Advances in Electronics and Electron Phisics. Vol. 53

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 53

CONTRIBUTORS TO THIS VOLUME

P. W. Baier P. H. Dawson H . Frohlich Ming Chiang Li D. B. McDermott T. C. Marshall M. Pandit S. P. Schlesinger Alan J. Toepfer

Advances in

Electronics and Electron Physics EDITEDBY L. MARTON AND C. MARTON Smithsonian Institution Washingfon, D.C.

EDITORIAL BOARD E. R. Piore T. E. Allibone M. Ponte H. B. G. Casimir W. G. Dow A. Rose L. P. Smith A. 0. C. Nier F. K. Willenbrock

VOLUME 53 1980

ACADEMIC PRESS A Subsidiary of Harcourt Brace Jovanovich, Publishers

New York London Toronto Sydney San Francisco

COPYRIGHT @ 1980, BY ACADEMIC PRESS,INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY B E REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM T HE PUBLISHER.

ACADEMIC PRESS, INC.

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United Kingdom Edifiori published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London N W l 7DX

LIBRARY OF CONGRESS CATALOG CARD NUMBER:49-7504 ISBN 0-12-014653-3 PRINTED IN TH E UNITED STATES OF AMERICA

80 81 82 83

9 8 7 6 5 4 3 2 1

CONTENTS CONTRIBUTORS TO VOLUME53 FOREWORD. . . . . .

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vii ix

Particle Beam Fusion ALANJ . TOEPFER

I . Introduction . . . . . . . . . . . I1. Power Flow and Energy Requirements for ICF I11. Particle Beam Generators for ICF . . . . IV . Power Flow in Vacuum . . . . . . . . V . Particle Beam Formation and Focusing . . . VI . The Light Ion Beam Option . . . . . . VII . Intense Beam Interaction with ICF Targets . VIII . Summary . . . . . . . . . . . . References . . . . . . . . . . .

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1 2 8 21 26 33 37 42 43

The Free-Electron Laser: A High-Power Submillimeter Radiation Source T . C . MARSHALL. S . P . SCHLESINGER. A N D D . B . MCDERMOTT

I . Scattering from Relativistic Electron Beams . . . . I1. Properties of Pulsed Intense Relativistic Electron Beams 111. Theory of Stimulated Scattering . . . . . . . . IV . Experimental Methods. Devices. and Results . . . . References . . . . . . . . . . . . . .

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48 57

59 67 82

The Biological Effects of Microwaves and Related Questions H . FROHLICH

. . . . . I11. Theory . . . . IV . Consequences . V . Experiments . . VI . Conclusions . . References . . I . Introduction

I1. General

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Ion Optical Properties of Quadrupole Mass Filters P. H . DAWSON I . Introduction . . . . . . . . . . . . . . I1. Ion Motion in the Quadrupole . . . . . . . . . I11. Outline of Ion Optical Techniques . . . . . . . v

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. 85 . 87 . 92 . 104 . 121 . 148 . 150

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153 155 161

vi

CONTENTS

IV . Source Characterization . . . . . . . . . . . . . V . Methods of Calculation . . . . . . . . . . . . . . VI . The Normal Quadrupole Mass Filter . . . . . . . . . . VII . Distorted Quadrupole Fields . . . . . . . . . . . . VIII . The Higher Zone of Stability . . . . . . . . . . . . IX . The RF-Only Quadrupole . . . . . . . . . . . . . X . Imaging Properties . . . . . . . . . . . . . . . XI . Conclusions . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . .

165 166 173 193 201 202 205 206 207

Spread Spectrum Communication Systems

P. W . BAIERAND M . PANDIT I . Introduction . . . . . . . . . . . . . . . . . 209 I1. Basic Spread Spectrum Techniques . . . . . . . . . . 214 111. Implementation of Spread Spectrum Communication Systems . . 226 IV . An Alternative Approach to Spread Spectrum Signaling . . . . 254 256 V . Limits of Spread Spectrum Techniques . . . . . . . . . VI . Examples of Realized Spread Spectrum Communication Systems . 263 References . . . . . . . . . . . . . . . . . 266 Electron Interference MING CHIANCLI

I . Introduction . . . . I1. Electron Wave . . . I11. Crystal Diffraction . . IV . Two-Beam Interference V . Interference Experiments VI . Proposed Experiments . VII . Discussion . . . . References . . . . AUTHORINDEX . SUBJECTINDEX .

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269 271 274 281 289 294 303 304

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CONTRIBUTORS TO VOLUME 53 Numbers in parentheses indicate the pages on which the authors’ contributions begin.

P. W. BAIER,Universitat Kaiserslautern, Fachbereich Elektrotechnik, Kaiserslautern D-6750, West Germany (209) P. H. DAWSON, Division of Physics, National Research Council of Canada, Ottawa K1A OR6, Canada (153) H. FROHLICH,Department of Physics, University of Liverpool, Liverpool L69 3BX, England (85) MINGCHIANGLI, Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 (269) D. B. MCDERMOTT, Plasma Laboratory, Columbia University, New York, New York 10027 (47) T. C. MARSHALL, Plasma Laboratory, Columbia University, New York, New York 10027 (47)

M. PANDIT,Universitat Kaiserslautern, Fachbereich Elektrotechnik, Kaiserslautern D-6750, West Germany (209) S. P. SCHLESINGER, Plasma Laboratory, Columbia University, New York, New York 10027 (47)

ALAN J. TOEPFER,Physics International Company, San Leandro, California 94577 (1)

vii

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FOREWORD While the contributions in this volume are not necessarily related to each other, four have a common thread in their concern with beam technology. This interesting tie is found in the articles on fusion, submillimeter lasers, quadrupole mass filters, and electron interference phenomena. Hence, the reader is provided with a good overview of the application of beams in contemporary technology. Given the interest in this subject by the public media as well as regulatory agencies, the contribution on the biological effects of microwaves is most timely. The remaining contribution on spread spectrum communication systems covers yet another subject of great current interest, given the search for solutions to the problems caused by the ever-increasing growth of information transmission and dissemination systems. We thank all of the authors for their excellent contributions. As is our custom, we include here a list of articles to appear in future volumes.

Critical Re\iews: A Review of Application of Superconductivity Sonar Electron-Beam-Controlled Lasers Amorphous Semiconductors Design Automation of Digital Systems, 1 and I1 Spin Effects in Electron- Atom Collision Processes Review of Hydromagnetic Shocks and Waves Seeing with Sound Large Molecules in Space Recent Advances and Basic Studies of Photoemitters Josephson Effect Electronics Present Stage of High Voltage Electron Microscopy Noise Fluctuations in Semiconductor Laser and LED Light Sources X-Ray Laser Research The Impact of integrated Electronics in Medicine Electron Storage Rings Radiation Damage in Semiconductors Solid-state Imaging Devices Spectroscopy of Electrons from High Energy Atomic Collisions Solid Surfaces Analysis ix

W. B. Fowler F. N. Spiess C. A. Cason H. Scher and G. Pfister W. G. Magnuson and Robert J. Smith H. Kleinpoppen A. Jaumotte and Hirsch A. F. Brown M. and G. Winnewisser H. Timan M. Nisenoff B. Jouffrey H. Melchior C. A. Cason and M. Scully J. D. Meindl D. Trines N. D. Wilsey and J. W . Corbett E. H. Snow D. Berenyi M. H. Higatsberger

X

FOREWORD

Surface Analysis Using Charged Particle Beams Sputtering Photovoltaic Effect Electron Irradiation Effect in MOS Systems

Light Valve Technology High Power Lasers Visualization of Single Heavy Atoms with the Electron Microscope Spin-Polarized Low-Energy Electron Scattering Defect Centers in 111-V Semiconductors Atomic Frequency Standards Reliability Microwave Imaging of Subsurface Features Electron Scattering and Nuclear Structure Electrical Structure of the Middle Atmosphere Microwave Superconducting Electronics Biomedical Engineering Using Microwaves, I1 Computer Microscopy Collisional Detachment of Negative Ions International Landing Systems for Aircraft Impact of Ion Implantation on Very Large Scale Integration Ultrasensitive Detection Physics and Techniques of Magnetic Bubble Devices Radioastronomy in Millimeter Wavelengths Energy Losses in Electron Microscopy Long-Life High-Current-Density Cathodes Interactions of Measurement Principles Low Energy Atomic Beam Spectroscopy History of Photoelectricity Fiber Optic Communications Electron Microscopy of Thin Films

F. P. Viehbock and F. Riidenauer G. H. Wehner R. H. Bube J. N. Churchill, F. E. Holmstrom, and T. W. Collins J. Grinberg V. N. Smiley

J. S. Wall D. T. Pierce and R. J. Celotta J. Schneider and V. Kaufmann C. Audoin H. Wilde A. P. Anderson G . A. Peterson L. C. Hale R. Adde M. Gautherie and A. Priou E. M. Glasser R. L. Champion H. W. Redlien and R. J. Kelly H. Ryssel K. H. Purser M. H. Kryder E-. J. Blum B. Jouffrey R. T. Longo W. G. Wolber E. M. Horl and E . Semerad W. E. Spicer G . Siege1 M. P. Shaw

Supplementary Volumes:

Applied Charged Particle Optics Microwave Field Effect Transistors Volume 54: Magnetic Reconnection Experiments Electron Physics in Device Fabrication, I1 Solar Physics Aspects of Resonant Multiphoton Processes

Fundamentals and Applications of Auger Electron Spectroscopy

A. Septier J. Frey

P. J. Baum and A. Bratenahl P. R. Thornton L. E. Cram A. T. Georges and P. Lambropoulos P. H. Holloway

FOREWORD Volume 55: Photodiodes for Optical Communication Microwave Systems for Industrial Measurements Cyclotron Resonance Devices Heavy Doping Effects in Silicon

Photodetachment and Photodissociation of Ions

xi J. Miiller W. Schilz and B. Schiek R. S . Symons and H. R. Jory R. P. Mertens, R. J. Van Overstraeten, and H. J. De Man T. M. Miller

As in the past, we have enjoyed the friendly cooperation and advice of many friends and colleagues. Our heartfelt thanks go to them, since without their help it would have been almost impossible to issue a volume such as the present one.

L. MARTON C. MARTON

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ADVANCES I N ELECTRONICS A N D ELECTRON PHYSICS,

VOL. 53

Particle Beam Fusion ALAN J. TOEPFER Physics International Company San Leandro, California

......................

I. Introduction 11. Power Flow 111. Particle Bea

1

VIII. Summary. . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This work is dedicated to J . C. Martin and T. H . Martin. Without their genius and innovation in pulsed-power technology, particle beam fusion could not have come into existence.

I . INTRODUCTION

One of the most serious problems facing mankind in the twentieth century is the need for an abundant, inexhaustible source of energy. A second and equally serious problem is the threat of a worldwide cataclysm brought about by the development of thermonuclear weapons with tremendous explosive power. It is a paradox then that a possible solution to man’s energy problems may spring from the very technology that was developed as part of nuclear weapons research. This energy source is inertial confinement fusion (ICF), and the technology is pulsed-power technology. The realization of inertial confinement fusion involves the ignition of a thermonuclear reaction wave in DT gas. This process requires the delivery of substantial amounts of energy to the fuel so that the reaction can be initiated and propagate before the fuel disassembles. The possibility of using intense beams of charged particles for driving an inertially confined 1 Copyright 0 1980 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-014653-3

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ALAN J. TOEPFER

mass of DT was recognized as early as 1963 by A. John Gale of High Voltage Engineering Corporation and 1964 by Donald Maxwell, then at Physics International Company. Because this work was highly classified at the time it was not published in the open literature although a patent was awarded to Gale on the concept. In 1968, F. Winterberg (1968a, b; 1971) independently proposed the use of electron beams from a pulsed highintensity field emission discharge to drive a small mass of DT fuel to ignition. The technological advance that led to these proposals was the development of pulsed-power generators capable of accelerating high-current beams of electrons for the production of intense bursts of X rays to simulate nuclear weapons effects in the laboratory. Pioneering work in this area was carried out in Great Britain by J. C. Martin and his colleagues at the Atomic Weapon Research Establishment, Aldermaston, and in the United States at Physics International, San Leandro, California; Ion Physics Corporation, Burlington, Massachusetts; and Sandia Laboratories, Albuquerque, New Mexico. At the same time, work was being carried out in the United States and the Soviet Union aimed at the use of high-power pulsed lasers to heat DT plasmas to fusion temperatures (Kidder, 1971; Krokhin, 1971). Since this early work, programs directed toward the use of intense particle beams have grown in the United States (Yonas et al., 1974) and the Soviet Union (Rudakov and Samarsky, 1973). The purpose of this chapter is to review the current status of particle beam fusion research with high-current electron and light ion beams. Since particle beam fusion research is a rapidly evolving field, there is always the chance that a new discovery or breakthrough may considerably reduce the significance of all earlier work. In that event, this chapter may be of more interest to the historian of science as the viewpoint of one of the original workers in the field. REQUIREMENTS FOR ICF 11. POWERFLOW A N D ENERGY In order to put the problem of particle-beam-driven ICF in perspective, it is useful to consider the levels of energy, power, and power flux necessary to initiate burn in an inertially confined plasma. The energy released through the DT fusion reaction

D

+ T + 4He (3.5 MeV) + n (14.1 MeV)

(1) amounts to 3.5 x 10" J/g. However, because of depletion of the reactants, not all the fuel is consumed in a thermonuclear burn. The reaction wave propagates due to absorption of energy from the 3.5-MeV a: par-

PARTICLE BEAM FUSION

3

ticles, which have a range of 0.3 g/cm2 in DT fuel at ignition temperature (20 keV). The bum fraction C#J depends on the areal density of the fuel and may be written (Nuckolls, 1974)

4

= pfRf/(HB

+ hRf)

(2)

where pf(Rf) is the fuel mass density (radius) and HBthe fuel depletion parameter. At 20 keV, HB = 6-7 g/cm2. Thus, a fuel mass with pfRt in the range 3-3.5 g/cm2 will have a theoretical burn efficiency off and yield -10" J/g thermonuclear energy. At the density of liquid DT (0.225 g/cm3), pfRr = 3 g/cm2 corresponds to a sphere with radius 13 cm and mass 2.2 kg. To heat such a mass of DT to ignition temperature would require 1013 J, delivered in a time

-

where y = 5/3 and T, is the characteristic time for a rarefaction wave to propagate into the fuel. These requirements (1013 J, lozoW) are well above the energy and power levels achievable in the laboratory using lasers or particle beams. The yield from such a reaction (- 1014 J) is equal to about 50 kilotons of high explosive. The central problem of ICF is to reduce the mass of fuel required for efficient burn and to reduce the energy and power required to bring the fuel to ignition. A solution proposed by Nuckolls ef al. (1972) is to compress the fuel to a density very much higher than solid (= 1000 g/cm3) in an isentropic manner, such that a small central region of the fuel with psRs = 0.3 g/cm2 is heated to ignition during the final stages of compression. The theoretical minimum energy required to compress DT fuel to a given density corresponds to the Fermi energy of the electrons. At 1000 g/cm3, this energy is 3 x lo7 J/g. The energy required to heat the central region of fuel with pR = 0.3 g/cm2 corresponding to a mass Ms = lob3Mf to ignition is about equal to the Fermi energy. Hence, using the principle of isentropic compression leads to a lower bound of - 6 x lo7 J/g absorbed in the fuel for ignition at 1000 g/cm3. Isentropic compression requires temporal shaping of the driver pulse. The pulse shape must have the characteristics that the implosion velocity of the piston working in the fuel increases from 1 to > 30 cm/psec. This results in coalescence of the hydrodynamic characteristics in the central region of the target during the final stages of implosion. The exact pulse shape is very sensitive to the details of pellet design and these considerations are beyond the scope of this chapter; however, power absorbed by the pellet characteristically increases by several orders of magnitude toward the end of the implosion. Peak power levels are of order 1015W

-

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ALAN J. TOEPFER

with fluxes I10lg W/cm2, and total energies are a few hundred kilojoules. Recent work indicates that for electron beams, pulse shaping has a negligible effect on power and energy required for breakeven because of fuel preheat by bremsstrahlung. For these designs specific energies of 4-5 x 1O'O J/gm were required for breakeven (Sweeney and Clauser, 1977). With light (or heavy) ions it may be possible to use bunching to achieve pulse shaping. The requirements cited above are for power and energy absorbed by the fuel in the target. As pointed out by Kidder (1976), only a few percent eLFof the absorbed driver energy is converted to internal energy of the compressed fuel (typically 5%). If ec is the ratio of the work required to compress the fuel isentropically at minimum energy to the driver energy absorbed by the pellet, then the minimum absorbed driver energy required to achieve a pellet gain G, is W,*

(4)

G,12~S~B915~LF-2/5e~3

and W,* = 6 x los J/g for G, = 200, ELF = 0.05, and eG = 0.02-0.04. We see from the above examples that the specific energy requirement for ignition of DT burn in an isentropically compressed spherical fuel mass, using the concept of central ignition and propagation burn, is z lo* J/g DT. Recent work by Nuckolls et al. (1977) considering hollow targets has resulted in designs that achieve bum at a specific energy of 2 x lo7 J/g, the theoretical minimum at densities of 600 g/cm3.

0.01

0.1

INITIAL DENSITY, g ~ c m 3

(a)

1.0 INITIAL DENSITY, g/crn'

(b)

FIG.1 . Ignition and failure regions in initial-temperature, initial-density phase space. Failure to ignite occurs in shaded regions. Initial implosion velocities are (a) 10 cm/psec and (b) 8.5 cm/psec (after Kirkpatrick, 1979).

PARTICLE BEAM FUSION

5

LOW DENSITY, PREHEATED DT GAS

MAGNETIC FIELD, B,

FROZEN DT LAYER

FIG.2. Magnetically insulated target.

An approach conceptually opposite to isentropic compression was studied by Kirkpatrick (1979), who considered the compression of spatially homogeneous, but nonequilibrium, DT by a piston (pusher) using a 12-parameter bum code. These calculations included radiation losses from the fuel into the pusher. Phase space plots of fuel temperature and density were made for various initial pusher velocities, and regions of initial density and temperature were defined that led to ignition for a given initial pusher velocity (Fig. 1). A major result of this work was to identify an island in phase space for very low initial pusher velocities ( 28.4 cm/psec) where ignition was calculated to occur (Wheeler mode). For these targets, preheat of the fuel implies higher specific energy requirements, lower final densities, and larger fuel masses than in an isen-

6

ALAN J. TOEPFER

tropic compression; however, the reduction of pusher velocity to less than 10 cmlpsec will possibly reduce power flux requirements to the target. Two methods that have been studied for reducing power requirements for ignition of ICF targets are: (1) to increase the acceptance time by using colliding shells to obtain velocity multiplication; and (2) to utilize magnetic fields in the fuel to reduce electron thermal conduction losses to the walls. Multiple-shell designs result in somewhat lower power requirements (- lOI4 W), but because they are hydrodynamically inefficient, specific energies of order 1O’O J/gm DT were required (Kirkpatrick et al., 1975). Because one of the main problems with existing particle beam sources is power flow rather than total energy, multiple-shell velocity multiplication targets may be well suited to this type of driver. Magnetically insulated targets (Fig. 2) usually employ preheat of the fuel, which has the effect of placing the fuel on a higher adiabat so that higher temperatures are attained by compression with a lower-velocity 1,000

-

I

I

I

I

’

“ ‘ I

I

I

I

I

1

! ‘ ‘ I

3

DEPOSITED POWER.,TW

FIG. 3. Thermonuclear yield vs. deposited power for proposed electron- and iondriven targets, compared with single-shell “conventional” targets (after Yonas, 1978).

7

PARTICLE BEAM FUSION

pusher (Chang et al., 1977; Bangerter and Meeker, 1977). A magnetic field in the fuel, which is either externally produced or caused by circulating currents in the fuel itself, serves to inhibit electron thermal conduction losses to the pusher. Radiative losses limit the fuel density and pR of these targets. This has the effect of reducing the power required by the target by almost an order of magnitude, but limiting the burn efficiency so that the “simple” magnetic target configurations are limited to low gains (- 1-3). By surrounding the low-density, magnetically insulated fuel with a high-density layer of frozen DT, it is possible to use the middle region as a central igniter and propagate a DT burn into the higher density fuel. The magnetically insulated target is similar in concept to the compression of a 2 pinch by an imploding liner (Lindemuth and Jarboe, 1978). Figure 3 plots thermonuclear yield vs. deposited power for proposed electron- and ion-driven targets that are magnetically insulated, compared with single- (but possibly multilayered) shell “conventional” targets (Yonas, 1978). Two conclusions can be drawn. First, it is clear that for both electron- and ion-driven targets, the power requirement for the magnetically insulated target is about a factor of five lower than for the conventional target. Second, ion-driven targets require less absorbed power because of the preheat of the pusher due to bremsstrahlung in the electron-driven target. From Fig. 3 it can be seen that the lowest power required for breakeven is 220 TW and the specific energy is -2.5 x log J/g DT. Table I lists specific energy and peak power requirements for ICF targets driven by electron and ion beams compared with those quoted for isentropic compression using lasers. In all cases, ion targets have a factor of 4-5 lower power requirement than electron-driven targets. This result TABLE I SPECIFIC ENERGYAND

REQUIREMENTS FOR ICF TARGETS BURNEFFICIENCY 4

POWER

WITH

Target

4

Isentropic compression Conventional ion Conventional electron Shaped-pulse electron Velocity multiplication, ion Velocity multiplication, electron Magnetic central igniter, ion Magnetic central igniter, electron

0.3-0.4 0.5

0.6 0.15 0.5 0.4 0.5 0.3

Specific energy (J/g of DT)

Power (TW

108 5 x 10’0 2.5 x 1O1O 5 x 1010 5 x 10’0 1.5 X 10” 2 x 100 1 x 10’0

100 260 1000 192 (max) 50 250 50 270

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ALAN J. TOEPFER

is basically due to preheat of the pusher by bremsstrahlung in the electron targets. Power requirements are reduced by a factor of 4-5 in velocity multiplication and magnetic targets as compared with conventional electron and ion single-shell targets driven with unshaped pulses. Lowest overall power requirements are for ion-driven targets. Specific energy requirements are reduced for magnetically insulated central igniter targets. Power requirements for electron beam targets employing shaped pulses are comparable to those for velocity multiplication and magnetically insulated targets. For all the particle beam targets, specific energy requirements are about two orders of magnitude higher than those for the most optimistic laser design employing isentropic compression. The radius of particle-beam-driven targets is limited, at least in the case of electrons, to a few millimeters because of limitations on beam focusing and electron range. For ion targets, beam-focusing limits also appear to be of order 1-2 mm. For 10-20 cm/psec implosion velocities required for breakeven, this places a range of 5-50 nsec on beam pulse lengths, corresponding to a few megajoules of beam energy at the 100-TW power level. Power flux requirements are in the range of 1014W/cm2 absorbed in the target. This corresponds to 100 MA/cmZcurrent density for 1-MeV electrons and 10 MA/cm2 current density for 10-MeV protons, which have similar stopping powers in high-2 materials. The next sections discuss the state of the art of pulsed-power technology as compared to the target requirements, and describe the approaches currently envisioned for meeting these requirements. 111. PARTICLE BEAMGENERATORS

FOR

ICF

High-voltage pulse technology for the production of high-current electron and light ion beams has developed over the past 20 years. This technology is to be distinguished from that associated with the particle accelerators of high-energy physics operating in the giga-electron-volt range. The largest existing high-current electron beam generator is the AURORA accelerator, which is capable of producing four 400-kA, 14-MeV electron beams with a pulse length of about 120 nsec (Bernstein and Smith, 1973). Because of its high voltage, this accelerator is not suitable for electron-driven fusion applications, but may be useful for light ion-driven fusion. Other high-current electron accelerators capable of delivering 5-10 TW to a matched load at 1-2 MV have been constructed and are currently being utilized for electron beam, ion beam, and imploding plasma research. The technology of these accelerators has been discussed by the author in previous review articles (Yonas and Toepfer,

PARTICLE BEAM FUSION

9

FIG.4. Sandia Laboratories PBFA-I accelerator (after Martin er a / . , 1977).

