access neutron spectrometer, • neutron optics and fundamental physics,

11.6 m

Reflector plug

552

17 The Accelerator-Based Neutron Spallation Sources Decoupled supercritical H2 moderators Al-alloy container Steel reflector Hg target

Be reflector Coupled supercritical H2 moderator (high intensity)

Fig. 17.36 The position of the three moderators in service position above the target. The moderators are inserted from below and above into the working position inside the reﬂector plug of the JSNS-MLF target station (after [629, 1086]). Coolant layer (H2O)

Viewed surface 10 × 10 cm2

13 cm

Decoupler (Ag-In-Cd)

4.0 cm

H2, 20 K

2.5 cm

Poison plate (Cd 1.25 mm) Decoupled moderators for high resolution with and without asymmetric poison

Fig. 17.37 The principle layout of the decoupled moderator for high-resolution instruments at the JSNS. The insertion of a Cd poisoning plate indicates an asymmetric poisoned decoupled moderator (after Arai [1088]).

• • • • •

high-resolution powder diffractometer, test port facility, high-resolution chopper spectrometer, cold neutron chopper instrument, neutron reﬂectometer with horizontal-sample geometry,

17.3 Spallation Neutron Sources Estimated neutron performance data of the three supercritical 20 K H2 moderators (all values are given at a distance of 10 m from the moderator surface for 1 MW proton beam power; data are from Refs. [629, 987]).

Tab. 17.13

JSNS moderator typea

Coupledb Decoupled Poisoned (thicker side) Poisoned (thinner side)

Number of viewing neutron beam ports

Time integrated thermal neutron ﬂux (n s−1 cm−2 )

Peak neutron ﬂux at 10 meV (n eV−1 s−1 cm−2 )

Pulse width in FWHM at 10 meV (µs)

11 6 3

4.6 × 108 0.95 × 108 0.65 × 108

6.0 × 1012 3.0 × 1012 2.4 × 1012

92 33 22

3

0.38 × 108

1.4 × 1012

14

a

All moderators are of supercritical 20 K H2 and depicted in Figure 17.36. The moderator is cylindrical (with diameter = 14 cm, height = 10 cm) with a H2 O premoderator and a viewed surface of 10 × 10 cm2 . b

• engineering diffractometer, • versatile high-intensity total diffractometer. The MLF experimental facility is available to national and international users for both academic research and industrial applications. As every large research facility, MLF is completed by the following committees: (1) An International Advisory Committee, (2) a User Consultant Committee, (3) a Neutron/Muon Program Review Committee, and (4) a Neutron/Muon Instrument Review Committee. Further information are given at MLF web pages of J-PARC [629]. Summary of accelerator systems and science issues at J-PARC The J-PARC complex consists of the following accelerators: (1) a 400 MeV normal-conducting (NC) Linac, (2) a 600 MeV superconducting (SCL) linac to increase the energy from 400 to 600 MeV, (3) a 3 GeV synchrotron ring (RCS), which provides proton beams at 333 µA, 1 MW, and (4) a 50 GeV synchrotron main ring (MR), which provides proton beams at 15 µA with 0.75 MW beam power. Neutron and muon beams are already available in the Material and Life Science Facility (MLF). The major highlights are materials sciences and structural biology using neutrons produced in proton–nucleus spallation reactions. The role of hydrogen atoms in biological cells is of particular interest in life science and, there, the neutron beams play a crucial role for these studies. In addition to condensed matter research with neutrons, muon beams are also important using muon spin as a probe (cf. [1094] and references therein). Research will be, e.g., muon catalyzed fusion (µCF), negative muon lifetime and muon capture rate in liquid hydrogen, µ− µ conversion, and high-precision spectroscopy

553

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17 The Accelerator-Based Neutron Spallation Sources

of muonium atomic levels. About 2% of the 3 GeV proton beam on the graphite target yields pions. The resulting muon yield is evaluated e.g. at the decay muon beam channel to be 5 × 106 µ+ /s and 1 × 106 µ− /s for around 60 MeV/c with 10% momentum spread [1094]. Radioactive beams produced from the 3 GeV RCS are also useful to nuclear/astrophysics research. Finally, the high current 600 MeV SC Linac will be used for R&D for the accelerator-driven nuclear transmutation (as will be discussed in Chapter 20 on page 593). At the 50 GeV MR proton synchrotron, nuclear and particle physics experiments using kaon beams, antiproton beams, hyperon beams and primary proton beams are planned. By high-intensity kaon beams the production of strangeness in nuclear matter becomes possible. Experiments on kaon rare decays, such as K0 → π 0 , or ν − ν conversion to measure CP matrix elements, and experiments on neutrino oscillation using the Super-Kamiokande as a detector will also be carried out. Although the beam power is sufﬁciently high for all the above-mentioned science at the 50 GeV main ring; however, a higher beam power will enrich, in particular, neutron science. Thus, plans to upgrade the accelerator from 1 to 5 MW beam power for spallation neutrons is envisaged. 17.3.7 Safety Aspects and Radiation Protection General remarks The classiﬁcation in terms of nuclear safety of different spallation neutron source complexes with the accelerators, the associated target remote and service cells, the sample handling laboratories, the waste disposal of components and long-lived nuclides, and at least the waste from the decommissioning and dismantling is depending on the country in which the facility is installed. Some countries are considering accelerators and target stations as a nuclear installation, while in others only the presence of ﬁssile material leads to a classiﬁcation as a nuclear installation. Extensive experience is available from the ISIS spallation source in UK, the SINQ in Switzerland, and from the complexes SNS in USA and J-PARC in Japan currently under commissioning. An overview about the international legal framework used in different countries, e.g., the European Union, Japan, USA, for the commissioning of high-intensity accelerators and spallation sources is given in Refs. [1061, 1095], where also the differences and the practice in the countries are discussed in more detail. Independent of the above classiﬁcation in nonnuclear or nuclear facilities, the radiation protection legislation determines the general rules that must be guarantee the protection of personal against ionizing radiation. These rules are based on the recommendations of the ‘‘International Commission on Radiological Protection’’ ICRP-103 [1096] and ICRP-60 [1097]. Any radiation protection policy must also comply with the fundamental As Low As Reasonably Achievable ALARA principle. All safety issues should be part of the overall design of the whole facility. It is therefore important to include questions of the radiation shielding, issues of the decommissioning of the facility, and waste disposal at an early design stage,

17.3 Spallation Neutron Sources

where differences in the requirements may lead to large cost differences. The legal framework for the licensing of a high-intensity spallation neutron source complex has to be concerned with the following questions: • radiological protection including decommissioning and waste disposal issues (e.g., long-living radioisotopes produced in the Hg or PbBi target materials), • requirements from the chemical toxicity of special used materials (e.g. the toxicity and volatility of mercury used by ESS, SNS, JSNS), • aspects of civil engineering. The estimation and later the control of the radiation doses consider the following pathways: • external irradiation: (a) direct radiation from the facility (b) radiation from radionuclides airborne from skyshine (e.g. 3 H, 7 Be, 11 C, 41 Ar) normal operation (c) radiation from radionuclides deposited or produced from ground shine • internal irradiation by incorporation: (a) inhalation of airborne radionuclides (b) ingestion of radioactivity of nuclides deposited on the ground or in surface water and incorporated via a food chain. Categories of facility failures There are mainly about three main categories of different facility failures, which are applied in the European Union and also in the most other countries. These failures are distinguished usually by their occurrence probability as follows: (1) normal operation and frequent abnormal failure events → >10−2 per year, (2) so-called design basis accidents (dba) events → 10−6 − 10−2 per year, (3) hypothetical failure events → <10−6 per year.

In addition of failures of the facility itself the impact and occurrence of external events must also be part of the safety analysis of the whole system. Such accidental events could happen due to, e.g., earthquakes, aeroplane crashes, etc. Radiation protection At SNS and at ADS facilities, the key components to be considered in safety analyses are the target stations, the accelerators, and other systems as experimental installations, beam stops, etc. In general the target system of a spallation source is the most important component, which (1) produces direct radiation, (2) contain considerable amounts of radiotoxic and chemical toxic materials, which are highly dependent on the target material6) , and (3) contains burnable liquid materials in moderators, which maybe evaporated in case of failure. The target is the component of a spallation source facility which requires an accident analysis for design basis accidents and 6) Except as uranium or uranium alloys, the most important target materials, which are mainly be considered are Ta, W, Hg, Bi, Pb,

or PbMo/PbBi eutectic materials (cf. appendix on page 683).

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17 The Accelerator-Based Neutron Spallation Sources

Comparison of the total induced radioactivity in Hg targets of ESS, SNS, and JSNS normalized to 1 MW proton beam power as a function of the cooling time (data are from [647, 649, 1098, 1099]).

Tab. 17.14

Cooling time (h)

Initial 72 8.76 × 103

Total Hg radioactivity in (TBq) normalized at 1 MW proton beam power ESS targeta 1.7 × 104 0.6 × 104 0.04 × 104

SNS targetb 3.3 × 104 1.3 × 104 0.26 × 104

JSNS target 1.0 × 104 0.4 × 104 0.2 × 104

a Inventory after 30-years continuous operation (1.334 GeV proton energy, 1 MW beam power). b Inventory after 30 years continuous operation (1 GeV proton energy, 1 MW beam power).

Tab. 17.15 Most relevant radionuclides produced in the ESS mercury target irradiated with a proton beam energy of 1.334 GeV and a beam current of 3.75 mA (assumed is a 40 years operation (5000 h/y) (data are based on simulations by Lensing et al. [647, 649]).

Nuclide

3 H/HTO 3 H/HT 124

J

125 J 126 J 193 Hg 194 Hg 195 Hg 197 Hg 203 Hg 90 Sr 148 Gd 172 Hf 195 Au

ESS target inventory (GBq)

Half life (d)

Radiation type

7.9 × 105 7.9 × 105 3.1 × 103 1.4 × 104 6.3 × 102 1.9 × 106 1.4 × 105 3.2 × 106 2.2 × 107 1.5 × 107 1.4 × 104 3.5 × 104 7.3 × 105 4.2 × 106

4500

weak β

4.2 60 13 0.16 1.4 × 105 0.42 2.67 47 1.05 × 104 2.72 × 104 683 186

β, γ γ β, γ γ γ γ γ β, γ β α γ γ

Boiling temperature (K) 373 14 387 387 387 629 629 629 629 629 1653 3546 4875 3081

17.3 Spallation Neutron Sources 1017

Activity [Bq]

1015

H3 Si 32 Co 60 Pm143 Gd150 Hg194

C 14 P32 Tc 99 Pm145 Au194 TOTAL

105

107

1013

1011

109

107 10−5

10−3

10−1 101 103 Time after shutdown [years]

Fig. 17.38 Decay of long-lived solid radionuclides of the Ess Hg target based on Monte Carlo simulations by Lensing et al. [647, 649]. The thick plotted blue curve (total) illustrates the decay of the total produced inventory of solid, liquid, and gaseous radionuclides.

hypothetical failure events. The shielding of the target station and the accelerator, which is an extensive task, must guarantee the protection of the personnel against ionizing radiation (cf. Chapter 7 on page 233). The main concern on radiation protection of the accelerator is shielding in normal operation and measures and protection against local beam losses. Also the contamination of soil and ground water is an important safety issue. A good example of radiation safety is the work on estimating the radioactive inventory induced in high-power mercury targets of the spallation sources ESS [647, 649, 1039], SNS [1098], and JSNS [1099]. A comparison of the total radioactive inventories for ESS, SNS, and JSNS mercury targets as a function of the cooling time is shown in Table 17.14. By analysis of the total inventory and the from the selected relevant nuclides of the Hg targets of ESS, SNS, and JSNS Moormann et al. [1039, 1100, 1101] concluded : (1) There is an excellent agreement for the total activity of short-lived nuclides, (2) the total inventories of all calculations are effectively identical up to a decay time of about 1 y, (3) there are no large discrepancies for the inventories of individual short-lived nuclides, too. Discrepancies between different estimations are mainly due to 163 Ho with half-life thalf = 4750 years and 194 Hg with half-life thalf = 520 years, whose inventories were calculated to much higher values at SNS

557

558

17 The Accelerator-Based Neutron Spallation Sources

than at ESS. The SNS data [1098] for 194 Hg are probably slightly conservative by a factor of about 2, but the 163 Ho concentrations were overestimated by about a factor of 80. A compilation of the radioactive inventory in Hg targets, as calculated by ESS, SNS, and JSNS, was summarized by Moormann et al. [1102] of about 500 nuclides. The radiologically most relevant nuclides are depicted in Table 17.15. The long-lived nuclide 194 Hg with thalf = 520 years with its short-lived daughter nuclide 194 Au shows a very pronounced radio toxicity. The nuclide 163 Ho with thalf = 4700 years is of particular relevance for long-term waste studies. The ESS calculations [647] are altogether in sufﬁcient agreement with the SNS-calculations, but lead to slightly smaller total activities than SNS particularly for long half-life (factor 2–3). A neglect of some chain reactions may result in underestimation of production rates particularly for low-mass nuclides and may explain the differences found between ESS and SNS calculations, e.g., for 148 Gd of about a factor 5. The mentioned studies are all theoretical. The accuracy of the estimations are depending mainly (1) on the initial calculated spallation product distributions resulting from the intranuclear-cascade-evaporation models, and (2) from the used decay chain algorithms and data libraries. The recently accomplished ARIA’08 workshop [1103] at PSI in Switzerland gives an overview about the current state-ofthe-art on accelerator radiation induced activation. 17.3.8 Parameter Overview of the Existing, Commissioned and Planned Spallation Neutron Sources with a Beam Power Above 0.1 MW

As mentioned in Chapter 17 on page 505, the low-intensity spallation sources KENS [679, 977] at KEK, Japan, and IPNS [641, 978] at ANL, USA, are the originators of all spallation sources. Therefore, in Table 17.16 some of their parameters are summarized. Table 17.17 summarizes the main characteristics of existing and proposed continuous and pulsed SNS with an incident proton beam power ≥ 0.1 MW. The peak and average ﬂuxes are typical maximum values. Precise numbers vary and are depending on the moderator systems. Tab. 17.16

Spallation source

KENS IPNS

The parameter of the KENS and the IPNS low intensity spallation sources. Type of accelerator

Proton energy (GeV)

Pulse frequency/ length (Hz)/(µ s)

Beam power/ current (MW)/mA

Target material

Peak thermal th ﬂux Φ (n/cm2 s)

Synchrotron Synchrotron

0.50 0.45

20/0.05 30/0.1

5 × 10−3 /10 × 10−3 7 × 10−3 /16 × 10−3

W U/W

3 × 1014 5 × 1014

Cyclotron

Cyclotron Synchrotron Synchrotron Linac + compressor Linac +compressor Linac + compressor Synchrotron Synchrotron Linac +2 compres. Linac Linac Linac

SINQ-I

SINQ-II ISIS (TS1) ISIS (TS2) MLNSC

251.0 50/1.0 50/1.4 16.66/2000 16.66/2000 100/100

1.334 1.334 0.6

60/0.695

60/0.695

Continuous 40/1.0 10/1.0 20/0.125

Continuous

Pulse frequency/ length (Hz)/(µ s)

3.0 3.0 1.334

1.3

1.0

0.59 0.8 0.8 0.8

0.59

(GeV)

Proton energy

5/3.75 5/3.75 0.3/ 0.5

1.0/0.333 5/ 0.333 5/3.75

3.0/2.3

1.4/1.4

1.8/2.8 0.16/0.2 0.048 / 0.10/0.125

1.35/2.3

Beam power/ current (MW)/mA

Liquid Hg Liquid Hg W/vol. H2 O

Liquid Hg Liquid Hg Liquid Hg

Liquid Hg

Pb rods/ D2 O Liquid PbBi Ta/vol. H2 O Ta/surf. D2 O W/ vol. H2 O Liquid Hg

target type material cooling

preparation Operating Operating Operating Operating

> 3 × 1014 2 × 1012 1 × 1012 1.1 × 1014

> 3 × 1014 2.3 × 1015 2.3 × 1015 3.0 × 1016

1.0 × 1014 2.5 × 1014 2.5 × 1014 3.0 × 1014 3.0 × 1014 1.5 × 1015

3.0 × 1016 2 × 1017 2 × 1017 1 × 1016 1 × 1016 -

Proposed Operating

Operating Proposed Proposed

Proposed

Operating

1.35 × 1014

1.35 × 1014

(n/cm2 s)

Status

Average thermal ﬂux Φth (n/cm2 s)

Peak thermal ﬂux th Φ

Europe Russia

J-PARC, Japan Europe

ORNL, USA

RAL, UK RAL, UK LANL, USA

PSI, Switzerland

Site

The peak and average ﬂuxes are typical maximum values. Precise numbers vary and are depending on the moderator systems. Unless otherwise noted all target materials are solid. The abbreviations vol. and surf. stand for volume and surface cooling, respectively. b Spallation neutron source. c Planned power upgrade.

a

ESS-I MMF

JSNS JSNSc ESS

SNSb

SNS

Type of accelerator

Spallation source

Tab. 17.17 Existing continuous and pulsed accelerator-based neutron sources (data based mainly on Refs. [57, 1104–1106] and on project information of [629, 681, 873, 1039]).a

17.3 Spallation Neutron Sources 559

561

18 Target Engineering 18.1 Introduction

Targets in ADS applications be it in neutron generation by spallation neutron sources (SNS) for solid-state scattering research, or for nuclear waste transmutation (ATW), or for energy amplifying (EA), or for basic science on neutrino and radioactive beam production are in any case the most important part of a spallation source system. The subsystems of a spallation source may vary depending on the special application, e.g., an SNS for scattering experiments have subsystems as moderators and reﬂectors surrounding the target where the neutron pulses, which are released from the target are tailored according to the instrument’s needs, while a transmutation system has a blanket surrounding the target fueled with radioactive waste. The main problems one has to deal with on the target side specially on high power accelerator applications are: • efﬁciency of neutron production and transport • heat removal • stress and fatigue • radiation effects (damage) • induced radioactivity and after heat. Examples of realized spallation source targets are discussed in the following section. Speciﬁc details are given recently by Bauer in Refs. [1107–1109], with more detailed information in the Proceedings of ICANS-I-XVII, and at special workshops on ‘‘High Power Targetry’’ [1110]. At the ﬁrst time high-power targets in the MW beam power range were studied during projects as the ING [58] during the 1960s, and the SNQ [142] in 1981, and then again during the ESS study phase [551] in 1996.

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

562

18 Target Engineering

18.2 Spallation Source Neutron-Generating Targets 18.2.1 Spallation Source Neutron-Generating Targets at Beam Power Levels of About Some 100 kW

At the ﬁrst meeting of ICANS-I [1111] in 1977 several neutron-producing spallation targets were presented, which were in the following technology basis for almost all the targets on a beam power level of about some 100 kW. Table 18.1 summarizes some of the main parameters of these early targets and Figure 18.1 illustrates the target concepts in this early days. With the target power ranging up to 500 kW, plate or rod target designs could be envisaged, although the IPNS-II neutron-scattering target foresaw NaK cooling to Tab. 18.1 The advanced neutron source targets as presented at the ICANS-I meeting in 1977 [1111].

Name of the spallation source Parameter

ANL-IPNS-Ia

ANL-IPNS-II

LASLb

RALc

Application

Neutron scattering U with 7–10 wt% Mo Zircaloy-2 0.51 mm thick 600

Radiation effects Ta or W

Neutron scattering Ta

None

None

1000

300

Neutron scattering U Springﬁelds Zircaloy-2 0.51 mm thick 600

Target material Target cladding Maximum target temperature (◦ C) Target coolant Target element dimensions Target length Proton beam diameter Beam intensity Pulse frequency (Hz) Target heating (kW) Beam intensity distribution a b c

NaK Stacked Discs Ø 10 cm, 2.54 cm thick 23 cm 7 cm

NaK Rod Ø 10 cm

H2 O Rod Ø 2.5 cm

22 cm 7 cm

15 cm 1 cm

H2 O Stacked discs 9–10 cm2 , 0.6–1.2 cm thick 26 cm 6 cm

5 × 1013 p/s 60

5×1013 p/s 60

5×1011 p/s 120

3×1013 p/s 53

490

200

230

420

Gaussian

Gaussian

Gaussian

Parabolic

Data are from [1112]. Now called MLNSC. Now the ISIS facility.

18.2 Spallation Source Neutron-Generating Targets

563

IPNS-I target About 22 cm

H2O cooling

Proton beam

Coolant flow channels width about 1 mm

Uranium disc 2.54 cm thick cladding 0.51 mm

LANSCE target H2O coolant inlet line

Void flux trap region Coolant gap

Upper target

7.25 cm

Proton beam

14 cm

H2O coolant outlet line

Lower target

Pressure vessel Solid tungsten cylinder Ø = 10 cm

27 cm

~ 48.25 cm ISIS target U target plates with graded plate thickness

Pressure vessel

19

20

21

22

16-8

16-8

26-2

26-2

6-9

5-0

4-5

2-0

23

18 16-8 8-3

26-2

17 16-8 9-8

0-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 7-7 7-7 7-7 7-7 7-7 7-7 7-7 7-7 9-7 9-7 9-7 9-7 9-7 9-7 9-7 9-7

Proton beam

12-3 12-0 13-2 13-0 12-8 12-4 12-6 12-6 12-6 11-4 10-4 9-4 8-4 6-9 6-4 6-4

D2O outlet temperature ~ 44°C

2-66 L/s 2-66 L/s 1-77 L/s

Coolant channel about 2 mm

~ 27 cm

Fig. 18.1 Target concepts of the neutron sources IPNS-I at ANL [1112], MLNSC of LANSCE at LANL [939], and of ISIS at the Rutherford & Appleton Laboratory [640, 1014]. Both IPNS-I and ISIS used plate targets, whereas ISIS applied a graded plate thickness (see Table 18.1). The actual MLNSC target is a tungsten target (cf. Table 17.17). The given ﬁgures are not to scale.

D2O inlet temperature ~ 38°C

564

18 Target Engineering

cope with the high heat ﬂux density. Nevertheless the IPNS-II never got approval. The ‘‘LASL’’ target, now called, MLNSC is now a solid surface cooled tungsten rod with a moderator surrounding it. By splitting the target in two parts (a ﬁrst short part with diameter of 10 cm and length of 7.25 cm, and a second part of diameter 10 cm and length of 27 cm) creating a ﬂux trap void (diameter=10 cm and length = 14 cm) in between the quality of the extracted neutron beams could be improved signiﬁcantly1) (cf. Russell [939]). The target designs of IPNS-I-ANL, MLNSC-LANL, ISIS-Rutherford, are shown in Figure 18.1. The KENS-KEK target, which is not listed or shown here is also a surface-cooled target, its design allows a particularly good neutronic target to moderator coupling, owing to the very low power dissipated in it. Both ISIS and IPNS were originally using uranium targets, but the experience was poor; all targets failed at less than 250 mAh of beam load. This prompted ISIS with its 200 µA proton beam current to move to tantalum and most recently to tantalum clad tungsten targets, while IPNS with a proton beam current of 16 µA have developed a method for recycling targets [1113] in order to be able to continue taking advantage of the higher neutron yield of the targets with uranium as target material. Volume-cooled plate targets applying H2 O or D2 O as a cooling medium as used for the IPNS and ISIS targets are a good solution at beam power levels up to a few hundred kilowatt. For sources with a beam power of a few megawatt or more liquid metal targets have long been considered as the best choice because the deposited heat can be transported out of the beam by circulation of the target material. Also there is no dilution of the target by cooling channels. In 1966 a target concept with a molten lead–bismuth-eutectic was ﬁrst considered by Bartholomew at the ING project [58] using a CW proton accelerator delivering a proton beam of an energy of 1 GeV with a beam current of 65 mA to the target. The concept to use Pb–Bi as target material was studied than again by Fischer et al. [645] at the PSI2) in 1979, which resulted ﬁnally in the construction of the Swiss spallation neutron source SINQ. At the same time other technical issues for high-power targets were investigated, which lead to the concept of a rotating wheel target during the SNQ project in Germany between 1979 and 1985 [142]. In the following section different target systems in the MW power range will be described. 18.2.2 Spallation Source Neutron-Generating Targets at Beam Power Levels in the MW Range

The choice of target material for high-power SNS in the MW range is determined by the following demands [1049]: (1) high Z, for a high production rate of spallation

1) In a split target design, all four moderators are charged with the same neutron intensity leaking out of the target and do not suffer from high-energy neutron

background compared to a four moderator wing system. 2) The former name was Swiss Institute for Nuclear Research (SIN).

18.2 Spallation Source Neutron-Generating Targets

neutrons, (2) high density, for high luminosity, (3) radiation stability, for high lifetime, (4) low neutron absorption, for high neutron intensity (not necessarily an issue for pulsed sources), (5) low after-heat and induced radioactivity, for easy serviceability and decommissioning, and (6) availability and cost, for economic reasons. Several basic options are conceivable at the power level of several megawatts: a circulating liquid metal target, a stationary solid target, and a rotating solid target. From the above considerations tungsten seems to be the best choice for a solid target material, while mercury or lead–bismuth–eutectic (LBE) are the candidates for a liquid target. The PbBi eutectic is the preferred target material in systems where neutron absorption must be minimized in order to obtain a high time average neutron ﬂux or where, as in power-generating systems as energy ampliﬁers (see Chapter 21 on page 613), a high operating temperature is desirable. Therefore this material was chosen for the MEGAPIE target at SINQ [1034, 1114]. The high thermal neutron absorption cross section of mercury is the main reason for not considering it as a target material in steady-state SNS, which require a long neutron lifetime in the moderator for high ﬂux densities. In the case of a highintensity pulsed source such as ESS, SNS, and JSNS, however, some moderators are surrounded by decouplers as neutron absorbers to prevent neutrons that are moderated elsewhere in the reﬂector or target to enter the moderator late after the main pulse and therefore widening the pulse or its tail. In this case, the high thermal neutron absorption cross section of mercury, whose energy dependence is very similar to that of the generally used decoupler material boron, helps to avoid or reduce the amount of decoupler material between target and some moderators, thus eventually increasing the neutron ﬂux and reducing complexity. Moderation is also avoided by the absence of water in a circulating liquid metal target, thus diminishing the probability of resonant absorption of neutrons. As already shown, Figure 8.8 on page 266 compares calculated neutron leakage distributions from surfaces of various targets [636, 1115]. The mercury target shows not only the highest peak intensity, but also wider downstream extension, which favors the neutronic coupling into geometrically extended moderators (or more than one moderator per side). 18.2.2.1 The SINQ Target Systems The initial concept of the SINQ PbBi target was a pumped horizontal liquid PbBi target presented at ICANS-III in 1979 [645]. After more detailed studies and investigations the SINQ team decided to use a target system in a fully vertical position [1116]. This was the birth of the world’s ﬁrst and only continuous SNS [478, 1029, 1117]. There are several advantages to use the target in a vertical position with an incident proton beam from below: (1) one is a higher buoyancy head [1109] and a cooling by natural convection to avoid the undeﬁned conditions during start up after a beam trip or shutdown, which helped to initiate the ﬂow at beam start up, (2) a vertical target has a radial symmetry in heat and stress distribution, (3) an easier handling and a symmetrical geometry for the

565

18 Target Engineering

surrounding moderator tank is possible, and (4) such geometry allows a 360◦ access around the target block for instruments. The geometry is very similar to that applied by research reactors. The solid Pb rod target Although a liquid metal target was planned for the SINQ project from very early [1028], there were still some concern about undeﬁned conditions during start-up after a beam trip or shutdown of the proton beam, about the coolability of the beam window by natural convection ﬂow, and the degree of polonium release in a case of a major accident [1109]. Therefore, the target concept ﬁnally chosen for SINQ, shown in Figure 18.2, is an arrangement of Pb

~ 499 cm

Target head

Pb rod array in stainless steel tubes (C) (SINQ target mark 3) Moderator vessel Outer container target shell Inner container target shell ~ 211 cm

566

Target case Target rods Row of empty ALMg3 tubes Vacuum

(A)

(B)

D2O moderator

Proton beam

Fig. 18.2 The SINQ solid Pb rod target. (A) Overall view of the target with rod array – the neutron producing zone – and the cooling bottle below, the upper shield plug with supply shaft, and target head, (B) the target rod array with double walled and separated cooled shell, and (C) the rod array container of the Mark 3 target, Pb in stainless steel tubes (after Bauer [1107, 1114]).

18.2 Spallation Source Neutron-Generating Targets

rods surface cooled in a cross-ﬂow conﬁguration similar to the one developed for SNQ target wheel of Pb-ﬁlled aluminum alloy tubes [1118]. The SINQ target Mark 3, shown in Figure 18.2, comprises an aluminummagnesium alloy block with a hexagonal lattice of about 351 stainless steel (316L) tubes ﬁlled with solid Pb, which are oriented perpendicular to the proton beam and cooled by a forced D2 O ﬂow. The dimensions of the target block are 44.5 × 13.4 × 13.4 cm3 , and the pitch of the hexagonal rod array is 12.75 mm. The diameter of a target rod is 10.7 mm and the cladding thickness is 0.5 cm with a length of 170 mm. The former Mark 1 target consisted of solid Zircaloy rods, while the Mark 2 target was of similar construction but with several test elements that led to the current design. The Mark 3 target increased the peak thermal ﬂux in SINQ by 50% relative to the solid Zircaloy rods [1119]. The lowermost part of the about 5 m long structure (cf. Figure 18.2) with the target structure is surrounded by a double walled and separately cooled shell of AlMg3 , which serves as a cooling water ‘‘bottle’’ container. The cooling water ﬂows downward between the target frame and this container, turns around at the bottom and cools the target rods as it ﬂows upward between them. It should be mentioned that like all other radioactive heavy water and light watercooling systems, the target and the target enclosure cooling system is equipped with ﬁlters, ion exchangers, and a recombinator to remove undesired products from the coolant (mainly radiolysis products and especially 7 Be) to maintain a low residual radiation level in the cooling system when shut down. For a continuous operation of the SINQ Mark 3 target at 1.4 mA proton beam current at an energy of 570 MeV results in a peak current density of 35 µ A/cm2 at the center of the target window. The mass ﬂow of 2.5 kg/s D2 O yields in a ﬂuid velocity at the window center of the target of 6 m/s. A special feature of SINQ relative to other SNS is its operation in a continuous, nonpulsed mode like a reactor, which prohibits the use of strongly neutron absorbing materials in and around the target in order to ensure a high stationary neutron ﬂux in its large D2 O moderator tank. The current SINQ target with Pb rods in thin stainless steel tubes yielded about 50% more neutron ﬂux in the surrounding large D2 O moderator compared to the solid Zircaloy rods, which had been used for the ﬁrst two target units. The latest target of the Mark 3 type used has been exposed to a total charge of more than 10 Ah, without any problem. This corresponds to about 20 displacements per atom, dpa, in the most highly loaded stainless steel tubes. Except for gas production and radiation damage in the lead this is not a problem due to the high operating temperature. During full power operation some part of the lead in some of the rods is most likely molten. A very important feature in the operation of the SINQ target is its use for associated radiation effects programs, e.g., STIP (SINQ Target Irradiation Program) [478, 919, 1120–1122]. Up to 20 of the total of 450 target rods may be used for experimental irradiation test capsules ﬁlled with different kinds of test specimens which range from 3 mm diameter for TEM discs via miniature tensile probes or to liquid metal probes, e.g., PbBi- or Hg-ﬁlled capsules or even massive rods

567

568

18 Target Engineering

of alternative target materials as W or Ta. This associated irradiation program at PSI together with a similar program at LANL [630] became the most signiﬁcant source on radiation damage data of materials under spallation-speciﬁc irradiation conditions. More details were published at regular ‘‘International Workshops on Spallation Materials’’ [1110]. The liquid PbBi MEGAPIE target With the interest of the ADS community on more powerful spallation targets and with a research grant from the European Union the so-called MEGAPIE (MEGAwatt PIlot Experiment) project, a joint initiative by six European research institutions, JAERI, Japan, DOE, USA and KAERI, Korea, was founded to design, build, operate, and explore a liquid lead–bismuth spallation target for 1 MW of beam power, taking advantage of the existing SNS facility SINQ. Based on an initiative of PSI, CEA, and FZK, the MEGAPIE project was started in 2000 to design, build and operate a liquid metal spallation neutron target as a key experiment on the road to an experimental ADS [1114]. The design of the MEGAPIE target for a beam power of 1 MW and 6000 mAh of accumulated current was completed in mid-2006. The target contains 82 l of liquid PbBi eutectic (LBE) serving as target material and primary heat removal ﬂuid. The 650 kW of thermal heat is removed by forced convection using an in-line electromagnetic pump with 4 l/s capacity. The heat is removed through 12 monowall cooling pins via an intermediate oil and a water-cooling loop. The beam window made of the martensitic steel T91, experiencing a peak current density of about 50 µA/cm2 , is cooled by a jet of cold LBE of about 1 m/s extracted at the heat exchanger exit by a second EM pump from the LBE mainstream. Figure 18.3 summarizes the main operating parameter of the target and shows an overall layout. The target is a fully pumped system with the PbBi loop completely enclosed in the target shell. In August 2006 the liquid metal target system MEGAPIE produced successfully the ﬁrst neutrons at SINQ-PSI: at a relatively stable and constant proton beam current of 40 µA, which corresponds to about 25 kW of beam power. After 4 months of operation, the beam on the MEGAPIE target has been stopped according to the original experimental plan. The target has performed almost perfectly over the whole period and about 2.8 Ah of charge were accumulated. The use of LBE as target material increased the amount of alpha-decaying isotopes considerably in comparison to solid Zircaloy or lead targets used up to now in SINQ. Special attention therefore has to be paid to the handling of the target material and the spallation products produced [1124]. Although the total activity of such a LBE liquid metal target is similar to that of the solid Zircaloy and Pb targets used presently in the SINQ (about 1016 Bq at the end of irradiation), its alpha-activity is with 3 × 1014 Bq, mainly from Po isotopes, three orders of magnitude higher compared to the SINQ Pb targets with about 3 × 1011 Bq [1124]. Special attention has also to be paid to the safe enclosure of the radioactive liquid metal and the gases and volatile elements produced during irradiation. Simulation has been shown [1119] that for the Mark 3 Pb-steel, and MEGAPIE PbBi targets, the unperturbed thermal ﬂuxes are 6.27 × 1013 (±0.23%), and 8.78 ×

18.2 Spallation Source Neutron-Generating Targets Beam energy: 575 MeV Beam current: 1.74 mA

Wetted surface: 8 m2

Upper shielding

Fill/drain pipe Heat exchanger

539 cm

Design life: 1 year of operation (6000 mAh) Target material: PbBi eutectic (Tm=125˚C) LBE volume: 82 l

Main pump

Deposited heat: 650 kW LBE Trange: 240–380˚C

Bypass pump 40.3 cm

Max. flow velocity: ~1.2 m/s Beam window:T91 steel Window temperature: 330–380˚C

Bypass duct

Radiation damage: 20–25 dpa

Central rod

209.55 cm

Safety hull

21.2 cm

Guide tube Target window Safety window

Fig. 18.3 Details of the liquid PbBi MEGAPIE target with some main operating parameters (after Dury [1123] and Groeschel [1124]).

1013 (±0.19%) (n cm−2 s−1 mA−1 ), respectively. This would imply that SINQ with the MEGAPIE target can be expected to be more intense than the existing Mark 3 target by about 40%. 18.2.2.2 The Mercury Targets for the Pulsed Spallation Neutron Sources ESS, SNS, and JSNS The PbBi eutectic is the preferred target material in systems where neutron absorption must be minimized in order to obtain a high time average neutron ﬂux or where, as in power generating systems, a high operating temperature is desirable. Since both is not the case in MW-class of pulsed SNS, these facilities prefer mercury as a target material, mainly because it does not require auxiliary heating, has a higher density than PbBi and does not produce alpha-active isotopes as Po. There are some other advantages as, e.g., (1) No radiation damage is induced directly in the target material but only in the container, (2) no reduction of target material density by the presence of cooling water in the target volume, (3) water contamination (e.g., by 3 H and 7 Be) is strongly reduced because the cooling is applied outside the beam area, and (4) the speciﬁc activity is reduced due to a large total mass of target material, avoiding active decay heat removal during service periods. The liquid metal in the target system must be fully enclosed since a pulsed proton source would eject the liquid from an open surface with a speed of about 10 m/s.

569

570

18 Target Engineering

The concept to use mercury as target material was ﬁrst proposed by Bauer [1049] for the 5 MW target of the European Spallation Source (ESS) [1114] and was then adopted and slightly modiﬁed for the SNS, USA [681, 1061] and the JSNS at J-PARC, Japan [1086]. All three concepts are using a horizontal beam injection and a laterally extended so-called slab target geometry. The three targets differ due to different proton beam power levels on the mercury target e.g., 5 MW at ESS, 1.4 MW at SNS, and 1 MW at JSNS and are different mainly by the way in which the liquid mercury ﬂow is directed across the window. In addition to the average power input, which causes thermal stresses in the window, the pulsed nature of the beam, especially in the short pulse targets, causes high-frequency stresses in the window and pressure waves in the liquid, which also generate stresses on the walls, which is not present in continuously operating targets. These phenomena, called cavitation damage erosion (CDE), was found by the JAERI team by Futakawa et al. [1125] and is a challenge for all high-intensity short-pulsed liquid metal targets. ESS follows mainly the MEGAPIE approach to direct part of the ﬂow across the window by providing a bottom inlet channel in addition to two side inlet channels (cf. Figure 18.4). The SNS target uses a double-walled container with a narrow channel to guide a partial ﬂow all the way across the window and out of the target again (cf. Figure 18.8), while for the JSNS target an elaborate system of blades was developed to establish a horizontal ﬂow across the window and in the whole beam interaction zone (cf. Figure 18.11). All these three mercury target systems are supported by extensive ﬂuid mechanics and thermal hydraulics calculations. The three targets have separately cooled outer shells, which serve to safely retain the mercury in the system in case the primary liquid metal container develops

Target flange manifold

Beam window

Proton pulse on target 100 kJ, 50 Hz

Upper duct Side duct Central duct Bottom duct LMTC GFSG H2O LMRH

Fig. 18.4 Schematic view of the liquid metal target container (LMTC) with liquid metal return hull (LMRH) and an exploded view of the LMTC with the components, the central part, side ducts, inlet support (after ESS-Update Report [1057] on pages 4.41/4.43).