1978; Toepfer, 1980) and in the collected notes of J. C. Martin (Martin et al., 1965-1970). The following paragraphs examine some of the design features of two generators currently under construction for particle beam fusion applications-the PBFA accelerator at Sandia Laboratories, Albuquerque, New Mexico, developed by T. H. Martin and his group (Fig. 4), and the ANGARA-V accelerator, now under construction at the Efremov Institute, Leningrad, by 0. P. Pechursky and collaborators, and to be put into operation at the I. V. Kurchatov Institute, Moscow, under the supervision of L. I. Rudakov (Fig. s).* The PBFA and ANGARA generators consist of the same basic building blocks but differ considerably in detailed design features. The designs themselves are evolving, and it is neither possible nor desirable to discuss all these features in detail, since details of switches, pulse-forming networks, diodes, etc., are sure to change in the future. In fact, PBFA-I, which started out initially as a 36-TW electron beam generator (Martin rt al., 1977), is now being converted to accelerate light ions at a somewhat lower power. A further modification, PBFA-11, is planned at the 60-280 TW level. The ANGARA-V accelerator (Velikhov et al., 1976),

* Details of the ANGARA-V accelerator given here were obtained through private discussions with members of the Efremov and Kurchatov Institutes and are not generally available in the published literature. Details of PBFA-I were taken from published reports and articles by the Sandia group.

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ALAN J. TOEPFER

FIG.5 . I. V. Kurchatov Institute/D. V. Efremov Institute ANGARA-V accelerator (after Velikhov ef al., 1976).

which was originally designed to produce 48 2-TW electron beams, is being considered as a possible low-impedance current generator for an electromagnetically driven imploding liner in another approach to ICF. These changes of program direction have been influenced on the one hand by realization of fundamental difficulties involved in focusing and combining intense relativistic electron beams above 10-TW/cm2 flux densities, and on the other hand by realization of the penalties paid in target design due to preheat of the pusher by bremsstrahlung produced in the electron beam -target interaction. Both PBFA and ANGARA-V are modular accelerators, with modules operating in parallel, and each module having the basic components illustrated in Fig. 6. In each stage, the efficiency of energy transfer is characterized by a subscripted parameter E . In both designs, the primary energy store is an oil-insulated Marx generator.* The basic Marx generator concept is shown in Fig. 7, which illustrates a two-stage voltage-multiplying network. The capacitors are charged in parallel through the charging resistors to a voltage V. GI is a switch, typically a gas-insulated spark gap, which is triggered by an external voltage pulse (trigger electrodes and circuitry are not shown). When gap G , is fired, its resistance drops to almost zero and the positive

* The first large oil-insulated multimegavolt Man generators were constructed at Physics International by D. F. Martin, D. Sloan, and B. Bernstein in 1964-1965.

r

.

r

GENE RATOR

PULSEFORMING NETWORK

VACUUM TRANSMISSION LINE

Oil-insulated capacitive energy store

Water-insulated with gas and/or water switches

Magnetically insulated

EWV

- LOAD

Electron beam Ion beam Imploding liner

FIG.6 . Block diagram for a particle beam fusion driver.

TARGET

‘BT

Beam combination or electromagnetic energy accumulation

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ALAN J. TOEPFER

-

FIG.7. A basic Marx circuit.

electrode of C , drops t o a potential near ground. The negative electrode of C1drops to - V, overvolting the gap G , , which breaks down. In this way the negative terminal of C, drops to a voltage - 2V and the generator discharges through the load R L . For N stages, with N capacitors charged in parallel to a voltage V, the magnitude of the output voltage of the Marx generator is NV. Nominal parameters of the PBFA-I and ANGARA-V Marx generators are given in Table 11. The PBFA-I Marx generator consists of 36 modules, each module consisting of four rows of eight 0.7-pF, 100-kV capacitors arranged in a configuration similar to that of Fig. 8a. Each module has 16 midplane triggered SF-6 spark gap switches. When positively or negatively charged to 100 kV, I10 kJ per module is stored. The output voltage rises t o 3.2 MV in 750 nsec into a 15-nF load. The Marx erection time is 300 f 3 nsec. A computer-generated equivalent circuit is given in Fig. 8b. The output inductance of the Marx generator is 6.7 pH. In comparison, the Hermes I1 18-MV Marx generator, which stores 1 MJ at 103 kV charge, has an output inductance 4 0 pH. The prototype of the ANGARA-V Marx module configuration, as determined through discussions with Efremov personnel in 1967, is shown in Fig. 9. Forty-eight of these or similar modules will form the ANGARA-V accelerator complex. Either oil or gas (up to 10 atm N, with COz and SFs) is the insulating medium. The total energy stored in each module when positively or negatively charged to 100 kV is -330 kJ. The TABLE I1 PBFA-I

AND

ANGARA-V MARXGENERATOR PARAMETERS PBFA-I

Number of modules Stored energy/module (kJ) Output voltage (MV) Run time (psec) Pulse capacitance (nF) Inductance ( p H )

36 110

3.2 0.75 22 6.7

ANGARA-V 48 330 2.8
13

PARTICLE BEAM FUSION

"I" BEAM RAIL,

CAPACITORS

TANK FLOOR MARX ROW

I

I

J 2 2 TF L M ~ R= ~6 . 7 ~ ~ CMARX

RSERIES= 30 fi R ~ H U N T= 560a (b)

FIG.8. PBFA-I Marx generator configuration and equivalent circuit.

output voltage is 2.8 MV and the Marx inductance was quoted as 4.0 pH. The switches were stated to be three-channel spark gaps with the working gas circulating through the switches under pressure. The energy transfer time to the pulse-forming network (PFN) was stated to be -1 psec with a jitter of -100 nsec. The Marx generator charges a PFN that is water insulated. The PFN

Screen for grading Tank thick enough for 10 atm operation

Epoxy or organic glass

Water Blumlein 10 switches 20 nsec risetime 150 k V trigger pulse 5 nsec total spread

Stainless Steel H,O coax strips of stainless connecting two tori for simplicity

3 levels of capacitors 2rH 300 kJ (9 f 100 k V Max 200 kJ (9 5 80 k V Typ 1 Psec transfer time to Blumleln

Initial insulator stacked, Final verston

(turbo pumps)

FIG.9. ANGARA-V prototype module (1967).

PARTICLE BEAM FUSION

15

consists of two or more stages connected by a number of low-inductance switches in parallel. Common geometries for PFNs are coaxial and parallel plate. The Blurnlein is essentially two transmission lines (coaxial or parallel plate) charged in parallel and discharged in series. An important requirement of modular designs such as the accelerators under consideration is the ability to switch energy from the Marx to the PFN and from the PFN to the output transmission lines with low jitter. For the 45-60 nsec fullwidth at half-maximum (FWHM) pulse lengths appropriate for the ICF application, a single-module jitter 5 5 nsec for switching energy out of the PFN is required. The PFNs are charged on a timescale of 0.75-1.0 psec and thus the jitter in Marx risetime can be quite a bit larger. The key to simultaneity in both PBFA and ANGARA-V is therefore the PFN switching. In PBFA there are three stages of switches. The first stage of the PFN is a 19.5 nF coaxial water capacitor, which is resonantly charged by the Marx to a voltage of approximately 3 MV. The output of this stage is a triggered gas switch of the trigatron type (Martin et al., 1965-1970). To date jitter times 5 5 nsec have been achieved. Energy from 36 intermediate store water capacitors is fed to 36 pairs of 2 . 2 4 triplate pulse-forming lines, each having a characteristic electrical length of approximately 20 nsec (Fig. 10). The charge time of these lines is approximately 270 nsec. They have a capacity of 16 n F and each pair of lines stores 46 kJ at 2.4 MV. The unique geometry of the PBFA pulseforming section surrounds each charged line with a ground plate that both

\

TRANSITION SECTION

I I

I

FIG. 10. PBFA pulse-forming section.

16

ALAN J . TOEPFER

increases the capacity of the line and reduces prepulse on the output section to only 0.3% of the charge voltage. This is an important feature for certain particle beam diode concepts. Energy is switched out of the PBFA pulse-forming lines to a transition section through two sets of five self-breaking water switches. The positive electrodes of these switches protrude through holes in the ground planes, which have a diameter sufficient to preclude breakdown of the water dielectric. Longer pulses require larger holes due to the fact that the field for breakdown varies with the inverse cube root of the effective pulse time. (The effective pulse time is defined as the time for which the voltage on the gap is greater than 63% of the breakdown voltage.) For low-jitter breakdown of these multichannel gaps, one requires mean electric field strengths at breakdown 2200 kV/cm and a correspondingly high rate of charge of the pulse-forming line ( 2IOl3 V/sec). At switching, the rate of rise of voltage on the output line is > 1014 V/sec. The ANGARA-V PFN is a coaxial, water-insulating Blumlein switched by 10 or 12 radially positioned, trigger gas switches, arranged azimuthally around the axis of the line (Fig. 11). The Blumlein principle

L FIG.1 1 ,

ANGARA-V coaxial Blumlein geometry with gas switch.

17

PARTICLE BEAM FUSION

FIG.12. Blumlein geometry: (a) center line is charged to voltage V,; switch S is closed line analysis.

at t = 0; (b) schematic for transmission

can be explained by a transmission'line analysis with the problem schematically illustrated in Fig. 12 for a line of length 1. For simplicity we assume Z1 = Z, = (L/C)'',, where L ( C ) is the inductance (capacitance) per unit length of the lines. The transmission line equations au/ax = L ailat,

ailax = C av/at

(5)

are solved by Laplace transform subject to the initial conditions i(x,O) = 0

u(x,O) = Vo,

aU/atl,,,

=

(6)

(7)

0

and the boundary conditions aU/axl,=,-

=

(continuity)

av/axl,,,-

u(O+,t) - v(O-,t)

=

(8)

i(0,t)R

(9)

av/axl,=-, = 0

v,,

(10)

t < 0,

v(1) = 0, t > 0. ( 1 1) The output voltage pulse into a matched noninductive load R = 2 2 is a square wave of amplitude Voand pulse length 21. Figure 13 shows two repu(1) =

V R = I(o,tlR

3 I VFI

413

v,

c

3 PIC419 v, 5PlC

PIC

I

PIC

3 PIC

7PlC 4127 V, QP/C

I

I

1

7PlC

5PlC

TIME

TIME

(a)

(b)

1

QP/C

llPIC

1

1

llPIC

FIG. 13. Output pulse from Blumlein into noninductive load for Z , = Z, = Z : (a) R =

22; (b) R = 42.

ALAN J. TOEPFER

I

+I

h\\Y

I

h\\\' L I

I

LY \

'

2D = LDITD

-1

4 -

WATER *& SOL1D

NEGATIVE TRIPLE POINT

VACUUM

4-

7R

FIG. 14. The transition from water dielectric to vacuum. Line is flared in the region close to solid dielectric-vacuum interface.

resentative cases. For a mismatched load in the general case Z1 # Z , , the initial wave has an amplitude

v; -- 2V,[R/(Z, = z, + R ) ]

(12)

The ANGARA-V Marx generator will charge the 70-nF Blumlein to a little over 2 MV in about 1.5 psec. The ratio Zl/Z, was chosen t o be 1.6 to assure a high-energy transfer efficiency from the Blumlein to the output line. The Blumlein is 2.5-m outer diameter and 1 rn long, with a nominal pulse length of 60 nsec. Due to stray capacitances, the output pulse is lengthened to between 85 and 90 nsec. The Blurnlein is charged by two lines running through two separate oil-water interfaces. The efficiency of energy transfer from the Marx to the Blumlein is quoted to 72%. No details of the ANGARA-V triggered gas switch have been published to date; however, the jitter has been quoted to be + 5 nsec. Energy from the PFN on ANGARA-V is fed to the vacuum diode via an approximately 5-m-long, coaxial, water-insulated transmission line. On the PBFA modules a transition is made from triplate geometry in the region of the pulse-forming line to coaxial geometry at the water-vacuum interface.

19

PARTICLE BEAM FUSION

Figure 14 schematically illustrates the transition region from waterinsulated transmission line to vacuum diode. Power flow in the water is limited by the breakdown strength of water fj'B D11/3A0.058 ef W =

k?

(13)

where in a coaxial system k' is a function of the polarity of a center electrode. If Aw is the electrode area in square centimeters, reff (defined above) is in microseconds, and E B D is in megavolts per centimeter, then .k+ ( k - ) = 0.3 (0.6). For a coaxial line, the maximum power flow in the water is

Pw

=

240EgD (TW/m2)

(14)

when E B D is in MV/cm. Depending upon geometry, power fluxes in the range of 40-60 TW/m2 should be achievable in the water transmission line section of PBFA and ANGARA-V. The breakdown strength of the solid insulator is EBDVi''o

=

k

(15)

where V, is the volume of the solid and k a constant characteristic of the material. The power fluxes that the bulk solid of the insulator can handle are comparable to those which can be transported in the water feed. I

I

1

1

I

I

1

I

1

l

l

I

l

-

I

1

1

1

1

1

1

l

TIME, nsec

FIG. 15. Typical data at the input to the magnetically insulated transmission (MITE) triplate line.

ET (MVlcm) WATER

I

INSULATOR

1

VACUUM

FIG. 16. Proposed ANGARA-V diode geometry, showing disk insulator and electric field stresses on water (I) and vacuum (11) interface.

I

PARTICLE BEAM FUSION

21

The limiting factor in power flow in both PBFA and ANGARA-V is the ability of the solid-vacuum interface to withstand flashover. Dielectric vacuum flashover is caused by field emission of electrons from the negative “triple point,” where metal, dielectric, and vacuum meet at the cathode. The flashover potential is a function of the angle formed by these surfaces. For example, for E,, 3 0.27 MV/cm, the limiting power flux at the vacuum interface is s 2 TW/m2. To reduce the power flux density at the vacuum interface, the line is generally flared in the region of the insulator as illustrated in Fig. 14. The effect is to actually increase the peak power that can be delivered to the diode load (VanDevender and McDaniel, 1978). This power is PL =

ffE/zD

(16)

where

with V othe maximum voltage across the interface and 2, = L D / T D the impedance of the transition region (L., is the inductance of the diode and T~ the electrical length). In Eq. (17), TR is the time to peak current at the output of the diode. For the PBFA diode, Z, = 4 R, L D = 38 nH, and TR = 45 nsec (Fig. 15). The length of the flare region is of order 50 cm, so that TD = 2 nsec. Hence Z, = 18 SZ and fy = 3. The EBFA module diode has operated at a peak power of 0.8 TW. A schematic of the proposed ANGARA-V diode is shown in Fig. 16, which shows the calculated electric field stresses on the insulator. Peak stresses for this design are less than 50 kV/cm. The insulator area is lo4 cmz and the peak power to be transmitted is = 2 TW. IV. POWERFLOWI N VACUUM The conversion of electromagnetic energy to particle beam energy is accomplished in a vacuum. Energy transported by the liquid-dielectric insulated transmission lines of the accelerator is fed through a soliddielectric interface to a vacuum region bounded by electrode surfaces. For a 1-TW,Zo = 7 . 6 4 line such as the PBFA-I module (2 MV), the electric fields in the line are +450 kV/cm, and electrons will be field-emitted from the negative conductor (cathode), modifying the energy flow in the vacuum line. Field emission of electrons occurring from microscopic whiskers on the cathode surface results in explosion of the whiskers and

22

ALAN J. TOEPFER

formation of a plasma on the surface of the cathode. Electrons are emitted from the boundary of the plasma sheath all along the transmission line surface. It is obvious that if the above electron current were not inhibited in some manner it would be impossible to transmit power in vacuum lines under these conditions. However, it has been observed that the selfmagnetic fields caused by current flowing in the surface of the conductor (boundary current) and the space-charge-limited electron flow in the gap will modify the emitted electron trajectories so they are confined to the region of the cathode in a sheath. The use of externally generated magnetic fields to limit vacuum gap breakdown was originally proposed by Winterberg (1968a). A selfconsistent equilibrium for the electron sheath in the steady state was arrived at by Lovelace and Ott (1974) for the case of an applied transverse magnetic field B, (Fig. 17). Under steady conditions, the electron energy in the gap is (in rest mass units) y(x) = 1

+ eV(x)/rnc2

(18)

If the system is uniform under translations in the direction of energy flow ( Z axis), the canonical momentum in the 2 direction is conserved so that

v,W

= eA,(x)/mcy(x)

(19)

where B,(x) = -(d/dx)A,(x) and, for convenience, A,(O) = 0. The minimum value of magnetic field necessary to prevent electrons from crossing the gap is that for which v,(d) = v = c(l - l / ~ : ) ~ ’so ~ ,that A,(d) = (rnc2/e)($ - l)In

(20)

If the applied field in the gap prior to application of the voltage V,, was B,, and the electrodes are perfect conductors, then flux is conserved so that

lod

B,(x) dx = Bud,

B,

=

(rnc2/ed)($ -

Add) = (parallel plate)

(21a)

where yo = 1 + eVo/mc2.For applied fields > B,, the transmission lines are magnetically insulated. For vacuum coaxial transmission lines such as those on ANGARA-V, the minimum applied field for magnetic insulation becomes

where r+ is the radius of the anode and ro (q)the radius of the outer (inner) cylinder. The details of the electron sheath structure for applied fields above cutoff are complicated and are given by Lovelace and Ott.

23

PARTICLE BEAM FUSION

X

'b

t

X'

I

2

FIG.17. Magnetically insulated parallel plate line.

Of particular application to ANGARA-V and PBFA-I is the case where the magnetic field restricting breakdown in the transmission lines is the self-field arising from the current flowing in the lines. An analytic model of this flow, after that originally proposed by dePackh for electron flow in high-current diodes, was developed by Creedon (1977). Creedon modeled the steady-state electron flow in the vacuum region using cold fluid equations

&/dt

V *E

=

+v

-e(E

= p/co,

J

x B)

V xB

= poJ

= PV

(22)

(23) (24)

assuming the flow to be along equipotential lines so that E + v x B = O

(25)

Equations (22)-(24) were solved in generalized curvilinear coordinates. The equilibrium current was determined to be

where ym is related to the potential at the edge of the electron sheath through Eq. (18), and

where Z o is the free-space impedance of the vacuum line. The parameter ym is not uniquely determined. In the parapotential theory, the ratio of total current to boundary current is given by ym, but the boundary current is not uniquely specified. Experimental data (Shope er ui., 1978) are consistent with so-called saturated parapotential theory obtained by setting -ym = yo when V < 1 MV. This is equivalent to having

24

ALAN J . TOEPFER

the electron sheath boundary at the anode, or x* = d in Fig. 17. Above 1 MV the data are consistent with setting ym = Z,Jo/Vo in Eq. (26). The above assumptions are admittedly ad hoc, but they permit reasonably accurate back-of-the-envelope calculations for magnetically insulated transmission lines. More accurate calculations involve the use of particle-in-cell numerical simulations of electron and ion flow in the vacuum (Poukey and Bergeron, 1978). These codes, as well as the parapotential theory, were originally developed to calculate self-consistent electron and ion flow in low-impedance diodes where pinching occurs and are applicable to “short” magnetically insulated lines where the pulse length is long compared to the transit time of the line. The magnetically insulated lines on PBFA and ANGARA-V are long compared with the pulse length. Results of a calculation using a twodimensional electromagnetic particle code for time-dependent electron and electromagnetic power flow in a long, self-magnetically insulated coaxial line are shown in Fig. 18. The line is driven by a trapezoidal voltage pulse, rising to 5 MV in 4 nsec, constant for 7 nsec, and falling to zero in 4 nsec. The quantitative results for IT = boundary (IB)plus electron (I,)

5

4

3

5

E

1

> 2

1

6.4

0

0

5

FIG.18. Voltage ( V )and electron envelope ( E ) as a function of axial position for a 3 1 - 0 coaxial line driven by a 5-MV trapezoidal voltage pulse with a 4-nsec risetime, at f = 15 nsec (after Poukey and Bergeron, 1978).

PARTICLE BEAM FUSION

H7.1

25

cm

I 1

FIG. 19. Prototype of PBFA (MITE): (a) side view schematic of MITE line; (b) cross section of triplate; (c) injected current (I,,) and transmitted current (IT2)for geometry shown; and (d) 1, and IT2for modified geometry (after VanDevender, 1979).

current are consistent with Eq. (26) when ym = ZT/ZBas specified by the parapotential theory. Other results, not predicted by the steady-state parapotential theory, are a sharpening of the pulse front due to leakage of electron current to the anode (the average energy of electrons reaching the anode is 1.5 MV, less than the applied voltage), and a propagation velocity of the pulse front given by (Bergeron, 1977) Of =

4% -

1Y2(y0 - 1)/(ymyo - 1)

(28)

Detailed comparison of the theories (particle code and parapotential) and experimentation (Bergeron et al., 1978) show that total current measurements agreed well with the calculations. However, the measured boundary currents were about 20% less than calculated, due possibly to

26

ALAN J . TOEPFER

diagnostic problems. It is interesting to note that comparisons between the parapotential and particle code theories indicate substantial discrepancies between the calculated values for the radial charge and electron current densities. The propagation of energy in magnetically insulated transmission lines is apparently not particularly sensitive to microscopic details of the electron trajectories as long as the basic conservation laws for charge, energy, and canonical momentum are obeyed. It has been shown experimentally on the PBFA-I prototype module MITE (Fig. 19) that the line geometry at the pulse injection point is crucial for setting up a stable flow with little power loss. In particular, VanDevender (1979) found that longitudinal and azimuthal variations in line geometry and magnetic field that are nonadiabatic (i.e., significant over an electron Larmor orbit) lead to the development of instabilities in the electron flow resulting in power and energy losses as shown in Fig. 19. The nature of these instabilities is still under investigation and their suppression is of importance because they limit energy flow in the vacuum. With Fig. the optimized injection geometry, an energy transfer efficiency (qB; 6) of 90% was observed on the MITE experiment. Power flow through the triplate line was 1.6 x 1O'O W/cm2. No similar experiments have been carried out on the ANGARA-V module. Considering a magnetically insulated transmission line as a circuit element, one must remember that the line impedance is afunction of voltage. Thus, efficient power transmission to a load will occur over a more limited range of voltage than for a constant-impedance transmission line. The ability to match this characteristic output impedance is crucial for efficient coupling to a load that is transit-time-isolated from the driver. For particle beam fusion applications, the load is a vacuum diode in which pulse energy is converted to intense electron and/or ion beams. The physics of these diodes is the subject of the next section. V. PARTICLE BEAMFORMATION A N D FOCUSING In the discussion of power flow in the magnetically insulated vacuum lines, it was stated that electron emission from cathode surfaces occurred when electric fields became of order 105-106 V/cm. The cathode processes that lead to the initiation of electron flow are complex and are dependent upon the material properties, initial conditions, and microscopic structure of the electrodes. The phenomena involved in vacuum breakdown under nanosecond pulse conditions have been studied by many researchers. Significant contributions to the understanding of these phenomena at the microscopic level have been made by G. A. Mesyats

a

X

a,

2 -

U

0 0

0 0

0 I

0

+€-

I

l

OO

0

o

0

I

0

TIME, nsec FIG. 20. Perveance comparison for the diode formed by positioning a 5.08-cm-diam graphite cathode a distance Of 6.05 mm from a planar anode (after Parker et al., 1974).