Components of the liquid metal container

18.2 Spallation Source Neutron-Generating Targets

a leak. The targets are mounted on movable carts that allow to pull them into maintenance cells for shell replacement after draining the mercury into a storage tank (cf. Chapter 17 on page 505). Because the issues and the parameter regime are similar comparing the liquid mercury targets of ESS, SNS, and JSNS some of the issues and challenges are discussed concerning only the ESS target. One reason for this argument is the ﬁve times higher proton beam power of ESS compared to SNS and JSNS. The mercury target of the European spallation neutron source ESS The horizontal proton beam injection in both ESS targets (SPTS /LPTS) with slab-type geometry and an oval cross section allows placing the moderators close to the beam axis giving optimum neutronic coupling, and reﬂecting fast neutrons by the wings. It also allows an elliptical beam cross-section thus reducing the current density, the associated heat load, and radiation damage in the window. To allow complete drainage of the liquid from the circuit during target exchange a slight wedge shape is used, which in addition reduces lateral losses of the broadening beam along its path through the target. A schematic view of the target geometry with liquid metal target container (LMTC) and liquid metal return hull (LMRH) is given in Figure 18.4. The target vessel length is about 800 mm with an additional length of the manifold and ﬂange system of 700 mm. The LMTC has inlet ducts on both sides and on the bottom, while the mercury is ﬂowing back through the central part and an upper duct. Upper and lower ducts have additional structure for mechanical stiffening, which is needed to avoid bulging, due to the pressure difference of about 2 bar between forward and return ﬂow channels (see the lower panes of Figure 18.4). A separately water-cooled, double-walled LMRH is added in the event of a mercury leak. Depending on the system pressure, water-cooling allows only surface temperatures below 150◦ C. The gas-ﬁlled safety gap (GFSG) between the LMTC and LMRH has an overpressure (e.g., helium, 10 bar) with respect to the LMTC, which allows early detection of cracking of the LMTC through a pressure increase in the target circuit and in addition reduces the mechanical stresses on both the LMTC and the inner wall of the LMRH. The GFSG is connected to the mercury storage tank via a return pipe. A more detailed description of the system is given in Ref. [1057]. The axial distribution of the power density in the central cylinder with 1 cm radius is shown in Figure 18.5 for the peak current density of about 80 µA cm−2 . A total deposited power of 2.37 MW, i.e., 47% of the total time averaged 5 MW, was estimated by Monte Carlo calculations for an elliptical beam cross section of 20×6 cm2 (constant throughout the target volume [636]). The remainder of the beam energy is accounted for by escaping particles (28% in other components, e.g., reﬂector, shielding, and structure) and by nuclear binding energy (25%). A 20% margin is added in the design base, giving a total power deposition in the target of 2.8 MW and a peak of 3 kW/cm3 . For the stainless steel window, the calculations yield a peak power density of 1.4 kW/cm3 , corresponding to a value

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18 Target Engineering 3.0 2.5 Deposition power in kW/cm3 in 1 cm radius

572

2.0 Axial fit Monte carlo 1.5 1.0 0.5 0.0 0.0

10.0

20.0 30.0 40.0 Target depth z [cm]

50.0

60.0

Fig. 18.5 Power density in the central cylinder with 1 cm radius of the mercury target for a proton beam power of 5 MW as obtained from Monte Carlo calculations (after [636]).

Fig. 18.6 Computed trajectories of 0.1 mm diameter helium bubbles. The helium bubbles are injected via the bottom inlet duct (after ESS-Update Report [1057, 1126, 1127] on page 4.51).

of about 2.3 kW/g(mA/cm2 ) at about 80 µA/cm2 [636] for the maximum beam current density [873]. In the early analysis for the ESS target it was therefore recognized that mitigation of the pressure pulses resulting from the pulsed heat input was necessary to limit the stress on the target container at 5 MW average power (100 kJ/pulse at 50 Hz). The method to achieve this was to be injection of bubbles of a noncondensable gas, e.g., Helium, in order to provide enough space into which

18.2 Spallation Source Neutron-Generating Targets

the heated mercury could expand. Figure 18.6 shows a (not yet optimized) result of initial simulations of trajectories for gas bubbles injected from the bottom bafﬂe in the ESS target [1057, 1126, 1127]. During the rarefaction phase of this pressure wave cavitation bubbles develop in the ﬂuid, since the liquid cannot sustain tensile stress. This leads to the well-known effect of ‘‘pitting erosion’’ on the container when the bubbles collapse and eject a high-velocity jet near the wall. The CDE effect was carefully studied in out-of-beam tests by Futakawa et al. [928, 1125, 1128–1130] as well as in in-beam tests by the LANSCE-WNR [1131–1133] at relevant pressure or power pulses. If these effects will be unmitigated, it might lead to unacceptably short lifetimes of the target shells, of the order of three weeks or less [1107]. While surface hardening was found effective in delaying the lifetime of target windows, this effects only a thin, 30 µm thick, surface layer and, therefore, will not be a realistic solution. Alternate materials and surface hardening treatments can provide therefore only a modest potential for extending target life. Required improvements in target life and power capacity must come by mitigation of the damage mechanism, either by reducing pressure wave magnitude at generation (e.g., through gas bubble injection, longor short-lived bubbles) or isolating the vessel wall from damaging bubble collapse by creating a layer of gas between it and the mercury [1132, 1134]. Despite enormous efforts and good progress made in the understanding of the above mechanism and its parameters, it is not quite clear yet how serious the problem will really be in the SNS and JSNS targets at about 1 MW proton beam power and how exactly it can be mitigated. Even if the pitting issue can be solved or the effect substantially mitigated, there remains the question of radiation damage in the target container window exposed to the proton beam, which is the other lifetime-limiting factor. Flow and temperature ﬁelds in the liquid mercury were studied for the ESS target by computational ﬂuid dynamics (CFD) with thermal hydraulics codes, e.g., [1135] using a realistic three-dimensional target model in material and geometry with all structures as shown in Figure 18.4. Investigations were done on the effect of inlet temperature, window thickness, and ﬂow partitioning between different inlet channels on the maximum window and mercury temperatures. For the ESS target these temperatures have to stay below certain limits, e.g., 400 and 300◦ C, respectively. The window material parameters in the calculations corresponded to 12% Cr steels. Figure 18.7 shows computed liquid mercury temperature ﬁelds in the horizontal mid-planes of the ESS target for a heat deposition of 2.9 MW in the mercury and 9.1 kW in the window. An inlet temperature of 100◦ C, an inlet velocity of 1.05 m/s, and a ﬂow distribution with 15% of the total mass ﬂow through the bottom duct were used in these computations (details are given in Refs. [1057, 1126, 1127]). Some major results from the CFD analysis are: (1) The window cooling is dominated by the ﬂow through the side ducts, (2) the optimum temperature distribution is obtained for less than 18% of the total mass ﬂow going through the bottom duct, and (3) a 2.2 mm window thickness, which was derived from stress considerations [1057], is still tolerable from a cooling point of view.

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18 Target Engineering

Max. temperature [K] 544.7

373.0 Min. temperature [K]

Fig. 18.7 Computed liquid mercury temperature ﬁeld in the horizontal mid-plane of the target for a ﬂow distribution with 15% of the total mass ﬂow through the bottom ducts (after ESS-Update Report [1057, 1126, 1127]).

Finally, based on all the detailed investigations on the ESS mercury target the selection of structural materials for the window and target container directed only to 9–12% Cr martensitic steels to qualify for the LMTC of ESS. Where the thickness of the window of about 2–3 mm is being considered as the ﬁrst approximation [1057].

The SNS target of the spallation neutron source at ORNL The SNS mercury target uses a double-walled container with internal mercury cooling and with a narrow channel to guide a partial ﬂow of the mercury all the way across the window and out of the target again. Figure 18.8 illustrates the inner target module indicating the direction of the ﬂowing mercury. Figure 18.9 shows the whole target module, the outer vessel, with the ﬂange connecting both vessels with a module section to the rear of the target. This is a block of stainless steel with machined internal passages that direct the ﬂowing mercury into the respective passages in the forward mercury vessel. The walls of the inner vessel, and the mercury vessel, are cooled by the ﬂowing mercury, while the outer vessel is cooled by circulating water. The SNS target assembly comprises as shown in Figure 18.10, a target module mounted on a target carriage that moves on a trolley system transport system originally used at ISIS and adapted also for ESS and JSNS at J-PARC. The target module is subjected to both irradiation and cavitation erosion and, therefore, must be replaced periodically. The target module is an assembly of stainless steel vessels that is mounted at a target plug at the end of the mercury loop piping assembly.

18.2 Spallation Source Neutron-Generating Targets

Proton pulse on target 33 kJ, 60 Hz Target container cooling channels

M ma erc in ury flo w Stainless steel target container Proton beam

0

30 cm

Fig. 18.8 Target module illustration showing the internal mercury ﬂow paths and the mercury target container (after SNS-Completion Report [1061]).

Target hull stainless steel 316L(LN) SST

~6

50

mm

70

mm

1 ~2

Fig. 18.9 The SNS target module with outer vessel and the ﬂange connecting the outer vessel with the inner vessel, the mercury vessel, to the rear of the target (after Lousteau et al. [1136]).

Part of the target module is shown at the target plug in Figure 18.10. The term target ‘‘plug’’ refers to the assembly that combines the target module, lengths of mercury loop piping, carriage, and shielding.

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18 Target Engineering

Fig. 18.10 SNS target modul installed on carriage in service bay cavern (photograph after Lousteau et al. [1136]).

The mercury vessel and water-cooled shroud provide additional barriers against the leakage of mercury into the core vessel. The target module is designed for periodic remote replacement. Before replacement of the target module, mercury is drained to the storage tank, piping connections are removed in the target service bay, and the target carriage locking mechanism is released. The target plug (i.e., the whole target carriage, including the target module) can then be driven from the operational position back into the target service bay, where the replacement can begin using specially designed remote manipulator equipment. The carriage is mounted on wheels that move along precisely aligned rails to allow the target to be installed and removed. The carriage assembly includes passive shielding surrounding the piping connecting the target module to the process systems (more details are given in [1061]). Table 18.2 summarizes the main technical parameters of the whole mercury target module. The JSNS target of the Japanese spallation neutron source at J-PARC As already discussed in Section 17.3.6 on page 548 the spallation neutron source JSNS installed at J-PARC has also a target with mercury to realize a 1 MW-class target station. The system is similar to the mercury target systems of ESS and SNS where also the mercury is forced to ﬂow through a target container in order to carry off the heat and to cool down the target container wall and the target window. In order to meet these technical issues, a cross-ﬂow type (CFT) target container was developed to realize a mercury ﬂow ﬂowing across the proton beam path [1086, 1087]. The CFT target has been optimized to the mercury ﬂow channel structure using ﬂow guides of steel plates as ﬂow distributors. A schematic view of the JSNS mercury target is depicted in Figure 18.11 showing the safety vessel and as a cutaway the mercury target which is mounted inside the safety vessel. The mercury container consists of a single vessel, while the double-walled safety hull covers the mercury vessel. This makes the whole system to a triple-walled

18.2 Spallation Source Neutron-Generating Targets Summary of SNS mercury target parameters (data are from Refs. [1062, 1132, 1136]).

Tab. 18.2

SNS target parameter

Value

SNS target parameter

Value

Operating power (MW) Incident proton Energy (GeV) Protons per second (p/s) Protons per pulse (ppp) Pulse frequency (Hz)

1.4 1.0

Total Hg Weight (kg) Total ﬂow (l/s) Window ﬂow (l/s) Average ﬂow (l/s) Window target pressure (bar) Bulk target pressure (bar) Maximum Hg temperature (◦ C) Total target module component weight with Hg (kg) Dimensions of target module (cm) (length/width/height)

21.5 × 103

Beam shape Beam size (mm2 ) Energy deposited in Hg (kJ) Maxiumum energy deposition (MJ/m3 ) Peak initial pressure (MPa) Hg weight (kg) Hg volume (l) Material of window/container

8.73 × 1015 1.4 × 1014 60 Elliptic 200 × 70 12 9.2 25 795 1450 316L(LN) SST

24.5 1.5 1.0 2.9 2.8 90 1925

217/65/70.6

structure. The safety hull works as a support of the target vessel and a boundary of the helium vessel. The mercury container and its window is cooled by the mercury ﬂow and the safety hull is cooled by D2 O ﬂowing through the double-wall gap. The space between the safety hull and the mercury vessel is kept by a reinforcement structure and is ﬁlled with helium. Figure 18.11(b) shows the mercury target without safety hull. Indicated are the six ﬂow guides of steel plates 10 mm thick placed in the mercury ﬂow path to realize the ‘‘cross-ﬂow,’’ to remove the heat generated by spallation reaction between mercury and the proton beam. The arrangement of the ﬂow guides to obtain appropriate mercury ﬂow distribution by thermal hydraulic (CFD) analysis and the structural integrity [1137] of the mercury target were optimized with the LS–Dyna system [1138]. The reliability of the models was conﬁrmed by water ﬂow experiments using the mockup model of CFT targets [1139, 1140]. The mercury target and the safety vessel are connected to each other by reinforcement ribs with bolts and welding. The wall thickness of 2.5 mm for the beam window with a half-cylindrical shape is very thin, in order to reduce the bulk heating by spallation reaction, while side walls have a thickness of 10 mm to ensure the rigidness of the target vessel and erosion allowance. The mercury target vessel is made of 316LN-stainless steel except for the proton beam window (PBW), which is made of INCONEL 718. The mercury target has an effective length of about 800 mm, a height of about 100 mm and a width of 260 mm at the front. The total length of the safety hull plus the mercury target is about 2000 mm with

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18 Target Engineering

D2O vessel cooling

Out

Flow guide D2O

Mercury In

Safety hull

Beam window Target inner vessel

Proton beam (a)

Flow guide mercury Mercury Mercury vessel

Proton pulse on target 40 kJ, 25 Hz Beam window 2.5 mm

Beam stop

Proton beam (b)

00

~ 260 mm

mm

~8

Flow guides mercury

Fig. 18.11 The schematics of the JSNS mercury target with the structure of the safety vessel (a) and a cutaway view of the main mercury vessel with the ﬂow guides. The cross ﬂow of the mercury is also illustrated (b) (after Haga et al. [1087]).

a maximum width of 1110 mm. The effective mercury volume of the CFT target is about 0.023 m3 [1140]. Figure 18.12 shows the target vessel and the mercury target container to be connected with the mercury pipelines and the target trolley for the remote handling. This is facilitated by using a link system with bellows [1087]. The target–trolley link system is based on the concept of the one-touch vacuum connector so as to be operated (fasten and loosen) with a power manipulator. This system is to be veriﬁed with a mock-up model. For the maintenance the lifetime of the PBW is essential. An estimated number of about 5 dpa per year yields a lifetime of the PBW of about 1 year. To receive a more precise measure of the lifetime, post-irradiation examination (PIE) preparations on the ﬁrst JSNS target have been started.

18.2 Spallation Source Neutron-Generating Targets

Mercury pipes (Ø 150 mm) Target inner system

Target outer vessel Target trolley system Fig. 18.12 A drawing of the JSNS mercury target with vessel and target trolley for remote handling (after Haga et al. [1087, 1140]).

Target trolley

Mercury target

Fig. 18.13 Photograph of the JSNS mercury target in the target cavern mounted at the target trolley (after Haga et al. [1140]).

Figure 18.13 shows a photograph of the JSNS target vessel mounted at the target trolley. Table 18.3 summarizes the main parameters of the JSNS mercury target system. 18.2.2.3 Rotating High-Power Targets The ﬁrst pulsed SNS in the multimegawatt beam power range was proposed and studied in detail in Germany during the SNQ project [1118, 1141] in 1980–1985. It was quickly clear that the goal of a 5-MW proton beam power spallation target could hardly be met by a water-cooled plate target as developed for the then existing low power sources IPNS [1112] and ISIS [1014]. Although a liquid metal target as originally proposed in the Canadian ING-Project with 60 MW proton beam power [58] was studied as an option, SNQ preferred a concept based on an idea used for high-power X-ray anodes, where the target rotates in order to dilute the average load on the material. The ﬁrst design, as shown in Figure 18.14, the SNQ rotating wheel target, foresaw a 2.5 m diameter disk of 12 cm height. The spallation internal structure in the outer part of this

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18 Target Engineering Tab. 18.3 Summary of JSNS mercury target parameters (data are from Refs. [1087, 1137, 1140])

JSNS target parameter

Value

JSNS target parameter

Operating power (MW) Incident proton energy (GeV) Proton current (mA) Protons per second (p/s) Protons per pulse (ppp) Pulse frequency (Hz) Beam shape Beam size (mm2 ) Energy deposited in Hg per pulse (kJ) Window material container material

1.0 3.0

Maximum energy Deposition in Hg (MJ/m3 ) Mercury ﬂow rate (l/s) Total power deposited in target (MW) inlet/outlet Hg Temperature (◦ C) dimensions of CFT Target modul (cm) (length/width/height) Overall vessel length (cm) Effective volume of the CFT target (m3 )

0.333 2.1 × 1015 8.4 × 1013 25 Gaussian 180 × 70 19.3 Inconel 718 316LN(SST)

Value 8.8 11.1 0.482 50/72 80/26/8

200 0.023

Wheel diameter 2.5 m

Rotating AlMg3 window Target wheel

Neutron leakage distribution from the target [z]

I[z]

Proton beam Target Rotating elements seal Coolant inlet Coolant outlet

Hydraulic bearing Driving turbine Water feed for turbine

Fig. 18.14

The SNQ rotating wheel spallation target (after [1118, 1141]).

wheel about 70 cm in depth, indicated in Figure 18.14, was planned to be made up of lead-ﬁlled aluminum alloy tubes which would be cooled by water ﬂowing between them. This water would ﬂow forward through bores in the upper and lower support structure of the disk and would, upon turning around, also cool the rotating beam entrance window. The support structure, the beam window and the tubes of the target elements were planned to be of the AlMg3 alloy.

18.2 Spallation Source Neutron-Generating Targets

With a diameter of the target pins of 2.5 cm in the outer region, indicated in Figure 18.14, and a water ﬂow gap of 1.5 mm between them, the degree of ﬁlling was much higher than what could have been achieved in a stationary system. The speed of rotation was to be such that consecutive pulses of the 100 Hz accelerator would hit adjacent areas on the target periphery, requiring ca. 8 m/s or, with a circumference of 7.8 m, a rotation frequency of about 1.0 Hz or even lower. This very moderate rotation rate was to be accomplished by a water driven turbine which would be fed from a controlled pressure loop and which would drain into the main cooling water circuit. A model of the target support and drive unit was built and with a dummy target load simulating the weight and inertia of the actual target, was run for nearly 1000 h without problems, albeit in the absence of radiation load. Two alternatives to the lead ﬁlled aluminum tubes were considered for the target structure: clad-depleted uranium rods and an edge-cooled array of hexagonal tungsten rods. While uranium was expected to yield nearly two times more neutrons than lead, its use was discarded on the basis of waste considerations because, although the rotating target kept most of the material outside the region of high thermal neutron ﬂux, production of plutonium and other higher actinides could not be excluded. This would generate a much more serious licensing and disposal problem than lead, in which virtually no long-lived alpha-activity is generated. On the other hand, an edge cooled tungsten target [1107, 1142], appeared as a very attractive solution because it would allow a more than 50% higher target density than surface-cooled lead pins and would largely avoid the difﬁculties resulting from radiolysis and formation of 7 Be in the water hit by the proton beam. As the SNQ project was terminated in 1985, the research necessary to qualify the edge-cooled tungsten target never took place. In Table 18.4, performance data of the SNQ wheel target are summarized. The concept of a rotating solid target was also investigated as a backup solution for the 5 MW ESS target [1054]3) in case there were problems with the liquid mercury target that could not be solved satisfactorily. For the 50 Hz pulse repetition rate a diameter of 1.5 m was chosen, leading to a slightly higher time average radiation load. This was considered acceptable since, in the mean time, data on material lifetime were compiled from irradiation experiments at SINQ indicating that the service time of the beam entrance window of AlMg3 has survived about 200 mAh/cm2 , which would correspond to more than 7.5×104 h of operation at 5 MW beam power for a 1.5 m diameter rotating target [1107]. The concept of a rotating solid target was recently investigated [1145] during a study phase for a pulsed spallation source planned for the BASQUE Country in Spain. The neutron source will be driven by a circular accelerator (synchrotron), in which the desired proton beam power of 250 kW can be reached by choosing a reasonably high proton energy of 2 GeV and a relatively modest average beam current of 125 mA. A disk-shaped target made of tungsten that can be rotated 3) In Report ESS03-155T, February 2004, Chapter No. IX. ‘‘Investigations of the

neutronic performance of the ESS using a tungsten wheel target,’’ p. 61.

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18 Target Engineering Tab. 18.4 Summary of SNQ rotating wheel target parameters (data are from Refs. [1143, 1144]).

SNQ target parametera

Value

Incident protonenergy (GeV) Operating power (MW) Proton current (mA) Protons per second (p/s) Protons per pulse (ppp) Pulse frequency (Hz) Beam shape and size

1.1 5.5 5.0 3.1 × 1016 3.1 × 1014 100 Gaussian, 4.0 cm FWHM Truncated at a radius of 4.0 cm Pbb (76.5%), H2 O( 16.6%), AlMg3 (7%) W (76.5%), H2 O( 16.6%), AlMg3 (7%) U (76.5%), H2 O( 16.6%), AlMg3 (7%) 2.9 (Pb), 3.4 (W), 11.4 (U) 0.06 (Pb), 0.11 (W),0.17 (U), AlMg3 (7%) 1.2 × 1015 (for dep U target) 6.0 × 1014 (for Pb target) 4.5 × 1016 (for dep U target) 1.2 × 1016 (for Pb target)

Target material

Average energy deposition in target (MW) Peak energy deposition in target (kW/cm3 ) Window/structure material Time average thermal ﬂux (n× cm−2 ×s−1 ) Peak thermal ﬂux (n× cm−2 ×s−1 )

a The detailed ﬁnal target speciﬁcations are given in Ref. [1141] in Chapter E on pages E4–E7. b Pb was ﬁnally chosen as backup solution.

to reduce radiation damage, which would serve the facility for at least 30 years without the need for exchange. The proposed diameter of the tungsten target disk was estimated to be 50 cm and height 5 cm. The thermomechanical investigations also show that this novel target, driven stationary, is capable of coping with the heat deposited by the proton beam of 250 kW, provided certain measures are taken to ensure sufﬁcient cooling and to avoid excessive local stresses. The heat removal capacity of the target can be signiﬁcantly increased by operating it with a continuous rotation at a very moderate revolution rate of a few turns per minute, which will allow an increase in the beam power to 500 kW or beyond [1145]. A wheel target concept [1146] is also under investigation at SNS-ORNL. 18.2.2.4 Windowless Liquid Metal Targets It should be shortly mentioned here that other high-power target concepts were studied and investigated, which may not be limited by the radiation damage in the beam entrance window or where the pressure wave issue plays no role. These target systems are mainly considered in continuously operating spallation sources. The idea at the ING project in the early 60s [58] was to inject the high-intensity proton beam directly into the liquid metal without a target window. Both parallel ﬂow, with the beam injected parallel to the ﬂow direction of the liquid metal, and cross ﬂow conﬁgurations have been considered in the recent

18.2 Spallation Source Neutron-Generating Targets

years. The latter is the preferred solution of the IFMIF project [1147], which aims at providing a high ﬂux of neutrons with spectral properties near to those prevailing in a fusion reactor ﬁrst wall by stripping 2 × 125 mA of 40 MeV deuterons of their protons in a ﬂowing lithium curtain target. A concept of this kind requires very high ﬂow rate of the liquid metal curtain and is possible only if the range of the injected particles, i.e. the required target thickness is small. For particles with a longer range injection of the beam parallel to the direction of the liquid metal ﬂow allows to take advantage of a higher temperature rise in the liquid and hence smaller ﬂow rates and heat exchangers. This conﬁguration is the preferred solution of most ADS studies. A project which is actively developing this concept is MYRRHA4) , a high ﬂux fast neutron irradiation facility proposed by SCK-CEN at Mol, Belgium [1148, 1149]. As in an ADS facility a spallation target will be used to drive a PbBi cooled sub-critical core which will then generate the high fast neutron ﬂux to be used for the planned experiments. MYRRHA is planned to be fed by an accelerator of 350–400 MeV with a beam current of 4–5 mA. A similar target was also studied in the German SNQ project [142]. The concept of a coalescing hollow jet is also an interesting idea in the target system considered for the next-generation radioactive beam facility ‘‘European Isotope Separation On-Line Radioactive Ion Beam Facility’’ (EURISOL) [1150] called the unconﬁned liquid jet target. Here it is proposed to inject a beam coaxially into a mercury jet formed in essentially the way studied for SNQ [142] but with a high-speed pumped horizontal ﬂow. It should be noted that a target with a free surface is in principle not suited for pulsed high-power operation, because the shape of the free surface will be destroyed at each pulse. Nevertheless consideration is being given to using a target of a design similar to EURISOL also for the next-generation neutrino factory NuFact [724] (see also Section 22.3 on page 638). The idea is to use a very high ﬂow rate to restore the conﬁguration between two pulses over the beam interaction length of about 60 cm. 18.2.3 Materials for Accelerators and Targets of Spallation Sources

This section summarizes the material issues for systems driven by high intensity and high-power accelerators. As mentioned before the purposes of all these facilities cover a broad range of basic and applied research, e.g., neutron spallation sources for research in the physical, chemical, and life sciences, for materials irradiation, and for isotope production, accelerator-driven sub-critical devices (ADS) for transmutation of nuclear wastes and for energy ampliﬁcation, radioactive beam facilities for fundamental nuclear physics research, and facilities that use muons or neutrinos for particle physics research. Some materials considerations are unique to some particular accelerators and facilities. For example, high-intensity stress waves and the resulting cavitation 4) Myrrha is a ﬁgure of the ancient greece mythology and was the mother of Adonis the divinity of beauteousness.

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18 Target Engineering

erosion in heavy liquid metal targets may occur where the sharpness of the beam pulse produces shock by thermal expansion. Other irradiation environment properties and materials response are similar to those for ﬁssion or fusion reactors. For example, the high displacement doses in the target structures of high-power accelerators, produced by the impinging beam and the spallation neutrons, are of similar magnitude to those in high ﬂux reactor cores and ﬁrst walls of future fusion reactors. In addition to the central issue of radiation effects in metallic structural alloys, designers will be concerned with radiation effects in polymers and ceramics, which may be employed as seals, sensors, or insulators. Other applications place demands on materials that are not related to radiation but to other aspects of aggressive environments, such as compatibility of materials with special purpose ﬂuids [1151]. In many cases, materials lifetime and performance are the key features that will determine the components lifetime, the remote handling issues, and the safety of the facility. Among the wide variety of materials employed in targets and target stations of high-power spallation sources, materials in or close to the proton beam will experience the most critical load. Whereas ‘‘conventional’’ loads such as mechanical stresses, temperatures and corrosion can be kept sufﬁciently small by a proper design and material selection, there are two effects, already mentioned (Chapter 6 on page 215), which will determine the lifetime of the targets and their surrounding components: (1) radiation damage due to high-energy protons and neutrons, and (2) possible stress waves excited by the a pulsed energy input [1152]. A number of reviews on the materials properties for spallation sources have been published previously. In particular, the reader is referred to comprehensive reviews, e.g., for metallic alloys [1153], for ceramics [1154, 1155], for structure, and target materials [483, 1108, 1156]. In the appendix on page 683, the physical properties of materials for spallation sources and ADS are summarized. At this point it should be mentioned, as shown in Table 18.1 on page 562, that many targets made of uranium as natural, depleted or enriched uranium, have been used so far in various spallation neutron facilities of small and medium proton beam powers (KENS (3–5 kW), IPNS (6–8 kW), and ISIS (160 kW)), due to their higher neutron yield per proton compared to other nonactinide heavy metal targets such as tantalum, tungsten, lead, etc. – about 1.7 times higher yield than the latter in case of a depleted uranium target, about four times or more in case of a highly enriched one. Also the SNQ project considered a target loaded with depleted uranium. However, the operational experience was not successful and the service life of uranium targets was much shorter than expected. The problems were associated with radiation damage and swelling, which led to these limited operational lifetimes [1157]. There are quite severe problems to overcome to get approval to use targets containing many critical masses of ﬁssionable material [1158]. Thus, the use of nonactinide target materials such as Ta, W, and Pb, became the unique solution suggesting to use solid targets at beam power levels far below of 1 MW and at higher power levels applying liquid metal target materials such as PbBi and Hg.

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19 Research with Neutrons 19.1 Introduction

This section is devoted to the ‘‘scientiﬁc case,’’ the research employing neutrons as probes in different scientiﬁc and technical domains. A detailed description of the activities in these domains is certainly beyond the scope of this book and the science case is such manyfold and voluminous that in the following only a small representative selection can be discussed in order to describe the the importance of the new generation of high-intensity neutron sources. A more detailed compilation about the utilization of spallation neutron sources (SNS) for neutron research can be found on the web pages of the operated and planned SNS, e.g., ISIS [643], SINQ [627], SNS [681], J-PARC [629], and ESS [837, 1037, 1043] or by information of the different national and international neutron scattering societies and associations, e.g., the ‘‘European Neutron Scattering Association’’ (ENSA) [1159], which is a platform for discussion and a focus for actions in neutron scattering and related topics within Europe, the ‘‘European Strategy Forum on Research Infrastructure’’ (ESFRI) [1048] of medium to long-term future scenarios for neutron-based science, the ‘‘Neutron Scattering Society of America’’ (NSSA) [1160] etc.. Neutron beams are uniquely suited to studying the structure and dynamics of materials at the atomic level. Neutron scattering is used to examine samples under different conditions such as variations in vacuum pressure, high temperature, low temperature, and magnetic ﬁeld, essentially under the real-world conditions. By using neutron activation analysis, it is possible to measure minute quantities of an element. Atoms in a sample are made radioactive by exposure to neutrons in a reactor. The characteristic radiation each element emits can then be detected. A neutron is an uncharged and electrically neutral subatomic particle with mass about 1839 times that of the electron. Neutrons are stable when bound in an atomic nucleus, while having a mean lifetime of approximately 900 s as a free particle, decaying through the weak interaction into a proton, an electron, and an antineutrino. The neutron, like proton, is the ground state of a three-quark system and consists of one ‘‘up’’ and two ‘‘down’’ quarks with spin 1/2 and baryon number 1. QCD allows the calculation of particle masses and magnetic moments; predictions, 939 MeV and −1.86 nuclear magneton, compare well with measured Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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19 Research with Neutrons

values, 939.6 MeV and −1.913 nuclear magneton. The neutron and the proton form nearly the entire mass of atomic nuclei, so they are both called nucleons. They interact through the nuclear, weak, electromagnetic, and gravitational forces. At the end of the second World War, researchers in the USA gained access to the large neutron ﬂuxes that even relatively modest nuclear reactors were capable of delivering. For more than a decade (Nobel Prize in physics to Chadwick in 1935 for the neutron discovery in 1932) neutrons had then been known as building blocks in the atomic nucleus. Fermi showed in 1942 that neutrons from ﬁssion of the uranium nucleus could support a controlled chain reaction. He had earlier made the important discovery that slowed-down or thermal neutrons show a much greater inclination to react than fast ones do (Nobel Prize for this discovery, among others, to Fermi in 1938). The special properties of these slow neutrons make them suitable for detecting the positions and movements of atoms. Even before the entry of the nuclear reactors into the research arena, results of using simple neutron sources had indicated that neutron beams could be used for studying solid bodies and liquids (condensed matter). However, there were many difﬁculties to overcome before these possibilities could be realized. The 1994 Nobel Prize in Physics was awarded to Brockhouse and Shull for their pioneering contributions to the development of neutron scattering techniques, neutron diffraction and neutron spectroscopy, for studies of condensed matter. In simple terms, they helped answer the questions of where atoms ‘‘are’’ and of what atoms ‘‘do.’’ Neutrons are an ideal probe for investigation of the structural and dynamical properties of matter. Their electrical neutrality enables them to penetrate deep into matter and due to the low energy the matter can be studied without being destroyed. The magnetic moment enables neutrons to explore microscopic magnetic structures and study magnetic ﬂuctuations. The energies of thermal neutrons are similar to the energies of elementary excitations in solids and consequently molecular vibrations, lattice modes and the dynamics of atomic motions can be probed. Very much the same is true for the wavelengths of thermal neutrons being similar to the atomic spacings and therefore a means to determine structural information from 10−13 to 10−4 cm or crystal structures and atomic spacings. Applying a method called ‘‘contrast variation’’ complex molecular structures can be differentiated since the scattering amplitude of neutrons depends strongly on individual isotopes. Due to the unique sensitivity of neutrons to hydrogen atoms, the best way to see a part of a biomolecule, nucleic acid or a protein in a chromosome is through isotope substitution replacing hydrogen by heavy hydrogen (deuterium) atoms. In particular for light atoms this physical property makes neutron scattering out-classing compared to investigations using X-rays, because neutrons scatter from materials by interacting with the nucleus rather than the electron cloud of an atom. This means that the neutron scattering power (cross section) of an atom is not strongly related to its atomic number (the number of positive protons in the atom, and therefore number of negative electrons, since the atom must remain neutral), unlike X-rays and electrons where the scattering power increases in proportion to the number of electrons in the atom. Therefore neutron scattering has three signiﬁcant advantages:

19.1 Introduction

• it is easier to sense light atoms, such as hydrogen, in the presence of heavier ones; • neighboring elements in the periodic table generally have substantially different scattering cross sections and can be distinguished; • the nuclear dependence of scattering allows isotopes of the same element to have substantially different scattering lengths for neutrons. Isotopic substitution can be used to label different parts of the molecules making up a material. Moreover, the absolute value of the X-ray scattering cross sections is particularly small for light atoms compared to neutron scattering cross sections. The capability of neutrons localizing other light atoms among heavy atoms allows scientists to determine the critical positions of light oxygen atoms in yttrium-barium-copper oxide (YBCO) – a promising high-temperature superconducting ceramic. The span of applications is ranging from the basic research of materials science (structure of new alloys or modern plastics and ceramics) up to the enlightenment of the structure and function of proteins, enzymes, and other biomolecules. Engineering scientists use neutrons for the investigation of highly loaded components (e.g., turbine blades) and measuring of the inner forces of workpieces, geoscientists for the research of rock samples or chemists for the acknowledgment of catalytical processes or the structure of redeveloped molecules. Neutrons scattered from hydrogen in water can locate bits of moisture in jet wings indicating microscopic cracking and early corrosion. 19.1.1 Solid-State Physics

Neutrons are the key to our understandings of solids. Nowadays advances in solid-state physics provide the backbone of many technologies. One example is molecular and organic magnets i.e. solids built from structurally well deﬁned clusters of magnetic ions in a complex environment. Such systems are of fundamental importance and could also serve as atomic scale information storage systems. Research on the electron–electron interactions underpinning such phenomena as high-temperature superconductivity and ‘‘colossal’’ magneto-resistance are at the cutting edge of solid state physics. The high neutron ﬂux anticipated at next generation facilities will enable experiments on excitation continua of metallic systems, among others, that will yield a wealth of new information. Alternatively NMR techniques yield valuable local data on the magnetic susceptibility of solids, but interpretation of these data requires knowledge of the material-speciﬁc hyperﬁne interactions. The interaction parameters are difﬁcult to calculate and to measure independently, especially for complex materials. Even if they could be calculated accurately, NMR would remain constrained to energies several orders of magnitude below those of electronic correlation effects. Synchrotron radiation is another valuable characterization tool for solid state magnetism. However, the cross section for charge scattering is several orders of magnitude larger than that for magnetic scattering of photons. Thus, even magnetic structure determinations

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of simple single-crystalline solids by magnetic X-ray scattering are exceedingly difﬁcult. A quantitative determination of the magnetic collective modes and excitation continua of complex electronic materials by inelastic X-ray scattering will not be feasible in the foreseeable future.

19.1.2 Materials Science and Engineering

The interaction of a neutron with the nucleus of an atom is weak (but not negligible) making the neutron a highly penetrating probe. This allows the investigation of the interior of materials, rather than the surface layers probed by techniques such as X-ray scattering, electron microscopy or optical methods. This feature also makes the use of complex sample environments such as cryostats, furnaces and pressure cells quite routinely, and enables the measurement of bulk processes under realistic conditions. High intensity SNS will allow for the ﬁrst time to investigate materials in real time with realistic dimensions and under real conditions. One example is the deformation of materials and the understanding of the mechanisms involved. New solid-state joining techniques require more accurate information about the generation of residual stresses that will add to in-service stresses and shorten component life. Finite element modeling has become the main method for the design and assessment of engineering structures. Such models cannot be developed reliably without accurate information to validate them. Neutron diffraction is the only technique that can do this, providing measurements deep inside most engineering materials.

19.1.3 Chemical Structure, Kinetics, and Dynamics

Neutrons are spin-1/2 particles and therefore have a magnetic moment that can couple directly to spatial and temporal variations of the magnetization of materials on an atomic scale. Unlike other forms of radiation, neutrons are ideally suited to the study of microscopic magnetism, magnetic structures and short wavelength magnetic ﬂuctuations. The cross sections for magnetic scattering and scattering from the chemical structure are fortunately of the same magnitude, permitting the simultaneous measurement of the magnetic and chemical behavior of materials. Chemists ask for higher performance materials, cleaner environments and improved efﬁciency in the use of chemicals. The aim is to develop molecular materials with useful and tuneable physical properties such as magnetism, superconductivity, nonlinear optical activity, polymorphism, etc. The understanding of intermolecular interactions that hold 3D arrays of molecules together as, e.g., weak hydrogen bonding interactions is mandatory. Neutron research will allow for more rational crystal engineering, enabling chemists to tailor properties by designing structures, e.g., of pharmaceuticals.

19.1 Introduction

19.1.4 Soft Condensed Matter

High penetrability, space time resolution at proper scales and variation of contrast qualify neutrons as a unique tool for studying the structural and dynamical properties of soft matter at a molecular level. One challenge of basic soft condensed matter science is the development of a molecular rheology, i.e. an understanding of mechanical and rheological properties on the basis of molecular motion. This aim requires space time resolution on widely differing length and time scales and the selective observation of key components. Neutrons are uniquely suited to meet these goals; however advances in instrumental techniques and neutron ﬂux are required, far beyond the present state of the art.

19.1.5 Biology and Biotechnology

Neutrons are nondestructive probes, even to complex and delicate biological or polymeric samples. Neutrons are of major importance, when information on hydrogen atoms – their positions, hydrogen bonds, the role of water, hydrogen motions – as well as contrast variation on larger scales and dynamical features in general are of interest. Unfortunately, present neutron intensities are too low to expect progress in a broad sense. Present neutron sources require large sample sizes, which are often not available. Their limited intensity renders multidimensional contrast variation schemes impossible and constrains time resolution severely. Next-generation sources will enable the miniaturization of neutron-scattering techniques and facilitate multiparameter studies. The future intention is to provide tools for ﬁnding molecular markers for early stage detection of illnesses. Neutron data on such complex systems become a prerequisite for the design of more advanced combinations of biological matter with solid surfaces for biochips, including biosensors.

19.1.6 Earth and Environmental Science

Thanks to the latest generation of diffractometers and spectrometers at the most modern neutron sources, neutron scattering has recently been added to the methods applied in earth science. However, as for example one of the most signiﬁcant issues in earth science related to the prediction of earthquakes and volcanic eruptions remains out of the reach of present day neutron instrumentation. The reliability of models crucially depends on the knowledge of the physical and chemical properties of the materials involved (oceanic crust, upper mantle, continental crust). Mineral structures and material behaviors under extreme temperature and pressure conditions simulating the real conditions deep in earth would be in the ﬁeld of in-situ studies when more intense neutron sources would be available.