ALAN J. TOEPFER

28

and co-workers at the Tomsk Institute of Atmospheric Optics in the Soviet Union. A systematic study of resulting macroscopic behavior of a diode fed by a nanosecond voltage pulse has been made by Parker r f nl. (1974). Formation of plasma at the cathode surface leads to a transition of current flow from field-emission-dominated to space-charge-limited. For planar diodes, the relativistically correct Child-Langmuir law can be written in integral form as

l1

1+eVlmez

dJl/(@ - 1)1‘4

=

d (2eZ/~,,mc~A)~’~

(29)

where A is the cathode area, d the gap, V the voltage, and I the current. For eV 4 mc2, Eq. (29) reduces to

I/A

=

2.34 x 103Vj’’/dL

(30)

where V is in megavolts and d is in centimeters. Motion of cathode plasma will cause the gap d to vary. By plotting diode perveance P = Z/v3’2 vs. time, and assuming d = do - uexpt, consistent with plasma velocities of 2-3 x lo6 cm/sec were obtained (Fig. 20). The latter stages of diode behavior are modifed by the formation of plasma at the anode due to electron deposition. This plasma can serve as a source of ions that are accelerated toward the cathode. The ions lead to a reduction of space charge in the gap, leading to increased electron flow, and deposit energy in the cathode and cathode plasma, leading to cathode heating and increased cathode plasma velocity. As the current builds up in the diode, self-magnetic-field effects begin to modify the flow. When the cutoff condition for magnetically insulated flow is satisfied, which for a cylindrical diode is just I 2 8 . 5 p y R l d (kA)

(31)

(where R is the cathode radius), the electrons will be focused toward the axis. Conditions for electron beam focusing in the diode are complicated by the effects of the anode plasma, which hopefully is not present in magnetically insulated transmission lines. The parapotential theory was originally developed to calculate selfpinched electron flow in high-current diodes (Fig. 21). By assuming saturated flow (ym = y o ) in cylindrical geometry ( g = R / d , the diode aspect ratio, where R is the cathode radius and d the width of the anode cathode gap), Creedon (1975) was able to obtain reasonable agreement with Eq. (26) with impedance measurements for diodes operating at 1 M V in the 1 -4-R regime.

-

PARTICLE BEAM FUSION CATHODE

29

CATHODE

fa)

b)

FIG.21. High-v/y diodes with (a) flat and (b) conical front surfaces. The radius of the cathode is R, . The hollow well of radius R, helps reduce the effects of plasma motion (after Creedon, 1975).

A fundamental problem with the parapotential model was the necessary assumption of the existence of a boundary current on the axis of the diode where, in the case of a hollow cathode, there is no physical boundary. In one class of experiments, a boundary current was introduced by placing an exploding wire on the axis of the diode (Yonas rt ul., 1973; Read and Nation, 1976). They showed that pinched flow was introduced by the current-carrying plasma on axis. However, this technique has not been generally viable because of the difficulty of controlling the plasma impedance on axis. Pinching was also experimentally observed in hollow diodes, where appreciable current flow on axis was hard to explain. Numerical simulation of high-aspect-ratio (large R / d ) diodes by Poukey (1976) and theoretical modeling by Goldstein and Lee (1975) indicates that ion flow in the diode from the electron-beam-generated anode plasma provides an equivalent “boundary current,” which is distributed radially throughout the diode. Poukey showed that I, + I, = I0 (32) where Z,(Z,) is the total electron (ion), and Zo is given by Eq. (26) with ym = y o . Using the assumption of space-charge-limited emission of ions and electrons from the anode and cathode plasmas, Goldstein and Lee showed that

Id4

= (2m,/m,)”2[y0/(yo

+ 1)1’21(R/d)

(33)

30

ALAN J. TOEPFER

L

ELP ANODE POTENTIAL

FIG.$2. Schematic illustration of the way that the operating point of a diode changes with time. The solid curves are I,, and I,. The crosses represent simultaneous measurements of voltage and current made at different times during a single pulse for a hypothetical diode. The diode passes through four distinct operating regimes which are, in the order of their occurrence, the emission-limited phase (ELP), the unpinched phase (UP), the pinched phase (PP), and the voltage-collapse phase (CP). The symbols T represent the transition regions (after Di Capua et al., 1976).

Equations (26),(32),and (33)indicate that as diode impedance drops, the percentage of current available in ions (mostly protons from hydrocarbon contamination of the anode) increases without limit, and the electron current has a maximum value I,

2 :

0.25(y0+ 1)'@ ln[yo +

(3- 1)1'2] (MA)

(34)

These results set the lower limit on diode impedance for efficient conversion of driver energy to electrons at 1 fl (or 1-2 TW per diode). This result, coupled with the difficulty of electron beam focusing in highaspect-ratio diodes, was an important factor, which led to the modular construction of PBFA and ANGARA-V. Several papers have been published that examine time-dependent pinching phenomena in parapotential diodes. Di Capua et al. (1976)studied the transition of diode impedance from unpinched Child-Langmuir flow to pinched parapotential flow (Fig. 22). In the transition region, the pinch was inferred to collapse to the diode axis at a velocity of -2 mm/nsec. It was also postulated that cathode plasma motion across the diode was impeded by the magnetic pressure. Johnson et al. (1978) showed a dependence of plasma closure velocity on the electric field risetime in the diode. 2 :

PARTICLE BEAM FUSION

31

Blaugrund et al. (1977) utilized an optical streak camera to observe light induced by bremsstrahlung deposition in a scintillator sheet on the anode of the NRL GAMBLE I and I1 accelerators to infer radial pinch motion, and demonstrated the dependence of pinch collapse velocity on the anode material. They proposed that the areal collapse velocity of the pinch is related to the anode surface heating rate, resulting in release of adsorbed gases from the anode surface and the formation of an anode plasma. The areal collpase velocity was defined as

with I, the electron current in the collapsing pinch, dE/dz the specific energy deposited by a beam electron in the anode material along the coordinants normal to the anode plane, and C the specific heat of the anode material. This work led to the realization of the importance of ion flow in the diode and the development of methods to efficiently produce intense ion beams in low impedance. The finite time required for pinch formation results in reduced efficiency for coupling diode energy to focused flow. Attempts to go to increased electron beam current in very high aspect ratio, low-impedance diode (< 1 a)have been frustrated by finite pinch formation time, closure of plasmas in the anode cathode gap resulting in diode shorting, increased coupling of diode energy to light ions produced in the anode plasma, and instabilities in the radial electron flow (see Fig. 23).

FIG.23. X-ray pinhole photograph of bremsstrahlung from pinched electron beam for Z = I a, R / d = 24 parapotential diode (after R. Genuario, unpublished).

32

A L A N J. TOEPFER

(bl 1.2,

I

I

I

0.4 0,o

12

0

50

100 TIME (nsect

FIG.24. ANGARA-I diode geometry (a) and characteristic voltage, current, power, and impedance (b) (dimensions in millimeters).

Maximum electron current densities achieved on the prototype PBFA-I MITE module have been in the few MA/cmZ range, with cathode diameters in the range of 4-6 cm. In other experiments, maximum current densities achieved in the United States have been on the PROTO-I accelerator at Sandia Laboratories ( 1 . 1 MV, 340 kA, 25 nsec,

PARTICLE BEAM FUSION

-

33

20 MA/cm2) and the CAMEL accelerator at Physics International (1 MV, 200 kA, 60 nsec, 10 MA/cm2). An entirely different type of diode behavior has been postulated by Rudakov to explain electron pinch phenomena in experiments carried out on the TRITON and ANGARA-I accelerators (Liksonov et al., 1977; Afonin et al., 1977). The cathode geometry (see Fig. 24) is claimed to result in a turbulent plasma channel 1-2 mm in diameter and < 1 cm long carrying a 200-kA electron current, and maintaining a voltage drop of 1 MV at peak power 2.5 x 10” W. A similar diode is proposed for the ANGARA-V accelerator. A current density of 10 MA/cm2 of 1-MeV electrons is a t least one and most likely two orders of magnitude less than that required to drive a thermonuclear capsule. It was therefore originally proposed t o transport the 36 PBFA-I electron beams to the target through plasma channels and overlap them at the target. This scheme also had the advantage of “standoff,” i.e., the electron beam source was isolated from the target region by a gas blanket (50 Torr to 1 atm) in which the plasma channels were formed. Freeman and Poukey (1979) have estimated the requirements for transporting a 500-kA, 2-MeV electron beam characteristic of the PBFA-I module through a 0.4-cm-diam channel to a target 3 m from the diode. For 77% energy transport efficiency, a channel conductivity -4000 R/cm is required. Slowing down and beam spreading due to electric fields induced in the channel by the injected beam and channel expansion due to beam pressure all tend to reduce the beam flux at the target. To date, 140 kA/cm2 has been propagated through 1.6-cm-diam, 50-cm-long beam channel (Miller and Mix, 1978), well below the current densities achieved by beam focusing in a diode.

-

-

VI. THE LIGHTION BEAMOPTION Most recent work on pulsed-power-generated, high-current particle beams has concentrated on the efficient production of light ion beams. As seen in Eq. (33), low-impedance, high-aspect-ratio diodes are efficient generators of ion current. The self-magnetic field of the current essentially cuts off electron flow but does not impede the ion flow. Also, the distribution of electrons in the anode-cathode gap results in an enhanced electric field at the anode plasma boundary, leading t o enhanced ion flow. Suppression of electron flow in high-current diodes can also be accomplished by using externally applied magnetic fields. Figure 25 illustrates a concept for a magnetically insulated diode fed by radial transmission lines. External toroidal field coils produce a magnetic field that is parallel

34

ALAN J. TOEPFER

F C

FIG.25. PROTO-I magnetically insulated ion diode (after Yonas, 1978).

to the curved anode-cathode surfaces, preventing electron flow in the gap. The diode illustrated has been fielded on the 2-MV, 20-nnsec pulse length PROTO I accelerator at Sandia Laboratories, producing a 280-kA ion beam focused to 2 2 5 kA/cm2. The ion current was 13 times higher than the value to be expected from conventional Child-Langmuir space-charge-limited flow assuming the diode voltage and anode-cathode gap. This enhancement is due to formation of a virtual cathode of electrons trapped on magnetic field lines running parallel to the anode surface (Yonas, 1978). An alternative method of enhancing ion flow relative to electron flow is to cause the electrons to reflex in the anode. The basic geometry of the “reflex triode” is shown in Fig, 26. Equations for steady onedimensional, nonrelativistic bipolar (electron-ion) flow in such a diode have been solved by Creedon ct a / . (1975). The solutions are parameterized by the ratio of electron range in the anode material to the anode thickness 7,and are dependent upon the form of the spectral distribution of electron energies in the diode. For a 6 function distribution, corre-

35

PARTICLE BEAM FUSION

sponding to the case of a mesh anode with transmission probability T [i.e., 7 = 1/(1 - T ) ] , the electron and ion current densities are

wherej, is the nonrelativistic Child-Langmuir current, given by Eq. (30). In the more general case of a continuous distribution a strong enhancement of ion flow was found to lead to a drop in diode impedance to a fraction of the Child-Langmuir value. This effect has been observed (Prono et al., 1975). More recently, the principle of the self-pinched magnetically insulated diode (Poukey et af., 1975) has been combined with that of the reflex triode to produce a “reflex pinch” diode (Goldstein et al., 1978). The geometry is shown in Fig. 27. Proton currents of 500 kA at 1.4 MV out of a total diode current of 1 MA have been produced on the NRL GAMBLE I1 accelerator and focused to 70 kA/cm2, corresponding to a power flux of 0.1 TW/cm*. Propagation of ion beams to an ICF target can be accomplished by means of geometric focusing onto the target, or geometric focusing, injection, and transport through a plasma channel, as discussed in the electron beam approach. Geometric focusing to a plasma channel as illustrated in Fig. 28 imposes less constraint on ion beam emittance than focusing over a distance of many meters to a target approximately 1 cm in diameter. Nevertheless, questions remain as to the energy losses from the ion beam in v = -v,

v=o

v = -v, TYPICAL ELECTRON

/ ORBIT

CATHODE

CAl

FLOW IN BOTH DIRECTIONS

% ION

EXTERNAL B - FIELD

FIG. 26. Reflex triode.

36

ALAN J . TOEPFER

FIG.27. Pinch reflex diode.

the channel and the hydrodynamic response of the channel to beam energy deposition. To increase the ion beam fluence at the target, it is proposed to bunch the beam by applying a time-varying voltage to the anode-cathode gap 1979). For paraxial motion, the ideal diode voltage wave(Mosher et d.,

'+ . \

Anode

1-

1-10 T o n

2- 5 cm

b-

2-5 m

1--

2 - 5 rn

-1-2-5-1 crn

FIG.28. Pinch reflex diode with ballistic focusing and propagation to target through a plasma channel (after Mosher et a / . . 1979). External capacitor bank provides channel current fchfor ion beam confinement.

PARTICLE BEAM FUSION

form (pulse length

37

T)

will result in all ions arriving at a target a distance

d

= uOta

(39)

away from the diode at the time t,. In Eq. (39), u,, = (2qV,,/rni)1’2,where mi is the ion mass and q the ion charge. A finite spread of axial momentum and diode voltage from the ideal waveform and dispersion of ion velocities due to scattering in the channel will, of course, limit the degree of bunching achievable. By utilizing a more complicated driving voltage waveform it may be possible to shape the ion pulse at the target to accommodate special driving requirements.

VII. INTENSE BEAMINTERACTION WITH ICF TARGETS The interaction of charged-particle beams with ICF targets is currently a subject of intensive theoretical and experimental investigation. To date, however, only electron beam experiments have been carried out, and these have been at power fluxes well below those required to achieve significant neutron yield. We therefore concentrate on particular aspects of the problem of interaction of intense electron beams with dense targets that are of interest for ICF. For purposes of this discussion, an electron beam is considered “intense” when the self-generated electric and magnetic fields associated with the beam modify the beam kinematics and the dynamics of the medium in which the beam is propagating. Intense electron beams are typically classified according to the Alfven-Lawson parameter v/y, where

and y is the usual relativistic factor corresponding to the beam energy. It is easily shown for a uniform electron beam carrying a current f in a charge-neutralizing medium that v/y = 1 corresponds to a critical current for which an electron at the outer edge of the beam has a Larmor radius equal to one-half the beam radius, so that the resulting electron orbit would be perpendicular to the beam axis. This critical current ZA = 17/37 kA was recognized by Alfven (1939) as a limiting current for propagation of a charge-neutralized electron beam. Lawson (1958, 1973) defines

38

ALAN J. TOEPFER

the current ZA as a transition from beam conditions to plasma discharge conditions characterized by the Bennett pinch relation

12

=

2NW,

(41)

where N is the electron density per unit length of the discharge and W , the transverse energy density. Since Z a u and N a Y, it follows that W, 0: V/Y.

When an intense electron beam is injected into a neutral gas or plasma where the electron mean free path is much greater than a Larmor radius, the beam dynamics are modified by charges and currents induced in the background medium. Low-energy electrons will be expelled from the beam channel, leaving behind a space-charge-neutralizing ion background. When the beam is space-charge-neutralized, an axial electric field will induce a return current in the beam channel, reducing the net magnetic field. Hence, intense beam propagation characteristics are determined by the conductivity of the background medium. Recent work of interest for ICF has concentrated on the interaction of high-current electron beams with solid density foils of thickness d , much less than an electron range, and experiments have been carried out to measure enhanced electron coupling to thin foil targets. Yonas el al. (1974) predicted that high v / y electron beams would undergo enhanced coupling with a dense plasma target in the case where rL/A -e 1, where r, = aZA/2Z is the instantaneous Larmor radius of a beam electron at the outer edge of the beam, and A is the mean free path for 90" scattering of a beam electron in the target material. Experiments by Bogolyubskii et al. (1976) on the Triton accelerator at the I. V. Kurchatov Institute reported enhanced coupling of a 120-kA, 500-keV, 30-nsec FWHM electron beam (corresponding to v / y = 4) with platinum and gold foils ranging in thickness from 5 to 30 pm. About one-half of the 1.2-kJ beam energy was coupled to the foil, ten times that expected from a Monte Carlo calculation that neglected the modification of beam electron orbits by self-generated electric and magnetic fields. It was claimed that enhanced coupling was obtained due to penetration of the beam magnetic field into the exploding foil, which was less than a skin depth thick. Electrons backscattered from the foil were returned due to the diode electric fields. Foil heating was independent of gas pressure behind the anode foil, indicating that space charge buildup behind the foil was not a significant effect. The first electron-beam-produced thermonuclear neutrons were claimed in these experiments. Since this first work, many experiments and theoretical calculations have been performed to investigate the coupling of intense electron beams with targets. Enhanced coupling has been attributed to magnetic stopping

PARTICLE BEAM FUSION

39

(Widner et al., 1979), beam stagnation and reflexing (Clauser et al., 1978), and collective interaction of the beam with the dense plasma target (Imasaki et al., 1975). Theoretical modeling of the interaction has utilized self-consistent particle-in-cell (PIC) codes to calculate electron motion in the diode region, coupled with Monte Carlo codes to calculate energy deposition and hydrocodes to calculate material response in the adjacent target region (Widner et al., 1977; Zinamon et al., 1975). The rate of energy deposition due to an intense electron beam interacting with a thin foil target may be written

dWb/dt = X(jb/ep)(d&/dx) where j , is the beam current density, dE,Jdx the stopping power corresponding to the incident beam electron energy, p the target density, e the electron charge, and x contains contributions due to scattering of the beam in the target and electron path modification due to self-magnetic fields and self-generated and applied electric fields. Modifications due to finite target temperature are usually included in dE/dx. In a high-Z target there is enhancement at the front surface due to electron scattering. This enhancement is a function of the angular distribution

nb =

10’5

cm-3

FIG.29. Electron trajectories in a 1 MV diode with (a) a target simulated by a region (lower right comer) with no E field (solid line trajectory), and (b) a flat anode with no target (dotted trajectory) (after Clauser er a / ., 1978).

40

ALAN J . TOEPFER

of beam electrons at the surface of the target, and for thick targets can lead to energy deposition rates corresponding to x = 2-3 for a hot beam. These effects are calculated using conventional Monte Carlo electronphoton transport codes. For intense beams interacting with targets of thickness much less than a range, target expansion and the effect of space charge buildup and self-magnetic fields generated by the beam in the target region lead to electron energy deposition enhancement. Clauser et al. (1978) observed that target geometry can alter the electric and magnetic field distributions in the diode, leading to a stagnation of the beam in the target region and enhancement factors in the range of 13-34. Figure 29 illustrates the effect of a cylindrical, space-charge-neutralizing target region placed on axis on the electron trajectories in the diode. Current density in the target region was 160-400 kA/cm2; however, observation with holographic interferometry indicated deposition levels equivalent to a 5.4-MA/cm2 cold beam interacting with the 800-pm-diam, 10-pm-wall-thickness, spherical nickel shell targets mounted on a 0.125-rnm-diam, 0.5-mm-long tungsten stalk in the center of the anode. More recent experiments have studied the enhanced coupling of intense electron beams to thin planar or hemispherical foils placed in the anode plane. Diagnostics employed have been holographic interferometry, bare and filtered aluminum photocathode X-ray diodes, XUV pin-

L

1

3.175 cm

1.27 cm

f -FOIL

1-

1-0.35cm

FIG.30. Diode geometry for experiment to study electron beam interaction with a thin foil (after Widner et a / . , 1979).

41

PARTICLE BEAM FUSION 2.37

0

1.07

Z,cm

FIG.31. Coupled PIC diode Monte Carlo code simulation of enhanced electron deposition in a thin foil target. Solid line illustrates a representative particle trajectory (after Widiier er d.,1979).

hole cameras, optical streak photography, and Faraday cup particle detectors. Target foils have been both high-Z (Au, Ta) and low-Z (CH2). Figure 30 shows the diode geometry employed in experiments on the PROTO-I accelerator by Widner et (11. (1979). This geometry is similar to the reflex triode geometry of Fig. 27, in the case where the region behind the target foil is evacuated so that a virtual cathode is formed by space charge buildup behind the foil. An enhancement in electron deposition corresponding to x = 3.5 was found due to electrons making multiple passes through the target foil, as shown by the self-consistent PIC calculations in Fig. 3 1. Peak energy deposition rates were > 50 TW/g and target temperatures were observed to be 15-20 eV at the front surface and 7-10 eV at the rear surface of the target foil. The lower rear surface temperature was attributed to radial beam spreading in the foil interior at distances greater than a skin depth. The calculation in Fig. 31 did not take this effect into account. In other experiments carried out at Valduc (Bruno et al., 1979) and the Kurchatov Institute (Babykin ef al., 1979), values of x in the range of 2-5 for similar beam parameters have been observed. Thus, to date, enhancement of electron energy deposition due to self-magnetic fields and electrostatic reflexing has been observed, but beam power flux levels are well below those required for inertial confinement fusion.

42

ALAN J . TOEPFER

VIII. SUMMARY In order to achieve fusion burn in a particle-beam-driven, inertially confined DT capsule, specific energies in the range of lo*- lo1*J/g of DT and absorbed power 2 5 0 TW appear to be required. Future advances in target design will hopefully reduce these requirements. The major facilities currently under construction, PBFA-I in the United States, and ANGARA-V in the Soviet Union, will provide drivers for study of the critical issues of beam production, propagation, focusing, and target physics in the 30-100 TW range. To date, the major feasibility question for particle beam fusion deals with beam focusing. High-current electron beams appear to be limited to power fluxes in the 10 TW/cm2 range, which are 1-2 orders of magnitude less than that required for fusion. Preheat of the pusher by bremsstrahlung in electron beam targets results in decreased target performance and more severe beam focusing and power requirements. Research on production and focusing of intense ion beams is just beginning. Power fluxes of 0.1 TW/cm2 of 1.3-MeV protons have been achieved, three orders of magnitude below that required for fusion. Projected accelerator requirements for ignition in the 2-3 MJ range with light ion beams are given in Table 111 (Mosher et al., 1979). PBFA-I and TABLE 111 LIGHTION BEAMIGNITION SYSTEMPARAMETERS" Power on pellet 200 TW

100 TW

3 24

16

Energy on pellet (MJ) Stored energy (MJ)

2

Pulse duration (nsec)

Focused power (TW) Bunching factor Focused current (MA) 5-MeV peak 2-MeV peak Min. channel length (m) 5-MeV protons 2-MeV deuterons

100

50

100

50

35 6

I0 3

.23 4.5

45 2

I 18

14 35

4.5 12

23

6 3

5 2

6 3

4 2

* After Mosher ef at. (1979).

9

PARTICLE BEAM FUSION

43

ANGARA-V are well below these requirements, but should be able to provide answers to the critical questions of physics and accelerator technology for assessing feasibility of particle beam fusion.