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19.1.7 Fundamental Neutron Physics

The features of neutrons appearing as both composite particles and quantum waves have been investigated with thermal, cold and ultra cold neutrons at many sources. Accurate measurements of the neutron β-decay conﬁrmed the number of particle families predicted in the Standard Model at three. Neutron experiments have made substantial contributions to our understanding of strong, electroweak, and gravitational interactions. A signiﬁcantly higher intensity and pulse structure of future generation neutron sources would provide new possibilities for fundamental neutron physics experiments. One of several questions concerns the handedness of the universe. The grand uniﬁed theory assumes a left–right symmetric universe and explains the evident left handedness of nature through a spontaneous symmetry breaking caused by a phase transition of the vacuum, a scenario which would entail a small right-handed component for the neutrinos. Looking at the decay of a neutron into a hydrogen atom could provide a deﬁnite answer, since one of the four hydrogen hyperﬁne states cannot be populated at all if neutrinos are completely left handed. The best way to check whether deviations in the singlet scattering lengths signal a breakdown of isospin invariance is a direct scattering measurement of the neutron – neutron scattering at very low energy as available at the ESS. Ultracold neutrons could be used to study elastic and inelastic surface reﬂections and quantum gravitational states.

19.1.8 Muons as Probes for Condensed Matter

Spallation neutron sources as discussed in the following chapter represent at the same time an intense resource of muons. Muons provide an alternative to the neutron as a probe of condensed matter and are frequently used in complementary experiments. The muon can be implanted into virtually any material and its spin polarization monitored to determine its site in crystal lattices or molecules, giving information about the local atomic structure and dynamics. Resulting from the decay of positive or negative pions into a muon and a neutrino, muons have spin 1/2, carry one elementary electric charge, and have a mass about 207 times the rest mass of the electron or 1/9th of the proton rest mass. Thus, from the particle physics point of view they are ‘‘heavy electrons,’’ whereas from a solid-state physics or chemistry point of view they are ‘‘light protons.’’ In the rest frame of the pion, the muon magnetic moment is antiparallel to the muon momentum, allowing muon beams with a very high degree of spin polarization (nearly 100% when the muons are collected from pions decaying at rest) to be produced. Free muons have a mean lifetime of 2.2 µs, decaying into a positron and two neutrinos, with the positron emitted preferentially in the direction of the muon spin, allowing the time evolution of the muon polarization to be measured by detecting the position of the decay positrons. Why using muons for condensed matter studies?

19.1 Introduction

• The muon is essentially a sensitive microscopic magnetometer with a magnetic moment three times that of the proton. In condensed matter, muons are repelled by the nuclei, and thus muons probe magnetic ﬁelds in the interstitial regions between the atoms. The frequencies of muon resonance or precession signals give a direct measurement of local magnetic or hyperﬁne ﬁelds. Measurements of the relaxation of the muon polarization characterize the distribution of these ﬁelds. • In contrast to the neutron, the muon is usually a perturbative probe since it represents a defect carrying a unit positive charge. The defect interactions are essentially identical to those of the proton, allowing, for example, studies of the isolated hydrogen defect centers in semiconductors via their muonium analogues. • In insulators, semiconductors, and in organic materials positive muons may capture an electron, to form hydrogen-like quasiatoms known as muonium (Mu). Due to the hyperﬁne interaction between muon and electron spin, muonium is an even more sensitive magnetic probe than the bare muon. Muonium can be used as a substitute for hydrogen in organic molecules or radicals, giving information on the structure, dynamics and reactions of these species. • Muons have approximately one-ninth of the proton mass, resulting in large isotope effects. This favors the observation of quantum effects, notably the inﬂuence of zero point energy in chemical bonds and quantum tunneling. Many questions in almost all research disciplines desire for higher intensities and better monochromatization than currently available with existing sources.

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20 Accelerator Transmutation of Nuclear Waste – ATW 20.1 Introduction

The production of radioactive waste and its long-term disposal is one of the most serious problems of electricity generation by nuclear power. There still exists the public concern about three problems using nuclear power, (1) the processing and storage of radioactive waste, actinides and ﬁssion products, (2) the proliferation of nuclear weapon material, e.g., high enriched uranium and plutonium, and (3) at least the reactor safety. At present about 450 Giga Watt electrical power are produced by about 440 nuclear reactors around the world. Transuranic elements (Np, Pu, Am, Cm, . . .) and ﬁssion products are produced by the operation of nuclear reactors, e.g., mainly light water reactors (LWR). Because of their radiotoxicity, these elements have to be safely separated from the biosphere and stored until their ﬁnal decay. Geological disposal of long-lived and highly concentrated waste is one option investigated in a number of countries. But many experts consider that longterm geological storage is an unacceptable issue because the waste ﬁnally will not be eliminated from the biosphere. Therefore, scientists and nuclear engineers are divided on the choice of geological repositories for long-lived waste disposal. It is in fact impossible to guarantee the integrity of this kind of storage for future generations and moreover over geological long periods. A deﬁnitive solution to the problem would be the complete elimination of the most offending isotopes with the help of nuclear reactions which would allow long-lived elements to ‘‘transmute’’ into stable ones. It should be mentioned here that the accelerator-based transmutation as a concept have been discussed since many years mostly for breeding ﬁssile material from fertile thorium and uranium [1161] and also several projects on accelerator production of tritium were investigated during the 1990s [1000, 1162] (details are given in Section 20.5 on page 607 of this chapter). The high-power accelerator needed for the transmutation techniques was not within technical reach until fairly recently. The accelerator development over the last decades for high-energy physics has prompted proposals to develop accelerator-driven systems (ADS) for nuclear waste incineration and energy production. There are several acronyms and abbreviations commonly used in the transmutation community, which may be useful for the following discussion, e.g., ADTT Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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(accelerator-driven transmutation technology), ATW (accelerator transmutation of waste), ADS (accelerator-driven systems), ADEP (accelerator-driven energy production), ADSS (accelerator-driven subcritical systems), AAA (advanced accelerator applications), and APT (accelerator-driven production of tritium, projects investigated in the US and in France). Basic deﬁnitions and terms in nuclear technology applied in transmutation are summarized in the appendix on page 681. The application of high-intense proton drivers for the transmutation of longlived radioactive in accelerator transmutation of nuclear wastes (ATW) is discussed as an alternative to the controversial geological storage and could strongly inﬂuence the debatable fuel cycle and future energy production. The topic ADTT provides an external spallation neutron source, offers signiﬁcant safeguards and nonproliferation advantages in burning weapons plutonium until it is ‘‘gone forever.’’ An ADTT program has the potential to burn commercial reactor spent fuel down to levels that do not require radioactive storage for hundreds of thousands of years, and ﬁnally, gives the opportunity for the production of energy from the abundant element thorium in a safe, subcritical assembly with minimal long-term nuclear waste. The idea to transmute the radioactive waste produced in nuclear reactors into stable isotopes or radionuclides with a much lower hazard was considered in the literature by Steinberg et al. [1163, 1164], Bartholomev and Tunniclife [58], Wolkenhauer et al. [1165] since 1958. Most of the work was restricted to transmute ﬁssion products , e.g., 85 Kr, 90 Sr, and 137 Cs as shown by an example in Table 20.1 of the transmutation of 90 Sr and 137 Cs using thermal neutrons. Claiborne [1166] demonstrated at the beginning of the 1970s, in detail, the feasibility of byproduct actinide recycling through a LWR. More details in ATW physics and technology can be found in report by Venneri et al. [1167], by Bowman et al. [996, 1168], and in a status report of the IAEA [481]. 20.2 The Concepts of Transmutation

There are still several transmutation concepts under discussion, e.g., • Thermal and fast ﬁssion reactors, which are an attractive concept based on near term technology. However, reactors are technically feasible only for ﬁssionable waste actinides, which could be recycled into the nuclear fuel cycle after a reprocessing of the spent fuel and a refabrication of the fuel charge (see , e.g., Refs. [1169–1173]). • Fusion reactors appear technically feasible for actinide transmutation and, perhaps, selected ﬁssion products. But this would presuppose that the controlled thermonuclear fusion could be accomplished. • High-intensity particle accelerators, ﬁrst discussed by Steinberg et al. [1174] and recently reviewed by Gokhale et al. [1175] and references therein, can meet the feasibility criteria for transmutation of both actinides and ﬁssion products. By the process of transmutation into stable, low hazard or ﬁssionable elements a signiﬁcant reduction of the amount and the radiotoxicity of transuranic elements

20.2 The Concepts of Transmutation

(TRU), Pu, minor actinides (MA), and long-lived ﬁssion products (LLFP) should be achieved. The storage time will be dramatically reduced by transmutation. Not only in the framework of intense spallation neutron sources, but also for acceleratordriven nuclear reactors, nuclear waste transmutation and also the application for radioactive beams the primary question is to determine the most efﬁcient way to convert the incident beam energy into neutron production. Powerful neutron sources also provide the backbone for various applications currently lively discussed as, e.g., the so-called subcritical spallation/ﬁssion hybrid systems [992, 994], the incineration or transmutation of radioactive nuclear waste, and the production of tritium [1000]. In the last years on several international conferences the physics, technologies, and economic aspects of energy generation and transmutation of nuclear waste by ADS were discussed and published in great detail [682, 708, 994–999, 1176–1179]. As for example, the International Atomic Energy Agency IAEA [481] reviews explicitly the existing projects and international activities such as, e.g., the JAERI OMEGA project in Japan, the Los Alamos and Brookhaven National Laboratory ADS projects, the CERN-group conceptional design of a high-power energy ampliﬁer, the ADS program in Russia and France as well as the European community projects. The physics design of ADS and the design of the so-called Energy Ampliﬁer (EA, cf. Section 21.2) is also presented, in detail, in several comprehensive compilations of the AIP (American Institute of Physics) conference contributions 346 [997] and the Proceedings of the Second International Conference on Accelerator Driven Transmutation (ADT) held in Kalmar, Sweden [995, 999]. A comprehensive and recent review article on ADS for energy production (see also Chapter 21 on page 613) and waste transmutation and the current international trends in R&D is compiled by Gokhale et al. [1175]. The article presents a content analysis of references and abstracts from three international CD-ROM databases: INIS, INSPEC, and Chemical Abstracts, including a total of 2336 bibliographic records on ADS for energy production and waste transmutation. The records were grouped under six separate categories: (1) target systems, (2) blanket/fuel systems, (3) material studies, (4) experiments and computer simulation codes, (5) chemical separation and fuel processing, and (6) accelerator systems and development. The basic possibilities to use high-intensity proton or deuteron accelerators and their beams for ADTT applications can be described as follows: (1) Spallation mode: Proton or deuteron beams with GeV energy are used to produce a particle cascade in a target system of nuclear waste. The transmutation of the radionuclides is then caused by the primary and secondary particles transported and created inside the target. (2) Spallation moderation mode: Neutrons produced in the spallation process in a heavy metal target made of W, Hg, Pb, or PbBi are moderated to generate thermal or epithermal neutrons. A most intensive continuous high-intensity neutron source with an average neutron ﬂux of more than 1016 neutrons cm2 s−1 will be possible.

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20 Accelerator Transmutation of Nuclear Waste – ATW Separations fission product removal recirculation loop

Initial waste preprocessed spent fuel removal of 238U excess

Out fission products

Transmuted actinides, long-lived fission products

Accelerator (linac / cyclotron) 0.5–2.0 GeV beam to target

Spallation neutron target (liquid PbBi or solid W) Subcritical reactor (spallator/blanket) target neutrons are multiplied in the surrounding fissionable fuel

Electricity generation 10–20 % returned to accelerator

Fig. 20.1 The general layout of an ATW system with different components indicating the different waste streams (after Venneri et al. [999]).

(3) Spallation moderation boost mode: This is an extension of version (2) containing a subcritical assembly to ‘‘ﬁssion boost’’ the low-energy multiplication. This concept could be used for breeding ﬁssionable material as Pu isotopes or 233 U or to generate additional energy, named the electro nuclear breeder or energy ampliﬁer. (4) Spallation hybrid mode: This means certain combinations of the above modes, which might be used for ﬁssion product transmutation, e.g., 137 Cs might be better transmuted by spallation fast neutrons than by low-energy neutrons. A general scheme of an ATW system with the components, the accelerator, the target and the subcritical reactor, the power generation, and different waste streams in the facility, is shown in Figure 20.1. 20.2.1 Balance Criteria for ADTT Systems

• Energy balance: The energy consumption of the transmutation process should be less or equal compared to the energy needed on producing the radionuclides. • Radionuclide balance: The transmutation process must destroy more long-lived nuclides as generated in the transmutation process. • Speciﬁc transmutation rate: The speciﬁc transmutation rate should be signiﬁcantly greater than the rate generated by the natural decay. • Total transmutation rate: The transmutation process should destroy a signiﬁcant fraction of the originally generated radionuclide inventory.

20.2 The Concepts of Transmutation Tab. 20.1

Time required for a 99.9% reduction of

Natural decay only Thermal neutron ﬂux 1015 (n cm−2 s −1 ) Thermal neutron ﬂux 1016 (n cm−2 s −1 ) Thermal neutron ﬂux 1017 (n cm−2 s −1 ) a

90 Sr

and

137 Cs.

90 Sr

137 Csa

Time (y)

Time (y)

288 112 17 1.8

302 245 91 12

Thermal cross sections are σSr = 0.9 b and σCs = 0.11 b.

Some helpful basic deﬁnitions as transmutation energy and effective half-life are given by Eqs. (20.1) and (20.2). The transmutation energy Etrans is given by the incident particle energy Eparticle and the number of reactions R in the system Etrans = Eparticle /R.

(20.1)

The effective half-life Teff is the time to reduce the number of target nuclides by a factor of 2 and is given by Teff =

0.693 , λnat + λtrans

(20.2)

where λnat is the natural decay constant and λtrans is the transmutation decay constant. The transmutation rate Trate for a mass inventory M irradiated with a thermal neutron ﬂux and a transmutation cross section σtrans could be estimated with the formula Trate = M · σtrans · . A simple example for the time required to reduce the 99.9% is given in Table 20.1.

(20.3) 90

Sr and 137 Cs inventory to

20.2.2 The Accelerator Issue of ATW/ADTT Systems

With the commissioning of high-intensity accelerators in the MW range for the spallation neutron sources, SNS at ORNL [681] and JSNS at J-PARC [629], the planned ESS accelerator of 5–10 MW beam power [1039, 1040], and MW accelerators designed for neutrino production [961, 962] (see also Sections 16.1 on page 497 and 22.3 on page 638) an ATW machine becomes feasible to satisfy experimental requirements for an XADS machine and moreover could

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lay the ground for an industrial ATW plant. The several performance options to satisfy the requirements of an experimental facility (XADS) were focused in [481, 483] on the accelerator, the spallation target and the subcritical reactor issues. As discussed in Ref. [483] the optimum proton energy for production of neutrons by spallation in a heavy metal target, in terms of costs, target heating, and system efﬁciency, lies in the range 0.6–1 GeV. Although speciﬁc neutron production efﬁciency (neutrons per unit of beam power) continues to increase up to about 2 GeV, a minimum-cost performance-optimized facility is generally obtained at somewhat lower energies due to other factors, such as the beam current, the accelerating gradient, and the accelerator electrical efﬁciency. For the envisaged power levels of a XADS accelerator the optimum energy in terms of minimizing the accelerator cost would be about 0.4 GeV, but target considerations drive the practical lowest beam energy up to 0.6 GeV. At lower beam energies, the power deposition density in the spallation target is too high, and the energy loss in the beam entrance window becomes signiﬁcant. For the industrial ADS plant, the range 0.8–1 GeV is optimum, with lower energies matched to lower beam powers. Two completely different kinds of machines can be considered for the acceleration of high currents of protons to an energy of 0.6–1 GeV: linear accelerators and sector-focused cyclotrons. Concerning cyclotrons, a ﬁnal energy of 0.6 GeV is well established, namely with the experience of the PSI cyclotron [627], and from this, it is felt in the cyclotron community, that a value of about 5 mA proton beam current should be considered as safely reachable. However, extrapolating up to 10 mA is more questionable, and might require a complex of at least two cyclotrons with the two beams being funneled together [1180]. For an industrial-scale ADS/ATW system, the logical accelerator choice would be a linac [483]. A proposed reference design of an experimental XADS accelerator is proposed in Ref. [1181] and illustrated in Figure 20.2. The XADS accelerator belongs to the category of high-power proton accelerators (HPPA) and is designed for a maximum beam current of 6 mA CW. Similar systems were suggested by Los Alamos [483] and by the J-PARC project [629, 1182]. The XADS is composed of a ‘‘classical’’ proton injector and a normal conducting RFQ structure followed by warm or/and superconducting drift tube linac (DTL) structures, which are used up to a transition energy between 5 and 50 MeV. At this point, a fully modular superconducting linac accelerates the beam up to the ﬁnal energy (Figure 20.2). A remarkable feature of the concept is its validity for a very different output energy range: (1) at 0.35 GeV the smaller scale XADS requires nine cryomodules of β = 0.65 elliptical cavities, while for 0.6 GeV simply 10 more cryomodules have to be added, 7 with β = 0.65, 3 with β = 0.85, and (2) 12 additional β = 0.85 may boost the energy up to 1 GeV, respectively. A proton beam vertically injected from the top is preferred for the spallation target (Figure 20.2).

ce

Sour

RFQ

Linac front end

ß = 0.47

ß = 0.65 ß = 0.85

0.35 GeV

Examples of superconducting sections

Beam dump

Spallation target & subcritical core

0.6 GeV

SC Spoke SC elliptical cavities (700 MHz, 3 sections) cavities (350 MHz, 1 or 2 sections) 0.1 GeV 0.2 GeV 0.5 GeV 0.6 GeV

ß = 0.35

- X MeV (between 5 and 50 MeV)

CH ? r SC IH o tructure s L T D

IH o DTL r SC CH struc ture ?

Fig. 20.2 The XADS reference accelerator layout with a doubled injector accelerator is followed by a fully modular spoke and elliptical cavity superconducting linac. Photographs of typical cavity prototypes are shown in the lower panels: From left to right: RFQ, CH structure, spoke, and an elliptical 5 cell structure (after Mueller et al. [1180, 1181]).

Sour

ce

100 ~ 5 MeV keV

RFQ

20.2 The Concepts of Transmutation 599

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20 Accelerator Transmutation of Nuclear Waste – ATW

20.3 The Spent Reactor Fuel and Transmutation

Spent reactor fuel elements exhibit a large radiotoxicity. The common classiﬁcation of the radioactive waste from nuclear reactors is given as: • HLW – high-level waste • MA – minor actinides • FP – ﬁssion products • LLFP – long-lived ﬁssion products Responsible for the radiotoxicity are essentially the long-living transuranium isotopes (TRU), the minor actinides (MA) and ﬁssion products (FP), respectively the LLFP. Large radioactive half-life of some isotopes are the main concern in ﬁnal disposal, since a safe enclosure of the radioactive inventory has to be ensured for millions of years. Table 20.2 summarizes the annual production of high-level Tab. 20.2 Annual production of Pu, minor actinides and LLFP of a 3.000 MWth PWR reactor (after 10 years decay or cooling time)a .

Isotope

Half-life in years

Amount in kg/y

Decay

Dose conversion factor of effective dose (ingestion) in Sv/Bq

Pu and minor actinides (TRU and MA) 237 Np 238

Pu 239 Pu 240 Pu 241 Pu 242 Pu 241 Am 243 Am 244 Cm

2.100.000 80 24.000 6.600 14 380.000 430 7.400 18

14.5 4.5 166.0 76.2 25.4 15.5 16.6 3.0 0.6

α α α α α, β α, ﬁssion α α α, ﬁssion

1.1 × 10−7 2.3 × 10−7 2.5 × 10−7 2.5 × 10−7 4.8 × 10−9 2.4 × 10−7 2.0 × 10−7 2.0 × 10−7 1.2 × 10−7

Long-lived ﬁssion products (LLFP) 79

Se

90 Sr 93 Zr 99

Tc

107 Pd 126 Sn 129 I 135 Cs 137 Cs 153 Sm

a

65.000 29 1.500.000 210.000 6.500.000 100.000 17.000.000 3.000.000 30 90

0.2 13.4 23.2 24.7 7.3 1.0 5.8 9.4 31.8 0.4

β β β β β β β β β β

The Sv/Bq ratio is related to ingestion[1183].

2.9 × 10−9 2.8 × 10−8 1.1 × 10−9 6.4 × 10−10 3.7 × 10−11 4.7 × 10−9 1.1 × 10−7 2.0 × 10−9 1.3 × 10−8 7.4 × 10−10

20.3 The Spent Reactor Fuel and Transmutation Most long-lived ﬁssion products (LLFP) produced annually by a 1 GW electrical power reactor.

Tab. 20.3

Isotope

Half-life

99 Tc

211.000 y 15.7 million y 2.3 million y 1.53 million y 100.000 y 650.000 y

129 I 135 Cs 93 Zr 125

Sn

79 Se

Weight (kg)

Radiotoxicity (Sv)

16.61 8.09 34.12 26.11 1.19 0.3

27670 19580 9870 2380 3200 745

Class A dilution (m3 ) 947.65 178.47 39.32 18.75 9.65 0.59

waste (HWL) of a 3000 MWth pressurized water reactor (PWR) after 10 years of decay and cooling time. The research on transmutation is not only aimed at the destruction of transuranium elements, which represent the most toxic part of nuclear waste, but it is also devoted to the elimination of the most dangerous ﬁssion fragments (cf. lower panel of Tables 20.2 and 20.3). Transuranium elements, e.g., 237 Np and Pu-isotopes are produced by successive neutron capture of 235 U and 238 U. Since transuranium elements and minor actinides are essentially α-emitters, the isotopes have high radiotoxicity. For ﬁssion fragments, the concern is not only the long half-life, but also the water-solubility of some elements. In case of water inﬁltration the elements could contaminate the ground water. Most of these elements have a lifetime that rarely lasts more than decades or centuries. 99.995% of the long-lasting radiotoxicity (>500 years) is in a few elements and in about 1% of the spent fuel mass. Once the MAs are successfully transmuted to a fraction of their initial mass (e.g., 1.0%) the overall radiotoxicity of PWR and LWR waste is determined by ﬁssion products (FP) (<500 years) and the remaining by MA radiotoxicity. This means that, by eliminating the few most offending long-lived ﬁssion fragments, one could dispose the rest in controlled secular repositories for a few centuries to eliminate all danger completely. This is clearly demonstrated by Figures 20.3 and 20.5. The biggest achievement would be the elimination of the need for geological repositories. Transmutation reduces the time till harmless declaration from a geological to a historical time-scale. Table 20.3 summarizes the annually produced LLFP by a 1 GW electrical power reactor. The volume of inert material is indicated on the right in which the elements should be diluted, to be considered as dangerous as industrial or medical radioactive waste, and to be stored in uncontrolled surface repositories, according to American regulations. The elimination of iodine and technetium, the most dangerous isotopes, would allow a consistent reduction in the volume of storage waste. Figure 20.3 shows the impact on the radiotoxicity by partitioning of Pu isotopes and MAs of spent reactor fuel as a function of the decay time in years. The ﬁgure indicates, that by partitioning of 99.9% of U, Pu and MAs the radiotoxicity of the

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20 Accelerator Transmutation of Nuclear Waste – ATW

109

108

Without reprocessing

107 Radiotoxicity [Sv/t burned fuel]

602

99 % U,Pu

106

99,9 % U,Pu

105

104

103

Natural uranium ore 99.9 % U,Pu,MA 99.9 % U,Pu,MA

102

101 1 10

102

103

104

105

106

Decay time [y] Fig. 20.3 The impact on the radiotoxicity by partitioning of Pu isotopes and MAs of the spent fuel (1 t burned nuclear fuel) of a PWR (4% 235 U enrichment, burn-up 40 GW/t). The radiotoxicity Sv/Bq is related to ingestion (after [1184]).

waste falls below the natural uranium ore radiotoxicity at a decay time of about 800 years [1184]. 20.3.1 An Example of a Transmutation Complex

As already discussed, transmutation/incineration is limited in thermal or fast nuclear reactor systems, while ADS in spallation mode or in hybrid, subcritical mode would be able to separate the long-lived nuclei from the high-level waste by transmuting such nuclei into short-lived or nonradioactive wastes. ADS or ATW operates in non self-sustained chain-mode and therefore minimize the power excursion concern. A transmutation system, when operated in a subcritical mode, stays subcritical, regardless of the accelerator being on or off. A transmutation complex schematically shown in Figure 20.4 is a technological approach to a possible reduction of the hazards of permanent spent nuclear fuel disposal. It utilizes two different ‘‘building blocks’’: (a) a nuclear power plant (1ststratum), and (b) an accelerator transmutation ATW complex (2nd stratum). The

20.3 The Spent Reactor Fuel and Transmutation

603

Superconducting proton LINAC

20 – 30% Proton beam

Nuclear power plant

to Grid

U, Pu

70 – 80% 1st Stratum

Commercial fuel cycle

Electric power generation

Spallation target

High level waste

Spent fuel Reprocessing

MA, LLFP

Partitioning MA, LLFP Fuel manufacturing Final geological disposal

Partitioning & Transmutation fuel cycle

Subcritical core with MA fuel 2nd Stratum

SF Radioactire waste without long-lived nuclides Shorter than 500years

Reprocessing

MA : Minor actinide LLFP : Long-lived fission products

Fig. 20.4 Double strata concept combining a PWR U-Pu fuel cycle and an accelerator driven transmutation system (after Takao et al. [1185]).

ATW complex consists of (1) a linear accelerator of delivering a proton beam with a MW beam power and an energy between 0.6 and 1 GeV, (2) a spallation target or a subcritical nuclear assembly where the proton beam is converted by spallation reactions into an intense neutron ﬂux, with which ﬁssile isotopes and LLFP are transmuted into short-lived radio-isotopes or stable nuclei, and (3) a chemical processing plant for treating nuclear waste to isolate long-lived radioisotopes and the transuranium isotopes for initial or recycle irradiation. Various solutions for fueling the system from traditional solid fuel to systems with liquid fuel (molten salt) are under investigation. In these liquid systems, the minor actinides are not reprocessed into solid fuel pins but dissolved into salt and transmuted, respectively, incinerated. Figure 20.5 demonstrates the relative radiotoxicity for the radioactive inventory of spent reactor fuel elements and the radioactive inventory by a 99.9% transmutation of the spent fuel normalized to the radiotoxicity of natural uranium ore as a function of time. The slow decline of the radiotoxicity due to radioactive decay is shown by the upper curve. Using ADS and applying transmutation, the decline of radiotoxicity can be signiﬁcantly increased, as indicated by the lower graph. Having applied transmutation, already after 1000 years the radiotoxicity resembles the level of natural uranium ore. The storage therefore reduces by three orders of magnitude from >106 to 103 years. By examining the radiotoxicity of long-lived ﬁssion fragments, it is clear that the most offending are few in number. In particular, 129 I and 99 Tc are by far the most dangerous for their solubility and mobility in the biosphere. These light elements

20 Accelerator Transmutation of Nuclear Waste – ATW

Radiotoxicity relative to natural uranium ore

604

104 103

Untreated reactor waste

102 101 100

Natural uranium

10−1

99.9% Transmuted reactor waste

−2

10

10−3 10

100

1000

10 000

Decay time [y] Fig. 20.5 The promise of transmutation: toxicity reduction of transmuted reactor spent fuel. With transmutation the used nuclear fuel reaches the toxicity of the source uranium ore within a few centuries [1183].

cannot ﬁssion like the transuranium isotopes, so a different technique has to be adopted to eliminate them. The technique consists of artiﬁcially accelerating their natural decay by using neutrons again. The goal is to let the dangerous elements capture a neutron, in order to increase their energy and become unstable, as they will rapidly decay in stable elements. This process also occurs in reactors, but it is not efﬁcient enough and the eliminated quantities are smaller than the produced ones. A solution to this problem has been suggested by Rubbia and his research on ADS. The advantage is to spoil particular neutron energies that massively increase the capture probability: the so-called resonances. If the energy of the neutrons emitted in nuclear reactions is decreased very slowly, it is sure that sooner or later the neutron will be captured by the resonance of the radioactive element that has to be destroyed. To do so, neutrons interact with a heavy element so that they are able to transfer only a small fraction of their energy: they will then lose energy in small steps. The element used is lead, which has the added advantage of having a small tendency to capture neutrons itself. This element, which is already ideal for transuranium transmutation, seems to be the key element for the elimination of any dangerous waste. The principle1) has again been demonstrated at CERN, with the TARC experiment (Transmutation by Adiabatic Resonance Crossing) [1187–1189]. The process is so efﬁcient that it can be applied not only to 1) This principle is applied in nuclear physics with the well-known ‘‘lead spectrometer’’ to measure neutron resonance parameter [1186].

20.4 Partitioning

ﬁssion fragments transmutation, but also to activate stable elements and produce radioactive isotopes to be used in medicine as tracers in radiological analysis or in cancer therapy. Computer simulation of the interaction of a single proton into a 334 ton lead block used in the TARC experiment at CERN show that on the average 147 neutrons are produced that, before being absorbed, will interact with the Pb atoms about 55,000 times. In such a cloud it is very easy for a radioactive element to capture a neutron and become stable. The spallation reaction is not the only mechanism involved in the destruction of the transuranium elements. In fact, the probability of breaking up a heavy nucleus like plutonium, instead of being captured by it, increases with the energy of the striking neutron. Therefore, it is necessary to maintain the neutrons produced in the cascade to a very high energy. This is particularly favorable if liquid Pb is used as coolant, a solution that has already been adopted in the alfa-class Russian submarines in the 1950s, but that has to be reproduced today using current standards observed by the industry in the west. The use of particle accelerators therefore seems to be the perfect solution to the problem of radioactive waste, but like all technologies connected with the nuclei of elements, it has to be studied in great depth and tested before being used on a large scale. The results of the research on the transmutation of radioactive waste allows to foresee a different strategy of energy production and nuclear waste disposal for the future, which is much more suitable for future generations, because it allows the elimination of contamination risks associated with a possible failure of geological repositories. Transmutation techniques can be applied to both military and civil waste: military plutonium is in fact an excellent fuel for ADS. The demonstration of the transmutation technique could bring about the elimination of all plutonium in the next 50 years! 20.4 Partitioning

For ADS, the salient hope exists that due to its subcriticality the deterioration of safety parameters can be coped with and a higher MA load can be deposited in the core surrounding the external spallation neutron source. The number of ADS facilities dedicated to destruct MAs will therefore be only a few within the reactor park. Possible realizations of transmutation and incineration of Pu and MAs within a reactor park are displayed in Figure 20.6. In the so-called single stratum concept, the nuclear waste is transmuted/ incinerated in a nuclear energy park, e.g., with critical reactors. This is accomplished by separating the uranium and plutonium vectors from the burned fuel and recycle their amount together with fresh fuel. In the double strata concept the problematic LLFP and MA elements are treated in an ADS waste burner [1172, 1173]. The double strata concept is therefore able to reduce the storage in the ﬁnal disposal considerably. Before the U, Pu, LLFP, and MA nuclides can be transmuted, they have to be separated from the spent reactor fuel elements. This process is referred to as partitioning.

605

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20 Accelerator Transmutation of Nuclear Waste – ATW

1st stratum of fuel cycle

Fuel fabrication

Reprocessing

1000 MWe 10 –14 LWRs HLW (TRU,FP)

99.5% U, Pu

2nd stratum of fuel cycle (P-T cycle) MA LLFP

Spent fuel storage

Transmutation system 800–1000 Mwth

U, Pu

MA nitrite fuel

Partitioning

HLW storage

MA, LLFP Reprocessing

SLFP

To final disposal Fig. 20.6 The double strata concept of JAERI, a combination of a power reactor fuel cycle and an independent partitioning-transmutation cycle (after Mukaiyama [1182]).

To this, two different techniques may be applied: the hydrochemical and the pyrochemical method. The best known hydrochemical method is the PUREX method, in which the spent fuel is dissolved in nitric acid (HNO3 ) and uranium and plutonium can be separated. For the minor actinides, this method is currently not yet available and in the process of being developed [1183]. Fission fragments are often separated in pyrochemical techniques by afﬁliation of molten salt solutions. 20.4.1 EU Projects on Partitioning and Transmutation

Already in the ﬁfth framework program, projects aiming at new nuclear data measurements and evaluations such as, e.g., HINDAS (High and Intermediate energy Nuclear Data for Accelerator-driven Systems) were supported by the EU. Within the 3 years program, HINDAS provided a wealth of new nuclear reaction

20.5 Advances in Accelerator Breeding of Fissile Material

cross sections in the energy range between 20 MeV and 2 GeV on three elements of crucial importance for ADS systems: Pb as a target element, U as an actinide and Fe as a shielding element. As a natural extension or successor of the FP5 HINDAS project, in FP6, the project EUROTRANS (EUROpean Research Programme for the TRANSmutation of high-level nuclear waste in an ADS) has been launched. Due to the lack of progress in implementing the radioactive waste disposal in geological repositories, the Partitioning and Transmutation (P&T) strategy has been put forward. In addition, P&T will both contribute to the sustainability of nuclear energy in those countries that pursue this source of energy, and will assist in combating global warming. In the Euratom Sixth Framework Program (FP6), one speciﬁc targeted research project on the study of the impact of P&T (RED-IMPACT) and two integrated projects: (i) EUROPART (partitioning) and (ii) EUROTRANS (transmutation) have been launched. EUROTRANS beneﬁts not only from the technological developments and scientiﬁc progress achieved in Europe during FP5, but also from worldwide co-operation (OECD/NEA, IAEA, USA, Japan, ISTC, etc.) in the ﬁeld of P&T. The FP5 R&D results in the areas of preliminary design studies of an experimental ADS, low-power coupling of an accelerator to the Masurca zero power reactor made subcritical for the purpose of the MUSE programme, studies on transmutation fuels, heavy liquid metal technology and high-energy nuclear data are available as a basis for the advancement of this integrated project (IP). The following sections are devoted to accelerator breeding of nuclear fuel and the production of tritium. 20.5 Advances in Accelerator Breeding of Fissile Material

The present-day nuclear technology and its various applications, electrical power generation, production of ﬁssionable materials, tritium, the bulk of commercial isotopes, etc., depend on the presence of a relatively small amount of 235 U in nature approximately 0.71% in natural uranium. If the supply of 235 U were limited, the problem of nuclear-fuel reproduction could be solved for many years by breeding nuclear fuel with accelerators, the ADS technique, using fast neutrons for the 238 U– 239 Pu cycle and thermal neutrons for the 232 Th– 233 U cycle [1190, 1191]. The early work considered in USA and Russia on breeding of ﬁssile material utilizing proton accelerators is summarized by Vasil’kov et al. in [1190]. Thus with ADS, by using the total ﬁssion energy content of the abundant natural elements the resources are enough to meet the world energy need for thousands of years2) [1193]. Also the proliferation risk of strategic materials can be diminished with the use of the thorium–uranium cycle by adding a few percent of 238 U to the initial feed, which will result in an inﬁnite critical mass of the uranium. Former 2) The global uranium resources with mining costs up to 130 US dollar per kilogram amount to about 3.3 million tonnes. With 3.3 million

tonnes, all 436 worldwide operating nuclear power plants could be supplied for several decades. [1192]

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20 Accelerator Transmutation of Nuclear Waste – ATW

Proton beam 1 GeV, 300 mA 425°C

61 cm

300°C

UO2

Pb Bi

or ThO2

Na cooling

Fuel

~ 183 cm

Blanket

~ 90 cm

608

Liquid metal target

~107 cm

Fig. 20.7 Schematic of the ORNL 239 Pu and 233 U fuel breeder with PbBi target and LMFBR blanket (not to scale) [1199].

studies and investigations conducted at Chalk River, Canada [58, 982], at BNL, USA [1194–1197], and at LANL, USA [1198], and at ORNL, USA [1199] indicted that ADS concepts, if the technology is available, will be competitive with that of the liquid metal fast breeder reactors (LMFBR) [1196]. ADS technology may overcome the safety and environmental issues with the present ﬁssion reactors, especially the LMFBR systems, considering the different proposed concepts of accelerator-driven subcritical systems for safe and clean nuclear energy production (cf. Chapter 21 on page 613) using the thorium–uranium or uranium–plutonium fuel cycles. A clean environment is given by using thorium–uranium fuel cycle that produces fewer heavy transuranium elements than the uranium–plutonium cycle or by using the uranium–plutonium cycle with a simultaneous incineration of long-lived elements [1193]. Two studies on accelerator breeding of ﬁssile materials investigated by Mynatt et al. [1199] at ORNL and by Taschek [1198] at LANL, investigated during the 1970s, may be mentioned. Some results of the ORNL group are shortly discussed below. The ORNL group assumed a coupled cavity linear accelerator with a proton beam energy of 1 GeV and a continuous beam current (CW) of 300 mA, which assumes a beam power two orders of magnitude higher than still the currently state-of-the-art accelerators. Different subcritical target–blanket systems were investigated, which look similar to the geometry concept of the Rubbia system in Figure 21.1 on page 614. A schematic sketch of a target with a LMFBR type blanket is shown in Figure 20.7. Considering a blanket system with a 238 U or 232 Th content, most of the neutrons from the spallation target are captured producing 239 Pu or 233 U. The presence of

20.6 Accelerator Production of Tritium-APT 239

Pu - cycle

238

U

Breeding

7.4 kg/d 239Pu

1980 MWe

11.4 kg/d 239Pu

Conversion ratio CR = 0.65

Processing Fabrication

Waste 232Th

Breeding

25.2 kg /d 233U

6818 MWe

28 kg /d 233U

Conversion ratio CR = 0.9

Processing Fabrication

233

U- cycle

Waste Fig. 20.8

General ﬂow charts for

239

Pu and

233

U cycles [1199].

this ﬁssile material and in the case of 238 U in the blanket lead to multiplication of neutrons in the blanket. If the blanket is subcritical only a ﬁnite number of daughter neutrons will be produced. The neutrons are absorbed in ﬁssion reactions, nonbreeding capture and in the fertile material to produce 239 Pu and 233 U. The whole process can be described by the equation of the neutron economy, Eq. (20.4), the time dependence of the total number of neutrons cm−3 produced in the ADS system, dn/dt = S + ν · R − (1 + α)R − C − L − E,

(20.4)

with S is the external source term (n/s), ν is neutrons per ﬁssion, R is the ﬁssion rate, α is the capture-to-ﬁssion ratio, C is the fertile conversion rate (loss of neutrons from conversion of fertile to ﬁssile material, e.g., 232 Th to 233 U), L is the neutron loss rate (from parasitic capture, leakage, and absorption), and E is the number of excess neutrons, which may be available to burn ﬁssion product waste. In the equation no cross sections are used; only the ratios are applied. For a steady-state system the term can be set to dn/dt = 0. For a given ﬁssion rate the acceleratorproduced neutron source term could be evaluated providing the number of excess neutrons required to burn waste or breed ﬁssionable material. Figure 20.8 illustrates material ﬂow for the Pu and 233 U cycles. Typical parameters for the PbBi target and the LMFBR blanket are given in Table 20.4.

20.6 Accelerator Production of Tritium-APT

Both programs on accelerator production of tritium (APT) at LANL in USA [1000, 1200] and TRISPAL [1162, 1201] in France were investigated to maintain their nations strategic deterrent during the 1990s, concerning the used tritium in nuclear weapons for boosting a ﬁssion bomb or the ﬁssion primary of a thermonuclear

609

610

20 Accelerator Transmutation of Nuclear Waste – ATW Tab. 20.4 Parameter of the liquid PbBi target and the LMFBR blanket concept (data are from Ref. [1199]).

Target/blanket Parameter

Value

Target material Dimension Neutron efﬁciency Neutron production (target leakage) Energy deposition Energy density Energy density Peak/average Neutron ﬂux at liner

PbBi Ø = 100 cm, length = 60 cm 25 neutrons/incident proton 5 × 1019 neutrons s−1 186 MW 0.4 MW/l 2.5 5 × 1016 neutrons cm−2 s−1

Blanket (LMFBR type) with sodium and steel 50% UO2 or ThO2 25% Na, 25% steel 316 640 MW

Material Blanket power

weapon. This is because tritium decays with a half-life t1/2 = 4.5 ± 8 d (about 12.33 y) to 32 He3) at a rate of about 5.5% per year, so it must be replaced continuously. Tritium is produced mainly in nuclear reactors as a byproduct4) . In contrast to reactors an APT facility would produce the required tritium without any ﬁssile material and will leave no HLW from the ﬁssioning of uranium. The production of tritium in a quantity large enough to supply the needs of a stockpile can only be accomplished through neutron capture by a stable isotope such as 3 He or 63 Li with the following reactions: 3 2 He + 6 3 Li +

n −→ p +31 T n −→ 42 He(2.05 MeV) +31 T(2.75 MeV).

(20.5)

3 2 He

has a very large cross section for the (n, p) reaction with thermal neutrons. The capture reaction with 63 Li is possible with neutrons of any energy, and is an exothermic reaction yielding 4.8 MeV. Only a reactor or an accelerator-driven neutron source can produce enough neutrons in the quantities which will be needed. Accelerator studies in this ﬁeld are given in Refs. [1201, 1202]. The TRISPAL study was started in 1992 and completed during 1998. The TRISPAL accelerator was composed of a normal conducting (NC) linear accelerator 3) 31 T →32 He + e− + ν e .

4) In nuclear ﬁssion, tritium is produced with a yield of about 0.01% (one per 104 ﬁssions).

20.6 Accelerator Production of Tritium-APT

in continuous mode operation (CW) with a proton beam energy of 0.6 GeV and a beam current of 40 mA, which would be a beam power of 24 MW [1201]. Two target systems were planned for the ﬁnal system consisting of lead rods clad in Al alloy acting as the SNS. While both projects are very similar, the APT program at LANL, USA–so far the most advanced project during the 1990s is described below in more detail. The basic parameters and the outcome of the APT-LANL project are shortly summarized as follows: (1) The APT system of LANL [1000, 1200, 1203, 1204] considered a family of accelerators with different energies and structures, depending on the quantity of tritium produced per year. – (a) an NC linac with nominal beam energy of 1.3 GeV with CW beam of 100 mA, 130 MW, (upgradable to 134 mA, 174 MW) with a tritium production of 2 kg/y for the 130 MW device and 3 kg/y for the a beam power of 174 MW, – (b) an SC linac with nominal beam energy of 1.7 GeV with CW beam of 100 mA, 130 MW, (upgradable to 1.7 GeV, 100 mA, 17 MW), with a tritium production of 2 kg/y for the 130 MW device and 3 kg/y for a beam power of 170 MW. (2) The tritium is produced in one or two target/blanket systems. The target consists of a tungsten target surrounded by a blanket of lead for additional neutron production. The neutrons are slowed down and captured in 3 He to produce tritium. The system uses a replaceable module design for most of the components. (a) The beam entrance window is a double wall Inconel structure which isolates the proton beam pipe high vacuum system from the low vacuum that maintains the target/blanket system. The high-intensity beam passes through a series of magnets, which expand the beam into a rectangular shape of approximately 16 × 160 cm2 . The nominal 100 mA, 1.7 GeV proton beam loses only about 6 MeV or 0.02% of energy inside the proton beam window. The heat deposited in the target window is about 600 KW. (b) After passing the beam entrance window the beam bombards a centrally located D2 O-cooled tungsten target. About 64 MW will be deposited in the tungsten. At an incident beam energy of 1.7 GeV 40 neutrons per beam proton were approximately produced in the target/blanket assembly of the APT. (c) The overall dimension of the target/blanket assembly has a length of 7.8 m and a width of 3.4 m, and is housed in a steel vessel with a diameter of 9.75 m. An exploded view of the target/blanket assembly is depicted in Figure 20.9. The target/blanket system will be assembled from a series of replaceable modules, e.g., the beam entrance window, the central tungsten target, the lead blanket, the reﬂector, and the shielding modules. The neutron-producing target consists of

611

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20 Accelerator Transmutation of Nuclear Waste – ATW

Cavity vessel

Lead blanket /reflector

Iron shield modules

Tungsten neutron source

Proton beam entrance window

Fig. 20.9

The APT-LANL target/blanket system (after Cappiello [1203]).

small Inconel-clad tungsten rods (diameter = 0.3175 cm) mounted horizontally in stainless steel tubes, which then manifolded in vertical inlet and outlet pipes (cf. Figure 20.9), which provide a coolant ﬂow of D2 O with an inlet temperature of 50◦ C. This target design of horizontal and vertical tubes make up a structure like a ladder. The peak power density inside the tungsten ladder target peaks in ladder two (cf. Figure 20.9) with a level of 2.45 MW/l. The target is surrounded by a H2 O-cooled aluminum decoupler and then by a blanket of lead cooled also by H2 O. Both systems have tubes ﬁlled with 3 He gas. The produced tritium inside the aluminum tubing will diffuse to a manifold, where it is carried away by ﬂowing 3 He gas. The 3 He/tritium/isotope gas mixture is then transported to a tritium separation facility for continuous tritium removal. An overall nuclear design of the APT facility leads to the following results: about 36% of the tritium is produced in the de-coupler region of the system, 56% inside the target rows, and 8% in the reﬂector regions. For a 1.7 GeV proton beam, the neutron production rate, n/p, is 75% of that achievable with an ideal target. The efﬁciency for tritium production, tritium per neutron, is 84%, which leads to a total tritium production of 40 tritium atoms per incident proton. At a beam current of 100 mA and by a system availability this leads to a total mass production of 3 kg of tritium per year [1204].

613

21 Accelerator Production of Electrical Energy – ‘‘Energy Amplifying’’ 21.1 Introduction

An energy ampliﬁer (EA) is a novel type of nuclear power reactor, a subcritical reactor, in which an energetic particle beam is used to stimulate a reaction, which in turn releases enough energy to power the particle accelerator and leave enough energy for electricity generation. The concept has more recently been referred to as an accelerator-driven system (ADS). Historically it is credited to Carlo Rubbia, a nuclear physicist and former director of Europe’s CERN international nuclear physics laboratory. He published a proposal for a power reactor based on a proton cyclotron accelerator with a beam energy of 0.8–1 GeV, and a target with thorium as fuel and lead as a coolant. On the basis of former ideas formulated starting from the 1950s, in 1993 Carlo Rubbia took up once again the challenge to operate particle accelerators not only for the transmutation concept as discussed in Chapter 20, but also for energy production [994, 995, 1178, 1183, 1205–1208].

21.2 Principle of the ‘‘Energy-Ampliﬁer’’

Typically the proposed concept of an energy ampliﬁer uses a synchrotron accelerator to produce a beam of protons. These hit a heavy metal target such as lead, thorium, or uranium and produce neutrons through the process of spallation. The interaction always results in the release of a large quantity of neutrons (up to a few tens for each proton sent) that can then be used to induce ﬁssion reactions, like in a reactor. The difference is that the ﬁssions are not enough to startup a (so-called critical) chain reaction, but only a cascade of ﬁssions that is called ‘‘subcritical’’ since it can be stopped in about a millisecond if the accelerator is turned off. This is an enormous advantage in terms of safety. The nuclear cascade, like in the case of a reactor, produces a large quantity of heat, generally much more than that used to operate the accelerator, which can be used to produce energy and ﬁnally generate electricity. For this reason Carlo Rubbia called his machine: the energy ampliﬁer (EA). The system is illustrated schematically in Figure 21.1. The main vessel is very tall about 6 m in diameter and about 30 m in height. Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

21 Accelerator Production of Electrical Energy – ‘‘Energy Amplifying’’

Proton beam Beam channel

Beam collimator

Heat exchanger

Heat exchanger

Beam window

Molted lead

614

Liquid lead Fuel

n

n n n n

Fission Spallation Breeding 232 233 U Th → 233U ⇓ (fission fragments) Fig. 21.1 The energy ampliﬁer scheme: a particle beam produced by an accelerator enters from top a subcritical system, similar to a traditional reactor, producing a cascade of nuclear reactions that can be used to destroy radioactive nuclear waste, to breed, e.g., 233 U from 232 Th, and in turn produce

energy. The system is embedded in a liquid lead ‘‘bath’’ which works as the neutronproducing target, is a moderator for the fast neutrons produced in the spallation process, and is simultaneously the cooling medium for the system. The ﬁgure is not to scale (after [1209]).

It might be possible to increase the neutron ﬂux through the use of a neutron ampliﬁer, a thin ﬁlm of ﬁssile material surrounding the spallation source. The use of neutron ampliﬁcation in CANDU reactors has been proposed [1210]. While CANDU is a critical design, many of the concepts can be applied to a subcritical system. Thorium nuclei absorb neutrons, thus breeding ﬁssile 233 U, an isotope of uranium which is not found in nature. Moderated neutrons produce in the 233 U ﬁssions and releasing energy. This design is entirely plausible with currently available technology, but requires more study before it can be declared as both practical and economical. The preferred fertile material 232 Th lead to the production of ﬁssile material via capture of neutrons. The well-known main chain is illustrated in Figure 21.2. The element 232 Th has an abundance of 100%. A detailed chart of the produced actinides is depicted in Figure B.1 on page 681. In steady neutron ﬂux conditions, the chain will tend to an equilibrium, namely in a situation in which each ﬁssioned 233 U nucleus is replaced by a newly bred

21.3 Feasibility of the ‘‘Energy Ampliﬁer’’ Th – U cycle [232Th 100% abundance] 232

234Pa

b− 6h

234U

+n b− b− 233 233 n → Th + → Th Pa → 233U 22.3 min 26.97 d

Fig. 21.2

The

232 Th

−→233 U cycle [1205].

fuel nucleus. At ﬁrst order, such a breeding equilibrium is naturally attained with a speciﬁc value of the fuel/breeder concentration ratio ξ determined solely by the ratio of cross sections [1178] ξ=

σcapture+ﬁssion (232 Th) 233 ( U), σTh capture + ﬁssion

(21.1)

where the cross sections are given in [1178] as • σcapture (b) (232 Th = 0.387, 233 Pa = 1.122, 233 U = 0.289), • σﬁssion (b) (232 Th = 0.006, 233 Pa = 0.039, 233 U = 2.784), • and σtotal (b) including σn,2n and σn,n (232 Th = 12.016, 233 Pa = 11.009, 233 U = 12.273). Equation (21.1) assumes no alternatives besides the main chain, justiﬁed as long as the rate of neutron captures by 233 Pa competing with natural decay is kept negligible with a sufﬁciently low neutron ﬂux. This is the ‘‘decay dominated’’ regime [1205] in contrast with the high ﬂux, ‘‘capture dominated’’ regime investigated by Bowman et al. [996, 1168], where the 233 Pa must be quickly extracted to avoid capture. The breeding ratio at equilibrium is about ξ = 1.35 × 10−2 for thermal energies [1178] and it rises to about ξ = 0.128 for fast neutrons and the above given cross sections. An EAc based on fast neutrons will then require a fuel concentration which is about nine times the one of a device based on a fully thermalized neutron device [1178]. However, it can operate with much higher burn-up rates and hence the total mass of fuel is correspondingly reduced with the same output power.

21.3 Feasibility of the ‘‘Energy Ampliﬁer’’

In 1994, Rubbia’s team demonstrated the working principle of an EA [993, 1207]. Rubbia has also simulated using lead as moderator. This involves working with neutrons of higher energy than in normal fast neutron reactors where the less agreeable liquid sodium is the moderator. Simulations show that the reactivity of the subcritical system using lead remains very constant since the effect of ﬁssion products (poisons) is considerably reduced. This allows more complete combustion before the fuel rods have to be reprocessed (they could stay in place for 4 years instead of a year with the light-water variant). Moreover, the constant reactivity

615

21 Accelerator Production of Electrical Energy – ‘‘Energy Amplifying’’

opens up the prospect of energy gain G1) increasing from about 60 to 100 or 120, with the assembly remaining subcritical. Fast neutrons open up interesting opportunities for the reprocessing of the irradiated rods. This reprocessing will be limited to the separation of the ﬁssion products since all actinides become combustible, sidestepping the plutonium problem. The only EA actinide waste (0.5%) comes from imperfections in the separation process. Fission products can be recycled in the rods, the neutron ﬂux transforming them into nonradioactive elements. However, unlike the ﬁssion of actinides, this transformation consumes neutrons and reduces energy production. A compromise solution would be to reserve this costly processing to sensitive elements such as 135 Cs, 129 I, etc., which are long-lived (several million years) and potentially polluting. A detailed description of the Pb-cooled subcritical system (keff = 0.98) designed for a thermal power of 1500 MWth is given in Ref. [994, 995, 1178]. Figure 21.3 shows the general layout of the energy ampliﬁer complex as given by Rubbia et al. in Ref. [994, 1178]. 30 MWe

Booster

Turbine

p beam

Cyclotron accelerator complex Energy amplifier Fuel discharge 27.6 t

Pump

Fuel loading

Power generation 675 MWe

Pump

Core

Reprocessing (partition)

Actinides 24.7 t

Fuel fabrication

Spent fuel Reprocessing complex (every 5 years)

Generator Condenser

Injectors

Heat exchanger

616

Fission fragments 2.9 t

Waste packaging (vitrification)

Thorium supply 2.9 t

To secular repository

Fig. 21.3 A general layout of the anergy ampliﬁer complex. The electrical power generated is also used to run the accelerators. Actinides, mostly thorium and uranium are refueled as new fuel into the EA refreshed with thorium. Fission fragments are stored in a secular repository, where after about 1000 y their radioactivity falls to a negligible level (after Rubbia et al. [1178]).

The ﬁgure shows also the mass ﬂow and the expected power. Only about 5% of the generated electricity is needed to power the accelerator system [994]. It is interesting to look more closely on the energy balance of the EA system of Figure 21.3. The proposed nominal power of the system of 1500 MWth requires 1) The energy gain G is deﬁned as the thermal energy produced by the EA divided by the energy deposited by the proton beam.

21.3 Feasibility of the ‘‘Energy Ampliﬁer’’

about 28 tons of mixed fuel oxide (ThO2 /233 UO2 ). The average power inside the fuel is set to be 55 W/g in the oxide fuel. This is only 1/2 of the level of UO2 experienced in LMFBR systems [1211]. To aim for 1500 MWth means then an energy production per second of 1.5 × 109 (J/s) · 6.2 × 1018 (eV/J) = 9.3 × 1027 (eV/s).

(21.2)

Furthermore, the following assumptions could be made: (1) 2.5 neutrons in average will be produced per ﬁssion releasing an energy of about 200 MeV, (2) assuming a keff = 0.98 [1168] of the subcritical EA system the additional number of ﬁssion neutrons Nneutron produced are determined to Nneutron = 1/(1 − keff ) = 50,

(21.3)

(3) 2.5 neutrons per ﬁssion yield 50/2.5 = 20 ﬁssions per neutron in the subcritical EA system, (4) the Pb target system [994] of the EA produces about 30 neutrons per beam proton at an incident proton beam energy of 1 GeV, about 40% of these neutrons will also cause ﬁssions inside the EA ampliﬁer. Using Eq. (21.2) and the above assumptions (1)–(4) the average number of beam protons per second or the beam current is then determined in the following way: 9.3 × 1027 (eV/s) (2.5 (n/ﬁssion) · 200 × 106 (eV/ﬁssion)· 20 (ﬁssion/n) · 0.4 (ﬁssion/n) · 30 (n/p))

= 7.75 × 106 (p/s)

(21.4)

and for the proton beam current it follows 7.75 × 106 (p/s) · 1.6 × 10−19 (C/p) = 12.4 (mA).

(21.5)

A beam current of 12.4 mA and a beam energy of 1 GeV delivered by the accelerator complex yield a proton beam power of 12.4 MW for the EA. The chosen nominal unit capacity of 1500 MWth thermal power corresponds to about 675 MWe of primary electrical power with ‘‘state-of-the-art’’ turbines and an outlet temperature of the order of 550 to 600◦ C. The thermodynamical efﬁciency of η = 45% is substantially higher than the one of a pressurized water reactor (PWR) and it is primarily due to the present higher temperature of operation. The nominal energetic gain of the EA is set to G = 120 corresponding to a multiplication coefﬁcient k = 0.98. The nominal beam current for 1500 MWth , is then 12.5 mA× GeV. Figure 21.4 shows the eventually possible scheme of performance of the EA design depicted in Figure 21.3. About 645 MWe may be delivered to the public electricity grid.

617

618

21 Accelerator Production of Electrical Energy – ‘‘Energy Amplifying’’ heff ≈ 45% 645 MWe to grid

675 MWe

Electrical energy convertor

30 MWe 1500 MWth 12.5 MW Accelerator

h ≈ 40%

Fig. 21.4

EA subcritical unit

The scheme of performance of the EA as shown in Figure 21.3.

In practice the proton accelerator must be able to produce eventually up to 20 mA × GeV in order to cope with the inevitable variations of performance during the lifetime of the fuel. The electric energy required to operate the accelerator is about 30 MWe about 5% of the primary electric energy production about of 675 MWe . Since the accelerator is relatively small and simple to operate, if more current is needed, several units can be used in parallel, with a corresponding increase of the overall reliability of the complex. In this case, the beams are independently brought to interact in the target region of the EA [1178]. 21.3.1 An Energy Ampliﬁer Test Experiment

The aspect of the energy gain has been studied in the FIRST Energy Ampliﬁer Test (FEAT) test experiment [1206]. A small subcritical system made of water and natural uranium was irradiated by a proton beam at CERN. The experimental setup and its main parameters are shown in Figure 21.5. It consists of an already existing subcritical assembly [1212] made of natural uranium rods, immersed in a stainless steel vessel ﬁlled with ordinary, demineralized water, which acts as moderator. The subcritical core has a diameter of 89 cm and height 107 cm. The central core was surrounded by a reﬂector of water with a thickness of about 12.5–15.5 cm. The beam from the CERN-PS hits a small target of depleted uranium, which is located in the center of the subcritical facility and provides the spallation source. A low-density channel from styrofoam removes most of the material along the beam path in its way to the target. The beam kinetic energy was varied between 0.6 and 2.75 GeV. The proton beam intensity has been typically of the order of l09 protons per pulse. From the heat released in the nuclear cascade about 1 W of energy was produced: too little to destroy nuclear waste, but enough to demonstrate the principle and to verify the precision of the calculations. From the analysis a keff = 0.895 ± 0.010 could be estimated as a preferred value. The gain factor G for additional neutron production from ﬁssions of the subcritical core is essentially

rods ~ 60 cm

natU

55

Stainless steel flang

5 12

Stainless steel vessel

35 15.8 50.8

21.4 Advantages and Disadvantages of the EA Concept

Proton beam 0.6-2.75 GeV Styrofoam Water moderator

Spallation target depU, ∅ = 35 mm

313 bar positions, 270 natU rods (∅ = 35 mm )

Fig. 21.5

View of the FEAT subcritical assembly (after Andriamonje et al. [1206])

constant above an incident beam energy of 1 GeV. The energy gain obtained from the experiment was G = 29 ± 2 for keff = 0.895, which was conﬁrmed also from Monte Carlo simulations. A G = 62 ± 8 is expected for larger more realistic EA devices and with a keff = 0.95, which is safely away from criticality [1206]. 21.4 Advantages and Disadvantages of the EA Concept

The possibility of having a neutron source external to a nuclear system, will allow the use of thorium in the future: a fuel much cleaner than uranium. This element is not ﬁssionable, but by capturing a neutron it can be transformed into 233 U, an isotope having favorable properties quite similar to the ones of 235 U, as for example being equally ﬁssionable and having resembling capture cross sections. The advantage is that thorium needs to capture seven neutrons to transform itself into 239 Pu, which is almost impossible given the fact that many other nuclear reactions are competing with capture in a subcritical core. Practically, over a thorium fast reactor lifetime only a few grams of plutonium can be produced and an even lower quantity of the other transuranium elements, which constitute the most toxic part of a traditional uranium reactor’s waste. Calculations show that in the EA, 233 U/thorium equilibrium is soon established. In this thorium cycle very little plutonium is produced – 1000 to 10,000 times less than in conventional reactors. Thorium, more abundant in the Earth’s crust than uranium, is fully used in the cycle (unlike natural uranium where only the 0.7% sliver of isotope 235 is ﬁssionable). Thorium energy reserves appear to be practically inexhaustible. The huge amount of thorium available in the earth’s crust opens the way to a source of energy which is exploitable for thousands of years. For the EA, different strategies for the transmutation of long-lived ﬁssion fragments are indicated. After 500 years, the toxicity of the radioactive waste is below that produced by Coal burning to produce an equivalent amount of energy.

619

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21 Accelerator Production of Electrical Energy – ‘‘Energy Amplifying’’

In conclusion, the advantages and disadvantages of the concept can be summarized as follows: Advantages: • Subcritical design means that the reaction could not run away – if anything went wrong, the reaction would stop and the reactor would cool down. A meltdown could however occur if the ability to cool the core was lost. • Thorium is an abundant element – much more so than uranium – reducing strategic and political supply issues and eliminating costly and energy-intensive isotope separation. There is enough thorium to generate energy for at least several thousand years at current consumption rates. • The EA would produce very little plutonium, so the design is believed to be more proliferation resistant than conventional nuclear power (although the question of 233 U as nuclear weapon material must be assessed carefully). • The possibility exists of using the reactor to consume plutonium, reducing the dangerously large world stockpile of the very long-lived element. • Less long-lived radioactive waste is produced – the waste material would decay after 500 years to the radioactive level of coal ash. • No new science is required. The technologies to build the energy ampliﬁer have all been demonstrated in the laboratory. Building an energy ampliﬁer requires some engineering effort, not fundamental research, unlike nuclear fusion. • The power generation might be economical compared to current nuclear reactor designs if the total fuel cycle and decommissioning costs are considered. • The design could work on a relatively small scale, making it more suitable for countries without a well-developed power grid system • Inherent safety and safe fuel transport could make the technology more suitable for developing countries as well as in densely populated areas. Disadvantages: • General technical difﬁculties. • Each reactor needs its own facility (particle accelerator) to generate the high-energy proton beam, which is very costly. • Apart from linear accelerators, which are very expensive, no proton accelerator of sufﬁcient power and energy (≤∼12 MW at 1 GeV) has ever been built. Currently, e.g., the spallation neutron source (SNS) in Oak Ridge utilizes a 1.4 MW proton beam to produce its neutrons, with upgrades envisioned to 2 MW [681], while the European ESS project, now again under consideration, is envisioned a beam power of 5–10 MW for a long-pulse spallation neutron source [1001]. An European effort at building such a machine in one of the EU countries could give a deﬁnitive answer in a few years to one of the most critical problems at the end of last century, opening up the way at last to a clean and potentially powerful source of energy. Elsewhere, several groups – at LANL, Los Alamos in USA, at BNL, Brookhaven in USA, at JAERI in Japan and in Russia, at least seven institutes around ITEP, Moscow – are planning accelerator-driven ﬁssion for a

21.4 Advantages and Disadvantages of the EA Concept

range of applications (waste and plutonium destruction, tritium production, energy production from thorium, uranium or plutonium). A joint report will be compiled under the aegis of the International Atomic Energy Agency. For a detailed concept of the EA, refer to Refs. [481, 682, 994, 995, 997, 1178, 1179, 1183, 1205–1207] and references therein. With the heavy ecological implications of present nuclear and conventional energy sources, it is surprising how little R&D work is being invested anywhere in this potentially rewarding alternative energy solution.

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22 Advanced Applications of Spallation Physics 22.1 Proton and Light Heavy Ion Cancer Therapy

The treatment of cancer with charged particles, ranging from protons to ‘‘light ions’’, e.g., carbon, oxygen, neon has many advantages. With the ﬁrst proton therapy facility at Loma Linda starting about 1990, currently, proton therapy is today a part of the medical business at many hospitals, whereas cancer therapy with light ions is just at the beginning. After some worldwide pioneering at research centers only a few were built. However, within the last years a remarkable dynamics can be observed with respect to the realization of new hadron therapy facilities [1213, 1214]. The reasons for an increased need of therapy facilities are the development of new treatment modalities like pencil beam scanning, light ion cancer treatment, and commercial aspects, arising from the number of patients that would proﬁt from the treatment. Another aspect is the reason that industrial companies offer ‘‘turn-key’’ facilities for proton treatment as well for light ions [1214]. Typically hadron cancer therapy requires, e.g., 250 MeV protons or 400 MeV/u carbon. Therefore it might be an option to beneﬁt from large scale neutron spallation sources typically driven by powerful linear accelerators, synchrotrons and cyclotrons to some extent also for cancer treatments. From the low energy required together with the rather moderate intensity needed, it is clear that the proton (and light ion) machines needed for cancer treatment would be quite different in size and costs than any accelerator for spallation neutron sources. For the three kinds of accelerators, cyclotron, linac and synchrotron and its advantages and disadvantages as they affect therapy, details are given, i.e., in Ref. [1215]. After the successful pioneering work carried out with accelerators built for physics research, machines dedicated to this new radiotherapy are planned or already in construction. The rationales for hadron therapy are based on the physical selectivity and biological effects of the respective beams. Fast neutron therapy began as long ago as 1938 and subsequently proton, α-particle, heavy ion, π, and neutron capture therapy have been used. To date it is estimated that in excess of 50 000 people have undergone some form of hadron therapy. In the future, it is expected that fast neutron therapy will be used for selected cancer types for which neutrons are known to show improved cure rates. The future trends in charged particle therapy will be driven by increasing commercialization. The future of neutron capture Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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22 Advanced Applications of Spallation Physics

therapy will depend on current clinical trials with epithermal neutron beams and the development of new cancer-seeking drugs. 22.1.1 History of Hadron Therapy

The history of proton beam therapy is surprisingly old. Robert Wilson ﬁrst proposed to use protons for the treatment of cancer in a scientiﬁc article in 1946 [958]. He recognized the importance of highly localized deposition of energy as a way of increasing the dose to the tumor while minimizing the dose to normal tissues. Two years later, researchers at the Lawrence Berkeley Laboratory (LBL) conducted extensive studies on protons and conﬁrmed the predictions made by Wilson. The ﬁrst treatments on humans consisted irradiation to destroy the pituitary gland in patients with metastatic breast cancer that was hormone sensitive. This treatment stopped the pituitary from making hormones that stimulated the cancer cells to grow. The pituitary was a natural site for the ﬁrst treatments because the gland location was easily identiﬁed on standard X-ray ﬁlms, well localized, and surrounded by sensitive normal structures. In the 1950s, the treatments were successfully duplicated on patients at the facility in Uppsala, Sweden. The Harvard Cyclotron Facility became interested in using protons for medical treatments after observing proton therapy in the 1950s at both LBL and Uppsala. The Harvard Cyclotron subsequently began treatment of the pituitary gland and developed specialized techniques for treating other lesions such as arteriovenous malformations (AVM). During the 1960s, these facilities worked to expand proton treatments to include choroidal melanomas, chondrosarcomas, chordomas, and various intracranial malignancies. However, this early work was limited due to the inability to perform 3D imaging and reliance on facilities primarily dedicated to physics research. With the development of the computed tomography (CT) scanner, improved target deﬁnition allowed the treatment of almost any site in the body. During the 1970s, the Massachusetts General Hospital conducted the ﬁrst research on mixed proton/X-ray radiotherapy for the treatment of prostate cancer, and the University of Tsukuba, Japan, started proton cancer therapy with a booster accelerator, a high-energy accelerator, for liver cancer, esophagus cancer, lung cancer, and brain tumor as its object diseases. Unfortunately, during this decade, the role of protons in radiotherapy was signiﬁcantly underestimated in favor of neutron therapy. However, proton therapy survived this time of limited acknowledgment and interest in this therapy is rapidly increasing. The subsequent development of MRI, SPECT, and PET scanning has further improved target deﬁnition and allows even further beneﬁts of proton therapy. In the 1980s, design and construction began on the ﬁrst dedicated clinical proton facility at Loma Linda University Medical Center. This facility was designed and built by Fermilab, where Wilson was the founding director. To date, the Loma Linda facility has treated over 6100 patients with proton therapy. The Proton Therapy

22.1 Proton and Light Heavy Ion Cancer Therapy

Cooperative Group (PTCOG) was also created during the 1980s for scientists to exchange ideas on the development of proton therapy. This group continues to meet on a regular basis to present both clinical and basic science research to the international proton therapy community. Proton therapy was further expanded during the 1990s. The Proton Radiation Oncology Group (PROG) was created speciﬁcally to sponsor the development of clinical trials involving proton therapy. As mentioned, over 50 000 patients have now been treated with proton therapy worldwide. Clearly proton therapy has a bright future in both the clinical and basic science areas. There has been a clear shift in the development of proton therapy systems this decade. Most of the centers opening and under construction are clinical proton facilities as opposed to physics research facilities that treat patients when beam time was available. A number of other facilities are considering the construction of clinical facilities worldwide. Without claiming to be complete, in summary the following proton therapy facilities for cancer treatment by proton and ions are operating or under construction worldwide: • North America – Loma Linda Proton Treatment Center at Loma Linda University Medical Center (LLUMC), California; a 250 MeV proton synchrotron, pulse width of 300 ms and frequency 2.2 s; – Eye Therapy at the Crocker Nuclear Laboratory, University of California, Davis, joined with LBL eye cancer therapy program; – The Northeast Proton Therapy Center (NPTC) at the Massachusetts General Hospital (see also Harvard Cyclotron Laboratory (HCL)); – Midwest Proton Radiation Institute at the Indiana University Cyclotron Facility; 210 MeV proton cyclotron with 0.5 µA current; – Cancer Treatment with protons at Triumf, Canada. • Europe – Radiation Medicine at Paul Scherrer Institute (PSI), Villigen, Switzerland; proton cyclotron with an active spot scanning system; – Heavy Ion Cancer Therapy at Gesellschaft f¨ur Schwerionenforschung mbH (GSI), Darmstadt, Germany; Synchrotron proton/ion accelerator with a raster scanning system; – Heidelberger Ionenstrahl-Therapie (HIT), Universitts Klinikum Heidelberg, Germany; – Proton therapy project at Kernfysisch Versneller Instituut (KVI), Groningen, The Netherlands; Proton cyclotron with a passive scanning system; – Clatterbridge Centre for Oncology; – The Center of Protontherapy of Orsay (CPO) near Paris, France; Proton synchrocyclotron with a passive scanning system; – Centre Antoine Lacassagne (CAL), Nice, France; MEDICYC 65 MeV proton cyclotron for proton and neutron therapy; – Department of Oncology of Uppsala University Hospital, Sweden or the Svedberg Laboratory (TSL) at the Uppsala University has a proton therapy research program;

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22 Advanced Applications of Spallation Physics

– Med-AUSTRON part of the Neutron Spallation Source Project AUSTRON, Austria; – The Prague Medical Synchrotron Project a joint proton therapy project of the Nuclear Research Institute in Rez and the First Faculty of Medicine of Charles University, Czech Republic; – CNAO Centro Nazionale di Adroterapia Oncologica, Pavia, Italy; – Rh¨on Klinikum AG, University of Marburg/Giessen, Germany; – Rinecker Proton Therapy Center (RPTC), Munich, Germany; – Medical Physics Department of ITEP at Dubna, Russia. • Africa – Medical Radiation Group of the National Accelerator Center (NAC) in South Africa. • Asia – Proton Medical Research Center (PMRC) at the University of Tsukuba; it uses the 500-MeV booster synchrotron of KEK operated at 20 Hz. A new facility is under development; – National Institute of Radiological Sciences (NIRS) Chiba, Japan; Research Center of Charged Particle Therapy with the HIMAC (Heavy Ion Accelerator in Chiba) facility. For neutron therapy, typically neutrons up to 50 MeV are used in speciﬁc human cancer. Neutron/Boron Neutron Capture Therapy (BNCT) is an experimental approach to cancer treatment, which combine boron and low-energy neutrons. Endeavors are undertaken in the following therapy facilities: • Medical Department of BNL at Brookhaven, USA • Lawrence Berkeley National Laboratory, USA • Fermilab Neutron Therapy Facility (NTF), Chicago/Illinois • Kyoto University Research Reactor, Japan • UCLA with a detailed introduction to BNCT, USA • The INEEL/MSU Center for Advanced Radiation Therapies at the Montana State University, USA. 22.1.2 What is Radiation Therapy and How Does it Work?

Tumors are made up of cells that are reproducing at abnormally high rates. Radiation therapy speciﬁcally acts against cells that are reproducing rapidly. Normal cells are programmed to stop reproducing (or dividing) when they come into contact with other cells. In the case of a tumor, this stop mechanism is missing, causing cells to continue to divide over and over. It is the DNA of the cell that makes it capable of reproducing. It is considered that the biological effect caused by ionizing radiation is a DNA damage. Radiation therapy uses high-energy X-rays to damage the DNA of cells, thereby killing the cancer cells, or at least stopping them from reproducing. The magnitude of the effect is determined by the amount of ionizing radiation per unit volume which is generated along the track of irradiation. The

22.1 Proton and Light Heavy Ion Cancer Therapy

average energy given per unit track length is called LET (linear energy transfer). The heavier the particles used and the deeper they pass into the body, the greater the LET. Radiation also damages normal cells, but because normal cells are growing more slowly, they are better able to repair this radiation damage than are cancer cells. In order to give normal cells time to heal and to reduce a patient’s side effects, radiation treatments are typically given in small daily doses. Currently available major approaches to cancer therapy are ‘‘surgery’’, ‘‘chemotherapy,’’ and ‘‘radiotherapy.’’ Considering the patient’s social rehabilitation, radiotherapy is achieving the desired effects with respect to quality of life improvement, fewer side-effects, and healthy organ preservation. In some cases, radiotherapy is used in combination with surgery or chemotherapy. 22.1.3 Differences Between Protons, Heavy Ion, and X-ray Therapy

The main difference between protons and X-rays is based on the physical properties of the beam itself. Protons penetrate matter to a ﬁnite depth based on the energy of the beam. X-rays are electromagnetic waves that have no mass or charge and are able to penetrate completely through tissue while losing some energy. These physical properties have a signiﬁcant bearing on the treatment of patients. To understand the effects of radiation on biological systems ﬁrst the physical interaction processes involved in the passage of radiation through matter have to be considered. Here the absorbed dose, the amount of energy deposited in a small mass element of the absorber medium, is an important measure (unit Gray, 1 Gy = 1 J/kg)1) . In contrast to electromagnetic radiation (X- and γ -rays), exhibiting an exponential decrease of intensity with penetration depth, heavy charged particles like protons or heavy ions have a well-deﬁned range in matter depositing their energy at the end of their range in tissue. The advantages of particle therapy in comparison to radiotherapy with photons are improved dose conformity inside the tumor as well as the lower integral dose deposited in the healthy tissue surrounding the tumor. The lower integral dose is a consequence of the physical differences of particles to photons. Having a nonnegligible mass, most of the energy of the particles is deposited inside the tumor at the depth of the so-called Bragg peak. In classical photon radiotherapy, the dose is deposited along the whole path of the radiation, with energy deposition at its highest within a short distance to the body surface. The depth of treatment in tissue for protons is related to the Bragg peak. This is due to a buildup of dose in the ﬁnal few millimeters at the end of the proton or light ion range. The depth of the Bragg peak is dependent on the energy of the beam; with increasing energy, the Bragg peak is located deeper in tissue [1216]. The slowing down process of heavy ions in matter is governed by inelastic collisions with 1) 1 Gy = 1 J/kg, a 250 MeV proton has 5 × 10−11 J, so 1 Gy is deposited by 2 × 1010 protons, if the protons stop inside 1 kg.

Typically 1/2 to 2/3 of the energy is deposited outside the tumor. Physician apply 2 to 10 Gy.

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22 Advanced Applications of Spallation Physics

atomic electrons of the absorber material and is very well described by the Bethe–Bloch formula (cf. Section 1.3.6.1 on page 33). The incident primary ions also undergo nuclear fragmentation reactions, resulting in a complex alteration of the composition of the particle ﬁeld. Detailed data on these effects are indispensable for the calculation and optimization of the biologically effective dose for treatment planning. The ‘‘inverted’’ depth-dose proﬁle (Bragg curve) of heavy charged particles represents the major advantage for the radiation therapy of deep-seated local tumors in comparison to conventional photon therapy. The favorable dose proﬁle is additionally enforced by an enhanced biological effectiveness (RBE) of heavy ions in the Bragg-peak region, which can be explained on a microscopic level by the high-ionization density in the particle track (biophysical model). Figure 22.1 shows such a Bragg peak in tissue as a function of penetration depth for 250 MeV carbon ions and 135 MeV protons. As can be seen, the entrance dose is relatively low, but as the beam penetrates deeper in tissue, there is a sharp rise in dose deposited. When traveling through tissue, the speciﬁc ionization of protons increases as they slow down toward the end of their trajectory. This is followed by a rapid stop in dose deposition. The beam stops at this point. Thus no tissue is treated beyond the Bragg peak. The relatively sharp peak needs to be ‘‘spread out’’ to ﬁt the width of the target (the tumor geometry) to be clinically useful. Several beam modulation methods were developed to spread out the Bragg peak to a desired size. The spreading out of the Bragg peak through energy modulation provides a homogeneous depth range, a Bragg plateau area, for the protons or the 12 C ions. Figure 22.1 also shows the ideal depth dose distribution as compared to the dose delivery characteristics of

140 Effective dose [arbitrary units]

628

Photons

12C

ions

100 Protons

Peak area Bragg peak protons

60

Plateau area

20

Tumor size

0 0

2

4 6 8 10 Penetration depth in H2O [cm]

Fig. 22.1 Effective dose in arbitrary units as a function of penetration depth in tissue for 250 MeV 12 C ions, 135 MeV protons, and 18 MeV photons. The Bragg plateaus by modulating the incident proton and 12 C beams and the Bragg peak for protons without beam modulation are indicated.