REFERENCES Afonin, I. P., Babykin, M. V., Baev, B. V., Baigarin, K. A., Bartov, A. V., Gavrin, P. 0.. Korop, E. D., Mizchirutskii, V. E., Pasechnikov, A. M., and Rudakov. L. I. (1977). Proc. All-Union Conf. Eng. Problems Thermonucl. Reactors, 1977 Vol. 2, p. 104 (in Russian). Alfven, H. (1939). Phys. R e v . 55, 425. Babykin, M. V., Baigarin, K. A.. Bartov, A. V., Gavrin, P. P., Gorbulin, Yu. M., Gubarev, A. V., Danko, S. A., Kalinin, Yu. G., Kiselev, V. N., Miziritsky, V . I., Rudakov, L. I., Skoryupin, V. A., and Shestakov, Yu.I. (1979). Proc. Int. Conf. High Power Electrun Ion Beam Techno/., 3rd (to be published). Bangerter, R. O., and Meeker, D. J. (1977). Proc. Int. Conf. High Power Electron Ion Beam Technol., 2nd. 1977 p. 183. Bergeron, K. D. (1977). J . Appl. Phys. 48, 3065. Bergeron, K. D., Poukey, J. W., Di Capua, M. S . , and Pellinen, D. G. (1978). Proc. Int. S y m p . Discharges Electr. Insul. V a c . , 8th, 1978 Paper E2. Bernstein, B., and Smith, I. D. (1973). IEEE Trans. Nucl. Sci. NS-20, 294. Blaugrund, A. E., Cooperstein, G., and Goldstein, S. A. (1977). Phys. Fluids 20, 1185. Bogolyubskii, S . L., Gerasimov, B. P., Liksonov, V . I., Popov, Yu. P., Rudakov, L. I., Samarskii, A. A , , Smirnov, V. p., and Urutskoev, L. 1. (1976).JETP L e t t . (Engl. Trans/.) 24, 179. Bruno, C., Cortella, J., Delvaux, T., Devin, A,, Nicolas, A., Patou, C., Peugnet, C., Roche, M., Wolff, G., Duborgel, B., Fedotoff, M., and Gouard, P. (1979).Proc. I n t . Con,/: High Power Electron Ion Beam Technol., 3rd (to be published). Chang, J., Widner, M. M., Farnsworth, A. V., Jr., Leeper, R. J., Prevender, T. S., Baker, L., and Olsen, J. N . (1977). Proc. Int. Conf. High Power Electron Ion Beam Technol., 2nd. 1977 p. 195. Clauser, M. J., Mix, L. P., Poukey, J. W., Quintenz, J. P., and Toepfer, A. J. (1978). Phys. R e v . Lett. 38, 398. Creedon. J. M. (1975). J . Appl. Phys. 46, 2946. Creedon, J . M. (1977). J . Appl. Phys. 48, 1070. Creedon, J. M., Smith, I. D., and Prono, D. S. (1975). Phys. R e v . Lett. 35, 91. Di Capua, M . , Creedon, J., and Huff,R. (1976). J . Appl. Phys. 47, 1887. Freeman, J. R., and Poukey, J. W. (1979). J . Appl. Phys. 50, 5691. Goldstein, S. A., and Lee, R. (1975). Phys. R e v . Lett. 35, 1079. Goldstein, S. A., Cooperstein, G., Lee, R., Mosher, D., and Stephanakis, S. J. (1978).Phys. R e v . Lett. 40, 1504. Imasaki, K., Nakai, S., and Yamanaka, C. (1975). J . Phys. SOC.J p n . 38, 1554. Johnson, D. J . , Goldstein, S. A., Lee, R.,and Oliphant, W. F. (1978). J. Appl. Phys. 49, 4634. Kidder, R. E. (1971). Proc. Int. Sch. Phys. “Enrico Fermi” 50, 306. Kidder, R. E. (1976). Nucl. Fusion 16, 405. Kirkpatrick, R. C. (1979). Nucl. Fusion 19, 69.

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Kirkpatrick, R. C., Cremer, C. C., Madsen, L. E . , Rogers, H. H., and Cooper, R. S. (1975). Nucl. Fusion 15, 333. Krokhin, 0. N. (1971). Proc. I n t . Sch. Phys. “Enrico Fermi” 50, p. 278. Lawson, J . D. (1958). J . Electron. Control 5 , 146. Lawson, J . D. (1973). Phys. Fluids 16, 1298. Liksonov, V. I . , Sidorov, Yu. L., and Smirnov, V. P. (1977).JETP L e f t . (Engl. Trunsl.) 19, 516. Lindemuth, I. R., and Jarboe, T. R. (1978). Nucl. Fusion 18, 929. Lovelace, R. V., and Ott, E. (1974). Phys. Fluids 17, 1263. Martin, J. C. et al. (1965-1970). Series of unpublished notes from the Atomic Weapons Research Establishment. Obtainable from AFWL (EL) Kirkland Air Force Base, New Mexico. Martin, T. H., Johnson, D. L., and McDaniel, D. H. (1977). Proc. Int. Conf. High Power Elecrron Ion Beam Technol., Znd, 1977 p. 807. Miller, P. A., and Mix, L. P. (1978). Bull. A m . Phys. Sac. [2] 23, 853. Mosher, D., Cooperstein, G., Goldstein, S. A., Colombant, D. G., Ottinger, P. F., Sandel, F. L., Stephanakis, S. J., and Young, F. C. (1979). Proc. Int. Conf. High Power Electron Ion Beam Technol., 3rd (to be published). Nuckolls, J. H. (1974). I n “Workshop on Laser Interaction and Related Plasma Phenomena” (H. J. Schwarz and H. Hora, eds.), Vol. 4, p. 399. Plenum, New York. Nuckolls, J. H., Wood, L., Thiessen, A,, and Zimmerman, G. (1972). Nuture (London) 239, 139. Nuckolls, J. H . , Bangerter, R. 0.. Lindl, J. D., Mead, W. C., and Pan, Y. L. (1977). Proc. Eur. Conf. Laser Interact. Matter. 1977. Parker, R. K., Anderson, R. E., and Duncan, C. V. (1974). J. Appl. Phys. 45, 2463. Poukey, J. W. (1976). Proc. In!. Conf. High Power Elecrron Ion Beam Technol.. I s t , I975 p. 247. Poukey, J. W., and Bergeron, K. D. (1978). Appl. Phys. Lett. 32, 8. Poukey, J. W., Freeman, J . R., Clauser, M. J., and Yonas, G. (1975). Phys. Rev. Lett. 35, 1806. Prono, D. S., Creedon, J. M., Smith, I. D., and Bergstrom, N. (1975). J. Appl. Phys. 46, 3310. Read, M. E., and Nation, J. A. (1976). J. Appl. Phvs. 47, 5236. Rudakov, L. I., and Samarsky, A. A. (1973). Proc. Eur. Conf. Controlled Fusiun Plusmu Phys., 6th, 1973 p. 487. Shope, S . , Poukey, J. W., Bergeron, K. D., McDaniel, D. H., Toepfer, A. J., and VanDevender, J. P. (1978). J. Appl. Phys. 49, 3675. Sweeney, M. A., and Clauser, M. J. (1977). Bull. A m . Phys. Soc. [2] 22, 1061. Toepfer, A. J. (1980). Proc. Scott. Univ. Summer Sch. Phys. 20 (to be published). VanDevender, J. P. (1979). J. Appl. Phys. 50, 3928. VanDevender, J. P., and McDaniel, D. H. (1978). Pruc. I n t . Symp. Dischurges Electr. Insul. Vuc., 8th, 1978 Paper El. Velikhov, E . P., Glukhiky, V. A., Gusev, 0. A,, Latmanizova, G. M., Nedoseev, S. L., Ovchinnikov, 0. B., Pasechnikov, A. M., Pecherskii, 0. P., Rudakov, L. I., Svin’in, M. B., Smirnov, V. P., and Chetvertkov, V. I. (1976). NIIEFA Preprint D-0301 (in Russian). Widner, M. M., Poukey, J. W., and Halbleib, J . A. (1977). Phys. Rev. Left. 38, 548. Widner, M. M., Goldstein, S. A,, Mendel, S. A,, Jr., Burns, E. J . T . , Quintenz, J . P.. and Farnsworth, A. V. (1979). Phys. Rev. Lett. 43, 357. Winterberg, F. (1968a). Phys. Rev. 174, 212.

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Winterberg, F. (1968b). Z. Nofurforsch., Teil A 23, 1396. Winterberg, F. (1971). Proc. Int. School Phys. "Enrico Ferrni" 50, 370. Yonas. G. (1978). Plostna Phys. Controlled Nucl. Fusion R e s . , Proc. Int. Conf., 7th. 1978 Paper IAEA-CN-37-17-3. Yonas, G., and Toepfer, A. J. (1978). In "Gaseous Electronics: Electrical Discharges" (M. N. Hirsh and H. J. Oskam, eds.), Vol. 1, Chapter 6. Academic Press, New York. Yonas, G., Prestwich. K . R., Poukey, J . W., and Freeman, J. R. (1973).Phgs. Rev. Lett. 30, 164. Yonas, G., Poukey, J . W.. Prestwich, K . R., Freeman, J. R., Toepfer, A. J., and Clauser, M .J . ( 1974). Nucl. Fusion 14, 73 I . Zinamon, Z., Nardi. E., and Peleg, E. (1975). Phys. Rev. Lett. 34, 1262.

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ADVANCES IN ELECTRONlCS A N D ELECTRON PHYSICS, VOL.

53

The Free-Electron Laser: A High-Power Submillimeter Radiation Source T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

AND

Plasma Luhorutory Columbiu University

New York, N e w York

I . Scattering from Relativistic Electron Beams. ................................ A. Front Scattering... . . . . . . . . .................. B. Body Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Basic Concepts.. . . . . . . . ......................... s ..................... 11. Properties of Pulsed Intense 111. Theory of Stimulated Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Gain Formula for Cold Beam ............................ B. Gain Formula for Warm Bea ............................ IV. Experimental Metho ............................ A. Classification. . . . ................... .... B . Apparatus and Di ......................... .... C. Superradiant Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Laser Oscillator ............................ ........... E. Future W o r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References ........................ ............................

48 49 49 53 57 59 60 66 61 61 68 71 75 81 82

The free-electron laser (FEL) is a device, tunable in frequency, that involves the stimulated backscatter of a pump wave from the “free” particles of a relativistic electron beam. In contrast, conventional lasers, which depend upon energy states of bound electrons in an atomic or molecular structure, are characterized by a finite number of discrete fixed frequencies. The type of FEL emphasized in this chapter, the collective free-electron laser, uses a magnetostatic ripple magnetic field component as a pump wave, and requires an intense (high-current) electron beam of up to a few MeV of energy guided along a strong magnetic field. This device, of great interest in connection with the generation of tunable, high-power coherent radiation in submillimeter and infrared spectral regions, in its initial version producing 1 MW of power at 400 p m (McDermott et al., 1978b),is capable of operating at high efficiencies-on the order of 1-5%. Possible areas of application might include heating of CTR 47 Cnpyrieht @ 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0~12-014653-3

48

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

plasmas, photochemistry, molecular spectroscopy, radar, and communications. In connection with conventional lasers, it should be noted that great strides have been made recently in the development of pulsed high power at a few fixed frequency locations in the submillimeter spectrum. Optically pumped gas lasers have operated with megawatt levels at 385 p m with D,O as the active medium (Evans et al., 1976), 496 pm with Y H 3 F (Evans et al., 1975), and 1220 pm using 13CH3F(Hackeret a / . , 1976). [For a complete review of pulse optically pumped far infrared lasers see DeTemple ( 1979).] Mention should also be made of the gyratron, a low-current (ampere) device with modest relativistic beam energy (- 50 keV) that is characterized by long-pulse, high-average-power operation. Although this oscillator performs optimally at the longer millimeter wavelengths, at the short wavelength limit of operation, 1-5 kW of power at 900 pm has been achieved with a 6% efficiency. Several survey articles are available to the reader and cover in detail all phases of theoretical and experimental gyratron development, the most recent being those of Hirschfield and Granatstein (1977) and Hirschfield (1979). Section I is a historical review of scattering research and develops basic expressions and concepts. Section I1 presents some physical principles associated with intense relativistic electron beams followed by a brief overview of high-voltage pulsed-power technology. In Section I11 a general theory for both the two- and three-wave stimulated scattering process for a cold relativistic electron beam is presented. After examining the temporal behavior of an amplified electromagnetic wave, we consider the question of efficiency. This section concludes with a Vlasov formulation of the gain for a beam of finite temperature. Section IV deals first with a description of apparatus and diagnostic methods; next the results of traveling wave stimulated scattering experiments that involve the growth of amplified noise are discussed; and finally a detailed review and interpretation is given of the results of the collective FEL oscillator experiment. 1. SCATTERING FROM RELATIVISTIC ELECTRON BEAMS

We present briefly an overview of radiation processes relating to the scattering of electromagnetic waves from relativistic electron beams. We distinguish between two principal types of scattering-front scattering, which involves double Doppler-shifted backscattering of the incident wave due to the discontinuity of refractive index presented by the leading edge of an electron beam moving near the velocity of light, and body scat-

THE FREE-ELECTRON LASER

49

tering, a process that in general involves a parametric interaction between an incident “pump” wave of power level above a fixed threshold, and results in the backscattering of an appropriately Doppler-upshifted backscattered wave. In this section we first present a brief description of the scattering processes together with a concise historical review of scattering research to date, follow by the development of a set of basic expressions common to all types of backscattering, and conclude with a physical description of the stimulated Raman scattering process. A . Front Scattering

The interesting features of electromagnetic wave interaction with a reflector moving at relativistic speed were first recognized by Einstein (1909, but it was Landecker (1952) who first described how the front of a magnetized relativistic electron beam may serve as just such a reflector. As will be discussed, if an electromagnetic incident wave has frequency u;, the backscattered-wave frequency is US 4y%; (+ = 1/[1 - ( v ~ / c ) ~ ] and vb is the beam velocity). By invoking conservation of momentum and energy it can be shown that for an ideal interaction, both scattered energy and power will increase by the same factor, except that for a perfect beam front mirror the power increases as y4 because of time compression. Granatstein er al. (1976) succeeded in actually realizing a relativistic mirror in an experiment that exploited the axial density gradient in the front of an intense relativistic electron beam pulse. Their first experiment demonstrated the conversion of a 3-cm incident wave into an 8-mm backscattered wave with power gain of about 2; and in subsequent studies scattering at 6 mm with a gain of one order of magnitude was achieved due to an increase in the average velocity of the beam front electrons brought about by a steepening of the accelerating voltage rise time (Pasour et a l . , 1977). The only other experiment on beam front scattering was reported by Buzzi et al. (1977). They observed an expected upshift of a masergenerated 3-cm incident wave to 8 mm with pulse compression as predicted.

-

B. Body Scattering In considering a historical review of stimulated scattering, two broad categories of experiments can be identified in terms of the nature of the incident wave. This wave, the electric field of which acts to drive the beam electrons at a “quiver” velocity thus initiating the excitation of an appropriate parametric instability, may take the form of a real incident electro-

50

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

magnetic wave or of a virtual wave. The latter case prevails when a periodic transverse magnetic field (a “wiggler” or “undulator”) is superimposed on the background axial magnetic field. In this case, 0,’ = 29v& (k; = 2 ~ 1 1and , 1 is the field period). We can further distinguish between a two-wave scattering process, wherein the stimulated electrons do not interact, and a three-wave collective (Raman) scattering, wherein the beat between the scattered and pump waves excites a collective mode of the beam. For the former case the gain is low, the spectral width is narrow, and finite length effects dominate. In the Raman case, an interaction that is generally associated with high density or intense relativistic electron beams, the gain is exponential and beam thermal spread must be narrow so that the collective beam mode is not excessively Landau damped. Within the parameter space that characterizes the Raman scattering process, Sprangle et al. (1979a) have identified two regimes associated with different physics-the strong- and weak-pump limits. In the weakpump regime the potential associated with the ponderomotive force is not large enough to appreciably alter the electrostatic body wave space charge potential, whereas for the strong pump case, the scattering mechanism is described by an idler electrostatic wave dispersion dominated by the ponderomotive forces. The stimulated scattering of photons by a group of electrons was discussed by Kapitza and Dirac (1933). The first analysis of highifrequency radiation from an electron beam in the presence of a modulating magnetic field was made by Motz (1951), while the first experiment on stimulated emission with an electron beam-“wiggler” configuration was reported by Phillips (1960). His device, the Ubitron (modulated beam interaction), utilized a low-current nonrelativistic beam and generated kilowatts of millimeter radiation. The first truly relativistic experiment demonstrating stimulated scattering was in the high-gain collective or Raman regime and was conducted at the Naval Research Laboratory (Granatstein et al., 1974). Utilizing a n intense relativistic beam (1 < V < 3 MV, Z = 30 kA) in a cyclotron maser apparatus devised by Friedman and Herndon (1972a,b), the group observed coherent radiation at submillimeter wavelengths at a power level orders of magnitude greater than could be accounted for by any cyclotron harmonic process. They speculated that the spurious radiation was due to the stimulated scattering by cold portions of the electron beam of the 100-MW centimeter-wavelength maser radiation that had been created further downstream, and were supported by an analysis of this process by Sprangle et al. (1979, subsequently confirmed in another redesigned experiment in which 1 MW of 400 pm radiation was observed (Granatstein et al., 1977).

THE FREE-ELECTRON LASER

51

Until recently these were the only successful experiments reported in which an electromagnetic wave was used as a pump to initiate the three-wave scattering process. In an experiment in 1979, a group at the Lebedev Institute, utilizing an undulating-wall, backward-wave oscillator to provide the hundreds of megawatts necessary to exceed pump threshold, reported observing several backscattered waves at a variety of upshifted wavelengths in the millimeter region due to the stimulated excitation involving a number of beam-waveguide normal modes (Zhukov er al., 1979). The first relativistic stimulated scattering experiments in the two-wave region were carried out at Stanford University. These experiments reported by Elias ef al. (1976) utilized a low-current electron beam in a linear accelerator ( I = 70 mA, V = 24 MV), and achieved 7% amplification at 10.6 ,um using a helical magnetic pump at 2.4 kG. Later a similar experiment was performed in the laser oscillator mode by Deacon et al. (1977) achieving a peak power of 7 kW at a wavelength of 3.4 ,um utilizing the same magnetic pump configuration with a more intense and somewhat higher energy beam (Z = 2.6 A, V = 43 MV). The 7 kW peak power output represented 0.01% of the energy in the beam. Since amplification is due to interference between several scattered waves, the gain is strongly dependent on undulator finite length. The initial analyses of the Stanford free electron laser were quantum mechanical (Madey, 1971; Sukhatme and Wolff, 1973; Madey et al., 1973). However, subsequent research has shown that a classical treatment of the stimulated scattering process is satisfactory (Colson, 1978). As discussed in Section 111, for the range of parameters that characterize the Stanford FEL experiment, an appreciable increase in gain would exist for a modest increase in beam current density due to space charge effects (McDermott and Marshall, 1980). The first series of experiments using a static magnetic field undulator as a “zero frequency pump” for the excitation of a true Raman scattering process was conducted by a group at Columbia University. Utilizing a 10-nsec pulsed intense relativistic beam at 700 kV and a variety of electron beam and undulator configurations, they conducted a parametric study that clearly established the salient characteristics of this 3-waveparametric scattering process. Efthimion and Schlesinger (1977), generating high-power pulses at wavelengths ranging from 6 cm to 3 mm, showed that the mechanism involved the coupling of waveguide modes to the negative energy cyclotron and space charge idler modes (Manheimer and Ott, 1974) and demonstrated the equivalence of stimulated Raman scattering to a waveguide normal-mode model. Marshall et al. (1977a), by reconfiguring the experiment and operating at higher magnetic pumping fields, succeeded in producing multimegawatts of power in the 1-3 mm range, and by using an electromagnetic undulator that permitted the

52

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

varying of pump field independent of bias field (Marshall et al., 1977b) established the linear dependence of growth rate on pump amplitude, implying that the interaction is in the weak-pump (Sprangle et ul., 1975) Raman regime. The detailed spectral characteristics of the radiation of the cyclotron and plasma idler modes were studied by Gilgenbach et u / . (1979a), and the role of cyclotron damping in accounting for output power variations with applied magnetic field was suggested (Gilgenbach et ul., 1979b). McDermott et ul. (1978a,b) reported on the realization of a collective Raman free-electron laser for the first time. This device, an examination of which forms the main focus of this chapter, followed the superradiant stimulated scattering studies mentioned above, and involved a cooperative effort with a group at the Naval Research Laboratory. The experimental configuration was redesigned to permit several passes of feedback by employing a quasi-optical cavity in the longer pulse (-50 nsec) NRL VEBA device (Parker and Ury, 1975). Laser output of 1 MW at 400 p m and line narrowing to Aw/w = 2% were observed, the latter figure to be compared with a typical value of Aw/w z 10% for the superradiant oscillator studies at Columbia. A detailed discussion of the collective freeelectron laser experiment together with an examination of new directions for performance enhancement is given in Section IV. In still another adaptation of the undulating magnetic-field configuration, Walsh et al. (1980) have recently conducted a series of experiments designed to demonstrate the feasibility of utilizing an accelerator with lower voltage and current (V < 100 kV, I < 30 A) to realize a millimeter wave oscillator (-4 mm) with repetitive microsecond-long pulsed output. Referred to as a Cerenkov-Raman maser, the device employs the magnetic wiggler for exciting a collective stimulated process in the presence of a dielectric medium that permits an additional frequency upshift. This latter effect may be described in terms of the approximate scattering up-shift expression given earlier, 0: = 2y2/kLVb, or more accurately 0; = khVb/(1 - p). (Here kh = 2.rr/l, the “wavenumber” of the zero frequency pump.) For the Cerenkov-stimulated scattering this latter expression becomes =khVb( 1 - np). For a given upshift we require a more modest p for a real index of refraction n . For n p > 1 we pass into the collective Cerenkov instability regime (Walsh er a / . , 1977). It is to be noted that the mechanism responsible for the operation of this maser is related to an earlier theoretical analysis by Schneider and Spitzer (1974), who proposed the exploitation of a synergistic effect combining (in their case) stimulated scattering with the shock wave produced when an electron beam moves faster than the speed of light in a background gas. Evolving in parallel with the experimental investigations touched on

THE FREE-ELECTRON LASER

53

above, various theoretical studies on stimulated scattering have been carried out. Sprangle et d . (1975) were the first to find the growth rates of the weak pump scattering process, and in a subsequent nonlinear analysis, growth rates pertinent to all high-gain processes and corresponding efficiencies were found (Sprangle and Drobot, 1979). The linear formulation of Kroll and McMullin (1978) not only yielded the growth rates for the high-gain regime, but also accounted for the low-gain two-wave scattering process. High-gain processes were further analyzed by Hasegawa (1978) using a relatively straightforward analysis carried out in the beam frame, and by Bernstein and Hirschfield (1979), who treated the process as an initial value problem. In Section 111 we reformulate the Hasegawa theory to account for arbitrary gain-scattering processes. Utilizing computational particle simulation codes, Kwan et a / . (1977) analyzed the nonlinear problem. Subsequently, using similar numerical codes, Lin and Dawson (1979) showed that efficiencies on the order of 25% could be achieved by an appropriate profiling of ripple length and pump amplitude (see also Sprangle ct a l . , 1979b). In concluding this overview of stimulated scattering research we note two recent review articles by Gover and Yariv (1978) and Sprangle et t i / . (1979a). It should also be mentioned that Gover and Yariv (1978) propose an FEL scheme that synergistically combines the Smith-Purcell effect with a three-wave scattering process.