12

14

22.1 Proton and Light Heavy Ion Cancer Therapy

protons and standard X-ray (18 MV) photons. X-rays deposit most of their radiation as they enter the body and continue depositing dose to the targeted region and surrounding normal tissue. As a result, the normal tissue near the entrance receives higher doses of radiation than the internal tumor itself. The sensitivity to radiation of normal tissue is what typically limits the dose that radiation oncologists can safely prescribe, especially when a tumor lies near vital organs. Extensive studies have been performed to determine the biological differences between protons and X-rays. A standard measure called the relative biologic effect (RBE) is used to compare the biologic effects of various radiation sources. An RBE of 1 is seen for standard X-rays. Neutrons have a much higher RBE of 3. It turns out that protons can be thought of exactly the same as X-rays in terms of its biologic effects because the calculated RBE is 1.1. Another measure of effect in biologic systems is the oxygen enhancement ratio (OER). Again, there is no difference in OER between protons and standard X-rays. The bottom line is that the only difference between protons and standard X-rays lies in the physical properties of the beam and not the biologic effects in tissue. Aside from the possibility of treating tumors resistant to classical photon therapy, the special physical properties of particles allow the treatment of deep-seated tumors with a high integral dose to healthy tissue while on its way to the tumor. Particle therapy is also favorable for tumors in the vicinity of sensitive or vital organs due to the higher accuracy of this treatment method. Because of the decreased energy deposition in healthy tissue, the probability of developing secondary cancer in the tissue surrounding the tumor is strongly decreased. Therefore, particle therapy is especially suited for pediatric tumors. This is especially important due to the long life expectancy of children after irradiation and the high risk of secondary cancer caused when treating them with classical photon therapy. The six images shown in Figure 22.2 compare the dose distribution of X-ray beams with proton beams. A tumor of the prostate gland appears in each image. The various colors indicate the intensity of the dose deposited in the tissue. The two images on the left compare the dose distribution of a single X-ray beam and a single proton beam. With the X-ray beam more dose is visibly deposited in the healthy tissue. The four images on the right show the effect of multiple beams. Even with multiple X-ray beams (top right) there is still substantial dose to healthy tissue. However, with the two lateral proton beams (lower middle), the dose nicely conforms to the shape of the tumor. Regardless of the quantity of X-ray beams used, there will be two to three times more integral dosage to normal tissue than with protons. As for (heavy) ion therapy, because of higher atomic numbers, the lateral and range scattering is much smaller for carbon or neon ions than for protons. One of the major advantages of heavy ion tumor therapy is the increase in RBE of particle beams, in particular, at the end of their penetration depth, i.e., in the tumor volume (see Figure 22.1). This increased effectiveness has to be taken into account for treatment planning. The RBE cannot be represented by a single number, but

629

22 Advanced Applications of Spallation Physics x-ray beam irradiation

X-ray beam

Proton beam

X-ray beam

X-ray beam

Proton beam

Proton beam

Proton beam irradiation

Fig. 22.2 Prostate cancer irradiated by X-ray and proton beam. The advantage of proton beams in respect to X-rays for cancer treatment is clearly visible. For details, refer to the description below. 2.5

2.0 Relative dose

630

Extended volume by different Bragg curves

Neutrons 14 MeV

1.5

60Co

Bragg plateau

Ne with sec. He

1.0

Neutrons 14 MeV 60Co

0.5

0.0

Pi-mesons

He Pi-mesons

Protons 0

2

4

6

8

Protons 10

Ne with sec. 12

14

16

18

20

Penetration depth [g/cm2]

Fig. 22.3

Penetration depths in tissue for various particles used for cancer therapy.

depends in a complex way on different factors like ion type and energy, depth in tissue, dose level and the tissue type. For applications of ion beams in tumor therapy, the increased RBE requires a corresponding general reduction in dose. In particular, due to the variation of RBE with depth, the shape of the depth-dose proﬁle has to be adapted accordingly. In general ions are better for radioresistant tumors, while protons minimize the risk of appearance of secondary tumors. In summary, Figure 22.3 shows the penetration depths in tissue for various particles used for the cancer therapy by radiation. It is seen that charged particle beams have particularly advantageous characteristics. Both protons and heavier

22.2 High-Energy Physics Calorimeter Tab. 22.1

Types of methods used in particle radiotherapy.

Type of radiation

Source of radiation

Features

γ -ray

60 Co

X-ray

Linac

Electron beam

Linac/betatron

Neutron beam

Cyclotron

Proton beam

Cyclotron & synchrotron

He, C, Ne ion beams

Synchrotron

Potential side-effects on the cells shallow from the body surface such as skin Potential damage to healthy cells between skin and the front of cancer cells, if cancer developed in deep part of body; Excellent in eliminating the cancer developed in relatively shallow part from the skin, potential damage to healthy cells between skin and front of cancer cells, if cancer developed in a deep part of the body; Highly effective in destroying cancer cells compared to γ -ray, X-ray and electron beam, but severe side-effects; Easily targeting cancer cells while avoiding healthy cells; Highly effective in destroying cancer cells Compared to γ -ray, X-ray and electron beam, Easily targeting cancer cells while avoiding healthy cells.

source

ions can be made to deliver the dose uniformly within a Bragg plateau. The various sources to produce this radiation are listed in Table 22.1. Comprehensive overview articles on the treatment of cancer with charged particles, ranging from protons to ‘‘light ions’’ (carbon, oxygen, neon) and hadron therapy projects in Europe are given, e.g., in Refs. [1213, 1215, 1217, 1218]. 22.2 High-Energy Physics Calorimeter 22.2.1 The Physics of Particle Calorimetry

In particle physics, a calorimeter is a component of a detector that measures the energy (and position) of entering incident particles or jets. Particles enter the calorimeter and initiate hadronic and/or electromagnetic showers as also described in detail in Section 4.2 on page 185. The particles’ energy is deposited in the calorimeter, collected, and measured. In the process of absorption showers are generated by cascades of interactions, hence the occasionally used name shower counter for a calorimeter.

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22 Advanced Applications of Spallation Physics

In the course of showering, eventually, most of the incident particle energy will be converted into ‘‘heat,’’ which explains the name calorimeter (calor = Latin for heat) for this kind of detector. In particle physics, no temperature is measured in practical detectors, but characteristic interactions of (essentially charged) particles with matter (e.g., atomic excitation, ionization, see Chapter 4 on page 185) are used to generate a detectable effect. Calorimetry is also the only practicable way to measure neutral particles among the secondaries produced in high-energy collisions. Calorimeters are usually composed of different parts, custom-built for optimal performance on different incident particles. The energy may be measured in its entirety, requiring total containment of the particle shower, or it may be sampled. Typically, calorimeters are segmented transversely to provide information about the direction of the particle or particles, as well as the energy deposited, and longitudinal segmentation can provide information about the identity of the particle based on the shape of the shower as it develops. Calorimeters are therefore made of multiple individual cells, over whose volume the absorbed energy is integrated; cells are aligned to form towers typically along the direction of the incident particle. The analysis of cells and towers allows one to measure lateral and longitudinal shower proﬁles, hence their arrangement is optimized for this purpose, and usually changes orientation in different angular regions. Typically, incident electromagnetic particles, i.e., electrons and gammas, are fully absorbed in the electromagnetic calorimeter, which is made of the ﬁrst (for the particles) layers of a composite calorimeter; its construction takes advantage of the comparatively short and concentrated electromagnetic shower shape (cf. Section 4.2) to measure energy and position with optimal precision for these particles (including π0’s, decaying electromagnetically). Electromagnetic showers have a shape that ﬂuctuates within comparatively narrow limits; its overall size scales with the radiation length X0 (cf. Eq. (1.72) on page 59). In contrast to the energy of particles that interact primarily via the electromagnetic interaction, a hadronic calorimeter, on the other hand, is designed to measure particles that interact via the strong nuclear force. Incident hadrons, may start their showering in the electromagnetic calorimeter, but will nearly always be absorbed fully only in later layers, i.e., in the hadronic calorimeter, built precisely for their containment. Hadronic showers have a widely ﬂuctuating shape; their average extent does not scale with the calorimeter’s interaction length λ (cf. Eq. (1.24) on page 32), but is partly determined by the radiation length. Discrimination, often at the trigger level, between electromagnetic and hadronic showers is a major criterion for a calorimeter; it is, therefore, important to contain electromagnetic showers over a short distance, without initiating too many hadronic showers. The critical quantity to maximize is the ratio λ/X0 which is approximately proportional to Z1.3 [1219] and hence the use of high-Z materials like Pb, W, or U for electromagnetic calorimeters. Calorimeters can also provide signatures for particles that are not absorbed: muons and neutrinos. Muons do not shower in matter, but their charge leaves an ionization signal, which can be identiﬁed in a calorimeter if the particle is sufﬁciently isolated (and the dynamic range of electronics permits), and then can

22.2 High-Energy Physics Calorimeter

be associated to a track detected in tracking devices inside the calorimeter, or/and in speciﬁc muon chambers (after passing the calorimeter). Neutrinos, on the other hand, leave no signal in a calorimeter, but their existence can sometimes be inferred from energy conservation: in a hermetically closed calorimeter, at least a single sufﬁciently energetic neutrino, or an unbalanced group of neutrinos, can be ‘‘observed’’ by forming a vector sum of all measured momenta, taking the observed energy in each calorimeter cell along the direction from the interaction point to the cell. The precision of such measurements, usually limited to the transverse direction, requires minimal leakage of energy in all directions, hence a major challenge for designing a practical calorimeter. The ultimate limit for the energy resolution of a calorimeter is determined by ﬂuctuations inherent in the development of showers, and by instrumental and calibration limits. The basic phenomena in showers are statistical processes. This explains why the relative accuracy of energy measurements in calorimeters improves with increasing energy. The intrinsic limiting accuracy, expressed as a fraction of total energy, improves with increasing energy as √ (σ/E)ﬂuct. ∝ 1/ E,

(22.1)

where E is the energy of incident particle and σ the standard deviation of the energy measurement. Over much of the useful range of calorimeters, this term dominates energy resolution. There are other contributions than statistics, though: a second component is due to instrumental effects, being rather energy independent (noise, pedestal); its relative contribution decreases with E: (σ/E)instr. ∝ 1/E.

(22.2)

This component may limit the low-energy performance of calorimeters. A third component is due to calibration errors, nonuniformities and nonlinearities in photomultipliers, proportional counters, ADCs, etc. This contribution is energy independent: (σ/E)syst. = const.

(22.3)

This component sets the limit for the performance at very high energies. The two types of showers have markedly different characteristics discussed as follows: 22.2.2 Electromagnetic Showers

For electromagnetic showers, the intrinsic limitation in resolution results from variations in the net track length of charged particles in the cascade; for homogeneous shower counters √ (σ/E)ﬂuct. ≈ 0.005/ E (GeV),

(22.4)

633

634

22 Advanced Applications of Spallation Physics

whereas in sampling calorimeters, one has to add the sampling ﬂuctuations: (σ/E)samp. ≈ 0.04/ 1000E/E (GeV),

(22.5)

with E the energy loss of a single charged particle in one sampling layer. There are also ﬂuctuations arising from the Landau distribution; a comparison can be found in [1219]. In practice, total energy resolution below the percent level for E ≤ 50 GeV can be achieved routinely in homogeneous calorimeters; the same seems more like a very tough lower limit for sampling calorimeters. At low energies and for crystal calorimeters, total energy resolutions √ (σ/E) ≈ 0.025/4 E (GeV)

(22.6)

have been reported. For more quantitative values, confer Refs. [1220, 1221]. 22.2.3 Hadronic Showers

For hadronic showers, the intrinsic limitation is due to ﬂuctuations in the fractional energy loss accounted for by the many interaction mechanisms leaving behind nonhadronic debris (including muons and the γ s and e± from π0 decays) and slow neutrons, along with fast hadrons. The ﬂuctuations in these production processes, much larger than that for electromagnetic processes, are the major ingredient of the ﬁnal performance of a hadron calorimeter. Intrinsic shower ﬂuctuations are typically given by √ (σ/E)ﬂuct. ≈ 0.45/ E (GeV)

(22.7)

and for uncompensated calorimeters, and with compensation for nuclear effects: √ (σ/E)ﬂuct. ≈ 0.25/ E (GeV).

(22.8)

Compared with the intrinsic ﬂuctuations, sampling ﬂuctuations are normally small: (σ/E)samp. ≈ 0.09/ 1000E/E (GeV),

(22.9)

with E again being the energy lost by a single charged particle in one sampling layer. Note that these numbers refer to single hadronic particles; the (σ/E) for jets is typically higher by a factor 1.3 or more. Hadronic showers can spread over a large volume; a major source of systematic errors, therefore, is the geometric limitation of a calorimeter. The resolution ﬁgures determined by intrinsic shower and sampling ﬂuctuations will not be reached if showers are not fully contained within the calorimeter volume. In practice some average fraction of the shower energy escapes through the sides (lateral leakage) or back (longitudinal leakage). While the corrections for longitudinal leakage are understood, and can partly be

22.2 High-Energy Physics Calorimeter

accounted for, corrections for lateral leakage need a careful inspection of the shower development and an estimate of the particle impact point. Another important effect which has to be considered in a calorimeter is the energy loss of minimum ionizing particles, or mips (cf. Section 1.3.6.1 on page 33). Minimum ionizing particles (mips) leave a very distinctive trail in the calorimeters: a continuous sequence of single hits. Sometimes a hit is missed because of inefﬁciency; sometimes there are two adjacent hits because of a delta electron. True mips are muons. Also energetic charged hadrons (e.g., a pi+ or K+) act like a mip as they travel through the calorimeter until they undergo a hadronic interaction and showers. 22.2.4 Combined Electromagnetic/Hadronic Calorimeters

In hadronic and combined electromagnetic/hadronic calorimeters, the energy resolution achievable for hadrons is critically dependent on the choice of absorber and active materials, and their relative thicknesses. It is important that the energy response at all energies is as independent as possible of the ﬂuctuations in shower development, in particular the content of electromagnetic particles (electrons and photons). This is of prime relevance for the measurement of jet energies, as in this case not only electromagnetic particles may appear during shower development, but the π 0 content (and hence the fraction of energy in the form of γ s) can be substantial in the jet before it impinges on the calorimeter. The response of a calorimeter can be described in terms of the e/h (electromagnetic to hadronic) ratio. This is the measure of how well a calorimeter responds to leptons or photons versus the hadrons. Ideally one would want a ratio e/h ∼ 1, this condition is called compensation. In general, the average ratio between signals from electromagnetic and hadronic particles of the same incident energy is calorimeter- and energy-dependent, and for noncompensating calorimeters there is a higher response for electromagnetic particles, typically e/h ≈ 1.1–1.35. Various phenomena in both active and passive layers of sampling calorimeters can be put to use to achieve e/h ≈ 1, thus optimizing energy resolution: adjusting the relative thickness of absorber and active layers, using 238 U as absorber for its ﬁssion capability for slow neutrons, or shielding the active layers by thin sheets of low-Z material to suppress contributions from soft photons in electromagnetic showers, are possible methods of active compensation [1222]. The photon absorption in the (high-Z) absorber material plays a signiﬁcant role, and so does the conversion of low-energy neutrons into signal, e.g., by detection of deexcitation photons; the hydrogen content in the active medium is relevant here. For a detailed discussion, see [1223]. If high resolution is not required during readout, e.g., for triggering, corrections corresponding to compensation may also be applied by an a posteriori algorithm (‘‘off-line’’), when the shower proﬁle (mostly the longitudinal distribution) is known. A good example is the ZEUS uranium calorimeter used at the HERA accelerator at DESY, Germany, during 1987–2007, whose issues is described in [1224].

635

636

22 Advanced Applications of Spallation Physics

Figure 22.4 visualizes schematically the important effects, which are involved in the physics of compensating sampling calorimeters, e.g., the ZEUS uranium sampling calorimeter [1225] with layer thicknesses of the depleted uranium absorber of about 3 mm and for the scintillator (SCNS-38) about 2.5 mm. The main emphasis lies in the production of neutrons via spallation reactions and gammas in the uranium absorber plates. A tuning of the compensation by means of layer thickness could be accomplished in a calorimeter with hydrogeneous scintillator material [1226]. Figure 22.5 shows an artists view of the ZEUS-DESY uranium sampling calorimeter. The ZEUS calorimeter [1228] is a uranium-scintillator sampling calorimeter, which is divided into three main sections: the BCAL (Barrel CALorimeter), FCAL (Forward CALorimeter), and RCAL (Rear CALorimeter). Each section is subdivided transversely into towers and longitudinally into EMC (electromagnetic calorimeter) or HAC (HAdronic Calorimeter). The smallest subdivision in the calorimeter is called a cell. Each cell is read-out by two photomultiplier tubes (PMT), this redundancy helps to ensure that there are no holes in the detector if a PMT fails. Uranium was chosen as an absorber because of its ability to compensate [1226, 1227]. Leptons (and photons) and hadrons deposit energy differently than each other. In general the proportion of energy deposited from an electromagnetic cascade (e) is different from that in hadronic cascade (h). In most physics experiments e/h > 1, which compromises the energy measurement. In the ZEUS calorimeter particles interact with uranium atoms to produce slow-moving neutrons, which Scintillator Absorber Detector Absorber

h

Migration effects of γ energy

EM shower

e−

U

n

Spallation and evaporation n’s (MeV, prompt)

γ h

γ

n U

Fission n

Uranium lead tungsten

Fission γ’s, n’s (prompt) n-capture in uranium (delayed γ ’s )

Scintillator liquid argon (LA) LA + CH4

Fig. 22.4 Important effects of the physics of sampling calorimetry are illustrated for uranium as absorber and liquid argon (LA) or scintillator of SCNS-38 as detector material (after Bruckmann ¨ et al. [1226, 1227]).

22.2 High-Energy Physics Calorimeter

Muon toroid magnets

82

0G

p eV

rot

on

s

Muon detector

Ele

o ctr

3 ns

Fig. 22.5

0G

eV

6m DE SY –P R

Kn au t/2 .90

Superconducting solenoid & Forward Barrel central tracker uranium uranium calorimeter calorimeter

Artists view of the ZEUS-DESY uranium sampling calorimeter (after [1228]).

are captured by the scintillator and increase the hadronic signal [1227]. Another advantage of using uranium as the absorber is that the natural radioactivity allows one to monitor the calibration of the experiment over time. Measurements and simulations of test experiments were carried out with electrons, hadrons and muons in the momentum range of 1–100 GeV/c at the CERN-PS and CERN-SPS. An e/h ratio was evaluated to be about 1.03 ± 0.01 in the momentum range between 1 and 10 GeV/c and 1.0 ± 0.01 in the momentum range 10–100 GeV/c. An average resolution for hadrons was estimated from the measured values to √ σ/E = 33.5%/ E ± 0.3. Details on experimental and theoretical investigations of ZEUS e/h ratios and resolutions are published in Refs. [1226, 1229–1232]. The ZEUS detector depicted in Figure 22.5 comprises many components, including a depleted uranium-plastic scintillator calorimeter, a central tracking detector (CTD), which is a wire chamber, a silicon micro-vertex detector and muon chambers. In addition, a solenoid provides a 1.43 T magnetic ﬁeld. The ZEUS experiment studies the internal structure of the proton through measurements of deep inelastic scattering. These measurements are also used to test and study the Standard Model of particle physics, as well as searching for particles beyond the Standard Model. From the construction point of view, one can distinguish between: • homogeneous shower counters: In homogeneous calorimeters, the functions of passive particle absorption and active signal generation and readout are combined in a single material. Such materials are almost exclusively used for electromagnetic calorimeters, e.g., crystals (crystal calorimeter), composite materials (like lead glass, PbO and SiO2) or, usually for low energy, liquid noble gases [1220].

637

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22 Advanced Applications of Spallation Physics

• heterogeneous shower counters(= sampling calorimeters): In sampling calorimeters the functions of particle absorption and active signal readout are separated. This allows optimal choice of absorber materials and a certain freedom in signal treatment. Heterogeneous calorimeters are mostly built as sandwich counters, sheets of heavy-material absorber (e.g., lead, iron, uranium) alternating with layers of active material (e.g., liquid or solid scintillators, or proportional counters). Only the fraction of the shower energy absorbed in the active material is measured. Hadron calorimeters, needing considerable depth and width to create and absorb the shower, are necessarily of the sampling calorimeter type. In practical constructions the ratio of energy loss in the passive and active material is rather large, typically of the order of 10. Although performance does not strongly depend on the orientation of active and passive material, their relative thickness must not vary too much, to ensure an energy resolution independent of direction and position of showers. Only a few percent of the energy lost in the active layers is converted into a detectable signal [1219]. Calorimetry is the art of compromising between conﬂicting requirements; the principal requirements are usually formulated in terms of resolution in energy, spatial coordinates, and time, in triggering capabilities, in radiation hardness of the materials used, and in electronics parameters like dynamic range, and signal extraction (for high-frequency colliders). In nearly all cases, cost is the most critical limiting parameter. Most large high-energy physics experiments use some form of calorimetry. In large colliding experiments like ATLAS or ZEUS, the calorimeter works in conjunction with other components as already mentioned like a Central Tracker and a Muon Detector. The span of possible solutions for calorimeters is much wider than for tracking devices. All the components work together to achieve the objective of reconstructing a physics event. For further reading, see Refs. [1219–1223, 1233–1235] and references given therein.

22.3 Neutrino Factories and Neutrino Super/Beta Beams 22.3.1 Some Words on Research with Neutrinos

During the past years neutrino physics has emerged as an expanding ﬁeld of particle physics. In this book, neutrinos have already been introduced in Section 1.2 as products of the decay of charged mesons and few of their properties are given in Table 1.7 on page 25. Details on the ν’s properties as they are understood within the standard model are given in references of the Particle Data Group (PDG) [19]. Neutrinos are special among the elementary particles having in mind that they are structureless, do not carry charge or color and, until recently, it was believed that they carried no mass either.

22.3 Neutrino Factories and Neutrino Super/Beta Beams

They are the most abundant constituent of the universe and have an important impact on astrophysical processes, from the ﬁrst minutes after the Big Bang itself to supernovae explosions observed today. The relevance of neutrino physics to the understanding of dark matter and dark energy, the connection between neutrino mass and leptogenesis and galaxy-cluster formation are currently addressed issues. The demonstration, using natural sources, that neutrinos have mass and that the three generations mix has been one of the major events in particle physics in the last decade. This observation constitutes the ﬁrst experimental evidence of new physics beyond the standard model. The processes leading to these unexpected masses and mixing parameters are thought to take place at energies never seen since the Big Bang, perhaps connected to the uniﬁcation of all forces. Precise determinations of the masses and mixing angles of the three families of neutrinos is a unique window of observation into these early times. The understanding of the ﬂavor and connection between quarks and leptons, the possible existence of hidden ﬂavor quantum numbers that may be connected with the small mixings among the quarks, the mass hierarchy of the quarks and charged leptons, and the relationship of these phenomena with the neutrino mass matrix are currently of highest interest. The recently discovered properties of neutrinos open the possibility of observing a difference in the oscillations of neutrinos and antineutrinos, so-called leptonic CP violation. This discovery would be extremely important and likely to give essential input to understand how the universe has evolved from the matter–antimatter equality at the time of the Big Bang to our present matter-dominated world. A comprehensive and well-elaborated report on the Physics case at a future Neutrino Factory and super-beam facility can be found in a recent contribution by the ISS Physics Working Group [962] 22.3.2 International Scoping Study of ν Factories and Superbeam Facilities

These fascinating physics questions mentioned above require an ambitious accelerator-based long baseline neutrino experimental program. Several neutrino sources have been envisaged to reach high sensitivity and redundancy well beyond the presently approved neutrino-oscillation program. A ν-factory is an intense high-energy neutrino source based on a stored muon beam (see also Eq.(1.74), page 61). These factories currently lively discussed, e.g., in the EU CARE integrated infrastructure initiative [1236] and the BENE network activity [1237] employ very powerful MW proton drivers and produce ﬁnally neutrinos from π and µ decay. These kind of facilities aim at ν-production rates of up to 1021 useful µ-decays/year. Studies so far have shown that a ν-factory gives the best performance over virtually all of the parameter space; its time scale and cost remain, however, important question marks. The main technical challenges involve construction of very intense proton beams, targeting, effective capture of produced particles, cooling, and subsequent acceleration of the resulting muons.

639

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22 Advanced Applications of Spallation Physics

An alternative scenario of producing intense ν-beams is currently proposed by the decay of stored beta-active emitters instead of a µ: 6 2 He 18 10 Ne

−→ 63 Li + e− + ν e −→

18 9 Li

+ e+ + νe

T1/2 = 0.8 s

(22.10)

T1/2 = 1.7 s.

(22.11)

As shown in Figure 22.6, the He production could be performed by converter technology using spallation neutrons from water-cooled W or liquid Pb on BeO concentric cylinders via the reaction n + 9 Be → 6 He + 4 He. A nominal production rate of 5 × 1013 ions/s might be achieved. For the 18 Ne-production a spallation 18 of close-by target nuclides 18 Ne from MgO 24 12 Mg(p, p3 n4 )10 Ne is assumed to be a realistic reaction – the beam hitting directly the oxide target. However for a few GeV proton beam and 200 kW dc power the estimated production rate will be more than one order of magnitude too low. Novel production scenarios will be required. For the production of the speciﬁc ions, usually an isotope separation (e.g., ISOL) is following the intense proton driver. These ions are accelerated to ﬁnal energies and stored in large (km) decay rings at high γ (6 He : γ ∼ 150, 18 Ne : γ ∼ 60) for providing neutrino sources to experiments. Post accelerating the parent ions to relativistic γmax has the advantage of boosted neutrino energy spectra and forward focusing of neutrinos: θ ≤ 1/γ . Two (or more) different parent ions can be used for ν and ν-beams on β + and β − -decay. The physics applications of beta beams are primarily neutrino oscillations [1238] νe ↔ νµ (in particularly the single ﬂavor decays as of Eqs. (22.10) and (22.11)) and CP violation studies, but also measurements on cross sections of ν-nucleus interactions. By far however not all technical issues are addressed and solved yet. Second-generation superbeam experiments may be an attractive option in certain scenarios. Superbeams have many components in common with the ν-factory. A betabeam, in which electron neutrinos (or antineutrinos) are produced from the decay

6He/ 4He

9Be

Transfer line to ion source

Spallation neutrons

n n

n p n

gy ner

s

ton

pro

n Spallation target: (a) Water cooled W (b) Liquid Pb

h-e

Hig

n

ISOL target (BeO) in concentric cylinder Fig. 22.6 6 He-production by converter technology using spallation neutrons (CARE 08 meeting, CERN, 2008).

22.3 Neutrino Factories and Neutrino Super/Beta Beams

of stored radioactive ion beams (see also Eq. (1.75), page 61), in combination with a second-generation superbeam, may be a competitive option. A scoping study is therefore currently reviewing the physics reach of the various proposed facilities and making quantitative performance comparisons [1239]. These comparisons will be used to deﬁne the programme needed to achieve international consensus on the facility or facilities required for an optimal programme of highprecision neutrino-oscillation measurements. This requires that the performance, cost and feasibility of the various proposed facilities, including the detector systems, be evaluated. The conceptual design of the beta-beam facility is being developed in the context of the EU Framework – Programme-6 funded EURISOL design study [683]. Therefore, the scoping study [1239] will focus on evaluating the various options for the ν-factory accelerator complex and neutrino superbeam. In recent years, feasibility studies of possible conﬁgurations for a ν-factory have been carried out in Europe, in Japan, and in the U.S. These studies have concluded that such a facility is feasible, although the performance speciﬁed for some components is unproven and the overall design remains to be optimized. The key R&D activities needed to demonstrate the required performance have been indicated. Many of these are already under way, most as international collaborations involving all three regions. Experimental demonstration of muon ionization cooling is the aim of the international Muon Ionization Cooling Experiment (MICE) [1026], at Rutherford and Appleton Laboratory’s ISIS accelerator [643]. It will test the operation and performance of an actual section of cooling channel under a variety of conditions, and will provide a solid indication of component fabrication costs. A second key area involves demonstrating a target technology capable of withstanding bombardment with a multi-MW proton beam while operating in a high solenoidal ﬁeld. This experiment, nTOF11 [1240], also proposed by an international collaboration, is approved to run at CERN since 2007 [1241]. Efforts to study the performance of ﬁxed-ﬁeld alternating gradient (FFAG) synchrotrons, the ν-factory design based on FFAG, and the acceptance survey of FFAG accelerators for the ν-factories are also ongoing [968, 1242–1244]. Two examples of prototype ‘‘scaling’’ machines have already been built in Japan, and a proposal to build an electron model of a nonscaling ring has been submitted in Europe by an international team from all three regions. What has not been done – and will be a focus of the International Scoping Study (ISS) [1239] – is to compare and contrast the differing approaches to a ν-factory to identify the optimum and/or the most cost-effective ones. This will be accomplished by an international group comprising experts in all the proposed technical approaches. Lastly, the ISS will serve to review the R&D plan in support of a ν-factory, modifying and augmenting it as necessary to make it consistent with the latest thinking on ν-factory design. In order to establish the cost and performance of the overall facility, the ISS will not consider the accelerator in isolation, but will examine it in conjunction with the cost and performance of the detector as well.

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Several technologies have been discussed to match the tremendous challenge of providing very large mass detector while preserving the ability to perform precision measurements. Superbeam or beta-beam provide essentially one ﬂavor of neutrinos and the emphasis is on large detector mass and muon and electron particle identiﬁcation. These requirements are well matched by megatonscale water Cherenkov detectors for low-energy beams or perhaps as well by liquid argon or large volume scintillator detectors. The ν-factory has the advantage of the golden channel – appearance of wrong sign muons – which requires a magnetic ﬁeld. This leads most naturally to the magnetized iron calorimeter design. Another unique feature of the ν-factory is the possibility to observe the silver channel, the νe ↔ ντ transition, which could be observed with either emulsion-based detectors, or a magnetized liquid argon time projection chambers. In all detector concepts, there are important questions concerning cost, feasibility, and time scales, as well as design optimizations to be made, e.g., between energy/angle resolution, and mass. A realistic set of performance estimates is also important to serve as input to the physics comparisons between different options. Finally, precise normalization of ﬂux and cross sections will be a fundamental requirement. The study of detector concepts for the near detector stations will be an important aspect of the international scoping study [1239]. 22.4 Ultracold Neutrons 22.4.1 History

It was Enrico Fermi who ﬁrst realized that the coherent scattering of slow neutrons would result in an effective interaction potential for neutrons traveling through matter, which would be positive for most materials [1245]. The consequence of such a potential would be the total reﬂection of neutrons slow enough and incident on a surface at a glancing angle. This effect was experimentally demonstrated by Fermi and Walter Henry Zinn [1246] and Fermi and Leona Marshall [1247]. The storage of neutrons with very low kinetic energies was predicted by Yakov Borisovich Zel’dovich [1248] and experimentally realized simultaneously by groups at Dubna [1249] and Munich [1250]. 22.4.2 Properties of UCNs

When using neutrons as probe for the investigation of material properties, scientists are increasingly interested in ultracold neutrons (UCN). In fundamental physics, research UCN sources even down to the neV range are requested nowadays. While neutrons of typically 0.3 − 50 µeV are classiﬁed as very cold neutrons, ultracold neutrons are considered to have energies even smaller than a 0.3 µeV.

22.4 Ultracold Neutrons

The kinetic energy of 300 neV corresponds to a maximum velocity of 7.6 m/s or a minimum wavelength of 52 nm. Due to the neutron magnetic moment, magnetic ﬁelds of the order of several Tesla provide potential energies of the same order as UCN kinetic energies. Also the change in the gravitational potential for height differences of a few meters is of the order of the kinetic energy. As a consequence UCN can be conﬁned in material traps, magnetic traps, and combined gravitational traps. UCN can be stored in material as well as in magnetic bottles or cells for times approaching the beta-decay lifetime of the neutron. The storage of UCN is a very important feature for a variety of fundamental experiments. After trapping them, researchers can measure such basic neutron properties as lifetime (Section 22.4.5.1) and decay correlations (Section 22.4.5.5) and search for possible new properties, such as an electric dipole moment (Section 22.4.5.2). They can be used for various quantum optical experiments and as a starting point for phase space transformation to higher energies. Such data can lead to accurate measurements of fundamental constants of nature, advances in the quest for new particles predicted by uniﬁed ﬁeld theories, and new insights into how matter began in the Big Bang. Although UCN offer greatly improved sensitivity and systematics compared to cold-neutron-based experiments, one main limitation of these experiments is the low UCN intensity. As their density is usually very small, UCN can also be described as a very thin ideal gas with a temperature of 3.5 mK. New cooling methods based on the moderation in solid deuterium predict intensity gains in the order of several 1000 compared to the existing UCN source at the ILL in Grenoble where UCN densities of about 50 cm−3 are available. Neutrons of such small temperature exhibit optical properties, i.e., with proper energy and angle of incidence they might be reﬂected on surfaces. The reﬂection is caused by the coherent strong interaction of the neutron with atomic nuclei. It can be quantum-mechanically described by an effective potential which is commonly referred to as the Fermi pseudopotential or the neutron optical potential. The corresponding velocity is called the critical velocity of a material. As the neutron optical potential of most materials is below 300 neV, the kinetic energy of incident neutrons must not be higher than this value in order to be reﬂected under any angle of incidence; especially for normal incidence. Neutrons are reﬂected from a surface if the velocity component normal to the reﬂecting surface is less or equal to the critical velocity. The properties of reﬂection have been, for the ﬁrst time, taken into account in the PHITS transport code system and are described by the following semiempirical formula [917]: R=

Q ≤ Qc

R0 1 2 R0 (1

− tanh[Q − mQc ])(1 − α(Q − Qc ))

Q > Qc .

(22.12)

Equation (22.12) describes the relation between the reﬂectivity R0 of the material, the length of the scattering vector Q, and the critical scattering vector Qc . m represents a parameter of the material of the neutron guide and considers the neutron guide material, the double-layer structure, and the numbers of layers. For

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22 Advanced Applications of Spallation Physics

Qc (natNi)

Qc (58Ni)

1 R0 = 0.99 R0 = 0.80

0.8 Relfectivity

644

0.6 0.4 0.2 0

0

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Scattering vector Q [Å−1]

Fig. 22.7

Reﬂectivity curves for

nat Ni

and

58 Ni

for different reﬂections R0 .

modern neutron guides the parameter equals m = 3, while simple Ni mirrors are generally characterized by m = 1. The parameter α denotes a linear behavior up to the cutoff at Q = mQc and W reﬂects its width. Figure 22.7 displays typical curves for the reﬂectivity as a function of length of the scattering vector Q for nat Ni and 58 Ni. 22.4.3 Reﬂecting Materials

Any material with a positive neutron optical potential can reﬂect UCN. Table 22.2 gives an incomplete list of UCN reﬂecting materials including the height of the neutron optical potential (VF ) and the corresponding critical velocity (vC ). The height of the neutron optical potential is isotope-speciﬁc. The highest known value of VF is measured for 58 Ni: 335 neV (vC = 8.14 m/s). It deﬁnes the upper limit of the kinetic energy range of UCN. The most widely used materials for UCN wall coatings are beryllium, beryllium oxide, nickel (including 58 Ni), and more recently also diamond-like carbon (DLC). Nonmagnetic materials such as DLC are usually preferred for the use with polarized neutrons. Magnetic centers in, e.g., Ni can lead to depolarization of such neutrons upon reﬂection. If a material is magnetized, the neutron optical potential is different for the two polarizations, caused by VF (pol.) = VF (unpol.) ± µN · B,

(22.13)

where µN is the magnetic moment of the neutron and B = µ0 · M the magnetic ﬁeld created on the surface by the magnetization. Each material has a speciﬁc loss probability per reﬂection, E cos 2θ µ(E, θ ) = 2η , (22.14) VF − E cos 2θ

22.4 Ultracold Neutrons UCN reﬂecting materials and their properties with VF being the height of the neutron optical potential, vC the corresponding critical velocity, and η the energy-independent loss coefﬁcient.

Tab. 22.2

Material

VF (neV) [1251, 1252]

vC (m/s) [1253]

252 261 252 304 180 210 168 54

6.89 6.99 6.84 7.65 5.47 6.10 5.66 3.24

Beryllium BeO Nickel Diamond Graphite Iron Copper Aluminum

η (10−4 ) [1253] 2.0–8.5 5.1

1.7–28 2.1–16 2.9–10

which depends on the kinetic energy of the incident UCN (E) and the angle of incidence (θ ). It is caused by absorption and thermal upscattering. The loss coefﬁcient η is energy independent and typically of the order of 10−4 to 10−3 . 22.4.4 UCN Production

Traditionally, UCNs are produced at reactors. The principal difﬁculty of UCN production is that their energy region is far out in the tail of a thermal Maxwell distribution. Additional losses in the extraction from the reactor cold source result in large suppression factors (e.g., for a thermal ﬂux 0 (cm−2 s−1 ) one typically obtains ρUCN = 10−13 0 cm−3 ). Methods to increase the UCN yield from a cold neutron source include vertical extraction, using gravity to decelerate neutrons of higher velocities into the UCN regime; and mechanical deceleration, using collisions of faster neutrons with a moving scatterer. These faster neutrons can more easily penetrate windows and can be transported over longer distances with few reﬂections. The distances for UCN transport to the experiments can thus be short and UCN losses small. Alternative UCN production schemes have been proposed and demonstrated, such as conversion of cold neutrons into UCN in superﬂuid helium or other suitable cold converters as, e.g., solid deuterium. Especially the solid deuterium based pulsed sources have the potential to produce high UCN intensities with densities of about 103 –104 cm−3 . The production of cold and ultracold neutrons can also be performed by a moving crystal lattice. In Ref. [1254] it is demonstrated that the diffraction properties of a moving crystal lattice can be employed for the production of very cold and ultracold neutrons. The necessary formulation for the calculation of the diffracted neutron intensity is developed in [1254]. It is shown that such a device is indeed possible and, as a source of ultracold neutrons, constitutes a practical alternative to existing mirror-reﬂection neutron turbines.

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In the following, a selection of some particular facilities/installations of worldwide UCN sources is described: LANSCE A new source of ultracold neutrons, using on a solid deuterium moderator, is installed at the Los Alamos Neutron Science Center (LANSCE). Closely based on an approximately two-thirds scale prototype that has been tested at Los Alamos, the new source is expected to use a 4 µA beam of 800 MeV protons to produce enough UCNs to ﬁll a 50 liter storage volume to a density of 300 UCN/cm3 , which will result in greater than 2 × 104 UCNs being delivered to the experimental area. Like the prototype, the new source uses a tungsten spallation target to produce fast neutrons, which are trapped and moderated by beryllium and other materials. The resulting cold neutrons are down-scattered to UCN energy by interacting with a solid deuterium moderator of about 2 l volume. The source is closely coupled to the liquid nitrogen-temperature storage volume. Initially, the new source was used in 2003 to supply UCNs to a proposed experiment to measure the A correlation coefﬁcient of neutron beta decay (see Section 22.4.5.5). The key to Los Alamos’ success dates back to 1994 and a collaboration to develop a solid deuterium source for UCN with the Petersburg (Russia) Nuclear Physics Group. Four years later, design work was completed and the team built a prototype superthermal source at the Weapons Neutron Resource, part of the Los Alamos Neutron Science Center. The 800 MeV LANSCE proton beam strikes a tungsten target; each proton that hits produces about 14 neutrons at energies of a few MeV, which are reduced to typical cold neutron temperatures of 40 Kelvin by scattering in polyethylene moderators. As they interact with the solid deuterium inside a guide tube coated with 58 Ni, the cold neutrons further reduce their energy and become ultracold. In effect, the weak crystal structure of the solid deuterium trap creates a one-way pipe that scatters the cold neutrons’ energy away and would not let them regain energy above this so-called ground state. The UCNs then travel through a guide tube and are detected by a 3 He detector. Previous sources, built at nuclear reactors, could not produce enough ultracold neutrons for key experiments, such as those under way at Los Alamos to measure neutron β-decay with sufﬁcient precision to tell whether massive subatomic particles exist that inﬂuence the so-called electroweak force, one of the fundamental forces of nature. Because the UCNs are produced at a neutron spallation source instead of a reactor, researchers can acquire data without a continual beam of protons striking the source, so sensitive experiments can be performed with much smaller backgrounds. PSI A powerful source for ultracold neutrons is being constructed by an international collaboration at the Paul Scherrer Institut in Switzerland. The source concept is based on the three-step process of neutron production, moderation and conversion. A several seconds long pulse of the full (2 mA, 590 MeV) proton beam produces neutrons on a spallation target. The fast neutrons are moderated, cooled, and ﬁnally down-scattered into UCN in solid ortho-deuterium. UCNs are extracted

22.4 Ultracold Neutrons

from the solid deuterium and guided into a diamond-like carbon (DLC) coated large storage volume from which they can be extracted into experiments. After the proton beam pulse, the production and storage volumes are separated by a shutter, allowing for UCN storage times of the order of magnitude comparable to the lifetime of the free neutron. Test experiments and calculations based upon them predict UCN densities of about 3000 cm−3 in a 2 m3 volume. While the UCN source at ILL in Grenoble achieves about 10 UCN/cm3 in a typical experiment – and up to 100 UCN/cm3 close to the UCN producing turbine – the new UCN source at PSI delivers densities considerably higher. FRM-II The new Munich high-ﬂux reactor FRM-II offers the possibility to install a unique source for UCN, the Mini-D2 UCN source. A small volume of solid deuterium, positioned close to the cold source of FRM-II and kept at a temperature of about 5 K, will be used as a converter. This new source, best suited for storage experiments, is designed to be superior to existing UCN facilities. In pulsed mode, it will provide UCN densities up to 104 n/cm3 for neutrons with energies below 250 neV, orders of magnitude larger than the source at ILL ( 50 n/cm3 ). Operated in the continuous mode, up to 5 × 105 n/cm2 s may be extracted. TRIGA At the pulsed reactor TRIGA Mainz production rates of UCN with a solid deuterium converter have been measured. Exposed to a thermal neutron ﬁnance of ≈1 × 1013 n cm−2 pulse−1 , the number of detected very cold and ultracold neutrons ranges up to 200 000 at 7 mol of solid deuterium (sD2 ) in combination with a pre-moderator (mesitylene). About 50% of the measured neutrons can be assigned to UCN with energies E of VF (sD2 ) < E ≤ Vp (guide), where VF (sD2 ) = 105 neV and VF (guide) = 190 neV are the Fermi potentials of the sD2 converter and the stainless steel neutron guides, respectively. Thermal cycling of solid deuterium, which was frozen out from the gas phase, considerably improved the UCN yield, in particular at higher amounts of sD2 . Currently, there is a variety of further laboratories operating or installing powerful UCN sources as, e.g., the LPSC Grenoble, PNPI (Petersburg Nuclear Physics Institute, Russian Academy of Sciences), California Institute of Technology, just to name a few. A (comprehensive) compilation of existing cold and ultracold neutron sources is recently given by Gobrecht [1255]. 22.4.5 Experiments with UCN

The production, transportation and storage of UCN is currently motivated by their usefulness as a tool to determine properties of the neutron and to study fundamental physical interactions. The large success in storage experiments has improved the accuracy or the upper limit of some neutron-related physical values. A nice review article on fundamental physics with UCN is given in the Annual Review of Nuclear and Particle Science by Pendlebury [1256].

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22.4.5.1 Measurement of the Neutron Lifetime In 1989, Mampe et al performed the experiment MAMBO I to measure precisely the lifetime of the free neutron [1257]. The experiment MAMBO II has been developed and built according to the experience gained with MAMBO I. It was taking data until the middle of 2000. In the new setup the basic concepts, namely storage of the neutrons in a rectangular glass box of variable size covered with Fomblin oil and counting of the surviving neutrons, were kept. While these direct measurements give the bottle lifetimes, an extrapolation to inﬁnite storage volume yields the lifetime of the free neutron. The main improvement in MAMBO II is that a pre-storage volume has been added allowing to shape and control the spectrum of the stored neutrons independent of the actual size of the storage volume. Recent success in magnetic conﬁnement of UCN in an Ioffe-type superconducting magnetic trap led to an improved measurement of the neutron lifetime τn . At the NIST, Gaithersburg facility a trap is loaded through inelastic scattering of 0.89 nm neutrons with phonons in superﬂuid 4 He. Trapped neutrons are detected when they beta decay; energetic decay electrons ionize helium atoms in the superﬂuid resulting in efﬁcient conversion of electron kinetic energy into light (scintillation). The advantages of this technique over previous experiments are continuous detection of scintillations from decay electrons and the elimination of wall losses and betatron oscillations. Analysis indicates that systematic errors due to neutron losses should be controllable to 10−5 τn . Backgrounds for a lifetime measurement are substantially reduced by having upgraded the apparatus by constructing a larger, deeper magnetic trap. These improvements result in an increase in the number of detected trapped neutrons by two orders of magnitude. In today’s world, average value for the neutron lifetime is 885.7 ± 0.8 s [19], to which the experiment of Arzumanov et al. [1258] contributes strongest. Ref. [19] measured τn = 885.4 ± 0.9stat ± 0.4syst s by storage of UCN in a material bottle covered with Fomblin oil. Using traps with different surface-to-volume ratios allowed them to separate storage decay time and neutron life time from each other. There is another result, with even smaller uncertainty, but which is not included in the World average. It was obtained by Serebrov et al. [1259], who found 878.5 ± 0.7stat ± 0.4syst s. Thus, the two most precisely measured values deviate by 5.6σ . 22.4.5.2 Measurement of the Neutron Electric Dipole Moment The neutron electric dipole moment (nEDM) is a measure for the distribution of positive and negative charge inside the neutron. A ﬁnite electric dipole moment can only exist if the centers of the negative and positive charge distribution inside the particle do not coincide. So far, no neutron EDM has been found. Today’s lowest value for the upper limit of the nEDM was measured with stored UCN. The current best upper limit amounts to |dn | ≤ 2.9 × 10−26 ecm. A permanent electric dipole moment of a fundamental particle violates both parity (P) and time reversal symmetry (T). This is quickly comprehensible by looking at the neutron with its magnetic dipole moment and hypothetical electric dipole moment. Under time reversal, the magnetic dipole moment changes its

22.4 Ultracold Neutrons

direction, whereas the electric dipole moment stays unchanged. Under parity, the electric dipole moment changes its direction but not the magnetic dipole moment. As the resulting system under P and T is not symmetric with respect to the initial system, these symmetries are violated in the case of the existence of an EDM. Having also CPT symmetry, the combined symmetry CP is violated as well. In order to generate a ﬁnite nEDM, one needs processes that violate CP. CPviolation has been observed in weak interactions and is included in the Standard Model of particle physics via the CP violating phase in the CKM matrix. However, the amount of CP-violation is very small and therefore also the contribution to the nEDM: |dn | ∼ 10−32 ecm. As the neutron is built up of quarks, it is also susceptible to CP-violation stemming from strong interactions. Quantum chromodynamics – the theoretical description of the strong force – naturally includes a term which breaks CP-symmetry. The strength of this term is characterized by the angle θ . The current limit on the nEDM constrains this angle to be less than 10 - 10 rad. This ﬁne-tuning of the θ -angle, which is naturally expected to be of the order 1, is the strong CP problem. In order to extract the neutron EDM, one measures the Larmor precession of the neutron spin in the presence of parallel and antiparallel magnetic and electric ﬁelds. The precession frequency for each of the two cases is given by hν = 2µB B ± 2dn E, the addition or subtraction of the frequencies stemming from the precession of the magnetic moment around the magnetic ﬁeld and the precession of the electric dipole moment around the electric ﬁeld. From the difference of those two frequencies one readily obtains a measure of the nEDM: dn = hν 4E . The biggest challenge of the experiment (and at the same time the source of the biggest systematic false effects) is to ensure that the magnetic ﬁeld does not change during these two measurements. Experiments with ultracold neutrons started in 1980 with an experiment at the Leningrad Nuclear Physics Institute obtaining a limit of |dn | < 1.6 × 10−24 ecm [1260]. This experiment and especially the experiment starting in 1984 at the Institut Laue-Langevin pushed the limit down by another two orders of magnitude yielding the above quoted best upper limit in 2006. During 50 years of experiments, six orders of magnitude have been covered thereby putting stringent constraints on more theoretical models than probably any other experimental value. A new measurement of the nEDM, using the Ramsey method of separated oscillatory ﬁelds, is being designed at the PSI UCN source. Already the current upper limit on nEDM (≤ 2.9 × 10−26 ecm) constrains some extensions of the Standard Model of particle physics. The new experiment aims at a two orders of magnitude improvement in sensitivity to ﬁnd an eventual nEDM. This will be achieved by better control of systematic effects and the higher UCN ﬂux provided by the new PSI source. 22.4.5.3 Observation of the Gravitational Interactions of the Neutron Due to the small kinetic energy of an UCN, the inﬂuence of gravitation is signiﬁcant. Thus, the trajectories are parabolic. The kinetic energy of an UCN can be transformed into potential (height) energy of 102 neV/m.

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Nesvizhevsky and collaborators have reported on the evidence of quantization of the vertical motion of neutrons bound by the gravitational ﬁeld of the Earth [1261]. Even though the conceptual aspects of the experiment were discussed back in the 1970s [1262], concrete steps toward the goal of the ﬁnal experiment were only realized more recently [1263]. The experiment consists in allowing ultracold neutrons generated by a source at the Institute Laue-Langevin reactor (Grenoble) to fall toward a horizontal mirror due to the inﬂuence of the Earth’s gravitational ﬁeld. This potential conﬁnes the motion of the neutrons which no longer move continuously in the vertical direction, but rather jump from one height to another, as predicted by quantum mechanics. This impressive experiment complements the Collela, Overhauser and Werner experiment [1264], where neutrons were split and allowed to interfere with the gravitational ﬁeld, even though in that situation the neutrons were not quantum states. In the Grenoble experiment [1], the minimum energy of the detected neutrons is 1.4 × 10−12 eV, corresponding to a vertical velocity of 1.7 cm s−1 . In that work, it is stated that a more intense beam and an enclosure mirrored on all sides could lead to an improved energy resolution, down to 10−18 eV, if the neutron can be kept conﬁned for all of its lifetime. In [1261], besides the ground state, three excited states were determined, although with a reduced accuracy. 22.4.5.4 Measurement of the Neutron-Mirror Neutron Oscillation Time If there exists the mirror world, a parallel hidden sector of particles with exactly the same microphysics as that of the observable particles, then the primordial nucleosynthesis constraints require that the temperature of the cosmic background of mirror relic photons should be smaller than that of the ordinary relic photons, T /T < 0.5 or so. On the other hand, the present experimental and astrophysical limits allow a rather fast neutron-mirror neutron oscillation in vacuum, with an oscillation time τ ≈ 1 s, much smaller than the neutron lifetime. This could provide a very efﬁcient mechanism for transporting ultra high-energy protons at large cosmological distances. The mechanism operates as follows: a super-GZK energy proton scatters a relic photon producing a neutron that oscillates into a mirror neutron which then decays into a mirror proton. The latter undergoes a symmetric process, scattering a mirror relic photon and producing back an ordinary nucleon, but only after traveling a distance (T/T ) 3-times larger than ordinary protons. This may relax or completely remove the GZK-cutoff in the cosmic ray spectrum and also explain the correlation between the observed ultrahigh energy protons and far distant sources as are the BL Lacs. The phenomenological implications of the neutron oscillation into the mirror neutron (n ), a hypothetical particle exactly degenerate in mass with the neutron but sterile to normal matter. The present experimental data allow a maximal n − n oscillation in vacuum with a characteristic time τ much shorter than the neutron lifetime, in fact as small as 1 s. This phenomenon may – besides the above-mentioned interesting astrophysical consequences – manifest in neutron disappearance and regeneration experiments perfectly accessible to present experimental capabilities. It has been noted by Bento and Berezhiani [1265] that if

22.4 Ultracold Neutrons −1 −1 these oscillations occurred at a rate of τNN , it would help explain putative ≈ s super GKZ cosmic ray events provided the temperature of the mirror radiation is ∼ 0.3–0.4 times that of familiar cosmic microwave background radiation. Such oscillation time scales can be realized in mirror models and it was found that the simplest nonsupersymmetric model for this idea requires the existence of a low mass (30–3000 GeV) color triplet scalar or vector boson. A supersymmetric model, where this constraint can be avoided is severely constrained by the requirement of maintaining a cooler mirror sector. It was also found that the reheat temperature after inﬂation in generic models that give fast nn oscillation be less than about 300 GeV in order to maintain the required relative coolness of the mirror sector. For details, the interested reader is referred to Refs. [1265–1267].

22.4.5.5 Measurement of the a-Coefﬁcient of the Neutron Beta Decay Correlation A free neutron will β-decay, with a lifetime of about 900 s, into a proton, electron, and antineutrino. This is one of the most fundamental processes in particle physics and it provides a rich laboratory for exploring the fundamental forces of nature. The coefﬁcients that describe the angular correlations between the emitted electron and antineutrino determine the weak coupling constants gA and gV . They are sensitive to new physical forces and phenomena that have been theoretically proposed but not yet discovered, such as supersymmetric particles, scalar and tensor weak forces, and right-handed weak forces. In particular when combined with µ-decay measurements, one can extract the Vud element of the CKM matrix, a critical element in CKM unitarity tests. The observable of interest in this experiment is the electron–antineutrino angular correlation coefﬁcient, also known as the ‘‘a’’ coefﬁcient. It quantiﬁes the correlation pe · pν ]. of the form: dN = F(Ee )[1 + a Ee Eν Various tests of the Standard Model can be made using the neutron-decay parameters. For example, their values can be related to the strength of hypothetical right-handed weak forces and scalar and tensor forces. At the present level of precision there is no evidence for these forces, but as the experimental technology improves and more precise measurements are made, a discrepancy may eventually emerge from these results, indicating the presence of new physics. So the neutron decay system acts as a low-energy frontier of particle physics which is complementary to the high-energy frontier of super-collider physics. The coefﬁcient ‘‘a’’ has been the most difﬁcult to measure, and therefore is the least precisely known of the neutron decay parameters. The antineutrino cannot be detected, but the inﬂuence of its momentum can be felt on the other particles (electron and proton) which are detected. The most obvious way to determine the value of a is to measure the recoil proton energy spectrum. The proton energies are very low (maximum is 751 eV), so a precise determination of the shape of the energy spectrum is very difﬁcult and prone to systematic error. The best measurement so far, by Stratowa, Dobrozemsky, and Weinzierl was published in 1978. The result was a = −0.102 ± 0.005. The quoted uncertainty is dominated by the estimated systematic error. This result required the proton energy spectral

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22 Advanced Applications of Spallation Physics

shape to be measured to a precision of less than 0.5%, a phenomenal technical feat. The fact that this measurement has not been improved over the last 20 years is a testament to its difﬁculty. As mentioned above by using a new sD2 superthermal source at LANSCE, large ﬂuxes of UCN are expected for the UCNA project. These UCN will be 100% polarized using a 7 T ﬁeld, and directed into the beta spectrometer. This approach, together with an expected large reduction in backgrounds, will result in an order of magnitude reduction in the critical systematic corrections associated with current n beta-asymmetry measurements.

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23 Space Missions and Radiation in Space 23.1 Introduction

As already mentioned in Section 1.2 on page 5 the space environment contains energetic charged particles (electrons, protons, and heavier ions), which must be taken into account as part of the considerations in the design and operation of space missions. The space radiation environment has taken on increased importance in recent years for several reasons: (a) For the longer duration missions being planned (e.g., space station, long-stay lunar missions, manned missions to Mars), the radiation dose to astronauts will be much higher than previously experienced, and, in some cases, the predicted doses are comparable to the allowable personal dose limits. (b) To achieve higher computing and signal-processing capabilities, modern electronics technologies use smaller size electronic devices, which are inherently more susceptible to radiation damage. Thus, an assessment of potential radiation effects on microelectronics is needed for all missions in selecting electronics parts and in establishing appropriate preﬂight electronics testing criteria. (c) As technology has advanced, the sensitivity of instrumentation for scientiﬁc missions (such as charged-coupled devices (CCDs) used in orbital observatories for measuring visible light), so has the radiation sensitivity of such sensors increased. A careful assessment of the radiation exposure is important in establishing the performance degradation and background noise for such sensitive instrumentation. There are three sources of energetic charged particles in the low-earth orbit (LEO) space: (a) trapped radiation, which consists of electrons and protons conﬁned in the magnetic ﬁeld around the earth, (b) galactic cosmic radiation (GCR), which is from sources outside our solar system and consists mainly of very energetic protons with a small contribution from heavier ions, and (c) solar particle events (SPE), in which large emissions of protons and heavier ions can be produced in conjunction with solar ﬂare activity. A good review of the origin of these different sources is given in Refs. [1268, 1269] and references therein and the discussion in Section 1.2 on page 5. The relative importance of these different sources depends on numerous facts, including spacecraft trajectory, mission duration, and shielding. There are three major categories of radiation effects concern from the space environment: (a) the radiation hazards to astronauts in the case of manned missions, (b) effects Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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23 Space Missions and Radiation in Space

on radiation-sensitive components and materials, and (c) radiation backgrounds to experiments. To predict radiation effects, the space environments are used as input sources with space experiments on particle reactions in conjunction with spallation models and radiation transport calculations. Also accurate nuclear interaction databases play a vital role in space missions [1270]. A large amount of these data were measured by Michel and co-workers [37–39, 1271] during the 1990s and validated with spallation interaction models. In the following applications of spallation effects on space experiments and radiation hazards associated with space missions are brieﬂy described.

23.2 Galactic Cosmic Ray (GCR) Induced Reactions in Moon and MARS Soil 23.2.1 GCR-Induced Neutron Flux Density in the Lunar Soil During Apollo Missions

The lunar soil and its surface serves as an ideal test model for ‘‘thick’’ target spallation reactions. Three different experiments, measurements of the neutron production in the lunar soil, of a variety of the ‘‘lunar Neutron Probe Experiments’’ (LNPE) investigated during the Appollo missions will be brieﬂy presented: (1) the 10 B(n,α)7 Li reaction measurements by Woolum et al. [1272], (2) the 235 U ﬁssion rate measurements by Woolum and Burnett [1273], and the production rate of 53 Mn from Fe by Imamura et al. [1274, 1275]. All experiments were designed to measure the lunar neutron spectrum induced by GCR in the soil by a cascade of hadronic particles. The reaction rates were measured as a function of depth. The primary GCR source bombarding the lunar surface was sampled using formula (1.3) on page 8. The proton and α-particles were then used as source in the energy range of 10 MeV≤ E ≤ 10 GeV performing proton and alpha-particle transport calculations by the HERMES system [88] with the lunar soil. Details are given in Ref. [1276]. The geometry of the planetary lunar surface was assumed to be a semiinﬁnite slab, approximated by a disk of radius r = 100 m and thickness d = 20 m. To provide a homogeneous and isotropic irradiation, a modiﬁed point source was placed closely above the center of this disk. The disk was sectioned into 46 layers of variable thickness, starting with 1 cm at the surface, 3.3 cm down to a depth of 70 cm, then 13.3 cm to a depth of 360 cm, and three more layers to the total depth of 20 m [1276]. The material composition of the lunar soil is given in Table 23.1 as investigated during the Apollo 11 deep-drill core. The calculated neutron ﬂuxes are normalized to a total 4π GCR ﬂux of 3.0 protons/(s cm2 ), assuming a GCR spectrum consisting only of protons. This normalization factor (3.0 ± 0.2) protons/(s cm2 ) was obtained via the experimental neutron density proﬁles [1276]. The total neutron yield calculated via the HERMES system is (25.5 ± 0.5) neutrons per incident GCR proton. The resulting neutron depth distribution proﬁle in the lunar soil is given in Figure 23.1.

23.2 Galactic Cosmic Ray (GCR) Induced Reactions in Moon and MARS Soil The lunar ﬁne soil composition from Apollo 11 deep-drill investigations.a

Tab. 23.1

Element

Wt%

Element

Wt%

O Mg Al Si

41.93 4.78 7.23 20.26

Ca Ti Fe Gd

8.99 4.36 12.45 0.0017

a The soil density = 1.5 g/cm2 . The Gd density substitutes the sum of all other trace elements (Gd, Sm, and Eu). Data are from Dagge et al. [27].

10−1

Neutrons per GCR−proton [1/g]

5

2

10−2

5

Source & equilibrium neutron density Source neutrons < 0.414 MeV, scaled

2

1−14.9 MeV, scaled 10−3 0

100

200

300

400

Depth [g/cm2]

Fig. 23.1 Depth proﬁle of neutrons in the lunar soil produced below 14.9 MeV or slowed down below 14.9 MeV. The proﬁle is normalized to the total number of neutrons per GCR proton. The equilibrium neutron density (per 1 g of lunar material) for

thermal neutrons (< 0.414 eV) and fast neutrons (> 1 MeV) is shown for comparison. The equilibrium neutron densities are scaled to the neutron source proﬁle at 450 g/cm2 (after Ref. [1276]).

In Figure 23.1 the neutron source proﬁle is presented together with the equilibrium neutron proﬁle for thermal neutrons and for neutrons of energies E > 1 MeV. The results are in good agreement with those given by Drake et al. [1277] for the Martian surface and a cutoff energy of 10 MeV. The depth distribution presented in Figure 23.1 is quite close to an exponential proﬁle. The thermal neutron ﬂux is not greatly affected by the input proﬁle, since the low-energy neutrons have undergone multiple scattering processes, as stated

655

23 Space Missions and Radiation in Space 100 90 Neutron density [10−7 n/cm3]

656

80 70 60 50 40 Via 10B(n,a)7Li reaction: 30

Calculated profile LNPE, Woolum (1975)

20 10 0

100

200

300

400

Depth [g/cm2]

Fig. 23.2 Lunar neutron density proﬁle obtained via the 10 B(n,α)7Li reaction rate. The calculated data are compared to the results from the LNPE (Woolum et al. [1272]). The calculations with the HERMES system [88] include the GCR α-particle contribution and are equivalent to a pure GCR proton ﬂux irradiation of 3.0 protons/(s cm2 ) (after Ref. [1276]).

by Lingenfelter et al. [1278]. Figures 23.2–23.4 show some examples comparing measured and simulated neutron reaction rate depth proﬁles, e.g., the 10 B(n,α)7 Li reaction rate, the 235 U ﬁssion rate, and the 53 Mn production from Fe samples. The measurements were chosen from the LNPE experiments. The 10 B(n,α)7 Li reaction rate (Woolum et al. [1272]) measured in the lunar soil is directly proportional to the neutron density since the reaction rate has a pure 1/v cross section. Therefore, the equilibrium neutron density could be calculated (1) via the 10 B(n,α)7 Li rates by folding the cross section with the neutron ﬂux at each depth and (2) directly from the differential ﬂux proﬁle. Both results are in excellent agreement. Simulations of an alpha-particle irradiation indicate that the alpha-particle contribution of the GCR ﬂux can be accounted for by scaling the proton GCR ﬂux with 3.0 protons/(s cm2 ). The proﬁles of 235 U ﬁssion rates presented in Figure 23.3 are obtained in the same way as described before, by folding the calculated neutron ﬂux with the 235 U ﬁssion cross section. Compared to the normalization discussed above, the calculated proﬁle has to be enhanced by a factor of 1.17 to obtain the best ﬁt to the experimental data from Woolum and Burnett [1273]. In order to check the high-energy secondary particle ﬂuxes, the production rate of 53 Mn from Fe was calculated, also including the production from protons. Since the

23.2 Galactic Cosmic Ray (GCR) Induced Reactions in Moon and MARS Soil 4

Fission rate [1/g sec]

3

2

235

U(n,f) rate:

1

Calculated profile LNPE, Woolum (1974) 0 0

100

200

300

400

Depth [g/cm2]

Fig. 23.3 Lunar depth proﬁle of the 235 U ﬁssion rate from the LNPE (Woolum and Burnett [1273]) compared to the theoretical proﬁle. The calculated data with the HERMES system [88] had to be enhanced by 17% compared to the standard normalization value of 3.0 protons/(s cm2 ). The calculations include the GCR α-particle contribution (after Ref. [1276]).

high-energy particle ﬂuxes do not change signiﬁcantly as long as the average atomic mass and charge remain approximately constant, the calculated Apollo-11 neutron ﬂuxes can also be applied for other lunar compositions for the calculation of this reaction rate. The cross-section data were provided by Michel [37] and were calculated with the ALICE LIVERMORE-82 code (Blann and Bisplinghoff [1279]). The theoretical proﬁle can be found in Figure 23.4, together with the experimental data from Imamura et al. [1274, 1275]. A long-term averaged GCR-proton ﬂux of 4.9 protons/(s cm2 ) for Apollo-15 data and 6.0 protons/(s cm2 ) for Apollo-16 data best represents the experimental depth proﬁle, assuming a constant irradiation for several million years (T1/2 = 3.7 × 106 y). A detailed discussion on the production of radionuclides from GCR by neutron and proton ﬂuxes can be found in Michel et al. [37]. 23.2.2 The Mars Observer Orbiter Mission to Measure the Spallation-Induced Gamma Flux Return of GCR on the Martian Surface 23.2.2.1 The Aim of the Mars Observer Mission The Mars Observer mission spacecraft was primarily designed for exploring Mars and the Martian environment. However, in addition to its planetary payload, Mars

657

23 Space Missions and Radiation in Space

103

5 Production rate [dpm/kg Fe]

658

GCR flux = 5.5 protons/cm2 s 2

102 53Mn

5

production from Fe

Calculated profile Apollo 15, Imamura (1973) 2

Apollo 16, Imamura (1974)

101 0

100

200 Depth

300

400

[g/cm2]

Fig. 23.4 Depth proﬁle of the 53 Mn production rate from Fe from lunar samples (Imamura et al. [1274, 1275]) compared to the theoretical proﬁle (calculated with the HERMES system [88]) normalized to 5.5 GCR protons/(s cm2 ). The GCR α-particle contribution is included in the calculations (after Ref. [1276]).

Observer carried some high-energy astrophysics instruments, including a gammaray spectrometer (GRS). Mars Observer was launched on September 25, 1992 from Kennedy Space Center aboard a Titan-III rocket. The spacecraft was lost in the vicinity of Mars after (most probably) an explosion of the fuel and oxidizer elements on August 21, 1993 when the spacecraft began its maneuvering sequence for Martian orbital insertion. While intended as a GRS for mapping the Martian surface composition from orbit, the GRS was also capable of suspending this function in order to make detailed observations of cosmic gamma-ray bursts. The n-type Ge detector for the gamma mapping was 5.5 cm in diameter and length. Passive cooling kept the crystal at less than 100 K. A combined anticoincidence shield and neutron system surrounding the Ge crystal rejected cosmic ray and neutron events when a burst mode had been triggered. Gamma-ray spectra from planetary surfaces provide a tool for the investigation of the chemical composition of the planet’s surface. Galactic cosmic rays (GCR), (cf. Section 1.2 on page 5), penetrate the upper few meters of the soil of planetary surfaces and produce a cascade of hadronic particles and gamma rays. Gamma rays from inelastic neutron scattering or neutron capture are a characteristic ﬁngerprint of the target nucleus, whereas several other gamma-ray sources make up a background spectrum. The gamma-ray spectrum from a planetary surface thus contains information about the elemental composition of the surface material. The

23.2 Galactic Cosmic Ray (GCR) Induced Reactions in Moon and MARS Soil

portion of the gamma-ray ﬂux transferred back through the soil and the atmosphere can be detected from an orbiting satellite. Planetary gamma-ray spectroscopy is an instrument for chemical mapping of planets with a sufﬁciently thin atmosphere like that of Mars. 23.2.2.2 Application to the Martian Surface To prepare the Mars Observer mission theoretical simulations [27, 1276] and experiments [1280–1282] have to be performed for a variety of expected material compositions in order to extract information about the Martian surface composition from measured gamma-ray spectra [27, 1276]. Calculations were carried out by various authors for the lunar surface, e.g., Armstrong and Alsmiller [1283], Lingenfelter et al. [1278]. Additionally, the lunar photon albedo was calculated by Armstrong [192] using Monte Carlo methods. Reedy et al. [1284] and Reedy [1285] calculated the gamma-ray leakage for a large number of gamma-ray lines using modeled particle ﬂuxes described by Reedy and Arnold [1286]. Experimental lunar gamma-ray spectra had a relatively poor energy resolution since a NaJ(Tl) detector was used. Experimental tests at the SATURNE accelerator with a Ge detector were carried out by Brckner et al. [1287]. Basic studies of gamma-ray emission spectra from the Martian surface were performed by Metzger and Arnold [1288]. The effects of hydrogen in the Martian soil and the macroscopic neutron capture cross section of the Martian gamma-ray spectrum were shown by Lapides [1289]. Evans and Squyres [1290] calculated the gamma-ray-line intensity ratios of selected gamma-ray lines for a variety of expected Martian material compositions and structures such as polar caps. Calculations of Martian neutron leakage spectra for various water concentrations and inhomogeneous material structures were carried out by Drake et al. [1277]. Although extensive calculations on planetary neutron and gamma-ray spectra were carried out in the past, the calculational methods showed some basic disadvantages and gaps. Various Monte Carlo codes for low-energy neutron transport were not coupled properly to the high-energy particle transport codes. Instead, modeled neutron distributions were used as input spectra for the low-energy neutron transport. Important gamma-ray sources produced by the π 0 -decay could not be calculated from ﬁrst principles. The applicability of spallation reactions of photon evaporation or induced gammaray spectra (cf. page 179) to analyze planetary surface compositions is shown as an example in Figure 23.5 bombarding the moon’s surface assuming a soil composition given in Table 23.1 with an average GCR spectrum (cf. page 10, Figure 1.5). Figure 23.5 shows the total prompt gamma-ray emission spectrum from the moon surface including several resolved gamma lines. The simulation was performed by using the HERMES system [88]. The calculational procedure for the Martian soil was applied to a standard Martian composition [1291] given in Table 23.2 with a water content of 0.9%. Both GCR proton and alpha-particle irradiations were performed. Compared to a simulated proton irradiation, the neutron yield, as well as the low-energy neutron ﬂux per source particle, is increased by a factor of 3.5 for an alpha-particle irradiation.

659

23 Space Missions and Radiation in Space

Gamma−ray flux spectrum in arbitray units dΦ(E)/dE [cm−2 s−1 MeV−1]

660

102 5 2 101 5 2

Fe Si Mg

C O

Fe

AI

100 5

Si

Ca AI

Gd −1

10

Cr

5 From O(n,nag)C

10−2 5 10−3 10

20

30

40

50

60

70

80

Gamma−ray energy [MeV ×

10−1]

90

100

Fig. 23.5 The simulation of the prompt photon ﬂux spectrum emitted from the lunar surface bombarded by the cosmic ray ﬂux (GCR). The solid line shows the continuum, which is the sum of the total photon albedo plus the photon contribution produced by the π 0 -decay originating from the intranuclear cascade process. The lines or peaks in the spectrum have a FWHM of about 10 keV (after Ref. [1276]). Tab. 23.2 Elemental composition for the Martian soil (0.9 wt% H2 O and the Martian atmosphere).a

Composition of Martian soil Element wt% Element wt% Element wt%

H 0.10 Si 21.50 Mn 0.34

C 0.60 S 3.00 Fe 13.50

N – Cl 0.70 Co 33 ppm

O 46.60 K 0.12 Ni 52 ppm

Na 0.81 Ca 4.40 Th 0.45 ppm

Mg 3.70 Ti 0.38 U 0.13 ppm

Al 4.10 Cr 0.15

Composition of Martian atmosphere Element C N O wt% 26.52 2.74 70.74 a

The atmosphere of the Martian atmosphere was set to 16 g/cm2 (data are from [1276]).

The low-energy neutron depth proﬁle originating from the GCR alpha-particle contribution was found to be close to that from the GCR proton case. The same results are found for the lunar surface. Therefore, further calculations are

23.2 Galactic Cosmic Ray (GCR) Induced Reactions in Moon and MARS Soil SCR

Observer

&

GCR

Protons & a's Gamma spectrum Prompt g 's, p0-decay, de-ex, of residuals, delayed g 's

Mars atmosphere

Polar ice cap

Mars soil

Fig. 23.6 Schematic sketch of the Martian solar cosmic ray (SCR) and the GCR irradiation environment with the Mars Observer orbiter as used in the simulations.

restricted to a pure GCR proton irradiation. To allow a direct comparison to the lunar calculations, a total 4π GCR ﬂux of 3.0 protons/(s cm2 ) is assumed. The alphaparticle contribution is included in this normalization by the appropriate scaling factor of (0.9 + 0.1 × 3.5)/0.9 = 1.39. The gradient of about 2%/AU of the GCR intensity was neglected for Mars, e.g. [1292]. Figure 23.6 illustrates schematically the Martian irradiation environment with the Mars Observer orbiter applied in the simulations. The geometry used in the Monte Carlo simulations is similar to the geometry applied for the lunar surface. The prompt gamma-ray emission spectrum evaluated for a standard Martian composition is presented in Figure 23.7. The gamma-ray lines shown were obtained by Monte Carlo simulation as applied at the moon soil (cf. Figure 23.5). The statistical errors are about 15%(±1σ ) for strong lines like those from the elements oxygen and iron and are increasing to 40%(±1σ ) for weak lines, e.g., like the capture line from Si. The gamma-ray line ﬂuxes are also determined and summarized in different tables and published in Refs. [27, 1276]. The gamma-ray background contribution from π 0 -decay is shown separately in Figure 23.7. The total gamma-ray ﬂux from π 0 -decay yields 1.95 ± 0.08 photons/(s cm2 ), which is about twice the value given by Armstrong [1293] for the Moon. About one-third of the total gamma-ray continuum up to 10 MeV is produced by π 0 -decay. One of the most important problems is the determination of the water content of the Martian soil. This can be accomplished by two methods: (1) the ratio of the thermal to the epithermal neutron leakage ﬂuxes may be used to determine

661

23 Space Missions and Radiation in Space

101 C

5 Diff. gamma-ray flux [1/cm2 sec MeV]

662

Fe

O

2

Fe

100

Cl

Si Si

Mg

Ca

Al H

S

5

Ti Mn

C

2

Al

10−1 5

Cr

0.9 wt% H2O Total photon albedo

2

From p0-decay 10−2 0

2

4 6 Gamma−ray energy [MeV]

8

10

Fig. 23.7 Total prompt gamma-ray emission spectrum from the Martian surface for an average GCR-spectrum including several resolved gamma lines. The dashed curve represents the continuum contribution from the π 0 -decay. The normalization is identical to the lunar case (after Ref. [1276]).

the water content of the Martian soil, and (2) by analyzing the gamma-ray line intensities. Figure 23.8 shows an example to determine the water content by analyzing gamma-ray line intensities (see the following discussion). It could be shown in [27] that the ratio of the inelastic scattering line from Si at 1.779 MeV and the capture line of Si varies signiﬁcantly for low water concentrations, while the ratio of the capture line from H to a Fe capture line is best suited for the determination of higher water concentrations. A variety of other gamma-ray lines may be used in a similar way. The ratio of the 1.779 MeV inelastic scattering line to the 3.539 MeV capture line from Si is depicted in Figure 23.8 as a function of the water concentration. For the calculation of these data, only the neutron ﬂuxes below 14.9 MeV were taken into account. The intensity of the 4.934 MeV line is about 14% higher than the 3.539 MeV capture line. Although these results are very promising, the interpretation of experimental gamma-ray spectra may be difﬁcult if statistical errors are large. Additionally, the prompt photon contributions to the 1.779 MeV line from neutrons above 14.9 MeV and residual nuclei have to be accounted for. Adding this contribution causes a substantial shift of the line ratios. Furthermore, since prompt and delayed photons cannot be separated experimentally, delayed photons have also to be taken into account. The Si line ratio may thus be suited to show relative changes of the water content, although absolute water concentrations cannot be deduced easily. As can be estimated from Figure 23.8, this method is limited to water concentrations

23.3 The Space Experiment LDEF (Long Duration Exposure Facility)

4 Homogeneous soil + H2O From neutrons <15 MeV Total prompt ratio Flux ratio Si (inel./capt.)

3

2

1

0 0

10

20 30 Weight-% H2O

Fig. 23.8 Calculations of the photon ﬂux ratio of the 1.779-MeV inelastic scattering line from silicon to the 3.539 MeV silicon capture line from the Martian soil with different amounts of water. Solid line: ratio from

40

50

neutrons below 14.9 MeV. Dashed line: ratio of the total prompt gamma-ray ﬂux at 1.779 MeV to the gamma-ray ﬂux at 3.539 MeV. Contributions from delayed photons are not included (after Ref. [1276]).

below 10%. Other inelastic gamma-ray line intensities are affected by the same difﬁculties or are too weak to give reliable experimental data. The simulations were partly validated on thick target experiments at the SATURNE accelerator [1282], but could never been demonstrated and validated in the Mars orbit due to the already mentioned lost of the spacecraft in the vicinity of Mars in 1993.

23.3 The Space Experiment LDEF (Long Duration Exposure Facility) 23.3.1 The Aim of the LDEF Mission

NASA’s Long Duration Exposure Facility (LDEF) was designed to provide long-term data on the space environment and its effects on space systems and operations. The objective of the Long Duration Exposure Facility (LDEF) mission was to investigate the long-term effects of the Earth orbital radiation environment on various materials, systems, and spacecraft components. A special issue of Radiation Measurements summarizes most of the results of LDEF [1294].

663

664

23 Space Missions and Radiation in Space

Orbit parameters

Magnetic field model

Trapped radiation model

Cosmic ray model

Solar particle event model

Geomagnetic shielding model Spacecraft mass/geometry model

Radiation transport model

Internal radiation environments

Radiation effects assessments Fig. 23.9

Radiation effects response functions databases

A general scheme of methods for predicting space radiation effects in the LEO.

One measurable effect is the build-up of induced radioactivity caused by bombardment by nuclear particles such as protons and secondary neutrons [1295]. The radiation ﬂuxes responsible for the activation are of signiﬁcant concern to spacecraft designers where manned missions are planned and also in cases where sensitive electronics or detectors are to be ﬂown in space. At least two components of the radiation environment can be sampled passively from the analysis of radioactive nuclides formed in proton- and neutron-induced reactions. One is the trapped proton ﬂux encountered in the lower Van Allen radiation belts (mostly the South Atlantic Anomaly) and the other is the high-energy cosmic ray ﬂux above the local cutoff-rigidity1) (about 3 GV for the LDEF orbit). In addition, the effect of shielding and the production of secondary particles can also be studied using induced radioactivity though, these require thorough modeling of the radiation environment and spacecraft geometry. Particle radiation transport in low-earth orbit Unlike the predictions of radiation effects in deep space where only GCRs or SPEs (Solar Particle Events) particle 1) A useful deﬁnition of the cutoff-rigidity is found in [1268, 1296]. The relation between rigidity R in units of giga volts, GV, and the

particle energy E in MeV is: R = (A/Z)(E2 + 1862 · E)/103 , where A is the particle mass number and Z is the charge number.