C . Busic Concepts Although the details of mechanisms associated with the various types of electromagnetic wave scattering from a moving electron beam may differ and depend upon such parameters as beam density, temperature, pumping field amplitude, and interaction length, there are certain basic properties common to all scattering processes. In what follows we identify some of these common elements. In the particle frame, an electromagnetic pump wave of frequency o,, and wavenumber ko is incident on the electrons, resulting in the development of a body "idler" space charge wave that we characterize by oi, ki, and a back-scattered electromagnetic wave at osrk,. Recalling the Manley -Rowe equations, which are based on conservation of momentum and energy, we have

To find the Doppler shift expression for the backscattered wave we

54

T. C. MARSHALL, S . P. SCHLESINGER, D. B. McDERMOTT

employ the relativistic transformation from the particle (unprimed) to the lab frame (primed): wo = y(w;

khvb),

w, = y ( 0 ; -

k;Vb)

(2)

where y = (1 - p2)-1’2 as identified earlier. Using Eq. (la) we have (a;

- kiVb)

=

(04 + k4Vb) - * / y

(3)

and taking w;/k; = w;/k; = c, we get

Three-wave scattering will be observed if the “beat” frequency of the two electromagnetic waves corresponds to one of the beam modes of oscillation, i.e., wi = w,, where wp = (47rne2/y~)1’2 is the electron plasma frequency of the cold beam, or q = = eBo/mc is the cyclotron frequency of the electrons within the guiding magnetic field B o . The general Doppler upshift equation is

a,

or

For the case that a, and o,are small compared to wo, 0,‘ = (1 which for p - 1 becomes CrJ;

= 4pw4

+ P)2ybA, (6)

the approximate expression used earlier. In practice these “Stokesscattering” relationships pick out the unstable combination of the three waves, in which the scattered usand idler wi waves grow from noise, feeding on the energy of the pump wave wo. Equations ( 5 ) and (6) represent the case for general body scattering, but two other cases of interest here follow easily. For the case that the incident electromagnetic pump wave is a magnetostatic ripple with period 1 and frequency zero in the lab frame, we simply use Eq. (3) with k; = 27~/1, yielding

THE FREE-ELECTRON LASER

55

or w,’ = 2y2kAVb

For the case of scattering from the beam front, wo = [Eq. (la)], yielding

(8) w, in the beam frame

or O;

(10)

= 4y2w&

For further physical insight, we consider a brief description of the pumping mechanism associated with the three-wave stimulated scattering process. Before doing that, however, we distinguish the Raman from the Compton process. As stated earlier, the Raman process, characterized by exponential gain, is based upon a three-wave interaction that involves the excitation of a space charge mode in the body of the beam. Such a collective action can exist only if the wavelengths of interest (i.e., A& andA6) are large compared to Debye length A; (see Section 11). That this is not just a simple matter of beam particle density can be seen from a consideration (particle frame) of AD = Vm/%, where v t h is the spread of beam parallel velocities and is related to the beam energy spread by c Ay/y. Thus, even though we are dealing with an intense relativistic electron beam in the kiloampere range, it is not obvious that we are in the collective regime until we examine the beam energy spread. On the other hand, given the ampere beams of the Stanford experiments, and considering the extremely small S y / y for their 50-MV accelerator, it is not obvious that space charge effects will play no role. For the intense-beam case with n b 2 lox2~ r n a- ~ typical value 6 y / y must be less than 3% for A; = A; = 1 mm. It would be of interest to consider still another way of looking at the differences between these two regimes of parameter space-this time in terms of the relationship between the phase velocity of the space charge wave and the electron distribution in velocityf(u,). For the case of stimulated Raman scattering the phase velocity of the plasma wave is much larger than the thermal velocity, i.e., milki uth, meaning that the entire electron distribution can participate in this wave-which takes the form of an electrostatic wave at q = %. Utilizing our equations and noting that k D = 2 n / h ~ ,

-

*

kD

k,

+ k,

( 1 1)

i.e., for stimulated Raman scattering the Debye wavelength must be smaller than either the incident (pump) or scattered wavelengths. When the electron beam is relatively warm the phase velocity of the body wave

56

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

falls “within” the beam velocity distribution, whereupon the conditions of Eq. (1 1) do not exist and only particles resonant with the beat disturbance between the pumped and scattered waves can participate in stimulated scattering-in this case called a Compton process. Assuming that the conditions for a Raman collective process do exist we turn next to a physical description of that process, taking as an example a,case where the forces that produce the electron quiver motion (i.e., the pump) derive from the transverse component of rippled magnetic field of period I, which in the beam frame appears to oscillate at wo = y ( 2 r / f ) V brad/sec. The transverse part of the pump field B; drives a transverse quiver motion of the electron V , , where V , = eyB;/rnwo. (For B; 500 G, less than 10% of Bo for a typical case, and I = 8 mm, V ; / c 0.04, which corresponds to what would prevail for an electromagnetic wave pump 100 MW/cm2-well above the threshold of this parametric process.) Assuming for the moment the existence of a strong transverse electromagnetic backscattered wave of frequency us, a beam space charge mode is developed at the difference frequency wo - w,, driven by the bunching action of a longitudinal nonlinear pondermotive V x B force. The space charge fluctuations Sn at wo - w, can combine with the transverse quiver velocity to yield a nonlinear current source term JNL for the scattered field Es: 0 2 E , = -4riwSJNL(ws), where JNL a Sn(w, wo)V,(wo).The backscattered wave E, appears in the laboratory upshifted in frequency. Further insight regarding the stimulated scattering process can be obtained by reference to the “Stokes” diagram of Fig. 1. Here we show the various w , k interrelations as first given by Eq. ( 5 ) in the beam frame. Whereas the pump and scattered signals are almost equal in the beam frame-the latter appears Doppler upshifted in the laboratory frame and m; = 0.

-

-

-

\

PUMP

lw

5

ELE TROMAGNETIC BRANCH

FIG.1. Dispersion curves and Stokes diagram for the electromagnetic and electrostatic modes of the electron beam @article frame, p = 1); the three-wave interaction is included.

THE FREE-ELECTRON LASER

57

11. PROPERTIES OF PULSEDINTENSE RELATIVISTIC ELECTRON BEAMS Briefly outlined here are some features relating to the propagation of intense (i.e., beam current of several kiloamperes) unneutralized relativistic electron beams in vacuum, along a strong guide magnetic field. The electrons have relativistic velocity p = vb/c =s 1 and are characterized by the relativistic factor y = (1 - pz)-l/z;hence the total particle energy is W = ymc2 and the particle kinetic energy is E = ( y - l)mc2. The electron density of the beam n can be measured in the laboratory frame by observation of the current density, once the beam cross section is determined from inspection of the damage pattern to a plastic or foil “witness plate.” The total current can be measured with a Faraday cup. The invariant plasma frequency w, = ( 4 7 r n ~ ~ / y m )characterizes ”~ the space charge effects of the beam. The beam configuration is typically either a thin cylindrical shell of radius a in a grounded metal pipe of radius b, or a pencil beam on the axis of the pipe, or “drift tube” (see Figs. 4 and 9). When the beam current density is high, e.g., z lo4 A/cm2, the beam should be positioned near the grounded wall -this reduces the depression of potential due to the space charge of the beam and prevents unnecessary reduction of y. A limiting current can be propagated, given by

for the shell beam, whereupon the electron energy - Y Q / ~ (Nation and Read, 1973). When the total current emitted from the cathode is small, it is advisable to form a well-focused pencil beam having cross section = 1 mm2 and current density = lo3 A/cm2. The space charge of the beam has two other important effects: modification of beam equilibrium and introduction of a shear in the electron momentum parallel to the guilding field. Space charge causes a radially outward force on the beam, whereas the pinching effect of the beam current from its azimuthal magnetic field is radially inward. These two forces cannot balance unless the beam is partly neutralized. On the other hand, if an unneutralized beam is guided by a strong magnetic field-several times as large as the azimuthal field-then an azimuthal rotation of the beam results in order to provide a balance of radial forces (Davidson, 1974). This situation obtains up to a limiting space charge density of the beam; the condition is that w i / @ 5 4/2. This is well satisfied for lo4 A/cmZ beams providing B, = lo4 G . The rotation of the beam will not

58

T. C. MARSHALL, S. P. SCHLESINGER, D. B . McDERMOTT

give rise to appreciable diamagnetism provided the beam rotation frequency is considerably less than SZ, (Lawson, 1977). The appearance of transverse particle motion in the beam detracts from the laminar flow property, which is very desirable in any device application. In order that radial components of particle motion be negligible compared with the component parallel to the guiding field, it is necessary that Z << ZA,where ZA 17,OOOpy A. Another way of stating this is to say that the characteristic beam parameter v / y e I , where Y = Ne2/Mc2 is Budker’s parameter ( N is the number of electrons in beam per centimeter of length). Thus the electron beams under consideration here are not particularly “intense” by the standards of contemporary intense electron beam generation ( v / y = 1). The change in potential across the beam radius (or shell thickness) xo can result in a spread of electron energies AE/E = o:d/cZ,If the radial electric field from the space charge distribution is nonuniform, there is also a shear in beam rotation; this effect can cause beam radial diffusion due to diocotron instabilities (Carmel and Nation, 1973). The growth rate of these instabilities is a small fraction of w, ( = 4 2 f i c ) and typically causes beam profile deterioration after 1-2 m of beam propagation along B,. Stability of the beam is improved-again for strong magnetic field-if WE < 2ySZcc/b(Wong et al., 1973). The space charge potential results in a spread of electron velocities parallel to B, and thus the electron beam equilibrium requires a “temperature” (Davidson and Uhm, 1979). However, collective (wave) effects will dominate the beam plasma physics providing that the wavelength A of these motions is larger than the beam Debye distance AD:

-

27rc 4 AA(lab) = YWP Y where by characterizes the spread of particle energy in the beam. It is interesting to note the appearance of the skin depth c/o, in this formula. and y -- 3 , the Debye distance falls near For a beam having A y / y = 100 pm. A beam having a current of several kiloamperes can be formed by cold-cathode emission in an electric field 2300 kV/cm. A suitable cathode material is graphite, which gives uniform and reproducible emission. The cathode is positioned in front of a step (see Fig. 4, p. 72) or can be inserted inside the drift tube. The geometry of the cathode, the diode chamber, and the beam and its drift tube determines the impedance of the beam; this generally falls in the range -20-50 R. The pulsed-power device that drives the beam usually involves a capacitor bank storage system that can be charged in parallel at low volt-

THE FREE-ELECTRON LASER

59

age (e.g., 50- 100 kV) and erected in series as a Marx (500-2000 kV). Energy storage in the Marx capacitor bank is on the order of several kilojoules. The Marx charges a transmission line, in a fraction of a microsecond, and this pulse-forming line generates a square pulse of voltage at the diode. The line may be a coaxial pipe filled with oil (dielectric constant E = 2.5) or water ( E = 80) as a dielectric; water is preferred because a long pulse results from a comparatively short line, although the typical impedance for a water pulse line is 5 10 R and this may require a transformer section between the line and the diode for a suitable impedance match. The output pulse of a terminated coaxial line is half the Marx output; however, use of the Blumlein configuration provides a pulse that can exceed the erected voltage of the Marx. The pulse length of the applied voltage to the cathode can be as long as 100-500 nsec, although a complication of long pulse operation is that the diode impedance becomes markedly time dependent. This occurs because of the emission of plasma from electron bombardment of anode surfaces. Systems for providing intense electron beams are manufactured by Maxwell (Poco-beam), Physics International (Pulserad) and HewlettPackard (Febetron). Systems similar to this have been tested for repetitive pulsing at rates E= 100- 1000 pulses/sec using advanced design machines.

111. THEORYOF

S T I M U L A T E D SCATTERING

Theory of the general stimulated backscattering process for a cold, relativistic electron beam propagating through a spatially periodic, transverse magnetostatic field is presented. The model not only describes the Columbia-NRL FEL, but also has ramifications for the earlier FEL experiments at Stanford for which collective effects were assumed negligible. We find that the oscillating two-stream instability contributed to the observed gain of the Stanford oscillator experiment. The amplification of an electromagnetic wave of arbitrary frequency by the relativistic beam within the undulator is derived (McDermott and Marshall, 1980). We look directly at the temporal behavior of the scattered wave by focusing on the nonlinear driving currents and by using the Laplace transform. The Laplace technique is necessary in order to uncover any finite-length effects. We invoke the simplifying assumptions of no transverse spatial dependence, and no self-electrostatic or guiding magnetic field-their existence can permit excitation of a transverse cyclotron wave. However, this derivation ignores that effect. Once the amplifier experiment is understood, the description of the oscillator experiment

60

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

follows trivially -the output radiation of the oscillator is dominated by the wave that has the highest gain. The process is analyzed in the electron beam’s moving frame of reference, where the magnetostatic rippled field becomes Lorentz transformed into an electromagnetic wave with phase velocity pc. The amplitude of the electric field of the pump wave EL is related to the transverse magnetic field by the relation EL = PB, = j3yBl = y B ; , where B; is the amplitude of the transverse ripple measured in the lab frame. Rather than use Vlasov theory and later assuming a 6 distribution in velocity space, in Section II1,A we derive the gain formula by using the fluid equations. The theory presented is then valid for an appropriately cold electron beam. The gain formula for a cold beam is evaluated in the strong and weak pump regimes in Sections III,B and III,C, respectively. In Section III,D we relax the requirement of a cold beam and discuss the effects of finite temperature; here a Vlasov treatment is necessary. A . Gain Formula f o r Cold Beom

The perturbative ordering is the same as that used by Colson (1978) in his analysis of the Stanford FEL-the pump and scattered radiation fields are first-order quantities and the velocity induced at the beat frequency is second order. As viewed in the beam frame, a strong, high-frequency velocity modulation is induced upon the electron beam as it flows through the pump field. For the Columbia-NRL FEL experimental conditions, the quiver velocity induced by this wave =c/25 in the beam frame. The pump wave quiver in the Stanford experiment is even larger, >c/2, and so we must use a relativistic formulation to describe the quiver velocity magnitude in terms of the pump wave: V , / c = (n,/mO)fp, where R, = eB,/mc, wo is the pump frequency, and = [l + ( f 2 , / ~ ~ ) ~ ] repre-”~ sents the relativistic correction. The pump wave varies like {exp[j(w,t + koz)] + c.c.} and the backscattered wave is chosen to be [E,(t)exp(-k,z) + c.c.]. After Fourier transformation of the spatial variable the coupled equations are (wi

+

$)

& t ) = -27ren0(l + f p ) n , V & f )exp(-jw,t)

E,(f) = 2nen, {O,u(r) exp(jw,f)

(14)

61

THE FREE-ELECTRON LASER

(d/dt)V,(t)= - (e/m)E,(t>

(17)

(d/dt)[n(t)/nol = j ( k 0 + k,)u(f)

(18)

where all quantities are defined in the beam frame. Equations (14) and (15) describe the generation of the longitudinal plasma oscillation (amplitude 6) and the scattered transverse wave E,(t), respectively, in terms of nonlinear currents. Equations (16) and (17) represent the force equations for the two fields in terms of the motion u(t) at the beat frequency and Vs(t)at 0 , . The continuity equation [Eq. (18)] for the longitudinal mode [density n ( t ) ]closes the set of equations. These equations are valid for either circular or linear polarization of the pump wave. Though both terms on the right of Eq. (15) are third order, the first term has 1 ; it is included for comlittle effect on the scattering rate as long a s h pleteness. The ponderomotive force from the pump and the scattered wave bunches the electrons [Eqs. (16) and (18)], strengthening the longitudinal plasma wave [Eq. (14)], while the nonlinear current from the mixing of the quiver velocity and the density bunches drives the backscattered wave [Eq. (15)]. We apply the Laplace transform to each equation. Then after algebraic manipulation-elimination of variables -the inverse Laplace transform is applied, yielding E,(t) in terms of a Bromwich integral:

-

where and where q = oo - w, is the beat frequency. In the derivation of Eqs. (1414 19) we have consistently neglected terms proportional to w:/&$ E,(r) can be written in terms of residues: e-jol

where

+

el, e2, and e3 are the roots of the cubic -epn = ere + (ei + e,)l[e + ce, - e,)]

with 8, =

-

w,t,

Oi = q f ,On = (fl:/2ws)t;

-A92

(22)

t represents the time duration of

62

T. C. MARSHALL, S . P. SCHLESINGER, D. B. McDERMOTT

the interaction as observed in the electron beam’s frame of reference ( r = L / y p c , L is the length of rippled field). The scattering rate is governed solely by the parameters On, 8,, and 0,. Exponential growth can occur for 6, = 6,; here, the beat frequency corresponds to the negative-energy (as viewed in the lab frame) normal mode of the beam. If we solve the last equation for 6, = 6, we find

-$en

=

#(e + 28,)

(23)

The following two sections deal with this equation in two limits. 1 . Strong Pump Regime

For 6,

9 6,,

which was true for the Stanford FEL, Eq. (23) becomes

-@,en = B (24) and the exponentially growing root has an imaginary component equal to fi/2(4,$)1’3. This case can be further divided into two regimes. If 4,8, 9 1, exponential growth is dominant; this is called the oscillating

t

-10

FIG.2. Dependence of normalized gain upon the pump signal mismatch with plasma frequency as a parameter: w,t = l O O O , ~ , f = 800; curve A -, w,f = 0.03, GN = 0.087; curve B--.-, %r = 0.1, GN = 0.87; curve C- - - , %f = 0.3, GN = 8.7.

63

THE FREE-ELECTRON LASER

FIG.3. Dependence ofnormalized ga& upon plasma frequency with pump strength as a parameter. w,r =_lOOO; A, fiLf= 20; B, fi,r = 40; C , a L r = 80. q f = 2.6: D,n,r = 160; E, ?i,f = 320; F, f i , t = 640.

two-stream instability (Hasegawa, 1978; Sprangle and Drobot, 1979). If 4 1, then exponential growth is unimportant and the gain mechanism is dominated by interference effects: since two of the roots of Eq. (22) lie near - Oi, the normalized beat frequency, two of the residues in Eq. (21) may be combined approximately into the form of a derivative. Taking the definition of gain to be independent of reference frame as

%en

gain =

E,*(OEd?)- E,*(O)E,(O) E*(O)E(O)

we combine the derivative with the remaining residue and take the limit OD + 0 to find gain

=

-4@,,---

a

sin(8,/2)

ae,(

e,

)

This functional dependence of gain has been found and discussed in earlier treatments (Colson, 1978). It predicts that for a given undulator length the gain will be maximized by a specific mismatch between the pump and signal frequencies, in particular, for w,, - w, = 2.6/r. Here the gain is gain (8, = 2.6,

e,

+ 0) = 0.2700882,8,

= GN

(26)

64

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

The previous qualitative arguments can be made explicit through numerical solutions of Eqs. (21) and (22). In Fig. 2, normalized gain is plotted as a function of e, with ep (density) as a parameter. The chosen value for en (pump strength) equals that of the Stanford FEL. Curve A corresponds roughly to the density they reported in the amplifier experiment (Elias et al., 1976)-6, = 0.03. As expected, the gain is governed by interference and fits the functional form of Eq. (25). Curve B corresponds to the oscillator experiment (Deacon et al., 1977), where Op 0.1; the maximum amplification is higher by 15% than that predicted by Eq. (25). In Curve C we have taken e, = 0.3; here the gain is dominated by the 0scillating two-stream instability. Normalized gains at Oi = 2.6 for various values of 0, (pump strength) are plotted in Fig. 3 as a function of 6,. Curve F corresponds roughly to the Stanford FEL value for 0,. Notice that for a weak pump the gain is reduced from the “isolated-particle” scattering rate [Eq. (25)] by the inclusion of space charge, whereas the gain is enhanced with a strong pump.

-

2. Weilk Pump Regime-Raman

Scattering

For On e e,, which is true for the Columbia-NRL FEL, the exponential growth rate given by Eq. (23) is (8,6,/2)1’2; if this number is > 1 , then the electric field of the scattered wave satisfies E&t) = E,(O) cosh(e,e,/2)*’* exp(jo,r)

(27)

Exponential growth at o, = o, - w, dominates the o, spectrum. The width of this peak is found by allowing a three-wave mismatch, i.e., set Oi = 6, - 6, and solving Eq. (22) for imaginary roots:

-%en = e(e - s)(e+ 26, = 2e,e(e - 6)

- 6)

(28) (29)

An exponentially growing solution exists if 16) < 2(~9,0,,/2)”~.Note that bandwidth and growth rate are linearly related to one another. When three-wave resonance (oi= 0,) occurs in this regime, it completely overwhelms two-wave interference effects. a . Trapping. The formalism of the last sections breaks down for electrons that become trapped in the idler wave. This effect is discussed by Louise11 et al. (1979) for two-wave scattering, where the signal and pump combine to form an effective potential. The trapped electrons do not appreciably influence gain here, which accounts for Louisell’s result that as the pump field is increased (and therefore the beat potential strength too) the normalized gain decreases.

THE FREE-ELECTRON LASER

65

In three-wave scattering, the dominant trapping potential is that of the electrostatic idler wave. As the idler wave grows, the percentage of trapped electrons increases -three-wave gain will diminish. At some point, growth will effectively shut off. However, we are not considering the difficult question of energy transfer of trapped particles (bounce effects). We estimate the effective shut-off of three-wave growth by (Hasegawa, 1978): le4mer/ml = [vB(idler phase velocity)]2

(30)

The electrostatic idler wave grows until this relation is satisfied, i.e., when an appreciable fraction of electrons becomes trapped. Since the idler frequency is =q,,the idler wave grows until (E(q)( 47noe/ki

(31)

where ki is the idler wavevector and E ( o ) represents the Fourier amplitude of the electric field at the frequency, o. Comparing with Poisson’s equation, Eq. (31) states that the electrons are mostly trapped when 6n = no (the perturbation ordering scheme breaks down here too). We are interested in the maximum value attained by the signal wave. In superradiance the two waves grow together out of the noise spectrum; the signal, however, grows at a faster rate governed by the Manley-Rowe relations since w, % q.[Equations (14)-(18) can be rewritten as explicitly parametric equations with the result that u2 - u2 = const, where u = ( k , / ~ ~ ) ~ ’ ~and E ( uo ,=) (ki/20i)1~2E(~i),] As the idler and signal grow at the expense of the pump, ( k , / w , ) 1 ~ 2 E ( yremains ) roughly equal to (ki / ~ U ~ ) ~ / ~ EThe ( O signal , ) . electric field will grow until it satisfies:

IE(o,)(= ( 4 q , ) 1 / 2 ( 4 7 w / ~ d

(32)

We obtain a useful dimensionless relation by dividing the last equation by the magnetic ripple strength: J ~ m , , ( ~ s ) / ~ ~= ~ 2ac4/w&n:)

(33)

Equation (33) signifies that no more than the above fraction of ripple pump energy (as measured in the beam frame) will be converted into scattered radiation. We should note that this is a rather liberal estimate, since trapping effects probably ensue earlier than implied by Eq. (30). b. Eficiency. What fraction of the electron energy is transferred t o the scattered wave? This is a complicated question because the answer depends on the saturation mechanism and can be determined only through complex particle -wave computer simulations. However, we can deduce several semiquantitative upper limits, which were first derived by Sprangle and Drobot (1979). If the three-wave parametric process runs to comple-

66

T. C. MARSHALL, S . P. SCHLESINGER, D . B. McDERMOTT

tion, i.e., until the pump is depleted, then the maximum energy density p in the scattered wave is so that we can expect an energy efficiency

All quantities are defined in the beam frame. The efficiency is reduced if trapping occurs fist, i.e., if W: < 4w,f&f, in which case,

’

= +(4!/wsfm

2

(w%)2 =

%PWS

(35)

For the Columbia-NRL FEL experimental conditions this implies a 4% efficiency. As the electrons lose their longitudinal energy to the scattered wave, they slow down and eventually the three-wave resonance is broken. For this case the efficiency of electron energy conversion into a particular mode is determined by the finite bandwidth of the dispersive growth rate: 17

=

AY/(Y - 1)

AY/Y == H A d 4

(36)

For the weak pump regime, from Eq. (29) we have 7) =

(%/80s)1’2(f&l/oo)

(37)

For the Columbia-NRL FEL conditions this efficiency = 1/2%. We have found three possible conversion efficiencies. The actual efficiency will be no greater than the minimum of these three values. Since the intercavity power level = 10 MW in the laser device (Section IV), this corresponds to an efficiency = 0.05%, and the first experiment was an order of magnitude shy of saturation.

B . Gain Formula for Warm Beam In Section III,A we used the fluid equations to describe the scattering rate, i.e., the thermal spread of the beam was neglected, which is valid if 4 2 k , % V,. If this criterion is not met, then we must use a Vlasov formulation. The general gain formula becomes

where

THE FREE-ELECTRON LASER

67

where f(O'(u,) is the initial electron beam velocity distribution function. If f(o'(u,) = S(u,), then this formula can be shown to equal our previous expression. The other interesting limit is q,/2k0 = Vth, where the collective behavior of the beam is lost; here the scattering is due to particles whose velocity nearly equals the phase velocity of the beat wave, q / ( k , + ks). In this limit, Eq. (38) is dominated by the pole near zero: E(t) exp(--jo,t)/E(O) = e x p [ j ( E ~ / 2 o , ) ~ ~ t 1

(40)

where

We have ignored this term compared to 1 in evaluating the denominator of Eq. (39), since the induced longitudinal field is nonresonant due to heavy Landau damping. Growth of the signal wave is due to the imaginary component of 8,. Using the Plemelj formula,

For a Maxwellian distribution, = [ ( 2 ~ ) ~ ~ % ~exp( , , ] --~ u2/2z+h2)

the growth rate is maximized when w1 = (k,

(44)

+ ks)uth,and is

This growth rate can be appreciable, but saturation is quickly reached because of bounce effects. Also, the efficiency is rather poor due to the small number of particles participating in the scattering process. IV. EXPERIMENTAL METHODS,DEVICES,A N D RESULTS A. Classification

It is possible to identify three configurations that will produce appreciable amounts of radiation in the submillimeter regime using stimulated Raman scattering from intense relativistic beams: (1) the superradiant amplifier, (2) the laser oscillator, and (3) the laser amplifier.

68

T. C. MARSHALL, S . P. SCHLESINGER, D. B . McDERMOTT

In the first case, we have a traveling-wave amplifier system with gain capable of amplifying to high level a noise signal present at the input. Since the gain is dispersive, a narrow band of frequencies is preferentially amplified and the output shows a certain degree of coherence. This situation is now understood rather well experimentally and theoretically; we can understand the operation using the three-wave parametric concepts of Section 111, taking the pump always to be very much stronger than the signal or idler waves. The second case involves the use of the system of beam and rippled field as an oscillator by means of quasi-optical reflectors that provide a recycling of the output radiation to the input. The desirable properties of the oscillator-frequency stability and coherence-can be purchased at the price of efficiency. There is a fair understanding of how this system works and some experimental data. One complication in the analysis is that now the signal wave, in the intercavity zone, can become-in principlealmost as large as the pump, namely, the magnetostatic ripple. Finally, for a system in which high power and high efficiency is called for, there is the laser amplifier, wherein a strong coherent signal is supplied at the input of the traveling-wave amplifier system described above. Filters can be used to reject unwanted modes, and the ripple period can be slowly changed as the beam and signal move down the amplifier so that the frequency of the system remains constant as appreciable energy is extracted from the beam (Sprangle et al., 1979a,b). Computation has been undertaken for this configuration: efficiency (beam energy + radiation) -20-30% can be achieved by appropriate “programming” of the rippled field amplitude in the undulator (Lin and Dawson, 1979). Thus, a laser oscillator, followed by a stage of traveling-wave amplification (perhaps using the same electron beam line) presents-as might be expected-the optimum choice for generation of high-power, high-efficiency, coherent radiation. In this section we review experimental data and conclusions relating to the first two configurations described above.

B . Apparatus und Diagnostic Methods

In what follows we consider the signals generated by the interaction of a cylindrical-shell electron beam, situated near the wall of the drift tube, as it passes through an “undulator” of about 50-cm total length and period 1 = 8 mrn. The beam y ranges from = 2 to 3, the beam density 3 X 10” to 3 x 10l2cm3, and the guiding field B, = 10 kG.

THE FREE-ELECTRON LASER

69

1 . Field Ripple Devices

Two types of undulator are used to ripple the guiding magnetic field: a ferromagnetic structure and a pulsed electromagnetic structure. The ferromagnetic structures used include a set of alternating brass and iron rings, and also a square-channel helical groove milled on the outer surface of an iron pipe that fits snugly into the beam drift tube. The radial magnetic field ripple amplitude at the beam is -0.05 B,. Unfortunately the ripple cannot be controlled externally with these ferromagnetic structures, and there is also a large depression of field (B,) in front of the undulator, which expels some fraction of the beam as it enters [this was observed by lining the wall of the drift tube with thermal-sensitive “Witness paper” (Gilgenbach et al., 1978)l. The electromagnetic undulators were low-inductance systems of two types: first, a sequence of slotted plates in which the current flows in alternate directions creating cusp fields that-when superimposed with Bo-generate the rippled field; and second, a bifilar helical winding sandwiched between two insulator tubes, which slides over the drift tube. A pulsed current, up to 10 kA, can be passed through these structures to generate a component of radial rippled field = 1 kG at the beam location. Cusp or iron ring undulators produce rippled fields

B: = B,, sin(kk)I,(&r),

B: = - B y , cos(kb)I,(k;r)

(46)

(Io and ZIare Bessel functions of imaginary argument and k;

= 2 7 ~ / 1 )This . transforms to a linearly polarized E M wave in the electron rest frame. The helical undulator has field components

B:

=

-B,, cos(e

- ka)z,(k;r)

B; = BrOsin(8 - kk)[lo(k;r)- (l/k;r)Zl(k;r)]

(47)

B; = B~~cos(e - GZ)Z,(~;~)/(,~;~) However, in the shell beam geometry neither undulator provides an equilibrium for the beam. Evidence that there is no equilibrium is provided by lateral Witness papers-which show that electrons are continually ejected from the magnetostatic field ripples along the entire undulator length. The helical undulator is superior in this respect, however. The current in the undulator can be controlled at the entry point of the beam into the rippled field zone, minimizing the initial transient that otherwise will heat the beam (Hasegawa et a/., 1976). This transient also sets up a strong cyclotron motion of the particles. A pencil beam in a helical pump magnetic field provides the best beam equilibrium. A bifilar helical

70

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

winding provides a pump field amplitude B; (mks units) on the axis of magnitude

where KOand K,are the modified Bessel functions of the second kind, and a is the radius of the helical winding. 2. Spectral Resolution The wavelength of power in the millimeter-submillimeter spectral region can be measured by reflection meshes, a spectrometer, or a quasi-optical Fabry -Perot etalon. Reflection meshes are available for submillimeter wavelengths but these will give only a crude indication of spectral content since the wavelength dependence of their reflectivity is difficult to determine (Stauffer, 1976) with accuracy. These reflectors can be mounted in the light-pipe system, which is suitable to convey the radiation from the source to a shielded screen room where detectors, oscilloscopes, and other measuring equipment must be located. A spectrometer (Pasour and Schlesinger, 1977), specially adapted to the millimeter-submillimeter spectral region (0.5-5.0 mm), is a considerable improvement over the meshes. A polyethylene lens collimates the radiation, which is then diffracted by an aluminum echelette grating. The grating uses right-angle grooves with a blaze angle of 30"; this has been shown (Loewen et al., 1977) to yield a flat grating efficiency for 0.7 < A/d < 2 when the radiation is polarized with the electric vector perpendicular to the grooves (d is the grating spacing). A spherical mirror reflects the diffracted radiation to an array of detectors. The insertion loss of this type of spectrometer is approximately 12 dB, independent of wavelength, and the resolving power is = 100. Measurement of wavelength and spectral width A A ' / A ' can be made with a quasi-optical version of a Fabry -Perot interferometer. Two plane-parallel screen meshes are mounted in the light pipe; the adjustable gap d between the reflectors is measured with a micrometer. A crystal detector monitors the incoming power and another crystal detects the signal transmitted through the Fabry-Perot interferometer; thereby, shot-toshot power fluctuations are normalized out. The distance between interference maxima yields g / 2 and the normalized width of a maximum Ad yields the spectral width AAi/g = Ad/d or instrumental resolution, whichever is greater. The resolution is influenced by mesh reflectivity ( ~ 4 0 %and ) parallelism, which contribute to a limiting resolving power = 50.

THE FREE-ELECTRON LASER

71

3. Detectors The power level of the radiation can be determined by focusing the radiation through a polyethylene lens onto a 1.2-mm2Molectron P-3.00 pyroelectric detector. This detector can be calibrated at A = 1 mm by measuring its response to the chopped output radiation from a carcinotron; sensitivity of somewhat less than V/W was obtained for response to 10 nsec signals. Coarse meshes are placed in the light pipe to screen the pyroelectric from radiation with A > 1/2 cm, which is omnipresent in intense relativistic electron beam (REB) devices, and which tends to excite the electronics following the detector. A detector with higher sensitivity and quicker temporal response than the pyroelectric was required to study the functional dependence, spectra, and time resolution of the scattered radiation. For these purposes, 75-GHz Schottky barrier diodes (Chaffin, 1973) were used. The sensitivity of these crystals decreases monotonically for wavelengths shorter than the optimum 4 mm due to junction capacitance. Still, their 1 nsec risetime) is orders of magnitude better response (- 1 mV/W, than that of the pyroelectric device even for A < 1/2 mm. The crystals were originally designed with cavity resonators to further increase their sensitivity. However, to avoid strong frequency dependence of the detector, these “tunable shorts” were removed and replaced by a microwave absorber, which functions as a “matched terminator.” Total integrated electromagnetic energy of the scattered radiation can be measured using a graphite pyramid calorimeter (Efthimion et a f . , 1976) with a thermistor bridge circuit. As little as 0.01 J of electromagnetic energy will cause a reliable signal.

-

C . Superradiant Experiments *

Initially, in order to confirm that the high-power radiation emitted from the system (Fig. 4) was due to the stimulated process, the dependence of power upon pump amplitude (Fig. 5 ) and undulator length (McDermott et al., 1978a) (Fig. 6) was obtained. Figure 5 shows that the radiation is exponential in pump amplitude, so that the growth rate is approximately linear in pump amplitude as expected. Not shown in Fig. 5 but existing at 50 G = B; nevertheless, is the effect of a threshold of pump amplitude, which is to be expected in all parametric pumping processes. The growth rate obtained from Fig. 5 is = log sec-’, in approximate agreement with the spatial growth distance observed in Fig. 6. (In Fig. 6, a * From Gilgenbach et al. (1979a).

72

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

SOLENOID

r

I

PO LY E THY LENE

H H O R N AND WAVEGU ID E

1 SHIELDED

kPULSERAD 105 MARX AND BLUMLEIN

SCOPES

Lmm

WAVE SPECTROMETER

FIG. 4. Experimental configuration of the superradiant apparatus (zero-frequency

10 0

6 4

c

2

3

z

c

U

w

3

1

0.8 0.6 0.4

0.2

0.1

0

400

200 Bd ,l,i

(GAUSS)

FIG. 5 . Dependence of Raman backscattered power from the cyclotron wave idler upon pump amplitude: Bo = 9 kG,y = 2 . 5 , l = 8 mm.

73

THE FREE-ELECTRON LASER 10

i

L L

25

1

30

1 35

I

40

L , UNDULATOR LENGTH ( c m l

FIG.6 . Dependence of superradiant signal on length of rippled magnetic field, showing zone of linear growth followed by saturation (cyclotron idler). Ripple amplitude = .5%(Bo), E, = 9 kG, I = 8 mrn, y = 2.

more powerful and different-i .e., iron ring-undulator was used, thereby providing a zone of saturation.) Figure 6 also shows that the stimulated process can be described as a convective instability. In these experiments there is no complication from signal feedback: the accelerator pulse was very short (=S-10 nsec). Spectral resolution of the emitted power permitted identification of both the cyclotron idler and space charge (plasma) idler stimulated scattering processes [Fig. 7; see Eq. (31. The cyclotron idler process has the more rapid growth at this beam density; at higher beam current, the cyclotron wave suffers comparatively less growth and more damping than the space charge wave idler process (Gilgenbach et al., 1979b). Stimulated scattering from the cyclotron wave idler is possible because the magnetostatic pump amplitude is nonuniform in the radial (transverse) direction. Figure 7 also shows that the resonance width of the radiation A A / A = 10%. The dependence of line width upon pump amplitude is given in Fig. 8; there it was found that the line width increases as pump amplitude (and power) are increased. This is in accord with theory (Lin and Dawson, 1975), which shows that the growth rate is dispersive and that the span of unstable wave numbers increases as the pump increases. Extrapolation to

100

90

9I

A

I I

I

I

I

I

80 U

W

I

I I I

I I I

70

I

I

I

I 60 . I

A

I

n w 50

1

I

I L I 40 . I I W I a 30 . I

5

I

20 10 0

I

- h I

0

I I

I I

0

I I I

2 I

I

1.5

I

I

2.0 A(mm)

1

I

2.5

I

3.0

FIG.7. Scattered radiation spectrum (iron ring undulator). Solid curves, y = 1.8; dashed curves y = 2.1; 1 = 8 mm. Longer-wavelength radiation is from excitation of the cyclotron idler, and the shorter-wavelength radiation is from the space charge idler (all resonance amplitudes separately normalized to 100%).

O. l 4 l

0.13

I

I

I

I

I

I

FIG.8. Spectral width of superradiant signal vs. rippled field pump amplitude; 1 = 8 mm, superradiant system.

THE FREE-ELECTRON LASER

75

zero pump shows that AA/A = 0.06, and therefore the energy spread of the beam is AE/E = 0.03; as mentioned in Section 11, part of this effect (-0.01) is unavoidably due to beam space charge, and the balance probably has to do with the cathode-anode geometry and the field emission process. It should be noted that this traveling-wave system can amplify a high-level coherent wave: the bandwidth of the amplifier is merely a few percent and-as long as the signal is unsaturated-the coherence of the input wave should be maintained. However, the problems in using the stimulated Raman backscattering process as a superradiant amplifier for noise suggest that the introduction of feedback should greatly improve the performance of this system as a desirable source of coherent radiation.

D . Laser Oscillator* 1 . Experiments

Feedback of the output signal of the superradiant amplifier using a quasi-optical cavity with two mirrors should improve the performance of the superradiant system, providing that (a) excitation of more than one unstable mode does not occur, (b) the accelerator’s pulse length permits several bounces of the radiation in the optical resonator, and (c) the accelerator voltage remains constant during that interval. The first requirement is met because scattering from the cyclotron mode did not occur in the new laser experiments. This absence can be explained either by damping (Gilgenbach et al., 1979b) due to the higher beam density cm-3) or because the cyclotron wave is harder to excite with higher beam energy (y > 3). The accelerator used in the laser experiments only marginally fits the last two requirements: The pulse top lasts about 40 nsec, permitting approximately four passes of the radiation, but the voltage had a 20 nsec ripple, which is 5-10% of peak energy. The experimental configuration is shown in Fig. 9: a I.2-MeV, 25-kA cylindrical electron beam was produced by the Naval Research Laboratory’s VEBA accelerator. The beam was guided along a rippled field, down a 5-cm drift tube, which also formed part of a quasi-optical Fabry-Perot cavity. The beam was expanded adiabatically into the ripple field zone (by decreasing the guiding field) in order to cool the beam and minimize the transient effect on the beam by entry into the undulator. Strong (megawatt) coherent radiation at A, = 400 pn, corresponding to excitation of the space charge idler, was obtained when the mirrors were aligned * From McDermott et a / . (1978b).

76

T.

c. MARSHALL, s. P.

SCHLESINGER, D. B. MCDERMOTT

FIG. 9. Experiment of high-gain F E L with quasi-optical cavity. The electron beam is emitted from a 2.8-cm-diam cathode and is propagated in a 5-cm drift tube. MI and M2 are polished flat aluminum mirrors. Radiation is emitted into the light pipe through a polyethylene vacuum window.

(Fig. 10a) but only low-level superradiance was obtained (Fig. lob) when the optical system was misaligned. The narrow laser pulse, less than 20 nsec, shows that the system was lasing for only about two passes of the radiation in the cavity (radiation bounce time is = l o nsec); during this, the diode voltage (Fig. 1Oc) shows a 5-10% fluctuation, which-as we shall discuss-also has a detrimental effect upon the power output. Despite this fluctuation in beam energy or y , it was found that the wavelength of the laser radiation was constant during the pulse. Positive gain is observed at the front of the laser pulse, while negative gain is observed as the diode voltage begins to fall: the laser signal is driven down rapidly,

FIG.10. (a) The laser signal: ( b ) signal from apparatus with one mirror misaligned; (c) diode voltage = 1.2 MV; horizontal axis is time, 20 nsec/div.

77

THE FREE-ELECTRON LASER

I

100

1

I

I

I

200

300

400

500

SB,,

GAUSS

Fic. 1 1 . Laser power vs. pump amplitude: upper curve, system lasing; lower curve, superradiant mode.

then-presumably when there are no energetic electrons left in the cavity-the remaining radiation decays exponentially by leaking out of the cavity. The positive gain T L [T is the spatial exponential growth rate; see Eq. (27)] was measured to be TL = 2.0 2 20%, whereas [Eq. (27)] theory {TL = [(rB,/m)2w,l/8.rryc5]”2L) predicts T L = 1.6. A rather linear dependence of laser power observed as ripple field was increased shows that the output is unsaturated: indeed, the conversion efficiency in that experiment, where only two bounces of the radiation were obtained due to pulse limitations, was an order of magnitude less than expected (Fig. 11).

2. Intc.rprrttrtion

In the case of superradiant emission, both the idler and signal grow out of noise: the signal will grow at a frequency such that the idler is a normal mode of the plasma, i.e., a plasma flave. However, in the laser mode, the signal frequency is now constrained to be that of the fed-back cavity radiation produced by electrons that have left the resonator. Here, the beat wave between the pump and signal may not be a normal mode of the beam depending on the instantaneous value of y. For this reason, voltage fluctuation has a detrimental effect upon amplification. We now endeavor to find the gain of the electron medium as a function of beam energy and scattered frequency. It follows from Section III,A,2 that there are but two beam energies for which a three-wave interaction

78

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

will occur in which the ripple field participates. The cavity radiation will be amplified if the beam energy is such that the ripple field assumes the role of the pump and the cavity radiation is the signal. Then the negative energy space charge wave is excited and the scattered wave is given by

(Stokes scattering). However, if the beam energy is such that the cavity radiation satisfies

k$3c + op/y 1 - P (anti-Stokes scattering), then this radiation will be absorbed, because here the cavity wave has assumed the role of the pump while the ripple field is the signal. The Manley-Rowe relations guarantee that the pump is depleted. This corresponds to the positive energy space charge wave becoming excited. The situation can be described quantitatively using the results found in Section 111,A,2. If, after obtaining Eq. (22), we take w, = -q,since the idler is now the positive-energy wave, we find o; =

E&)

=

E,(O) c o ~ [ 3 ( q , o ~ ) ” ~ ( ~ ~ / o o ) t ] e ~ ~ ~(51)

assuming the idler wave is initially zero. If damping had been included, the solution would be similar to a strongly damped RLCcircuit. The result is strong absorption of the cavity radiation. The accelerator voltage difference between the two cases corresponds to y+ - y- = q,/k;c (McDermott, and Marshall, 1979). There is also a “parasitic” three-wave interaction, which is independent of the ripple field. At any energy the cavity radiation will act as a pump upon another electromagnetic wave as signal that must grow from noise. This is analogous to the existence of a multitude of scattered lines in any Raman scattering experiment: a signal wave can act as a pump upon another signal. Fortunately, the growth rate for this interaction is appreciably less than that of the positive gain process. The rate of growth depends linearly on the dominant quiver velocity, which is the quiver induced by the rippled field only if this wave is involved in that interaction: if not, as in the parasitic interaction, then the cavity radiation induces the dominant quiver motion, which is usually at least an order of magnitude less intense. A possibly useful (McDermott et a l . , 1978a) “parasitic” interaction occurs in the laser since the scattered radiation (A; = 1/24)is trapped between the mirrors and grows to high amplitude in the cavity. Then this radiation will serve as an electromagnetic wave pump for a new scattered wave at Ad, -- A6/4?; thus a relatively low y beam could pro-

79

THE FREE-ELECTRON LASER

GAIN / L E N G T H ( F O R SPECIFIC u;)

A

y

%

G % 2c

BEAM y

y+-y-

x

RESONANCE ENERGY

WP

K; C

FIG.12. Qualitative picture of gain/length for radiation at w, as a function of beam energy (parasitic interactions included).

duce short-wavelength radiation at wavelength

AA

= 1/8y4

(52)

The gain processes for a cold beam are summarized in Fig. 12; the electron beam is viewed as an amplifying medium with the radiation frequency as a parameter. The positive gain process occurs for a spread of electron energies Ay due to the dispersive growth rate, as given by Eq. (36),which is less than I% in our experimental conditions. Weak negative gain to the parasitic interaction exists at any energy, whereas at the beam energy corresponding to anti-Stokes scattering, the negative gain peak is strong enough to absorb the interacting cavity radiation in a single pass. For optimal performance of the collective free electron laser it is necessary that the beam y be held constant within narrow tolerance. This has two ramifications: (1) The accelerator voltage fluctuation must be kept to a minimum ( < 3 % in our case) so that the gain remains at least nearly positive. (2) If the beam density is too high and the geometry improper, the shear in y across the beam due to space charge may result in emission from the outside layer of the beam and absorption in the interior.

3 . Coherence and Line-NurroM!ing

Experiments with the superradiant emission from the laser system (no mirrors) using an external Fabry-Perot cavity detector showed that the linewidth was > lO%-similar to the exDeriments discussed in Section IV,C. (This could be anticipated in view of the fact that the accelerator voltage fluctuation was =5-lo%, and thus, since A: = 1 / 2 4 , AA; = 2(Ay/y)Ah .) In a conventional laser, we would expect a remarkable improvement in coherence, due to the narrow spectral linewidth and exci-

80

T. C. MARSHALL, S. P. SCHLESINGER, D. B. McDERMOTT

tation ofjust one or a few cavity modes. Unfortunately, these possibilities are not within our grasp-the cavity is long and the gain bandwidth for the three-wave process is enormous by atomic standards. Nevertheless, an improvement in linewidth-in the range A h / h = 1-2%-was observed in lasing, and can be understood simply. A similar improvement in coherence occurred in the example of the Stanford F E L oscillator: however, the Stanford electron beam had a much better energy spread than the beam used in our experiments on the collective FEL. Besides improving the unidirectionality of the emission-waves that do not satisfy k l mirror surface are not returned through the mediumthe mirrors allow feedback: This was their primary function. Effectively, the mirrors extend the undulator’s length. It would not be worthwhile to simply build a longer undulator because the superradiant experiments had attained saturation within 50 cm of interaction region (see Fig. 6 ) for reasons not completely known. The most obvious explanations are decay of beam quality and/or saturation of the idler-the idler has the smallest phase velocity and is therefore most susceptible to trapping and/or damping. Either explanation would suggest an optimum length undulator. We then must apply feedback to attain higher output power. A major contribution to linewidth improvement comes from the feature of the laser (optical feedback) system to regenerate and amplify radiation in the cavity, which lies only within the narrow range of wavenumbers [Eq. (29)] necessary to maintain three-wave resonance. This effect stabilizes the frequency of the laser against changes due to fluctuations in beam energy. The price that must be paid for this is a net loss in efficiency in the oscillator-a situation that is not serious, since the oscillator can always be followed by a stage of high-efficiency amplification attached to the same electroil beam. Equation (37) shows that the spectrum should have a bandwidth 1-2% due to this effect. Indeed, experimental data, obtained with a Fabry-Perot, show (Fig. 13) that the signal linewidth is of this order. Another source of coherence improvement has been demonstrated (Gamo et al., 1973) in experiments with high-gain laser media. If radiation having a bandwidth Amo is introduced into a single-pass traveling-wave amplifying medium having bandwidth Amo, the bandwidth of the radiation emerging from the system is

-

~ ~ ~+ r/ L( y i

(53) assuming a gaussian spectrum. Since r L = 2 for the original experiments, a two-pass system would give a 50% improvement in linewidth. Thus a net linewidth = 1% (somewhat beyond the capability of the submillimeter Fabry-Perot instrument, which had a resolving power -50) is to be expected. =

81

THE FREE-ELECTRON LASER

-

b f2.4 ’

2:6

’

28

% fi.4 ’

216

’

2 2

2.0

2.0

FIG.13. Fabry-Perot interferometer data at 10-nsec intervals; the peak laser radiation occurred at the time of (b) and (a) corresponds to an earlier instant. Note the laser wavelength at (a) and (b) is the same, but the fringes are sharper in (b). Horizontal axis is d, interferometer spacing (mm); & = 0.4 mm.