23.3 The Space Experiment LDEF (Long Duration Exposure Facility)

sources with some few parameters are needed spallation effects in the LEO generally involve a more detailed description of the source term. The schematics are depicted in Figure 23.9. The following steps may be needed: • speciﬁcation of orbit parameters (inclination, altitude, etc.); • orbit calculation, in which the radiation environments are computed at time steps to obtain the orbit-average radiation exposure; • magnetic ﬁeld model is needed in computing the trapped radiation exposure; • radiation transport calculation to determine the radiation environment at locations internal to the spacecraft (3D Monte Carlo); • folding of these results with ‘‘response functions’’ for the radiation effect of interest. Examples here are folding computed particle ﬂuxes with LET spectra with quality factors to predict personnel doses, or folding with LET-dependent upset cross sections to predict single-event upset rates to electronics, using computed ﬂux spectra with atomic displacement cross sections to predict solar cell damage etc. (details are given in Refs. [1297–1301]). Recently NASA established a consortium to lay standards on radiation transport computer codes for NASA human exploration applications [1302]. This effort involves further improvements of Monte Carlo particle collision models, particle transport features, particle sources, and includes nuclear reaction databases. 23.3.2 The LDEF Orbiter System and Results on Induced Radioactivity of LDEF Materials

LDEF was deployed in orbit on April 8, 1984 by the Shuttle Challenger. The nearly circular orbit was at an altitude between 480 and 474 km and an inclination of 28.5◦ . The attitude control of the spacecraft was achieved with gravity gradient and inertial distribution to maintain three-axis stability in orbit. Therefore, propulsion or other attitude control systems were not required. After 2114 days remained in space and about 32,322 orbits (about 741,928837 miles) LDEF was retrieved on January 11, 1990 by the Shuttle Columbia. It experienced one-half of a solar cycle, as it was deployed during a solar minimum and retrieved at a solar maximum. Figure 23.10 shows a photo of LDEF in space taken through a window of the space shuttle. One can clearly see the bays and rows for experiments mounted at the outside. LDEF had a nearly cylindrical structure, and its 57 experiments were mounted in 86 trays about its periphery and on the two ends. The spacecraft measured about 9.14 × 4.27 m2 and weighed about 9752 kg with mounted experiments, and remains one of the largest shuttle-deployed payloads. In cross-section, LDEF was a Dodecagon or a 12-sided regular polygon that was 4.27 m wide. The 12 ﬂat sides accommodated experiments, while the nearly cylindrical shape ﬁts efﬁciently into the space shuttle’s payload bay. The structure was composed primarily of aluminum, with some structural elements composed of steel and titanium. LDEFs 9.14 m length was divided equally between six bays for the experiment trays, with a center ring midway along the length that was constructed of aluminum

665

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23 Space Missions and Radiation in Space

Fig. 23.10 An overall side view of the LDEF orbiter showing the bays and rows for experiments. The remote manipulator system arm is depicted in the upper part of the photo. The lower side of the photograph is blanked by the frame of the aft ﬂight deck window of the shuttle. The original photo is rotated by 90◦ . (Photo from: JSC S32-85-060, 01/12/1990, LDF Retrieval Survey, Photo Credit: NASA-JSC.)

Structure clips (Ti) Trunnion (steel)

12

11 12

10

Structure clips (Ti) 1

1

9

2

Detectors (Co, V, Ta, In, Ni)

Ballast 8 (Pb) 2

3

Ballast (Pb)

Clamp assembly (Al)

7 6

Tray clamps (Al)

3 5

4

Trunnion (steel) Fig. 23.11 The structure of LDEF and the components for induced activity measurements. The support structure shown on the left side with the trunnions is the earth-facing end of the spacecraft (after Harmon et al. [1295]).

with welded joints. The experiments involved the participation of more than 200 principal investigators. Figure 23.11 shows the overall outside structure of LDEF with the location of detector materials for induced radioactivity measurements.

23.3 The Space Experiment LDEF (Long Duration Exposure Facility) Galactic protons (cone half-angle = 100° at 450 km)

L D E F

Trapped protons

Trapped protons

Atmospheric neutrons (cone half-angle = 70° at 450 km)

Fig. 23.12 Sketch of the nonuniform angular variation of LDEF exposure to ionizing radiation (after [1297]).

The radiation measurements on LDEF were contained in 14 experiments at various locations and shielding depths, and encompassed many disciplines within the ﬁeld including nucleosynthesis of cosmic rays, radiobiology, dosimetry, and validation of radiation environment and transport models. The LDEF experiments were unique not only due to the extended length of the mission, but also due to the scale of the experiment, e.g., on results from the Ultra Heavy Cosmic Ray Experiment (UHCRE), which consisted of about 10 m2 of plastic nuclear track detector arrayed around the perimeter of LDEF to measure tracks from cosmic rays with a charge Z > 65. This experiment has increased the world sample of ultra heavy cosmic ray measurements by nearly 15 times [1303, 1304]. The radiation exposure experiments including induced radioactivity, absorbed dose, and LET spectra has been extensively modeled [1299, 1300]. With the attitude stability of LDEF, the effects of directional characteristics of the primary environment (trapped protons and heavy ions, cosmic rays, solar energetic particles) (cf. Figure 23.12) could be studied (see [1294, 1295, 1300] and references therein). These measurements lead to the discovery of an ‘‘anomalous’’ quantity of 7 Be [1305]. Other signiﬁcant results were on radiations emerging from LDEF important on the assessment of risk to crew during long duration spaceﬂight to determine proton-induced target fragments to the high LET (≥100 keV/µm) region of the LET spectrum [1306]. The radiation quantities and dosimeters applied for the radiation measurements aboard the LDEF satellite are summarized in Table 23.3. Activation results Interesting are the results of the extraction of speciﬁc activities from the Al activation tray clamp plates. These were some of the most valuable results from LDEF [1295]. Signiﬁcant amounts of the two radionuclides, 22 Na and 7 Be (cf. Figures 23.13 and 23.14), were observed, and were found of different

667

668

23 Space Missions and Radiation in Space Tab. 23.3 Radiation measurement methods and dosimeters applied at LDEF (more details are given in [1295] by Harmon et al.)

Radiation quantity

Dosimeter

Total absorbed dose Dose in microscopic volumes LET spectra Neutron ﬂuence and spectra Heavy ion ﬂuence and spectra Proton ﬂuence and spectra Trapped proton directionality

TLDsa microspheres PNTDb Fission foils activation PNTD PNTD/activation foilsc TLDs/activation foils

a

Thermoluminescent dosimeters. Passive nuclear track detectors. c Activation materials include speciﬁc metal samples for activation measurements, e.g., Ni, Ta, Va, In, Co, etc. and selected components, e.g., Al, Ti, Pb, steel, and stainless steel trunnions (see also Figure 23.11). b

origins. 22 Na is produced from trapped protons and cosmic ray interactions with higher energy particles in the Al clamps and spacer plates throughout the spacecraft. The distribution of the 22 Na activity on the clamp plates as a function of angle from the leading edge of the spacecraft is shown in Figure 23.13. The 1D approximate calculations were performed using the Watts model [886] simply assuming proton activation along a normal direction to a semiinﬁnite slab of aluminum. The 3D calculations are more realistic and treated time-dependent proton ﬂuxes, the effects of shielding, and secondary particle production [1297, 1299, 1300]. The models under predict the measured activation by about 30–50%, depending on the strength of the calculated anisotropy. This is also indicted by the model calculations on the dosimetric studies at LDEF [1306]. The regular placement of the clamps over the entire surface of the spacecraft allowed the activation due to the anisotropic proton ﬂuxes to be mapped. The 22 Na activity, with a half-life 2.6 y and a gamma-ray energy of 1.275 MeV from the experiment tray clamp plates allowed the sampling of the ﬂux in a plane aligned with the East, West, North, and South directions. The results indicate a clear peak in the southwest direction for the activation that reﬂects the maximum in the anisotropic ﬂux of trapped protons [886]. In contrast, there was a major surprise of the LDEF measurements [1305, 1307], comparing the 22 Na distribution with the distribution and the level of the 7 Be activity. A large concentration of 7 Be was discovered on the exposed metallic parts on the leading edge (i.e., the ram direction, the left part of the spacecraft shown in Figure 23.11) of the LDEF as seen in Figure 23.14, while the 22 Na distribution is present in the material from all sides.

23.3 The Space Experiment LDEF (Long Duration Exposure Facility) East 12

North

West

South

East

Measured 22Na activity

10

Approx. calculation, slab geometry, singel altitude = 450 km

Activity [Bq s−1 kg−1]

3D calculation with LDEF mass model, ESA AP8 fluences

8

6

4

2

0

45

90

135

180

225

270

315

360

Angle from LDEF leading direction (east) [degree]

Fig. 23.13 Comparison of measurements and calculations for 22 Na production rates of LDEF Al-clamp-plates as a function of angle from the leading side of the spacecraft. A measured and calculated anisotropy on West versus East is clearly indicated. (The clamp plates are used on outer surface of the LDEF spacecraft to secure experimental trays.) (after Harmon et al. [1295]).

Additional measurements of 7 Be applying a large bank of germanium detectors unevenly distributed around the spacecraft gave similar results [1308]. The conclusion of these exceptional 7 Be isotope distribution could only have been a result of atmospheric deposition combined with adsorption to the metallic surfaces caused by spacecraft motion [1305]. The 7 Be isotope is known primarily as a spallation product of relatively energetic cosmic ray interactions with N and O target nuclei in the atmosphere. Estimations have shown, that the measured concentration of 7 Be per unit mass of air at an altitude of 320 km is three orders of magnitude greater than it would be if it had been produced by cosmic-ray spallation at that altitude. Michel et al. [1309, 1310] have developed various sets of activation cross sections for 22 Na and 7 Be production from aluminum by protons and neutrons in the energy range from about 10 MeV to 1 GeV. The production cross section of 7 Be is in this energy range from about 0.1 to 10 mb very small. One simple explanation is that 7 Be is very fast transported upward from regions of the atmosphere, where its concentration is much higher. This transport has to take place on time scales similar to or shorter than the radioactive half-life = 53.2 d of the 7 Be [1305]. 23.3.3 Hazard Radiations in Space

Hazard sources faced by crews and spacecrafts in LEO or in deep space is the exposure to ionizing radiation in the space environment. The main sources of

669

23 Space Missions and Radiation in Space 160 140 Clamp plate activity per sample in [pCi] or [×3.7 Bq]

670

7Be 22Na (× 5)

120 100 80 60 40 Trailing edge

20 0 −270

−225

−180 7

Leading edge −135

−90

−45

0

45

90

22

Fig. 23.14 A comparison of Be and Na activities for the Al tray clamps taken from all around the LDEF spacecraft. The leading edge is at 0◦ and the trailing edge at 180◦ (after Gregory [1305]).

these radiations are the trapped particles in the Van Allen belts, consisting mainly of protons in the inner belt and electrons in the outer belt, the GCR background, composed of all naturally occurring elements and solar energetic particles, produced by events, such as coronal mass ejections and associated phenomena on the sun. Solar energetic particle events (SPE) are composed of protons and multiple-charged ions, with protons being the main source of concern for human exposures. As these radiations pass through spacecraft and the habitat shielding, their energies and composition are altered by interactions with the shielding. Hence, the radiation ﬁelds that actually produce biological damage may be substantially different from the external space environment. The modiﬁcations to the radiation ﬁelds arise from spallation and atomic processes whereby the charged particles lose energy with orbital electrons and occasionally undergo nuclear collisions. The spallation and fragmentation processes result in the formation of heavy ions that are lighter than the fragmenting nucleus and in the production of large numbers of light ions and neutrons. The potential hazards of space radiation are of concern in several areas: • Understanding the biological effects of space radiation is to be an important research area [1301, 1311]. While in the past, manned missions have been of relatively short duration and the astronaut doses have been relatively small[1312], for new missions such as the international space station (ISS), lunar bases, and Mars visits, the radiation protection to astronauts have to take on increased importance. • As space missions and operations nowadays become more complex and more extensive and higher speed automation requirements increase, more advanced

23.3 The Space Experiment LDEF (Long Duration Exposure Facility)

electronic technologies are needed. Such advanced microelectronics are susceptible to radiation damage, particularly to temporary failure due to single event effects (SEE) and single-event-upsets (SEU) [1313]. Also certain materials and components, such as optical coatings and solar cells, can have their performance degraded by radiation exposure[1314]. As the sensitivity of instrumentation for space observatories has increased, so has the susceptibility to radiation damage increased in many cases. Examples here include star sensors used in spacecraft orientation, CCDs used for visible light detection, and UV detectors [1314]. • Electrons with energies Eelectron > 100 keV can produce a buildup of charge on internal spacecraft structures, spacecraft charging, leading to electrical breakdown and current injection to sensitive electronic components [1315]. • Some satellite experiments include cryogenic systems for cooling instrumentation, and the heating effect of space radiation on these systems is often of concern. • The space radiation environment is a major source of background interference to some types of experiments, and in some cases the induced radioactivity in the spacecraft provides an important background to experiments [1316, 1317]. Astronaut dose limits The biological damage of radiation depends not just on the energy deposition produced but on the density of deposition. The density of energy deposition along a charged particle track is commonly expressed as the Linear Energy Transfer (LET). In radiation protection work, the quality factor (QF) is used to deﬁne a ‘‘dose equivalent’’ to relate LET to biologica1 damage. The LET is a physical quantity, representing the energy deposition by ionization processes, and can be calculated for a given ion charge, speed and material composition. Effects of this type are also important in other ﬁelds, notably in space physics since a strongly localized LET may induce failures in computer microchips. The QF as a function of LET is set by regulatory commissions and advisory groups based on experiments for various biological systems (ICRU [1318] and NCRP [1319, 1320]). The dose equivalent, H, which is expressed in units of Sieverts (Sv) is deﬁned as H = QF × D with D in (Gy). For example, NASA dose limits for astronauts are given in Table 23.4 set by the National Council on Radiation Protection Measurements (NCRP) [1319]. The limiting criterion is usually the BFO dose, which is the dose at the location of Blood Forming Organs, usually taken to be at a depth of 5 cm in tissue for dose estimates. Dose estimates for manned missions The importance of different space radiation sources (trapped, cosmic, and solar radiation) depends strongly on the mission and associated orbit parameters. Table 23.5 shows dose estimates (taken from various estimates in the literature [1319]) for different types of missions. For missions in LEO, e.g., below about 800 km, most of the exposure is from trapped proton exposure during passage through the South Atlantic region, with contributions from GCR and possible solar proton events (SPE) increasing for increasing orbit inclinations due to the decrease in geomagnetic shielding. The trapped exposure

671

23 Space Missions and Radiation in Space Tab. 23.4 Dose limits set by the USA National Council on Radiation Protection and Measurements (NCRP) for space activities (data based on Ref. [1319]).

Recommended organ dose equivalent limits all ages BFO (Sv) Eye (Sv) Skin (Sv) Career See below 4.0 6.0 Annual 0.50 2.0 3.0 30 days 0.25 1.0 1.5 Career whole-body dose equivalent limit (Sv) for a lifetime excess Risk of fatal cancer of 3% as a function of age at exposurea age

25

Female Male

35

1.0 1.5

55

1.75 2.5

3.0 4.0

Based on 10-y exposure duration. 1.4

.7

1.2

.6 Dose equivalent [Sv/y]

a

Dose equivalent [Sv/y]

672

1 .8 .6

Solar maximum

.4 Solar maximum

0

Aluminum shield

.4 .3 .2 Water shield

.2

(a)

.5

.1

5

10

15

20

25 2

Water thickness [cm or g/cm ]

30

0

10

(b)

20

30

40

50

Shield thickness [g/cm2]

Fig. 23.15 Shielding effectiveness for GCR radiation: (a) dose equivalent in water at solar minimum and solar maximum; (b) dose equivalent behind varying water and aluminum shielding thicknesses.

is strongly dependent on altitude. Outside the earth’s magnetosphere, there is the possibility of very large doses from SPEs, and shielding must be provided. Given that a SPE ‘‘storm shelter’’ is provided for SPEs in the spacecraft design, the main remaining contributor for deep space missions is the GCR. In Figure 23.15 the shielding effectiveness for GCR is illustrated for galactic cosmic rays for hydrogenous material (water) and aluminum shields [1321]. In the trapped electron environment, electrons and secondary photons (bremsstrahlung) are important at small shielding depths. Proton transport is needed in estimating the effects of trapped protons and cosmic ray protons, with the importance of secondary neutron and proton transport. Normal spacecraft

23.3 The Space Experiment LDEF (Long Duration Exposure Facility) Importance of various space radiation environments in terms of biological doses for different space missions (examples from various estimates in the literature, e.g., [1317, 1322]).

Tab. 23.5

Orbit Attitude

Mission Inclination

LEO

Low

LEO

Medium

LEO

High

GEO

0◦

Deep space Deep space

Radiation dose from Trapped protons (Sv/y)

Space Station 450 km, 28.5◦ Skylab 450 km, 50◦ Polar-Platform 450 km, 90◦ Geosynchronous 35790 km 160◦ west long. Lunar base Mars landing

Trapped electrons (Sv/y)

GCRs (Sv/y)

SPEs event (Sv/event)

0.32

∼0

0.03

0.21

∼0

0.06

0.04

0.19

∼0

0.09

0.29

0.47

5.07

0.30 (surface) 0.45 (transit) 0.12 (surface)

3.4

0.04

0.18

0.02

∼0

0.02

∼0

∼0

3.4

shielding, typically about 10–20 g/cm2 on average, is effective in shielding the trapped and SPE radiation, but has limited effectiveness for GCR as shown in Figure 23.15. Heavy ions make an important contribution to biological dose and electronics upset for small shielding thicknesses. Single event effects (SEE) of spacecraft microelectronics exposed to cosmic rays As advanced technology electronic devices have become increasingly smaller, it has become possible that a single charged particle hitting the device can produce sufﬁcient energy deposition and charge release that the logic state of the device is changed. Thus, for example, single-event-upset (SEU) phenomena can change a ‘‘0’’ or ‘‘1’’ bit in an on-board computer, resulting in such effects as a change in the orientation of the spacecraft. A related SEE is latch up, which can cause permanent damage to the device. SEU effects and Multiple Bit Upset (MBU) can be produced both by HZE comic rays, and by cosmic, solar, and trapped protons via the highly ionizing products from proton nuclear interactions. SEE have caused problems on numerous satellites in recent years and costly redesign for spacecraft [1323]. MBU has been observed since 1990s and increase exponentially when the gate length decreases [1324]. One concern is that the dominating sensitivity to SEE arises simply from a cosmic-ray track induced inside the sensitive volume of the device as depicted in Figure 23.16.

673

674

23 Space Missions and Radiation in Space Cosmic-ray track q Surface of silicon chip (greatly enlarged)

≈ 25m Sensitive region Charge cloud

Fig. 23.16 Illustration of SEE phenomena produced by primary and secondary particle collisions inside the sensitive region of a silicon chip.

Various types of SEE have been reported. As mentioned before, the SEU denotes a soft failure which upsets a bit memory from a state to another. This failure is called ‘‘soft’’ because the bit can be restored. In contrast the ‘‘Single Hard Error’’ may cause a permanent device damage, which is then called ‘‘hard’’ [1313]. Some of these problems may be circumvented if the radiation environments are much better understood, which could be done by spallation research on radiation–components interaction. But some problems are only solved by circumvention implementation, e.g., the choice of less sensitive components, the use of redundancy mode, or software protections. Such work was done during the ARIANE 5 design work [1324].

675

Appendix A Values of Fundamental Physical Constants and Relations In this appendix, a selection of the values of fundamental physical constants, units, symbols, conversion factors, and some relations relevant for the spallation physics are summarized in tabular form. For more detailed information, the reader is referred to the standard manifold literature. The 11th General Conference on Weights and Measures (1960) adopted the name Systeme International d’Unites (International System of Units, international abbreviation SI), for the recommended practical system of units of measurement. The same conference laid down rules for the preﬁxes, the derived units, and other matters. The base units are a choice of seven well-deﬁned units which by convention are regarded as dimensionally independent: the meter, the kilogram, the second, the ampere, the kelvin, the mole, and the candela (cf. Table A.1). Derived units are those formed by combining base units according to the algebraic relations linking the corresponding quantities. The SI unit is not static but evolves to match the world’s increasingly demanding requirements for measurement. The base units are deﬁned as follows: • The meter is the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second. • The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. • The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperﬁne levels of the ground state of the 133 Cs atom. Tab. A.1

SI units.

Measure

Unit

Measure

Unit

Meter Kilogram Second Ampere Kelvin Mole Watt

m kg s A K mol W

Newton Farad Joule Coulomb Tesla Hertz Candela

N F J C T Hz cd

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

676

A Values of Fundamental Physical Constants and Relations Tab. A.2

Some useful conversion factors.

Unit

Conversion unit

1u 1 eV 1J 1 MeV c−1 1C 1T 1 Bq 1 Ci 1 Gy 1 Sv 1 A˚ 1 fm 1b

Tab. A.3

= = = = = = = = = = = = =

1 mu = 12 m(12 C) 1.60217733(49) × 10−19 J 107 erg 5.3443 × 10−17 g cm s−1 10−1 e.m.u. = 2.99792458 × 109 e.s.u. 104 G 1 disintegration s−1 = 2.7 × 10−11 Ci 3.7 × 1010 s−1 1 J/kg = 104 erg/g = 100 rad 100 rem 10−10 m = 10−8 cm 10−15 m = 10−13 cm 10−28 m2 = 10−24 cm2

General constants.

Measure

Symbol/relation

value

Unit

Speed of light in vacuum Planck constant in electron volts, h/e h/2π in electron volts, /e h/2π hc Elementary charge

c h

299792458 ×1010 6.6260755 ×10−34 4.1356692 ×10−15 1.05457266×10−34 6.5821220 ×10−16 197.33 1240 −19 1.602008 √ ×10 1200 MeV fm 9.1093897 ×10−31 2.81794092 ×10−15 1.8835327 ×10−28 105.658389 2.406120 ×10−28 2.4880187 ×10−28 134.9630 139.5673 1.6726231 ×10−27 938.27231 1.6749286 ×10−27 939.56563 6.022045 ×1023 1.30658 ×10−23 8.617385 ×10−5

cm/s Js eV s Js eV s MeV fm/c eV nm C

Electron mass Classical electron radius Muon mass in electron volts, mµ c2 /e Pion mass Pion mass in electron volts, mπ 0 c2 /e in electron volts, mπ ± c2 /e Proton mass in electron volts, mp c2 /e Neutron mass in electron volts, mn c2 /e Avogadro constant Boltzmann constant in electron volts, k/e

hc e e me re mµ π0 π± mπ 0 mπ ± mp mn L k

kg m kg MeV kg kg MeV MeV kg MeV kg MeV mol−1 J K−1 eV K−1

A Values of Fundamental Physical Constants and Relations

• The ampere is that constant current which if maintained in two straight parallel conductors of inﬁnite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 N m−1 of length. • The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. • The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kg of 12 C. When the mole is used, the elementary entities must be speciﬁed and may be atoms, molecules, ions, electrons, other particles, or speciﬁed groups of such particles. • The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensity in that direction of 1/683 W sr−1 . Other useful relations (a) The de Broglie wavelength, with E = kinetic energy, is given: • λ = /p = (2m0 E + E 2 /c2 )−1/2 = (2m0 E)−1/2 (1 + E/2m0 c2 )−1/2 , √ • for nucleons and E m0 c2 the de Broglie wavelength is λ = (4.55/ E) (fm). (b) The relation between frequency and wavelength: • E λ = = 197.33 (MeV fm) 1/3 1/3 (c) The energy of the Coulomb threshold with R = r0 (A1 + A2 ) (fm): 2 • Vc = Z1 Z2 e /R = 1.44 Z1 Z2 /R (MeV)

677

679

Appendix B Basic Deﬁnitions in Nuclear Technology Concerning the Fuel Cycle Some terms, the breeding gain, the conversion ratio, and the reproduction factor, applied in nuclear technology and in the context of transmutation are summarized with examples in Tables B.1, B.2, B.3, and B.4. • η = number of neutrons produced per neutron absorbed in the fuel of a nuclear system. An η > 2 implies breeding is possible. • η = (σﬁssion /σabsorption ) · ν, where ν = number of neutrons produced per ﬁssion. Note that a fast spectrum yield higher reproduction factors. • Thus, a fast reactor or ‘‘fast’’ energy ampliﬁer is better suited for breeding fuel. • The highest possible reproduction factor is 239 Pu with an η = 2.7. • Conversion ratio (CR)/breeding gain (BG): ﬁssile nuclei produced CR = ﬁssile = η − 1, where for a CR > 1 the breeding ratio nuclei consumed (BR) is used. • breeding gain (BG) = BR – 1

Tab. B.1

Breeding and conversion of fertile and ﬁssile isotopes.

Fertile isotopes

→

Fissile isotopes

232 Th

→ → →

233 U

238

U 240 Pu

239

Pu

241 Pu

Reproduction factor η for thermal and fast neutrons for different ﬁssionable isotopes.

Tab. B.2

Isotopes

Thermal neutrons

Fast neutrons

233 U

2.30 2.07 2.11

2.45 2.30 2.70

235 U 239 Pu

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

680

B Basic Deﬁnitions in Nuclear Technology Concerning the Fuel Cycle Tab. B.3

Conversion and breeding ratios of different reactor types.

Reactor type

Fuel

Conversion

CR or BR

BWR PWR CANDU HTGR LMFBR

2–4 wt% 235 U 2–4 wt% 235 U nat U 5–90 wt% 235 U 10–20 wt% 239 Pu

238 U

0.60 0.60 0.80 0.80 1.0 to 1.7

Tab. B.4

to 239 Pu to 239 Pu 238 U to 239 Pu 232 Th to 233 U 238 U to 239 Pu 238 U

The status of commercial LMFBRs in 2006.

Reactor

Site

Year

Phenix Superphenix PFBR Monju BN 600 BN 800 Dounray

France France India Japan Russia Russia UK

1974-a 1986–1998 2010 1993–1995 1981-a 2012 1976–1994

a

Power MWe

Type

233 1200 500 246 560 750 250

Pool Pool – Loop Pool – Pool

In operation.

Overview on conversion and breeding ratios for different reactor types and commercial LMFBR reactors1) The most shutdowns or plant closures of fast reactors in the past were the result of sodium leaks in the cooling circuits of LMFBRs. Some shutdowns were caused by ﬁnancial or political reasons, e.g., the CRBR project (Clinch River Breeder Reactor Plant) in USA or the SNR-300 (Schneller Natriumgek¨uhlter Reaktor) in Germany. With low uranium prices, the costly reprocessing and the fuel cycle, the breeder reactors has had unfavorable economics.

1) Detailed information is given in the ‘‘Fast Reactor Database 2006 Update’’ of the Int. Atomic Energy Agency (IAEA) with a brief history on ‘‘Technology Advances in Fast Reactors and Accelerator Driven Systems,’’ (http://wwwfrdb.iaea.org/auxiliary/history.html).

1.1

232

−4

3.5×10

0.13

2

0.6

1.4

U

0.04

0.2

2.3

0.61

27 d

Pa

(n, 2n) (En: ≥ 6 MeV)

s (bam) Fission

0.31

0.20

22.3 mn

Th

233

233

233

(n, g) capture

U

0.007

0.24

1.3 d

Pa

Th

232

232

t 1/2 b -decay ≤ 10 a (isomer)

s (bam)

Pa

0.0017 25.5 h 0.18

Th 0.04

1.5

0.35

U 0.37

1.55

24.4 mn

Pa

7.2 mn

Th

235

235

235

236

U 0.4

0.08

237

0.35

0.69

1.1

0.3

6.75 d

U

Np

237

238

238

U

0.3

1.8

0.22

0.03

Pu 0.37

1.1

2.12 d

Np

238

239

1.27

Pu 0.31

1.65

2.35 d

Np

0.49

23.5 mn

U

239

239

240

0.4

61.9 mn (7.2 mn) 0.35

Np

14.1 h

U

Pu

240

240

Among the 60% of neutrons not used for fission, 20% are lost and 40% are used to breed 233-U from 232-Th. In this way, new fissile material replaces what is used for fission.

Note the difference between 232-Th and 238-U in terms of TRU access!

U

6.7 h (1.17 mn) 0.3

Pa

0.003 0.25

24.1d

Th

234

234

234

241

241

0.27

2.1

Am 1.2

0.2

14.3 yr

Pu

242

Pu

Am

242

0.47 (0.2)

2.7 (3.1)

0.34

0.24

243

0.24

0.64

1.0

0.17

4.96 h

Pu

Am

243

Fig. B.1 Chart of the actinides: The choice of fuel, Thorium[232 ThO2 (+233 UO2 )]. Thorium is about 5 neutron captures away from the transuranium elements (TRU) one wants to destroy (after Kadi [1325]).

231

231

n + 232Th (1.4 × 1010 a) → 233Th (22.3 m) → 233Pa (27 d) → 233U (1.6×105 a)

B Basic Deﬁnitions in Nuclear Technology Concerning the Fuel Cycle 681

683

Appendix C Material Properties of Structure and Target Materials

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

balanceFe-(50-55Ni)-(17-21Cr)-(4.75-55)Nb -(2.8-3.3)Mo-(0.65-1.15)Ti-(0.2-0.8)Al -(1.0)Co-(0.08)C-(0.35)Mn-(0.35)Si-(0.015)P -(0.015)S-(0.3)Cu balanceFe-(10-14)Ni-(16-18)Cr-(2-3)Mo -(2)Mn-(0.75)Si-(0.1)N-(0.045)P-(0.03)C -(0.03)S balanceAl-(0.4)Si-(0.4)Fe-(0.1)Cu-(0.5)Mn -(2.6-3.6)Mg-(0.3)Cr-(0.2)Zn-(0.15)Ti

INCONEL718b

balanceFe-(11.68)Cr-(1.1)Mo-(0.66)Ni -(0.47)W-(0.63)Mn-(0.29V-(0.45)Si -(0.2)C-(0.03)Nb balanceFe-(8.8)Cr-(0.96)Mo-(0.24)Ni -(< 0.01)W-(0.43)Mn-(0.24)V-(0.32)Si -(0.099)C-(0.3)Nb balanceFe-(12)Cr-(1.8)Si-(0.9)Ni-(0.7)Mo -(0.7)Mn balanceFe-9Cr-1.1W-0.4Mn balanceFe-(7.65)Cr-(2.0)W-(0.2)V-(0.04)Ta -(0.003)B-(0.1)C

2.65

7.9-8.0

8.19

Density (g cm−3 )

15.9 at 273–373 K

∼ 1333

24.0

13.0 at 294-366 K

≥ 1609

863-918

Thermal expansion (µm m−1 K−1 )

Melting point tm (K)

960

500

435

Speciﬁc heat (J kg−1 K−1 )

Tantalum is also applied as structure material to clad tungsten targets. For the many details about the properties and applications the comprehensive literature mainly published in handbooks should be considered, e.g. [926, 1153, 1326–1328]. b INCONEL is a trade mark of the Special Metals Corporation group of companies. 316LN/L is the most common stainless steel.

a

Eurofer97 F82H

EP823

T91

HT9

Ferritic–martensitic steels for ADS

AlMg3

316LN/316L

Material composition (% wt)

Properties of common structure materials for spallation neutron source target systems and for proposed ADS applicationsa .

Material

Tab. C.1

684

C Material Properties of Structure and Target Materials

W

82 83

nat Bi

74 73

nat Pb

Solid and liquid target materials:

nat Ta

nat

Solid target materials:

Charge number Z

209

207.2(1)

183.84 180.95

Atomic mass A (g mol−1 )

11.34 (solid) 10.66 (liquid) 9.78 (solid) 10.05 (liquid)

19.25 16.65

(g cm−3 ) at r.t.

Density

544.7

600.61

3695 3290

Melting point tm (K)

1837

2022

5828 5731

Boiling point tb (K) at 1 atm

28.9 (solid) 40 (liquid) 13.4 (solid)

4.5 6.3

Thermal expansion (µm m−1 K−1 )

25.52

26.65

24.27 25.36

Speciﬁc capacity (J mol−1 K−1 )

(continued)

0.034

0.17

18.5 22

Thermal cross section (b)

Material properties of target materials for spallation neutron sources and ADS applications. W with about 5 %wt Re and Udep with 7–10% wt Mo were also investigateda .

Tab. C.2

C Material Properties of Structure and Target Materials 685

(continued)

208.2 200.6

(82.5) 80

Isotopic compositions of W, Ta, Bi, Pb, and Hg:

202.6

Atomic mass A (g mol−1 )

(82)

Charge number Z

13.534

10.5 (liquid)

10.6 (liquid)

(g cm−3 ) at r.t.

Density

234.32

398

523

Melting point tm (K)

629.88

Boiling point tb (K) at 1 atm

60.4

40 (liquid)

Thermal expansion (µm m−1 K−1 )

• nat W (180 W(0.12%), 181 W(26.4%), 183 W(14.31%), 184 W(30.64%), 186 W(28.43%)], • nat Ta (180m Ta(0.012%), 181 Ta(99.988%)], • nat Pb (204 Pb(1.4%), 206 Pb(24.1%), 207 Pb(22.1%), 208 Pb(52.4%)], • nat Bi (209 Bi(100%)], • nat Hg (196 Hg(0.15%), 198 Hg(9.97% ),199 Hg(16.87%), 200 Hg(23.1%), 201 Hg(13.18%), 202 Hg(29.86%), 204 Hg(6.87%)]

a

LME (Pb 97.5%, Mg2.5%) PbMg eutectic LBE (Pb 45%, Bi55%) PbBi eutectic nat Hg

Liquid target materials:

Tab. C.3

27.98

31.2

28.4

Speciﬁc capacity (J mol−1 K−1 )

389

0.11

0.17

Thermal cross section (b)

686

C Material Properties of Structure and Target Materials

687

Appendix D Moderator and Reﬂector Materials Tab. D.1 Physical properties of compound moderator and reﬂector materials. Data based on Bauer [57].

Compound moderator materials Parameter

H2 O

D2 O

CH4

(CH2 )n

NH3

TiH2

A ρ (g cm−3 ) N (1024 cm3 ) σfree (b) σbound (b) σa (b) free =N·σfree (1/cm) ξ κ (2 MeV→1 eV) v · ts (cm)

18 1 0.033 44.8 168.3 0.665 1.5 0.926 15.7 2.15

20 0.001 0.033 10.5 19.5 0.001 0.35 0.510 28.5 14.24

16 0.453 0.017 86.8 333.6 1.334 1.48 0.954 15.2 2.12

14 0.94 0.040 45.7 169.6 0.669 1.85 0.913 15.9 1.77

17 0.682 0.024 71.5 257.6 2.898 1.73 0.879 16.5 1.96

49.92 3.978 0.048 42.43 163.3 6.755 2.04 0.811 17.9 1.81

σfree (b) = free scattering cross section, σbound (b) = bound scattering cross section, σa (b) = thermal absorption cross section, free (1/cm) = N · σfree (1/cm) = macroscopic cross section, ξ = logarithmic energy decrement, κ (2 MeV → 1 eV) = number of collisions for slowing down from an energy E to thermal energy, v · ts (cm) = slowing down length.

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

H 1 0.07 0.042 2.51 82.02 0.3326 0.86 1.000 14.5 3.47

A ρ (g cm−3 ) N (1024 cm3 ) σfree (b) σbound (b) σa (b) free =N·σfree (1/cm) ξ κ (2 MeV→1 eV) v · ts (cm)

Element

2 0.163 0.049 3.4 7.64 0.0005 0.17 0.725 20.0 21.37

D 9.01 1.85 0.124 6.18 7.63 0.0076 0.76 0.206 70.3 13.58

Be 12.01 2.3 0.115 4.73 5.51 0.0035 0.55 0.158 92.0 24.51

C 14 0.804 0.035 10.03 11.51 1.9 0.35 0.136 106.5 44.48

N 16 1.13 0.043 3.75 4.232 0.0002 0.16 0.120 121.0 108.83

O 55.85 7.9 0.085 11.21 11.62 2.56 0.96 0.035 410.0 59.86

Fe

58.71 8.9 0.091 17.89 18.5 4.49 1.63 0.034 430.8 36.77

Ni

Physical properties of common elemental moderator and reﬂector materials (data are from Bauer [57]).

Parameter

Tab. D.2

200.6 13.55 0.041 26.53 26.8 372.3 1.08 0.010 1460.1 187.06

Hg

207.19 11.3 0.033 11.01 11.118 0.171 0.36 0.010 1507.9 576.49

Pb

688

D Moderator and Reﬂector Materials

689

Appendix E Shielding Materials Tab. E.1

Element O Si Al Fe Mn Ti Ca Mg K Na

Soil composition for earth shielding of accelerators (data are from [1329]). Soil composition (wt%) 43.77 28.1 8.24 5.09 0.07±0.06 0.45±0.043 3.65 2.11 2.64 2.84

The density of soil varies between 1.7 and 2.25 g cm−3 depending on the water content and the soil sort.

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

690

E Shielding Materials

Tab. E.2

Typical compositions of representative concretesa . Concrete partial density (g cm−3 )

Element

Ordinary

Magnetite

Barytes

Magnetite steel

Limonite steel

Serpentine

H O Si Ca C Na Mg Al S K Fe Ti Cr Mn V Ba

0.13 1.165 0.737 0.194 – 0.040 0.006 0.107 0.003 0.045 0.029 – – – – –

0.011 1.168 0.091 0.251 – – 0.033 0.083 0.005 – 1.676 0.192 0.06 0.007 0.011 –

0.012 1.043 0.035 0.168 – – 0.004 0.014 0.361 0.159 – – – – – 1.551

0.011 0.638 0.073 0.258 – – 0.017 0.048 – – 3.512 0.074 – – 0.003 –

0.031 0.708 0.067 0.261 – – 0.007 0.029 – 0.004 3.421 – – – 0.004 –

0.035 1.126 0.460 0.150 0.002 0.09 0.297 0.042 – 0.009 0.068 – 0.002 – – –

Density (g cm−3 )

2.35

3.53

3.35

4.64

4.54

2.1

a Remark: The hydrogen content strongly inﬂuences its effectiveness for shielding against neutrons below energies of about 100 MeV (data are extracted from the American National Standard ANSI/ANS-6.4-1985 and from [1330].

Tab. E.3 Comparison of different shielding materials applied for spallation neutron source and accelerator shielding.

Shielding materials

Soil Normal concrete Heavy concrete Steel Cast steel Stainless steel Lead Tungsten

Density (g cm−3 ) 1.8 2.3 4.3 7.85 7.1 7.85 11.3 18.5

Attenuation length λatt [1329] (g cm−2 ) 108 115 130 160 160 160 210 194

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Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

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757

Index a A-coefﬁcient 651 abrasion–ablation 154 absorbed dose 627 absorber 37, 39, 124, 189, 200, 436, 467, 627, 628, 635–638 absorption 3, 15, 27–29, 31, 32, 51, 58, 75, 82–84, 95, 111, 121, 180, 251, 272, 341, 356, 382, 385, 395, 396, 426, 432, 434, 436, 444, 458, 459, 478, 483, 565, 569, 609, 631, 635, 637, 638, 645 abundance 7, 138, 281, 310, 356, 368, 408, 460, 614 accelerator – breeding 607 – driven system 3, 101, 185, 215, 269, 409, 594 – driven transmutation 548, 554, 594, 603 – production of tritium 609 acceptance 307, 320, 326, 340, 373, 500, 641 accumulation 19, 540 accumulator 269, 498, 501–503, 526, 528, 538–541, 547 achromat 526, 527 actinide 153, 173, 594, 607, 616 activation 233, 263, 333, 369, 379, 381, 388, 389, 411, 413, 420, 422, 455, 469, 488, 489, 492, 503, 509, 517, 519, 524, 558, 585 after-heat 565 albedo 250 ALICE program 116, 212, 657 alloys 471, 472, 510, 555, 584, 587 aluminum 35, 43, 44, 220, 225, 300, 303, 321, 324, 325, 361, 374, 385, 482, 516, 567, 580, 581, 612, angular dependent neutron production 380 ANISN program 245–247 anisotropic 128, 361 annealing 463

annihilation 59, 60, 111, 186, 283, 425, 426, 428 anomalous abundance 281, 356 antineutrino 585, 651 antinucleon 111 antiproton 112, 283, 425, 426, 554 antisymmetric 29 aperture 294, 295, 307, 457, 502 ASTE 380, 413, 419–423, 466–468, 482, 491, 493 atmosphere 4, 5, 7–10, 254 attenuation length 43, 44, 234–237, 241, 242, 246, 255, 484–487, 489, 490, 494 Audi-Wapstra 144 Auger-electrons 426 average neutron multiplicities 400 Avogadro 32, 34, 200, 397, 484

b backscattering 254, 511, 513, 518 balloon ﬂights and cosmic rays 5 baryon 26, 28, 74, 130, 585 Becquerel 268 benzene 447, 453 beryllium 259, 483, 487, 543, 646 beta-asymmetry 652 beta-beam 640–642 beta-decay 643 betatron 648 Bethe–Bloch formula 33, 34, 60, 61, 414 Bevatron 233 BGO 29 Bhabha scattering 59 binding energy 70–72, 103, 106, 121, 122, 137, 145, 160, 164, 168, 176, 182, 267, 282, 353, 571 biochips 589 biological effectiveness (RBE) 628 biosphere 593, 603

Handbook of Spallation Research: Theory, Experiments and Applications. Detlef Filges and Frank Goldenbaum Copyright  2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40714-9

758

Index biotechnology 589 bismuth 227 blanket 410, 412, 413, 561, 608–612 Bohr 136 Bohr–Wheeler 137, 162 Boltzmann constant 459 Boltzmann equation 191, 192, 194 booster 624, 626 borax 305 boron 361, 365, 444, 458, 565, 626, 651 Bragg angle 458, 465 Bragg peak 359, 360, 414, 627, 628 break-up 117, 136, 154, 158, 159, 176 breeding 383, 431, 593, 596, 607, 608, 614, 615 Breit–Wigner 208 bremsstrahlung 13, 39–41, 57–60, 186, 189 buckling 436 build-up 235 bulk shield 233, 234, 241, 248–250, 252, 253, 270, 482, 484, 487, 488, 490, 532, 541 bunches 421, 540 burn-up 211, 505, 543, 602, 615

c cadmium 384, 444, 457, 459 caesium 515 calcium 414 caloric equation of state 282 calorimeter 124, 211, 212, 631–638, 642 calorimeter ATLAS 638 calorimeter towers 632, 636 calorimeter ZEUS 635–638 cancer treatment 185, 623, 625, 626 capture 205, 287, 319, 336–338, 382, 383, 385, 386, 388, 391, 392, 428, 434, 437, 553, 591, 601, 604, 605, 609, 610, 614, 615, 619, 623, 639 cavitation 530, 570, 574, 583 cavity 482, 488, 525, 528, 540, 599, 608 Cd layer 535 central-tracker 638 chain-mode 602 charge-exchange 27, 82–84, 112, 324 Cherenkov 211, 491, 642 chopper 291, 503, 518, 531, 535, 552 cladding 562, 567 cluster 82, 103, 105–109, 183, 348, 368, 478 coalescence 105–109, 117, 347, 368 coherence 283, 426, 450 collider 185, 497 collimation 294, 511

collision length 31–34, 260 combustion 615 compensation 634–636 composite particle 104, 344 compound 18, 114, 135–138, 140, 144, 153–155, 159, 164, 165, 176, 181, 283, 351, 352, 370, 435, 439 compressibility 129 conditional barriers 137, 161 conﬁnement 25, 648 constituent 26, 180, 639 containment 215, 418, 632 contamination 254, 271, 296, 370, 557, 569, 605 continuum 180, 298 conversion 17, 169, 180, 181, 237, 238, 245, 268, 380, 383, 385–387, 450, 538, 553, 554, 600, 609, 635, 645, 646, 648 converter 307, 640, 647 coolant 521, 543, 562, 567, 605, 612, 613 corrosion 413, 414, 584, 587 cosmic 3–5, 7–12, 75, 119, 133, 185, 193, 194, 207, 215, 281, 356, 369, 379, 650, 651, 669, 672 Coulomb – barrier 51, 52, 65, 70, 106, 113, 142, 143, 145–147, 155, 177 – ﬁeld 38–40 – repulsion 15, 70, 166, 174, 354 – scattering 33, 37–39 coupling 57, 102, 106, 131, 137, 159, 168, 180, 233, 242, 243, 246–249, 258, 361, 441, 532, 564, 565, 571, 607, 651 CsI 363 CT-tomography 624 cycle 171, 269, 333, 516, 526, 540, 615, 619 cyclotron 13, 269, 288, 319, 320, 325, 380, 383, 388, 497–499, 519–522, 559, 598, 613, 623, 625, 631

d DT fusion, 13 Dalitz-decay 205 damage 185, 199, 207, 215–217, 219–225, 227–233, 261, 262, 280, 281, 356, 413, 431, 453, 462, 471, 479, 480, 503, 542, 561, 567–571, 573, 582, 584, 626, 627, 631 damping 155, 156, 158 debris 20, 634 deBroglie wavelength 18, 88, 120 decay constant 441, 443, 458, 460, 461, 597 decay width 137, 138, 145, 152, 154, 157, 159–162, 164 deceleration 645

Index decoupler 545 decoupling 437, 449, 543 deep penetration 198, 233, 243, 248–250, 252, 253, 481, 482, 494 defect 217, 218, 222, 223, 230, 341, 478, 591 deﬂection 39, 127, 333, 474, 475 deformation 15, 156–158, 160, 166–168, 170, 284, 350, 476, 588 degeneracy 68 degradation 219, 480 degrader 374, 472 depletion 88, 90, 97, 109, 113, 119, 121, 269, 340 deposit 636 destruction 105, 601, 605, 621 deuterium 47, 327, 374, 376, 512, 521, 586, 643, 645–647 deuteron 13, 59, 83, 90, 103, 110, 143, 258, 259, 327, 425, 429, 595 diffraction 478, 517, 518, 548, 586, 588, 645 diffractometer 513, 514, 552, 553 diffusion 157, 338, 391, 435, 436, 472 dilution 564, 601 dipole 179, 307, 515, 519, 643, 648, 649 discrete ordinates coupling 242–244, 246, 249 disintegration 3, 58, 59, 117, 136, 176, 282 dispersion 96, 149 displacement cross sections 220, 227, 229, 479 displacement dose 471, 473, 478 displacement rate 218 displacements per atom 207, 218, 219, 225, 231, 232, 245, 471, 472, 478, 479, 567 disposal 105, 554, 555, 581, 593, 600, 602, 605, 607 dissipation coefﬁcient 157 dose equivalent 236, 237, 239–241, 249, 253, 255, 256 down-scattering 194, 252 dpa numbers 231 ductility 475, 477 dynamics 55, 64, 162, 166, 168, 169, 186, 217, 218, 275, 284, 351, 414, 505, 517, 538, 573, 585, 586, 588, 590, 591, 623

e effective half-live 597 elastic 3, 4, 16, 30, 32, 41, 42, 44, 47, 48, 50, 59, 74–76, 81, 83–86, 93–97, 111, 115, 116, 123–126, 128, 130, 137, 201–205, 220, 230, 245, 274–276, 307, 391, 398, 432, 433, 491, 590

electromagnetic – cascade 23, 44, 636 – drain 57 – force 24, 186, 512 – shower 57, 59, 185, 189, 631–633, 635 electron-cooling 333 electroweak force 646 elongation 476, 477 embrittlement 232, 471, 510 emission 23, 55, 89, 91, 103–110, 115, 122, 124, 127, 128, 135, 136, 138, 142–144, 147, 148, 152, 154, 155, 158–160, 162–165, 167–169, 171, 172, 174–176, 178–182, 184, 189, 193, 194, 266, 279, 282, 285, 287, 293, 294, 300, 307, 311, 312, 331, 338, 342, 344, 348, 350–353, 360–363, 367, 368, 402, 408, 452, 545 emittance 520 ENDF 209, 211, 227, 245 endothermal 257 energy – ampliﬁer 259, 561, 595, 596, 613, 615, 617, 620 – conservation 276, 633 – deposition 10, 13, 15, 33, 43, 44, 57, 124, 199, 207, 267, 338, 379, 380, 413, 414, 416–419, 423, 502, 582, 610, 627, 629 – loss 10, 34, 35, 37, 39–41, 59, 60, 189, 194, 200, 211, 219, 257, 287, 299, 317, 324, 341, 356, 359, 361, 374, 408, 414, 432, 433, 598, 634, 635, 638 – resolution 296, 297, 634 enrichment 384, 467, 602 entropy 139, 155, 169 epithermal 16, 459, 511, 595, 624 equilibration 135, 285, 426 equilibrium 16, 114, 115, 117, 132, 135–137, 164, 167, 170, 181, 182, 234, 237, 246, 283, 284, 350, 353, 435, 450, 485, 614, 615, 619 equivalent neutron ﬂux 442 erosion 480, 570, 573, 574, 577, 584 ESFRI-EU research program 537 estimator – boundary crossing 196, 198 – collision density 197 – ﬂuence 196 – ﬂux at a point 198 – particle ﬂux 190 – statistical 198 – track length 190, 196, 197 euclidian 191 EURISOL project 287, 583, 641 eutectic 524, 555, 564, 565, 568, 569

759

760

Index evaporation 4, 15, 19–23, 55, 57, 88, 90, 91, 98, 100, 102–106, 108, 109, 113–115, 117, 135, 136, 138–140, 142–144, 148, 149, 153–155, 158, 159, 165, 170, 171, 176, 178–182, 184, 189, 191, 212, 279, 282–285, 300, 312, 331, 338, 342, 344, 345, 347, 348, 352, 356, 362, 363, 365, 368, 370, 375, 377, 398, 418, 426 event generator 110, 126, 207–209, 212, 220 excitation function 152, 370 exciton 109, 117, 136 EXFOR 299, 310, 316, 370, 371, 373, 376, 408 exothermal 17, 18 expansion 166, 182, 183, 203, 333, 584 exposure 12, 219, 281, 469, 480, 585

f facility failures 555 fatigue 232, 413, 414, 561 FERFICON experiment 379, 383–386, 388 Fermi – Dirac-gas 65 – gas 65, 68, 69, 74, 111, 112, 138, 139, 145, 155, 161 – momentum 28, 68–70, 74, 283 – sphere 97 fermion 69 ferritic 476 fertile 287, 431, 593, 609, 614 Feynman diagrams 26, 27 FFAG 500, 641 ﬁssility 164, 167, 350 ﬁssion – barrier 137, 149, 164, 166, 168, 172, 173 – cross-section 170, 350, 385 – decay 137, 154, 157, 162 – hindrance 351 – width 157, 158, 172, 173 ﬁssion process 15 ﬂavor 639, 640, 642 ﬂuctuation 40, 169 ﬂuence 195, 196, 236–238, 254, 255, 389, 471, 472 Fokker–Planck equation 169 forces and particles 23 four-momentum 96, 123 fragment separator 373, 374 fragmentation 3, 18, 128, 166, 181, 183, 184, 282–284, 331, 352, 370, 374, 628 freeze-out 181

Frenkel pairs 218, 221 fuel-cycle 594, 603, 606–608, 620 furnaces 588 fusion 147, 207, 216, 219, 231, 251, 257, 471, 506, 553, 583, 584, 594, 620 fusion cycle in stars 13

g gadolinium 334, 336, 338, 391, 543–545 galactic 5, 10–12, 215, 369 galaxy 5 gas production 207, 227, 230, 245, 480, 567 geological repository 593, 594, 601, 605, 607 geometric cross section 142 germanium 488 giant resonance 58, 59 gluon 24, 29 granularity 340 graphite 443, 448, 457, 458, 489, 518, 527, 549, 551, 554 gravitation 645, 649, 665 grooved moderator 441 ground state 68, 74, 138, 140, 144, 152, 155, 164, 165, 167, 168, 183, 298, 585, 646, 650 groundshine 233, 254 GZK-cutoff 650

h hadron 21, 22, 27, 41–44, 57, 58, 63, 64, 75, 89, 105, 110, 121, 124, 186, 209, 236, 267, 333, 334, 425, 428, 482, 548, 623, 631, 634 – therapy 624 hadron cascade 41–43, 75, 191, 195, 658 half-life 57, 144, 410, 489, 600, 601, 610 Hamiltonian 129, 168, 169 handedness 590 hardening 256, 444, 459, 471, 474, 475, 573 harmonics 195 Hauser–Feshbach 159, 176 hazards 207, 602, 669 hazards in space 670 heat capacity 283, 422 heavy-ion 49, 89, 97, 119, 282, 283, 353, 373 Heavyside step function 74 heliosphere 7 helium-bubbles 224, 572, 573 hemisphere 335 high altitude particle rays 5 high power proton accelerators 497, 502 high-energy ﬁssion 20, 23, 139, 148, 166 high-power proton accelerators 598 HINDAS project 159, 369, 606, 607 hodoscope 307 Hofstadter 65, 111, 121

Index hybrid 439, 440, 442, 443, 506, 595, 596, 602 hydrate 447, 452, 461–464, 466 hydrogen 6, 7, 13, 34–36, 41, 75, 76, 88, 186, 215, 224, 227, 229–232, 245, 296, 307, 321, 322, 327, 336, 350, 361, 369, 373, 376, 433–435, 439, 446–448, 450, 453, 461–463, 472, 491, 515, 516, 518, 525, 533, 535, 549, 553, 586–591, 635 hyperﬁne 587, 590, 591 hyperon 554

i ice moderator 436, 447, 460, 461, 466 illumination 508 IMF 145, 152, 162, 181, 182, 282, 284, 340, 344, 348, 352, 354, 355, 365 impact parameter 90, 98, 112, 129 imperfections 616 impurity 488 incineration 506, 593, 595, 605, 608 inclination 586 incorporation 105, 555 indium 422, 482 inelastic 3, 4, 17, 32, 92–95, 122, 123, 127, 251, 274–276, 280, 290, 311, 341, 350, 414, 461, 491, 518, 588, 590, 627, 637, 648 inertia 156, 162, 581 inﬂation 651 ingestion 555, 600, 602 inhalation 555 injector 291, 497, 515, 519, 598, 599 instability 502 insulators 584, 591 inter-nuclear-cascade 391 interference 230, 450, 483 intermediate mass fragments 147, 154, 159, 181, 331, 350, 360, 365 internuclear-cascade 57 interstellar medium 10 interstitials 217, 218 intranuclear-cascade 64, 71, 75, 87, 119, 212, 350 inventory 556–558, 596, 597, 600, 603 inverse cross section 142, 146 ionization 10, 21, 33–35, 37, 39–41, 43, 44, 59, 186, 189, 200, 201, 205, 217, 219, 223, 257, 258, 263, 317, 358–360, 374, 414, 425, 502, 519, 527, 628, 632, 641 irradiation 9, 216, 218, 219, 221, 223, 231, 232, 234, 238, 262, 268, 371, 373, 390, 414, 417–419, 471, 472, 474–479, 483, 484, 506, 510, 520, 555, 567, 568, 574, 578, 581, 583, 584, 603, 624, 626, 629

irradiation softening 474, 475 isobar 27, 58, 76, 78, 110, 111, 321 isobutane 359 isospin 26–28, 30, 95, 96, 98, 113, 124, 128, 130, 140, 142, 590 isotope 53, 180, 345, 348, 359, 368, 369, 372, 373, 377, 509, 519, 583, 586, 591, 600, 610, 614, 619, 620, 640, 669

j Jacobian 105 JESSICA experiment 252, 333, 436, 454–458, 461–463, 465

k kaon 7, 8, 28, 29, 44, 124, 405, 425, 548, 554 KARMEN experiment 61 kerma factor 244, 245 kernels 209, 447, 454, 532, 544 kinematics 63–65, 87, 89, 95, 96, 128, 151, 289, 367, 373, 375 Kox formula 51 Kramers factor 162 krypton 304

l Landau distribution 37, 634 Langevin equation 169 LANSCE 263, 439, 471, 472, 482, 497, 498, 505, 510, 512, 516, 548, 563, 646, 652 Larmor precession 649 lattice 184, 216, 218, 221, 222, 232, 458, 464, 528, 567, 586, 645 LDEF experiment 667, 668 – activation 668 lead–bismuth 142, 524, 568 leakage 15, 242, 254–256, 258, 264–266, 280, 379–381, 397, 403, 404, 407, 419, 422, 423, 432, 435, 436, 439, 443, 488, 545, 565, 576, 609, 610, 633–635 LEAR accelerator 284, 329 Legendre 245, 247 lepton 26, 189 level density 100, 135, 137–142, 145–148, 153, 155, 156, 160–162, 168, 171–173, 176, 180, 351 licensing 249, 530, 555, 581 lifetime 7, 28, 61, 152, 169, 194, 205–207, 250, 272, 435, 471, 505, 518, 542, 553, 565, 573, 578, 581, 584, 585, 590, 601, 618, 619, 643, 647, 648, 650, 651

761

762

Index Lindhard theory 219, 221 liquid drop model 15, 136 liquid PbBi target 565, 610 lithium 54, 305, 363, 583 logarithmic energy decrement 432, 433 long-lived ﬁssion products 600, 601, 603 long-term disposal 593 Lorentz 19, 31, 34, 95, 114, 123, 290 Lorentz-invariant 64 LPTS (long-pulse target station) 525, 527, 530–533, 535, 536 luminosity 273, 565 lunar soil composition 655 LWR 216, 509, 593, 594, 601

m macropulse 291 magnetometer 591 magneton 585, 586 MAMBO experiment 648 Mandelstam variable 95 manganites 522 MANIAC computer 4 Markovian assumption 169 Martian soil composition 660 Martian soil water content 661, 663 mass asymmetry 161 material damage 219, 233, 262, 431 Maxwell–Boltzmann 69, 459 Maxwellian distribution 459 Maxwellian energy range 470 mean free path 32–34, 112, 119, 196, 206, 434 MEGAPIE (MEGAwatt PIlot Experiment) 568 meltdown 620 mercury 252, 263–266, 380, 385, 394, 395, 398, 400, 413–416, 419–423, 454, 466, 491–493, 529, 530, 532, 536, 538, 541, 542, 547, 549, 550, 555–557, 565, 569–581, 583 mesitylene 447–450, 452–454, 461–465, 647 meson 28, 29, 55, 58, 74, 89, 92, 110, 170, 425, 519 metastable 15 metastatic 624 meteorites 10, 281 meteoroids 4 methanol 447, 453 methyl 453 Metropolis algorithm 136 microhardness 473, 474 micropulses 291

minimum ionizing 35, 341, 635 minor actinides 600, 601, 603, 606 model – ABLA 102, 108, 135, 138, 154, 156, 158, 159, 170, 211, 212 – ABRABLA 154, 212 – BERTINI 63–65, 68, 71, 74–80, 82, 84–90, 92, 109–112, 114, 116, 117, 119–121, 123, 124, 152, 153 – BRIC 117, 212 – BURST 154 – BUU 64, 89, 127, 212, 362, 363 – CALOR 65, 88, 139, 211 – CASCADE 121, 162 – Cascade-Exciton 117 – DISCA 212 – DOORS 243 – DORT 243, 245 – Dresner 135, 140–142 – EVAP 135, 139–143, 146, 148, 178 – FLUKA 65, 88, 176, 197, 210–212 – GEANT4 42, 45, 47, 52, 65, 88, 159, 176, 179, 180, 186–188, 197, 202, 204, 205, 210–213 – GEMINI 104, 115, 117, 135, 137, 138, 159, 162–165, 170, 212, 342, 344, 348, 353–355 – GEMJAM 211 – HERMES 65, 88, 159, 179, 190, 202–204, 211, 212, 245, 263, 264, 346, 397–401, 418, 422, 654, 658 – HETC 65, 208 – INC 85, 87, 353 – INCE 230, 343 – INCL 49, 63, 64, 88–98, 100–103, 105, 109–111, 113, 114, 116, 117, 124, 130, 153, 211, 212, 346 – ISABEL 63, 64, 90, 110–114, 116, 117, 123, 151–153, 211, 212 – JQMD 212 – LAHET 45, 65, 88, 110, 135, 139, 142, 144, 148, 153, 173, 179, 346, 479, 480 – LAQGSM 115, 117, 211 – MARS 210–212, 491, 522 – MCNP 212, 251 – MCNPX 65, 88, 110, 139, 153, 159, 176, 179, 197, 210–212, 245, 251–253, 390, 397, 398, 400, 412, 413, 450, 460, 462–464, 489, 493, 494, 532 – NMTC-JAM/PHITS 469 – PHITS 210–212, 643 – QMD (quantum molecular dynamics) 89, 127, 128 – Rutherford-ﬁssion 386 – TIERCE 65, 88, 211

Index – TORT 243, 245 – VEGAS 110–112, 114, 121–123 moderating ratio 434 moderation 193, 252, 263, 270, 432, 434, 444, 595, 596, 643, 646 moderator – ambient 280, 306, 436, 444, 445, 447, 454, 458–461, 466, 491, 516, 517, 522, 530, 533, 535, 536, 543, 545, 547 – cold 252, 333, 444, 446, 450, 455, 521 – cold advanced 454, 531 – ice 436, 447, 460, 461, 466 – nonexplosive 453, 454 moderator technology 276 moderator temperature 435, 446, 462 molecules 453, 461, 466, 508, 587, 588, 590, 591 Moliere scattering 211 momenta 68, 70, 75, 93, 94, 97, 114, 125, 126, 137, 164, 168, 169, 181, 283, 355, 427, 428, 633 Monte Carlo 4, 12, 63–65, 74, 85, 86, 119, 138, 151, 159, 162, 163, 186, 190, 195–199, 208–210, 233, 239, 242–244, 246–249, 251, 252, 255, 269, 298, 338, 339, 341, 368, 386, 389, 390, 396, 398–401, 408, 410, 412, 414, 416–418, 420, 422, 450, 454, 457, 458, 460, 468, 469, 491, 532, 544, 557, 571, 572, 619, 659 moon 4 Moyer model 235, 236, 238, 239, 242, 494 multifragmentation 158, 282 multiplet 27 multiwire 326 muon 5, 21, 24, 25, 34, 41, 43, 44, 288, 497, 518, 519, 549–551, 553, 554, 590, 591, 633, 637, 639, 641, 642 muonium 554, 591 MUSE experiment 607 MYRRHA experiment 583 Møller scattering 59

– lunar neutron probe experiments 654 – multiplicity distributions 334, 339, 340, 397, 400, 404 – performance 276, 447, 450, 453, 455, 529, 532, 535, 553 – production 13, 14, 56, 58, 59, 88, 101, 102, 117, 142, 170, 259–263, 280, 288, 289, 299, 303, 306, 308, 310–312, 316, 318, 319, 334, 341, 343, 371, 380–383, 388, 402, 409, 425, 429, 463, 506, 517, 541, 548, 561, 595, 598, 610–612, 618, 646 – production economy 263, 425, 609 – research with 585 – scattering kernels 209, 454 – temperature 459, 646 – therapy 623, 625, 626 neutron-mirror 650 niobium 482 nitrogen 179, 299, 365 nonelastic 3, 4, 17, 32, 33, 40–42, 44, 45, 47–49, 63, 74–78, 80, 85, 112, 115, 116, 128, 130, 220, 245, 260 nonproliferation 594 nuclear friction 168 nuclear fusion 13 nuclear power plants 431, 607 nuclear safety 554 nuclear waste transmutation (ATW) 561 nucleosynthesis 9, 281, 650 nuclides 10–12, 144, 151, 245, 268, 281, 341, 369, 370, 373–375, 548, 554, 555, 557, 558, 596, 597, 605, 640

o OPAL experiment 508 ORION experiment 264 ortho–para catalyst conversion 451 ortho–para hydrogen mixture 450 ortho–para ratio of hydrogen 444, 450, 451

p n n-body molecular dynamics 127 NESSI 103, 106, 264, 284, 327, 329, 330, 332–335, 337–339, 341–346, 348, 350–352, 355, 356, 362, 367, 368, 380, 385, 390–395, 397, 398, 400, 403, 405, 406, 413, 425, 426 neutrino factory 61, 583 neutrino super/beta beams 638 neutrino-oscillation 641 neutron 303 – depth proﬁle in lunar soil 655–657 – generator 381

pair production 40, 59, 186, 189, 321 para moderator 535 para-hydrogen 447, 450–454 parity 28, 648, 649 Particle Data Group 7, 24, 28, 77, 79, 81, 638 particle properties – baryons 26 – leptons 25 – mesons 29 – quarks 25 particle transport low-earth orbit 665 partitioning 573, 601, 602, 605–607

763

764

Index Pauli blocking 52, 53, 73, 89, 90, 97, 109, 113, 128, 130 Pauli principle 97 PAW program 90 pedestal 633 pellet 13 penetration 5, 143, 145, 191, 243, 258, 627–630 percolation 89, 103, 105, 110, 136, 184 permutation factor 178 PET(positron-electron tomography) 624 phase-diagrams 182 phase-space 184, 193, 253 phase-space occupation 97, 98, 105 phonons 648 photodisintegration 58, 59 photon 23, 40, 58, 59, 178–181, 186, 189, 244, 245, 254–256, 627–629, 635, 650, 659 – lunar surface photon ﬂux 660 – Martian surface gamma-ray lines 661 photonuclear interaction 40 photopion 58 pile-up 338 pion 4, 21, 27–30, 43, 44, 58, 65, 71, 74–86, 88, 110, 111, 121, 124, 186, 205, 209, 260, 264, 280, 283, 288, 318–322, 325–327, 329–331, 425, 428, 548, 590 pion-absorption 28 pion-charge-exchange 30 PISA experiment 327, 329, 330, 332, 355–357, 359–368 pitting 573 plasma 282 plateau area 628 plutonium 510, 581, 593, 594, 605, 606, 616, 619–621 poison 449, 543, 544 poisoning 436, 437, 448, 532, 545, 552 polarization 326, 518, 522, 590, 591 polonium 566 polyethylene moderator 440, 442, 488 polymers 584 positron 23, 59, 60, 472, 590 post-scission 351 postﬁssion 165, 171, 173 postirradiation 471 postsaddle 351 potential – Paris 103 – Skyrme 129 – Woods–Saxon 91, 92 – Yukawa 24

pre-equilibrium 19, 22, 88, 90, 98, 104, 106, 109, 113–115, 117, 127, 128, 136, 279, 285, 331, 338, 344, 345, 347, 348, 352, 413 pre-moderator 647 preﬁssion 173 premoderator 437, 443, 445, 448–450, 452, 453, 544, 553 presaddle 351 prescission 169 primordial 10, 334, 650 proliferation 593, 607 propagation 7, 43, 44, 57, 186, 189–191, 201, 237, 246, 356, 361 protection 185, 207, 234, 238, 241, 249, 369, 414, 481, 503, 554, 555, 557 protein 586 proton driver 497, 499, 519, 640 proton therapy facility 623 pulse width 272, 317, 436, 437, 441, 452, 460, 461, 464, 469, 536, 547, 553, 625

q Q-value 152 QCD theory 186 QED theory 186 quadrupole 156, 179, 320, 515, 540 quark 24, 26–29

r radiation length 39, 44, 59, 60, 186, 632 radiation protection 185, 234, 241, 249, 256, 369, 481, 554 radiation therapy 185, 369, 626, 628 radio-isotopes 603 radioactive 10, 13, 19, 55, 180, 185, 193, 194, 207, 267–269, 280, 281, 373, 377, 431, 506, 557, 558, 561, 567, 568, 583, 585, 593–595, 600, 601, 603–605, 607, 614, 619, 620, 641 radioactivity 13, 199, 209, 254, 257, 262, 267, 268, 280, 281, 373, 379, 420, 516, 536, 547, 555, 556, 561, 565, 616, 637 radiobiology 3 radiography 510, 512 radioisotope production 268, 280 radiology 238 radiolysis 455, 567, 581 radionuclide 555–557, 594–596 radiotherapy 3, 623, 624, 627, 631 radiotoxicity 593, 594, 600–603 range straggling 37, 200 Rayleigh dissipation function 169 reaction probability 395, 397, 398, 426 reactivity 615 recombination 224, 232, 359

Index recycle 603, 605 redundancy 636, 639 refabrication 594 reﬂection 65, 72, 105, 114, 121, 458, 518, 642–644 reﬂectivity 643, 644 reﬂectometer 545, 552 reﬂector 245, 272, 436–441, 444–446, 448, 449, 454–456, 466, 487, 491, 516, 517, 519, 530–533, 535, 541, 543, 547, 550, 552, 565, 571, 611, 612, 618 refraction 65, 72, 112, 114, 121, 127 relativistic kinematics 30 relaxation 115, 117, 158, 169, 354, 530, 591 remnant 181 repository 616 reprocessing 594, 616 research reactors 445, 505–510, 522 residual 20, 23, 24, 42, 87, 88, 98, 115, 117, 121–123, 136–138, 140, 146, 148, 151, 155, 160–162, 165, 170, 177, 178, 181, 209, 267, 280, 350, 361–363, 369, 372–375, 427, 482, 503, 567, 588 residue 108, 352, 374 residuum 103, 151 resolutions 288, 295–297, 518, 634, 637 resonance 16, 28, 29, 58, 76, 78, 80, 92, 95, 97, 124, 141, 152, 208, 432, 459, 591, 604 resonance decay 27 rigidity 374 – cutoff 664 Russian Roulette 251, 253

s saddle point 136, 137, 155, 160–162, 166–168, 284, 351 safeguards 510, 594 sampling 63, 64, 86, 121, 122, 252, 253, 358, 634–638 sandwich 638 scalar 192, 196, 247, 651 scanning electron microscopy (SEM) 478 scintillation 290, 307, 338, 356, 360, 467, 648 scintillator 186, 188, 189, 200, 296, 297, 305–308, 315, 316, 326, 334–336, 338, 360, 380, 391–394, 458, 467, 469, 636, 637, 642 scission 15, 162, 166–169, 284, 350–352 screening 227 secondaries 87, 632 secondary particle production 13, 27, 56, 244, 257, 379, 498, 502

segmentation 632 semiconductor 363 separation 3, 98, 113, 155, 160, 172, 177, 291, 312, 326, 340, 342, 359, 360, 365, 528, 583, 595, 612, 616, 620, 640 septum 333, 516 sequential decay 162 shield 185, 201, 233–241, 246, 248–253, 292, 307, 315, 320, 482, 484, 485, 488–494, 566 shielding calculations 198, 234, 243, 244, 246, 481, 672 shielding experiments 256, 281, 481, 482, 491, 494 short-lived 373, 557, 558, 602 shower 57, 119, 125, 185, 186, 189, 190, 205, 333, 631–635, 637, 638 shutter 531, 647 Sihver formula 50 silicon 340, 341, 356, 360, 363, 391, 509, 637 single-event-upsets (SEU) 671, 673, 674 skyshine 233, 256, 555 slowing down process 432, 434, 627 slowing-down power 433, 434 sodium 610, 615 soil 240–242, 557 solar activity cycle 5, 9 solenoid 326, 519, 637 solubility 603 space missions 281, 653 – Apollo LNPE experiments 654 – charged particles 653 – dose limits 671, 672 – galactic cosmic rays (GCR) 653 – gamma ray Martian surface mapping 658 – Long Duration Exposure Facility (LDEF) 663, 665, 666 – low-earth orbit (LEO) 665 – mars observer 657 – neutrons in lunar soil (LNPE experiments) 654 – planetary gamma-ray spectroscopy 659 – radiation environment 653 – solar particle events (SPE) 653 – trapped radiation 653 spacecraft 281 SPALADIN experiment 367 spallation neutron source targets – liquid metal targets 565, 568, 569, 571, 574, 576 – liquid metal windowless targets 582 – solid targets 562, 566 – target materials 583 – wheel targets 579

765

766

Index spallation neutron sources 4, 55, 101, 185, 207, 215, 216, 232, 233, 242, 250, 257, 261, 263, 267, 269–272, 279, 280, 369, 391, 413, 425, 432, 436, 437, 439, 445, 453, 455, 461, 481, 497, 498, 500–502, 505–507, 509, 510, 555, 561, 565, 569, 585, 588, 595, 597 – AUSTRON 626 – ESS-project-Europe 524 – ISIS-Rutherford Appleton Laboratory 514 – JSNS at the J-PARC complex 548 – MLNSC-LANL 510 – parameter overview 558 – SINQ-PSI 519 – SNS-ORNL 538 spallation reactions 10, 19, 21–23, 58, 64, 109, 114, 115, 127, 129, 130, 139, 154, 159, 165, 178, 181, 187, 188, 209, 211, 212, 215, 220, 221, 225, 227, 282, 283, 319, 342, 344, 355, 370, 429, 482, 505, 553, 636, 659 speciﬁc heat 283, 422 spectator 90, 109, 158, 159 spectrometer 275, 305–307, 310, 319–321, 326, 327, 373, 377, 488, 489, 518, 522, 545, 551, 552, 604, 652 spent reactor fuel 600, 603, 605 spin 24–28, 83, 90, 139, 144, 152, 159, 160, 162, 165, 177, 178, 283, 350, 426, 450, 553, 585, 590, 591, 649 spinodal 183 splitting 15, 163, 166, 167, 170, 184, 251, 253, 564 SPTS (short-pulse target station) 525–527, 530–533, 535, 536, 571 stability 141, 142, 144, 216, 267, 294, 414, 503, 565 standard model 23–25, 638 stockpile 610, 620 stopping power 34, 35, 191, 193, 200, 257, 414, 415 stopping-length 299, 407–409 storage 269, 337, 338, 458, 498–501, 510, 511, 546, 571, 576, 587, 593–595, 601, 603, 605, 642, 643, 646–648 strangeness 26, 554 strata concepts – double strata 605 – single stratum 605 stress 413, 420, 475, 476, 530, 561, 565, 572, 573, 583, 584 stress–strain curves 476 strong force 24, 25, 78, 186, 649 sub-thermal 208, 270

subcritical 594, 596, 598, 602, 603, 608, 609, 613, 615, 617–619 subthermal 432 super-beam 639 Super-Kamiokande experiment 554 superbeam 640–642 supercritical 543, 547, 549, 550, 553 superﬂuid 155, 645, 648 supernova 10 superthermal transport theory 434 survival probability 395, 396 susceptibility 587 sustainability 607 symmetry 96, 129, 156, 190, 565, 590, 648, 649 synchrotron 233, 243, 269, 288, 304, 312, 327, 332, 373, 379, 380, 390, 407, 454, 456, 488, 497–499, 501–503, 506, 515, 516, 519, 548–550, 553, 554, 558, 559, 613, 623, 625, 626, 631

t tailoring 447 tallies 197, 210 tandem 549 tantalum 220, 226, 227, 264–266, 385, 471, 472, 487, 488, 491, 516, 564, 584 TARC experiment 604, 605 target heating 257, 266, 562, 598 target wheel 266, 440, 564, 567, 579–582 target–moderator–reﬂector 252, 258, 270, 272, 431, 432, 436–439, 440, 445, 446,448, 455–457, 466, 469, 484, 491, 521, 523, 532, 541, 543, 544, 550 technetium 601 teﬂon 411 telescopes 308, 340, 341, 345, 360, 363 tensile test 476, 477 tensor 169, 651 ternary 171 terrestrial 10, 13 tertiary 217 therapy facilities 623, 625, 626 thermal neutron ﬁeld 440 thermalization 336, 338, 432, 437 thermocouple 421 thermoluminescence 414 thick target experiments 299, 381, 403, 407 thick target neutron multiplicity 390 thorium 20, 327, 350, 380, 384, 385, 387, 593, 594, 613, 616, 619–621 thorium-uranium cycle 607 three-point bending 472–475

Index threshold-foil technique 482 time-of-ﬂight 263, 273, 274, 289–296, 298, 299, 303, 305–310, 312, 315, 317, 326, 356, 360, 374, 380, 381, 393, 403, 407, 408, 438, 441, 447, 457–460, 465, 467–469, 508, 513, 518, 522 titanium 13, 158, 373 TLD detectors 414 toroidal 211, 212 total neutron yields 380 toxicity 555, 558, 604, 619 tracers 605 track 195, 197, 359, 360, 403, 626–628, 633 track-length 190, 191, 196, 197 trajectories 109, 307, 572, 573, 649 transient time 157, 168, 351 transmission coefﬁcients 137, 138, 160 transmission electron microscopy (TEM) 472, 478 transparency 50, 52, 53, 86 transport code systems 197, 208–210, 391 transport equation 191, 192, 195, 243 transport in matter 12, 23, 185, 191, 205, 234 transuranium 600, 601, 603–605, 608, 619 Tripathi formula 52 triplet 651 TRISPAL project 609, 610 triton 90, 103, 110, 143, 348, 363 tumor 624, 626–630 tungsten 20, 21, 45, 215, 220, 224–227, 258, 260, 263–266, 358, 380, 385, 394, 395, 398, 400, 482–484, 506, 511, 512, 516, 517, 563–565, 581, 584, 611, 612, 646

uranium 13–15, 20, 41, 44, 47, 165, 220, 258, 259, 267, 268, 295, 300, 303, 350, 376, 380, 384–387, 509, 516, 555, 564, 581, 584, 586, 593, 602–607, 610, 613, 614, 616, 618, 619, 621, 635–638

v vacancies 217, 218 Van Allen radiation belts 664 Van-der-Waals gas 282 vanadium 382 vaporization 136, 181, 182, 282, 284, 352–355 vertex 26, 123 vibrations 586 Vickers hardness 473 violation – CP 61, 548, 639, 640, 649 – Pauli principle 113 viscosity 162, 168, 283, 284 volatility 555

w water-bath experiment 382, 389 wavelength 183, 273, 274, 446, 449, 450, 457–460, 464, 465, 467, 518, 532, 535, 546, 588, 643 weight window 251–253 Wellish formula 45 WNR 55, 290, 291, 295–299, 303, 385, 437, 438, 481, 482, 505, 510, 511

x XADS experimental accelerator

597, 598

u UCN (ultracold neutrons) 642 ultra-cold 436, 642, 646, 647 ultra-heavy 10 unitarity 651 up-scattering 193 upscattering 645

y YBCO superconducting ceramic

z zircaloy 521 zirconium 482

587

767