A considerable improvement in coherence can be anticipated* by locking the multimode (mode spacing = c / 2 L C ;L, is cavity length) laser cavity to a high-Q, short, external interferometer (Smith, 1965). Another approach that seems promising is to employ distributed feedback (Degan, 1976). A central coaxial conductor, onto which is milled a helical groove (spacing A,/?), can provide both an internal grating and feedback within the laser cavity, and allows elimination of the mirrors. Another technique is that of distributed resistive feedback, in which the helix is made of dissipative material wound upon the coaxial conductor; this has the desirable feature of suppressing radial cavity modes (P. Dvorkis and A. Gover, private communication, 1979). These techniques purchase improvement in linewidth at the expense of tunability. E . Future Work

Experiments with a 100-nsec, 1-MV, 20-kA beam are planned for the near future at Columbia University’s Plasma Laboratory. The fluctuation * P. Efthimion, private communication.

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in beam energy in these new experiments can be held to = I % , thereby permitting the laser signal to regenerate over ten cavity passes. This should be adequate to drive the laser into saturation. As beam technology improves, one can foresee the availability of lower-power, repeatedly pulsed beam experiments such that the entire laser system (including the beam system) becomes more compact. Experiments using pencil beams and different undulator geometries need further work. Already the collective free election laser has a convenient size (= I m) and cost; thus commercial availability depends on reducing the complexity of the electron beam source. Extension of the collective FEL laser range into the infrared (10- 100 pm) is also expected soon. Bell Laboratories plans to build such a device to probe solid-state phenomena. For this spectrum range, there exists the possibility of using an intense beam (= 100 A, j = 103-104 A/cm2, y = 20) so that collective effects dominate, resulting in amplification 2 100% per pass. Operation in the laser mode would create a powerful spectroscopic tool. A microtron-type accelerator (Kapitsa and Melekhin, 1979) is to be used to generate the beam; this will operate at 1000 pulses/sec with a duty factor of 0.001; about 1 kW average power is expected from the laser. Exploitation of the second-order Raman backscatter effect [Eq. ( 5 2 ) ] should permit operation of combined microwave cavity -Fabry -Perot laser devices with submillimeter output, using beam energy 5200 kV. Development of the Cerenkov-Raman device (Section 1,B) should permit a similar reduction of beam potential. We believe the most promising collective FEL design is to combine the good coherence property of an oscillator with a high/gain efficient amplifier. The electron beam first propagates through a weak ripple field within a cavity and then through a strong ripple field. The cavity output radiation will be relatively low power, but have a narrow bandwidth. This cavity emission will then be amplified in the strong field region to multimegawatt power levels. The advantage of this approach is that the emission will retain the narrow bandwidth achieved within the oscillator. These experiments can be readily implemented by testing the travelingwave FEL system by injecting a coherent pulse of submillimeter radiation from an existing laser (e.g., the methyl fluoride system). In this case, optimization of laser efficiency is a primary objective, and if theory is correct, power levels = 108-109 W should be obtainable. REFERENCES Bemstein, I. A . , and Hirschfield, J. L. (1979). Phys. Rev. A 20, 1661. Buzzi, J . M . , Doucet, H. J . , Etlicher, B . , Haldenwang, P . , Huetz, A . , Lamain, H . , and Rouille, C. (1977). J . Phys. Lett. 38, L397.

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Carmel, Y., and Nation, J. (1973). Phys. Rev. Lett. 31, 286. Chaffin, R. J. (1973). “Microwave Semiconductor Devices: Fundamentals and Radiation Effects.” Wiley, New York. Colson, W. B. (1978). In “Physics of Quantum Electronics” ( S . F. Jacobs, M. Sargent, and M. 0. Scully, eds.), Vol. 5 , p. 157. Addison-Wesley, Reading Massachusetts. Davidson, R. C. (1974). “Theory of Nonneutral Plasmas,” p. 36. Benjamin, Reading, Mass. Davidson, R. C., and Uhm, H. S. (1979). Phys. Fluids 22, 1375. Deacon, D. A. G., Elias, L. R., Madey, J. M. J., Ramian, G. J., Schwettman, H. A., and Smith, T. L. (1977). Phys. Rev. Lett. 38, 892. Degan, J. J. (1976). Appl. Phys. 11, 1. DeTemple, T. A. (1979). In “Infrared and Submillimeter Waves” (K. J . Button, ed.), Vol. 1, p. 129. Academic Press, New York. Efthimion, P. E., and Schlesinger, S. P. (1977). Phys. Rev. A 15, 633. Efthimion, P., Smith, P. R., and Schlesinger, S. P. (1976). Rev. Sci. Instrum. 47, 1059. Einstein, A. (1905). Ann. Phys. (Leipzig) [4] 17, 891. Elias, L. R., Fairbank, W. M., Madey, J. M. J., Schwettman, H. A., and Smith, T. I. (1976). Phys. Rev. Lett. 36, 717. Evans, D. E., Sharp, L,.E., James, B. W,., and Peebles, W. A. (1975). Appl. Phys. Lett. 26, 630. Evans, D. E., Peebles, W. A., Sharp, L. E., and Taylor, G. (1976). O p t . Commun. 18,479. Friedman, M., and Herndon, M. (1972a). Phys. Rev. Lett. 28, 5 5 . Friedman, M., and Herndon, M. (1972b). Phys. Rev. Lett. 28, 210. Gamo, H., Ostrem, J . S., and Chuang, S. S. (1973). J . Appl. Phys. 44, 2750. Gilgenbach, R. M., McDermott, D. B., and Marshall, T. C. (1978). R e v . Sci. Instrum. 49, 1098. Gilgenbach, R. M., Marshall, T. C., and Schlesinger, S. P. (1979a). Phys. Fluids 22, 971. Gilgenbach, R. M., Marshall, T. C., and Schlesinger, S. P. (1979b). Phys. Fluids 22, 1219. Cover, A., and Yariv, A. (1978). Appl. Phys. 16, 121. Granatstein, V. L., Herndon, M., Parker, R. K., and Schlesinger, S. P. (1974). IEEE Trans. Microwave Theory Tech. 22, 1000. Granatstein, V. L., Sprangle, P., Parker, R. K., Pasour, J., Herndon, M., Schlesinger, S . P., and Seftor, J. L. (1976). Phys. Rev. A 14, 1194. Granatstein, V. L., Schlesinger, S. P., Herndon, M., Parker, R. K., and Pasour, J. A. (1977). Appl. Phys. Lett. 30, 384. Hacker, M. P., Rozdowicz, Z., Cohen, D. R., Isobe, K., and Tempkin, R. J. (1976). Phys. Lett. 57, 328. Hasegawa, A. (1978). Bell Syst. Tech. J . 57, 3069. Hasegawa, A., Mima, K., Sprangle, P., Szu, H. H., and Granatstein, V. L. (1976). Appl. Phys. Lett. 29, 542. Hirschfield, J . L. (1979). In “Infrared and Submillimeter Waves” (K. J. Button, ed.), Vol. 1, p. I . Academic Press, New York. Hirschfield, J. L., and Granatstein, V. L. (1977). IEEE Trans. Microwave Theory Tech. 25, 522. Kapitza, P. L., and Dirac, P. A. M. (1933). Proc. Cumbridge Philos. Soc. 29, 297. Kapitza. S. P., and Melekhin, V. N. (1979).In “The Microtron” (E. M. Rowe, ed.). Harwood Press, New York. Kroll, N. A., an3 McMullin, W. A. (1978). Phys. Rev. A 17, 300. Kwan, T., Dawson, J. M., and Lin, A. T. (1977). Phys. Fluids 20, 581. Landecker, K. (1952). Phys. Rev. 86, 852. Lawson, J. D. (1977). “The Physics of Charged-Particle Beams.” Oxford Univ. Press, London and New York.

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Lin, A. T., and Dawson, J. M. (1975). Phys. Fluids 18, 201. Lin, A. T., and Dawson, J. M. (1979). Phys. R e v . L e t t . 42, 1670. Loewen, E. G., Neviere, M., and Maystre, D. (1977). Appl. Opf.16, 2711. Louisell, W. H., Law, J., Copeland, D. A,, and Colson, W. B. (1979).Phys. R e v . A 19,288. McDermott, D. B., and Marshall, T. C. (1979). Proc. I n t . Conf. Energy Storage. Compression Switching, 2nd. Plenum, New York (in press). McDermott, D. B., and Marshall, T. C. (1980).In “Physics of Quantum Electronics” (S. F. Jacobs, H. Pilloff, M. Sargent, M. 0. Scully, and R. Spitzer, eds.), Vol. 7, p. 509 Addison-Wesley, Reading, Massachusetts. McDermott, D. B., Marshall, T. C., annd Schlesinger, S. P. (1978a). Comments Plusmcr Phys. Cantrolled Fusiorr 3, 165. McDermott, D. B., Marshall, T. C., Schlesinger, S. P., Parker, R. K., and Granatstein, V. L. (1978b). Phys. R e v . Lett. 41, 1368. Madey, J. M. J . (1971). J . Appl. Phys. 42, 1906. Madey, J. M. J., Schwettman, H. A.. and Fairbank. W. M. (1973). IEEE Trtrns. Nucl. Sci. 20,980. Manheimer, W. M., and Ott, E. (1974). Phys. Nuids 17,463. Marshall, T. C., Talmadge, S., and Efthimion, P. (1977a). Appl. P h j s . Lett. 31, 302. Marshall, T. C., Gilgenbach, R. M., and Sandel, F. (1977b). Proc. I n t . Top. Conf. High Power Electron Ion R e s . Technol.. 2nd. 1977 p. 697. Motz, H. (1951). J. Appl. Phys. 22. 527. Nation, J . M., and Read, M. (1973). Appl. Phys. Lett. 23, 426. Parker, P. K., and Ury, M. (1975). IEEE Trans. Nucl. Sci. 22, 983. Pasour, J. A., and Schlesinger, S . P. (1977). R e v . Sci. Instrum. 48, 1355. Pasour, J. A., Granatstein, V. L., and Parker, R. K. (1977). Phys. Rei.. A 16, 2441. Phillips, R. N. (1960). IRE Trons. Electron Devices 7 , 231. Schneider, S., and Spitzer, R. (1974). Nature (London) 250, 643. Smith, P. W. (1965). J. Qunnt. Electron. qe-1, 343. Sprangle, P., and Drobot, A. T. (1979). J. Appl. Phys. 50, 2652. Sprangle, P.. Granatstein, V. L.. and Baker, L.. (1975). Phys. R e v . A 12, 1697. Sprangle. P., Smith. R. A., and Granatstein, V. L. (197Ya). In “Infrared and Submillimeter Waves” (K. J. Button, ed.), Vol. 1, p. 279. Academic Press, New York. Sprangle, P., Tang, C. M., and Manheimer. W. M. (1979b). N R L Memo. R e p . N o . 4034. Stauffer, F. J . (1976). “Observations of Synchrotron Radiation from the University of Maryland Magnetic Mirror Experiment,” Tech. Rep. 77-013. University of Maryland, Dept. of Physics, College Park. Sukhatme, V. P., and Wolff, P. W. (1973). J . Appl. Phys. 44, 2331. Walsh, J . E., Marshall, T. C., and Schlesinger, S . P. (1977). Phys. Fluids 20, 709. Walsh, J. E.. Felch, K., Busby, K., and Layman, R. W. (1980). In ”Physics of Quantum Electronics” (S. F. Jacobs, H. Pilloff, M. Sargent, M. 0. Scully, and R. Spitzer, eds.), Vol. 7, p. 301. Addison-Wesley, Reading, Massachusetts. Wong, H. V., Sloan, M. L., Thompson, J. R., and Drobot, A. T. (1973). Phys. Fluids 16, 902. Zhukov, P. G., Ivanov, V. S., Rabinovich, M. S., Raizer, M. D., and Ruchadze, A. A. (1979). Proc. Inr. Canf. High Power Electron Ion Beom Technol.. 3rd, 1979, Novosibirsk. (preprint).

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The Biological Effects of Microwaves and Related Questions H. FROHLICH Department of Physics Uniwrsity of Liivrpool Livrrpool. Engltrnd

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ B . Metastable Highly Polar States C . Excitation of Coherent Vibratio ............................ IV. Consequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Long-Range Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Models for Nonthermal Actions of Microwaves.. , . . . . . . . . . . . . . . . . . . , . . . . D. Multicomponent Systems and the Cancer Problem.. . . . . . . . . . . . . . . . . . . . . . . E. Brain Waves ... V . Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Experiments with Millimeter Waves . . C. Rarnan Effect . . . . . . . ... . . . . _ . . . _. _. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Conclusions.. . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85 87 87 89 92 92 95 98 104 104 106 109 113

118 121 121

127 140 148 150

I. INTRODUCT~ON Microwaves, and particularly millimeter waves, are strongly absorbed in water, which represents a most important constituent of biological systems. As a consequence, when irradiated by microwaves the temperature of the biological material is raised and temperature-dependent processes are influenced. Well-documented biological effects exist, however, arising from irradiation at very low intensities where thermal effects are excluded. This article deals with these effects and with their prediction 85 Copyright 0 1980 by Academic Preys. Inc All rights of reproduction in dny form reserved ISBN 0 12 014653 3

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from theoretical considerations. It must be emphasized at once that an appropriate discussion of experimental results with regard to nonthermal effects must frequently consider thermal effects as well. Much prejudice has arisen from an inadequate knowledge of the basic differences between thermal and nonthermal effects. Thus the amount of energy transfer from the radiation to the material varies slowly with frequency and is largely governed by the dielectric loss. Within reasonable limits this loss is proportional to the intensity of the radiation. Nonthermal effects, on the other hand, occur in certain frequency regions only, and usually exhibit saturation at rather low intensity. As a consequence, nonthermal effects might be drowned by thermal ones. This is in particular to be expected when the sign of the considered effect in the nonthermal region is opposite to that of the thermal effect. As an example, consider the reduction of the rate of growth of certain bacteria arising from irradiation at 73.6 Hz, as discussed in Section V. Temperature increase, on the other hand, increases the rate of growth, thus canceling the nonthermal effect at sufficiently high intensity. It might be tempting to link frequency-dependent biological effects of a resonance type to absorption bands in certain biomolecules. We shall demonstrate, however, that such resonances are properties of the whole system, and may depend on the biological activity. It is of importance, in this context, to realize that in some instances biosystems can exhibit properties of the most refined electronic instruments, as discussed in Section II,A. They achieve this with the use of biomolecules in a way that is not yet understood. How is it possible that extremely weak electromagnetic radiation can have large biological consequences? To answer this it must be realized that an active biological system is very far from thermal equilibrium and has considerable amounts of energy stored for appropriate use. The microwave might then be considered as a trigger for certain bioeffects. The electronic engineer might like the analogy of a radio receiver that under the influence of an extremely weak electromagnetic wave (from a sender) will produce large sound effects (corresponding to bioeffects) when appropriately tuned. Switched off, however, it would be very difficult, though not impossible, to observe resonances. A great number of experiments have been published in which the influence of irradiation by microwaves of 2450 MHz-a frequency at which water absorbs strongly -on a variety of biological effects has been investigated. While not completely useless, this type of research does not lend itself to systematic discussion, which will require variation of frequency or of intensity-preferably of both. In the interest of a systematic presentation, the theoretical (physical)

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background is first presented on the basis of certain models. It must be recognized, however, that theoretical physics cannot make predictions in the way it does, e.g., in the realm of the linear response of more usual physical materials. Biological systems are in some respects very far from equilibrium, quite outside the regions of linear response. They have developed to fulfil a certain purpose, and usually there is no unique way in which this can be performed. Theoretical physics must, however, provide the relevant concepts, and it is here that the possibility of trigger action of microwaves arises. This holds in particular for the excitation of coherent electric vibrations pumped by energy derived from metabolism. These will be shown likely to have frequencies that can resonate with those of microwaves -although other frequencies are also likely to be relevant. For this reason it is not desirable to restrict our discussion to microwaves only. Such excitations can have far-reaching consequences on biological activity. While theory can point out a number of possibilities, it cannot predict in which way evolution has progressed. It is only in collaboration with experiment that the possibilities that have actually been established can be found. The attitude we thus must take is to consider biological systems in terms of their activities, which require a high degree of organization. Such organization may be of a complex nature, but it does require consideration of the systems as a whole. In microscopic terms it thus requires the introduction of collective properties that in some cases might go beyond those normally used in physics. It is sometimes asserted that experimental proof of the obedience of microscopic laws of physics and chemistry invalidates the existence of collective properties, but such conclusions are illogical. Thus a particular chemical process will be determined in terms of the atomic constitution of the systems undergoing a chemical transformation, i.e., will be determined microscopically. The fact, however, that the particular systems are brought together at a particular time in a particular place may well arise from certain collective properties of a larger region.

11. GENERAL A . Biology

Frequently the opinion has been expressed that the activity of biological systems can be understood in terms of standard chemical reactions in conjunction with diffusion of molecules. On this basis the biological ef-

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fects of weak microwaves would have to be considered as nonsense. For this reason it is necessary to point to a few biological properties that equally might have been considered as nonsense were they not so extremely well documented. In the first place we note that the biological sensitivity to certain external influences can equal that of the best available instrumentation. This will be illustrated on two cases showing that high sensitivity to microwaves need not be an isolated feature. In a careful analysis, Rose (1970) has demonstrated that at low light intensities the human visual system has a quantum efficiency of about 10% with a threshold signal to noise ratio of 4: 5. This sensitivity thus is close to the theoretical limit. By comparing the energy of a light quantum with that of a nerve impulse he finds a gain of more than lo6. Clearly the light quantum acts as a trigger for a nerve impulse whose energy is provided by the biological system. The usual system thus can be considered as an image converter of highest sensitivity. Yet the materials it uses are completely different from those used in technical image converters. Another example is provided by the sensitivity of certain fish to electric signals. They make use of such signals in various ways as discussed by Bullok (1977). The lowest electric field that has been observed to evoke a response is of the order of lo-* V/cm. Again in its receptor organ, the fish has none of the materials that would be used for construction of instruments of such high sensitivity. Controls of activities represent another important set of in vivo biological properties. Control of chemical activity is, of course, frequently well understood in terms of relevant enzymes. But these enzymes have to be in their activated state in the right place, at the right time. Control of cell division, however, is not understood at all. Its absence consists in cancer. We return to this problem in Section IV,D. Among material properties, most remarkable perhaps is the maintenance of an electric potential difference of about 100 mV across biological membranes. It is well known how this voltage is involved in nerve conduction, but all cells apparently maintain this voltage, leading to the high field of loJ V/cm within the membrane (thickness cm). Such a field leads to strong electric polarization of the materials within the membrane. It is discussed in Section 111 how this might be involved in the interaction with microwaves. Of particular interest among materials are enzymes, which through their catalytic action regulate most biological chemical processes. Enzymes are proteins, i.e., they consist of a linear string of amino acids, which in globular proteins are folded in a very definite way. The structure of many enzymes has now been analyzed. They all contain an active group at which,

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according to the laws of chemistry, the respective chemical reactions can take place. Yet as shown in a review article by Koshland and Neet (19681, the essential mystery of their enormous catalytic power remains. Clearly the system as a whole, not only the relatively small active group, should play a role in understanding the action of enzymes. It had been hoped that the spatial arrangement of the amino acids would exhibit a certain spatial order. Nothing of this kind was found, so that according to Monod (1972) knowing the arrangement of 199 amino acids would not permit us to predict to 200th. He concludes that the arrangements are “random. ”

B. Physics From the point of view of physics Monod’s conclusion is wrong, for physics knows other types of order and organization, besides spatial order. Thus order of motion is widely known and exists in thermal equilibrium (liquid helium 11, superconducting electrons) as well as away from equilibrium (lasers, sound waves in air). Another type of order, better termed organization, exists in a well-working machine in contrast to a broken-down one. Thus absence of spatial order need not imply randomness. Macroscopic organization, to which we alluded in the case of a machine, is, of course, uniquely correlated to details of microscopic structure. But this does not mean that knowing all microscopic details will reveal the interesting macroscopic properties (cf. Frohlich, 1973a). Not only is the number of microstates so enormous that it cannot be handled but, still more important, the relevant macroscopic properties are expressed in terms of concepts that do not exist in microphysics-they are collective properties. In the case of an enzyme, after appropriate folding, the system must also act as an enzyme, i.e., it must have very specific properties, although at present they have not yet all been found. F. Frohlich (1977) has compared the restrictions of the arrangement of words in a language to a restriction of the arrangements of amino acids in an enzyme. Among the known conditions are, in a water-soluble globular protein, the placement of the charged groups on the outside, where they can lower the free energy through their interaction with water. This does not, however, completely determine the folding, which is always exactly the same. If we assume this to be determined through thermodynamic considerations, then the particular conformation must have a free energy sufficiently lower than all the others such that establishment of any of the others becomes extremely unlikely.

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This, however, is not the only consideration, because on formation, the linear chain must fold itself, and the initially favorable first steps in folding are not necessarily those that lead to the lowest free energy when folding is completed. We might conjecture that in actually realized enzymes these two types of conditions coincide, so that for them the most favorable pathways also lead to the most favorable free energy. In addition, of course, they will have to have the relevant specific catalytic properties. One would expect that sueh conditions select only relatively few linear sequencies, but the total nwnber of possible sequences is enormous. Thus since there exist 20 amino acids, the total number of linear arrangements of 200 of these equals (20)200.This number, of course, is immense compared with the known number of proteins of 200 amino acids, or even of any length. It is very small, however, compared with the total number of possible microstates in even very small systems. For this reason the use of the concept of information, being equal to negative entropy, in this context cannot be successful. For selection of the one protein (of length 200) would have the information content 200 log 20. However, since this does not describe any relevant quality, it is equal in magnitude to small deviations from thermal equilibrium in very small regions. Thus, at temperature T , the imposition of a small temperature difference AT 4 T on a region containing N particles is of the order N ATIT. While negative entropy is not a useful concept for the description of the organization existing in biological and some other systems, one would hope that an appropriate concept does exist, and that it satisfies certain quantitative laws. Such concepts are, of course, used in particular cases, but they have not been unified. Most of them have in common that they involve only relatively few degrees of freedom such, however, that they govern the behavior of the rest. We presently describe in some detail two physical systems, relevant for biology, in which a certain order is established through the supply of energy (Section 111). More frequently, supply of energy to simple physical systems leads to heating, i.e., to disorder, while removal of energy increases order. An essential feature in our present two cases is the basic importance of nonlinear characteristics in conjunction with a supply of energy. The established new order will be found in the one case to be dynamic in terms of coherent excitation of electric vibrations. This will be seen to lead to long-range selective forces that thus supplement short-range forces, including those leading to standard chemical processes. The selectivity of the long-range forces depends on the frequency of the oscillating systems, which in turn depend on their structure.

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A general line of development can thus be seen whereby, e.g., (1) two selected systems attract each other, (2) when meeting they undergo chemical reactions and other rearrangements, (3) this leads to a change of relevant frequencies, and hence (4) to new types of long-range effects. It is a general feature of active biological systems that energy is always available, through metabolic processes, and that this causes nonlinear changes in molecules, or large subsystems. It is dangerous, therefore, to extrapolate from properties of biological molecules, obtained by extracting them from the living system, to their behavior in vivo, although in certain cases this can be done. The above discussion on the folding of proteins shows that these molecules have remarkable dielectric properties, different in many ways from more ordinary, small molecules (cf. Frohlich, 1975a). The latter possess a certain vacuum dipole moment that is slightly modified when they are brought into solution. In the case of water-soluble proteins, however, the interaction of these charged groups with water is an essential ingredient in determining the conformation, and hence the dipole moment. Moreover certain groups will become charged, depending on the ion concentration in the water. This latter also seriously affects the long-range interactions of charged groups. For statically all charges surrounded by cell water are screened within a very short distance through mobile ions. Dipole or higher poles are not necessarily completely screened because short-range interactions may affect positive mobile ions in a different way from negative ones so that the screening in such cases need not be complete. Such screening does not hold, however, in the case of dynamic interaction arising from the fields of oscillating charges in the frequency regions that we consider. Such interaction is governed by the appropriate dielectric constant at the particular frequency. In the range of interest, this dielectric constant depends on frequency but not on wavenumber, whereas the relevant dielectric constant in the static case depends on wavenumber. Clearly then we must expect particular physical properties of molecules or larger units within a cell to depend on the state and activity of their surroundings, and hence on time. This means that, with some exceptions, we cannot speak of definite molecular properties without referring to the state of the whole cell. From the point of view of physics we are thus involved in nontrivial nonlinear effects that change with time and are maintained through constant energy supply. As a consequence, nonthermal effects of microwaves should be expected to act at certain frequencies and at certain periods of biological development only. To find these presents a formidable task. Measuring overall properties might thus yield a small effect,

92

H . FROHLICH

when in fact such an effect might be large but effective during certain periods only. Thus, from the point of view of physics, biological systems are relatively stable from a microscopic point of view, e.g., the thermal vibrations of single atoms are practically the same as in a corresponding nonbiological system. In some respects, however, involving relatively few degrees of freedom, they are very far from thermal equilibrium, and these degrees of freedom dominate the overall behavior of the rest. They may be described in terms of collective properties or organizations that a1e carried by a great number of atoms, but use concepts that involve many atoms, i.e., do not exist in individual particle physics. These collective properties evolve as a consequence of supply of energy (metabolism), and usually represent extreme nonlinear displacements. Their detailed characteristics may depend on large-scale configurations and involve activities that in turn will change these configurations, and hence the characteristics of the collective properties. Among the forces that cause these changes are selective long-range forces and short-range forces, including standard chemical ones. Attention must therefore be drawn to the occurrence of multiple causes. Thus systems might attract each other through selective long-range forces requiring equality of certain frequencies (of Section IV). When they meet, questions of shape may arise to permit certain reactions to start (lock and key principle). Establishment of one does not exclude the other. For this and other reasons, therefore, great care must be taken when transferring methods of procedure in nonbiological sciences to biology.

111. THEORY

In this section we intend to consider on the basis of simple models the two basic collective excitations, relevant to our treatment. They both rest on the high dielectric polarizability of biological materials. One is quasi-static, showing that under very general conditions metastable states with very high electric polarization exist. The second shows that under more stringent conditions coherent electric vibrations may be excited by random metabolic energy (cf. Frohlich, 1968, 1969, 1977a). A . Mutrrial

Biological membranes have a thickness of about cm. Oscillations with displacement perpendicular to the surfaces exist so that for the longest wavelength the membrane thickness equals half the wavelength.

THE BIOLOGICAL EFFECTS OF MICROWAVES

93

Assuming elastic properties corresponding to a sound velocity of loJ cm/sec, we find a frequency 0.5 x 10" Hz. It must be realized now that the membrane usually contains a considerable number of proteins, dissolved in it, so that small sections of the membrane (e.g., between two proteins) might vibrate separately from the rest. In Section I1 it was mentioned that the membrane is very strongly polarized electrically, in a field of lo5 V/cm. Hence excitation of vibration of a particular section of the membrane is connected with a vibrating electric dipole. Vibrations with shorter wavelengths, i.e., with higher frequencies, also exist although electrically they would correspond to multipoles. Inhomogeneities within the membrane might, however, yield some dipolar contributions also in these cases. Individual proteins within the membrane will also be strongly polarized. Their oscillations may also give rise to oscillating dipoles, usually-though not necessarily -with higher frequencies. Optical modes of membranes also contribute to higher-frequency vibrations. Clearly molecules outside the membranes may, in principle, also oscillate as may other sections of a cell, and a great variety of possible frequencies will exist. Thus Prohofsky and Eyster (1974) by detailed calculation find a great number of giant breathing and rocking modes in double helical RNA, with frequencies reaching down to values below lo9 Hz. Brill (1978) has estimated a frequency of 1 X Hz for certain vibrations in blue proteins; Careri (1969) has observed that the stretching vibration of a hydrogen bond lies in a similar frequency region (5 x 10l2 Hz). He also observed (Careri, 1973) that a collective excitation might occur in hydrogen-bonded amide structures at about 5 x lOI3 Hz. Higher collective modes based on other degrees of freedom may well occur. Another source of electric vibrations arises from the plasma modes of unattached electrons. Such electrons might find themselves, for instance, in the conduction band of proteins through charge transfer mechanisms (R. Pethig, 1978), who reports a density up to 1OI8 cmP3).If ma is their effective mass and E an appropriate dielectric constant then the plasma frequency vp satisfies

.", = e 2 n / m m "

(1)

n being their density. Thus a frequency of 10" Hz then requires n = 1 0 1 4 ( m * / m ) ~~ m - ~

(2)

It is clear that the actual development of a plasma vibration of this magnitude involves a substantial number of electrons, which at the low density following from ( 2 ) would require a volume of the order of a cell's; thus using Em*/m = 10 would require one electron in a cube of side

94

H. FROHLICH

length cm. The dependence of n on 6 should be remembered here so that for 10l2 Hz the required volume would be 100 times smaller. Spectroscopic evidence for frequencies that are integer multiples of about 1013 Hz has been obtained by Biscar and Kollias (1973a,b) on specially prepared poly-L-glutamic acid, and may well be a general feature of very high molecular weight compounds. Now all these possible oscillating systems interact and on the basis of experience from solid-state physics one would expect the appearance of bands of modes. Some of these modes will extend spatially over relatively large regions; others may be restricted to regions around certain molecules-corresponding in solid-state physics to localized vibrations. Now in contrast to the usual experience in solid-state physics a new feature may arise in our case, due to the large size of the individual systems. As a simplified example (Frohlich, 1972) consider two large systems at distance R , larger than their linear dimensions L , capable of giant dipole vibrations with circular frequencies w1 and w2, respectively. Then through their interaction two frequencies o+,w- of the joint system arise, where E~ is the dielectric constant of the intermediate medium at frequency w2, and p measures their interaction. If, in particular, the two systems contain z1and z 2 elastically bound particles of mass M and charge e then

p2 = y?-e4zlzz/M2R6 where y is of order unity but depends on various angles. Due to the interaction of the two systems a softened mode arises. If in particular w1 = wz, z1 = z2, and R = R, such that

(4) w-

thus (5)

wf = e2z/E-MRi

then 05 = 0. In this case nonlinear and other neglected interaction terms will have to be employed. From (3) we note that mode softening will be particularly effective where w1 = w2. In this case using z1 = z2 = 100 and the proton mass for M we have with R = cm, ( e 2 ~ / ~ ~ 3= ) 11013 /2

HZ

(6)

which is indeed very large. It should be stressed that nonlinear terms arising from the deformation of molecules under the influence of vibrations will lead to further softening when a vibrational mode is strongly excited, as shown later. This

THE BIOLOGICAL EFFECTS OF MICROWAVES

95

may be of great importance in conjunction with the idea of strong excitation through metabolic activity. Then frequencies occuring in the active (metabolizing) system will differ from those of the resting system. Also the influence of interaction on frequencies (3) imposes a further divergence from the frequencies of extracted molecules. It should also be remarked that both transverse and longitudinal normal modes exist in an infinite homogeneous medium, and that very few of them are optically active. In our case, however, of strong inhomogeneity together with the existence of inner surfaces, a number of these characteristics are changed. Thus, a giant dipole oscillation of a molecule or of a section of a membrane corresponds to a wavelength of the electric polarization wave, large compared with the linear size of the oscillating region. In this case the division into longitudinal and transverse becomes irrelevant. Due to the existence of surfaces, however, such a system has always some optical activity, even for shorter waves.

B. Metastable Highly Polar States Consider a finite material, weakly polarized with finite polarization P. An electric self-energy can then be defined (cf. Frohlich, 1958), which is proportional to P 2 . The proportionality factor depends on the polarizability and on the shape of the material. Deformation of the material will, in general, cause a change in the electric self-energy, which may be positive or negative. A change in elastic energy, due to the deformation, will also occur, but this is always positive if the material was elastically in equilibrium before it was deformed. As a consequence, polarization of a material will cause its deformation, as is well known. Consider now an example in which the deformation can be described by a single parameter q (Frohlich, 1969, 1977b). The change U of elastic and of electric energy upon polarization and deformation then has the form

u = 3yP2(1 + c1q + 3c2q2) + icq2

t 7)

where C > 0 and y > 0, respectively, are elastic and electric material constants, and the signs of the parameters c1and c2 depend on the particular situation. Minimizing with regard to q for fixed P2 yields r) = -clrp/(C2rp

+ C)

(8)

and hence

u = HypP

- 3[(c,rpa)2/(czy~ +

C,l)

(9)

Thus with increasing polarization, U increases more slowly than it would

96

H. FROHLICH

without deformation. Furthermore, a maximum Urn,, of U exists provided cz > 0, and provided 2cz < c:

(10)

When P2 > PkaXthen U will decrease with growing P2.At this stage, however, higher powers in p2 as well as in q are likely to intervene such that a minimum of U is reached at a certain value of P2 i.e., when the material is strongly polarized. If this minimum Urninof U should be negative then the material would be ferroelectric. If, however, Umin> 0, then this highly polarized state is stable against small displacements only and represents a metastable state. Suppose now that we deal with a large molecule, e.g., a protein, dissolved in a membrane. Assume it to possess a metastable state with dipole moment po. If this p o has the correct direction, then the system gains the energy p$ if F is the membrane field. The previously metastable state will then become the stable state if

’

Urnin

(14)

It must now be emphasized that displacements corresponding to higher powers in 7 include what biochemists denote as conformational changes, e.g., large displacements of single ions such as H+, or of whole groups. Frequently the energies involved are discussed in terms of localized chemical bonds. This may lead to serious errors as the energy due to relatively small displacements of all the ions may be very substantial. It must be remembered in this context that the interaction between all the electric dipoles arising from the displacement of individual ions does not converge as the total energy arising from this depends on the shape of the molecule. Another situation arises when the molecule that has been brought into the highly polar metastable state is in solution in the cell water, which contains many small ions. Such ions will then accumulate near the molecule and screen the electric field of the dipole within a very short range.

THE BIOLOGICAL EFFECTS OF MICROWAVES

97

At the same time this will ensure further stabilization of the metastable state. As a consequence of this screening, such highly polarized systems will not be involved in long-range interaction. Forces are, however, exerted on ions inside the system, and this may be of considerable importance for reducing activation energies in enzymatic reactions. For systems within membranes, however, this screening is restricted to the regions outside the membrane. We now quantitatively introduce terms proportional to p4 in the energy so as to perform the above-mentioned stabilization (Frohlich, 1973b). At the same time we also consider the dynamic case of giant dipole oscillations. Essentially we thus deal with the case of a space- (x) and time- ( t ) dependent polarization field P(r), coupled nonlinearly to the longitudinal elastic field A(x). The parameter r] must then be replaced by div A, and we use the potential energy density Win such units that if wo is a frequency,

W

= + w P

+ (tu2(divA)2 + cP2 div A)(1 - d 2 P 2 )

(15)

Our U in (7) would correspond to the spatial integral over W; u , c , and d are parameters and the d 2 P 2 term has been introduced to ensure convergence at large polarization. Terms corresponding to cpterms in U have been neglected. The equations of motion can then be derived in a wellknown way from the appropriate Lagrangian density L by ( t represents time) 6

I

L d3xdt

=

6

I

( K - W) d3x dt

=

0

(16)

where K is the density of kinetic energy of the two fields. We consider now the case of absence of acoustic phonons so that the kinetic energy of the elastic field can be neglected, and of homogeneous polarization waves so that x dependence of P and div A does not arise. In this case div A takes on a time-independent mean value, obtained by differentiating the integrand in (16) with regard to div A. This yields div A = - ( c / u 2 ) p where p is the time average of P 2 , p

(17)

= P2

and it has been assumed that the fluctuation ( p - P2)* is negligible. Equation (16) then yields

P

+ av(P)/aP = 0

(19)

98

H. FROHLICH

where the effective potential energy V(P) has the form V(P) = A

+ B,P + B2PP

(20)

with

At first sight, (19) with (20) represents a simple anharmonic oscillator. In fact, however, it is highly nonlinear as the potential (20), though (21) and (18), depends on the mean amplitude of the oscillation. As a consequence, for small amplitudes, i.e., smallp, the anharmonic B2 term is negligible and the system oscillates harmonically with frequency ao.Increasing amplitudes introduce some anharmonicity through B2 but also reduce the frequency by reducing the magnitude of B1. Thus simultaneously the mode softens and becomes more and more anharmonic. A drastic change takes place, however, for still larger amplitudes when B , becomes negative. The minimum of the effective potential at P = 0 now turns into a maximum, but two minima now arise at certain values of P. In this case for a definite amplitude ? P o , static solutions of (19) exist, i.e., the system is strongly polarized and stable against small displacements. This then represents the metastable state. At amplitudes at which p = Pi, two branches of vibrations exist. At one the system oscillates weakly around the metastable state; in this case the mean value of P is Po. The other case is a large vibration such that the mean value of P disappears, but = p"0. In the case discussed here, the transition from the nonpolar to the highly polar metastable state thus becomes established when the system is forced into large vibrations through supply of energy. The characteristic feature in our model arises from the behavior of the term B 1 ,Eq. (21), which at a certain value of the mean square amplitude p turns from positive to negative values. A similar feature arises in a great number of other processes where supply of energy causes a change of behavior, comparable to a phase transition. Haken (1973) has discussed such questions where the same mathematical description often holds for widely different processes. On the basis of this he suggested a new discipline, synergetics. C . Excitation of Coherent Vibrations

In this section we come to the crucial consideration that engenders the possibility of trigger action by microwaves. We show that when certain conditions are fulfilled, random energy supply to the modes of a band of electric polarization waves may lead to strong, i.e., coherent, excitation

THE BIOLOGICAL EFFECTS OF MICROWAVES

99

of a single mode provided the energy supply s exceeds a critical value so (Frohlich, 1968, 1969, 1977a). If the supply s by metabolic energy is slightly less than so, then a small additional supply, e.g., from microwaves, can trigger off the strong excitation, whose consequences will be discussed in Section IV. We consider a band of polarization waves consisting of z normal modes with circular frequencies o,, O 1 ~ O j 5 O x ,

j=l,2,.

..

,z

(22)

For readers not quite familiar with all aspects of normal modes it must be pointed out that excitation of a vibration with time dependence cos(qt + cp), say, for a limited time period does not represent excitation of a single normal mode though it can be represented as a superposition of normal modes. Similarly, a vibration that changes its phase cp from time to time does not represent a normal mode because then cp is time dependent. Strong excitation of a normal mode is always coherent. Our band of normal modes rests on a selected relatively few degrees of freedom in a cell or larger unit. We shall assume it to be embedded in a heat bath of temperature T with which it interacts. As a consequence even when energy is supplied to our modes they tend to be excited according to temperature T as closely as possible. We show that when s > so this leads to the strong excitation of a single mode similar to the phenomenon of Bose condensation. Let n, be the number of quanta in the mode with frequency oj, and let s, be the rate of energy supply to this mode. Interaction with the heat bath will lead to emission and absorption of quanta by this mode and we consider processes involving one and two quanta. The heat bath is, of course, a very complex system. The interaction will involve dipoles of water and other molecules, mobile ions, certain electronic degrees of freedom, and to some extent also elastic displacements, e.g., when a coupling of the type presented in (15) is involved. The transition probabilities are therefore complicated quantities. The assumption that the heat bath be in thermal equilibrium enforces, however, the principle of detailed balance at its temperature. This means that the kinetic equation for the rate of change of nj has the form rij = sj - +,(n,e@OI- (1 + n,)) - uz[nj(l + nl)epOj- nt(1

2

+ n,)epwl]

I

Both

and

+j

uZ= X N will in general depend on temperature; we use =

ti/kT

(23)

H. FROHLICH

100

We discuss the stationary solutions of this rate equation, i.e., the case ti, = 0. On summation o v e r j we find for the total rate of supply of energy S,

s =

x

sj =

2 +j[nrePwJ- ( 1 +

nj)]

(25)

On introduction of the excess mj over the thermal equilibrium distribution nj’ n j = nT

we obtain s

=

x

+ m,,

nT

= (ePwi -

I)-l

+jmj(ePwu- 1) < N&ax(ePwz - 1)

(26) (27)

where N = x m j

(28)

and &, is the largest of the +j. Thus we have a lower limit of the total number N of excess quanta, which increases proportionally to the total rate of supply of energy. Furthermore, on introduction of pj by

we can present a formal stationary solution of the rate equation (23),

From (29) and (26) we have

i.e., p, = 0 in thermal equilibrium, ml with (30), since n, cannot be negative,

=

0 (or when xil = 01, and hence

0 5 pj < wj We note with (29) that (30) can be rewritten as

or using (31),

(32)

THE BIOLOGICAL EFFECTS OF MICROWAVES

101

We now consider the simple case that all #j are equal to 4, and all xtl are equal to x. Equation (25) with (26) then becomes s =

4 x rnj(eBWi-

1)

J

From (29) it then follows that all pj are equal to p such that O I p < w ,

Expression (34) for nj then reads

or making use of ( 3 3 ,

Thus using (26), (28), and NT=xnr

we find

because sj 5 s and p < wl. If in particular the supply sl to all modes is the same, then zsj = s, and

Dependence of both (40) and (41) on s is implicit through p only. Furthermore, through (27), N must increase with growing supply s. In both (40) and (41), once N, i.e., s, has surpassed a critical value N o , so, this is possible only if p closely approaches o1[cf. (36)] in which case n , will become very large. This is exactly the situation met in Einstein condensation of a Bose gas that arises in equilibrium below a certain critical temperature. In our case the corresponding phase transition is enforced by the supply of energy-again a specific case of Haken’s (1973) rules in synergetics. It will be seen from (29) that pj = 0 when the ul = 0. It is thus the two-quanta interaction with the heat bath that is mainly responsible for the condensation; large x favors our effect.

102

H. FROHLICH

In the more general case we make use of (27) and write (34) in the form

instead of (38). Here the factor of s5/s in general varies only slowly with s. Forming Znj, the same argument as that following (41) holds again. In the present case, however, only one of the pl need approach w, very closely, in which case the particular n, becomes very large. From (31) we would is much conclude that if for a particular j the transition probability smaller than that of all other states then its pj may approach ojbefore the others and therefore this particular n5 will be much larger than the others. On the other hand, supplying energy to a particular state only does not necessarily mean that this state will be strongly excited, for the xrl transitions distribute energy appropriately over all states and, as remarked before, large x favors our effect. It therefore seems reasonable to neglect the s, term in the expression for n,. Going back to (38) then, we have approximately

Clearly s = 0 implies p = 0, while for sufficiently large s/+ we can neglect z. p is then determined by S/C#L In the usual way, transforming the sum into an integral, assumed to converge as p approaches wl, one finds so for p = wl. Condensation into w1 then arises for s > so. In this approximation it is irrelevant into which states the energy is fed as the large value of x leads to immediate distribution. If now through metabolic processes the value of s is below so, say s =

SO

-

AS

(45)

then supply of energy at the small rate As into any of the modes wl is sufficient to cause condensation. Also if s > so, then energy supplied into any of the wj will be largely channeled into the condensed state. Rate equation (23) can, of course, be derived from more explicit models, as has been shown by Bhaumik et al. (1976) and by Wu and Austin (1977, 1978a) using different interaction terms between the electric vibrations and the heat bath (cf. also Mills, 1979). Both impose temperature equilibrium on the heat bath, so that detailed balance at this temperature, and hence Eq. (23), must arise. These papers permit, however,

THE BIOLOGICAL EFFECTS OF MICROWAVES

103

giving explicit interpretation to the transition probabilities 4 and x, although so far they have not dealt with the important cases of water dipoles and of unattached ions in the heat bath. Wu ef al.’s interaction term is closely related to our P2div A term in Eq. (15) if the elastic A field represents the heat bath. Such a term, in view of In, leads to two-quantum processes, not only to a combination of absorption and emission, as in the x processes, but also to absorption or emission of two quanta. Probability for such terms, however, is much smaller than of x processes as Wu and Austin (1978b) prove in detail. This arises because in the x processes the energy h(wl - wl), in the other processes, however, the energy h(wl + wl), has to be exchanged with the heat bath, if quanta with frequencies wj and o1are involved. In addition, the total wave vector must be conserved, which in view of the small magnitude of the wave vector of our polar modes permits only very small energy transfer. This is always possible for the difference o1 - wl but not for the sum. The reader is reminded at this stage that in analogy to the case of ionic crystals, a very low wave vector of polarization waves (very long wavelength) implies a very high wave vector of displacements of mass, as positive and negative ions then move in the opposite direction. It is easy to see that a similar result holds for the interaction of polarization waves with unattached ions, say of mass M , energy kT, and wave vector k. The important point here is that k is very large, of order lo8- lo9 cm-I if M is the proton mass. The transferred wave vector g has very much smaller magnitude. Thus the wave vector g of a giant dipole oscillation is g = 0; for a mode carried by interacting oscillating systems l / g equals at least their mean distance. Thus through the interaction, k changes into k + g, so that (k + gI2 - k2 = g2 + 2kg cos 6 where B is the angle between k and g. Conservation of energy then yields

(h2/2M)(g2 + 2kg cos 8) = h(wj

*

(46)

and hence since the g2 term can be neglected [COS

61

=

* oil -k

1 h)wl 2 kT

-

g

5 1

(47)

Clearly this can always be satisfied for wj - wlr i.e., a combination of absorption and emission, in spite of the very large magnitude of k / g . The wj + wi case, however, is largely excluded unless frequencies very much lower than 10” Hz were contemplated.* This also holds for +type single-quantum emission processes. * This discussion also shows that Livshits’ (1977) dogmatic conclusion is incorrect.

104

H . FROHLICH

It should be emphasized at this point that the required importance of x transitions represents a material property that we would expect to have been established in the course of evolution of biological materials. It is easy to demonstrate possibilities that counteract Bose condensation. As a simple example we might assume the absence of x processes, but the presence of strong interaction between polarization waves without the help of the heat bath with which they are assumed to be weakly coupled through 4 processes only. In this case, the supply of energy would simply result in hot polarization waves without strong excitation of a single mode. Thus we have shown that depending on certain microscopic properties, the supply of energy either may make a system hot or may result in the creation of a new type of order-a feature very important in many other aspects of biology. Theoretical investigation of the quantitative detailed microscopic requirements would be extremely difficult. At the present time, therefore, it should be left to experiments to decide on the existence of coherent excitations. Present evidence is strongly in favor. It was the task of the theory to point out the possibility and to pursue its consequences. It should also be pointed out that time-dependent solutions of the kinetic equation (23) will be of considerable importance for estimates of the time required to establish the strongly excited state. A first step in this direction has been taken by Wu and Austin (1979).

IV. CONSEQUENCES A . General

The theoretical models discussed in Section 111 are based on the dielectric behavior of biological systems in conjunction with nonlinear excitation. One of them shows that single modes of electric vibrations can be strongly excited provided certain conditions are fulfilled. The other illustrates under rather more general conditions, that strongly polarizable systems will possess metastable states with very high polarization. It has also been shown that interaction between two systems may lead to mode softening. Clearly if these possibilities are realized in biological systems, then system properties of a much more complex nature may be considered. Among these, the establishment of the strongly excited mode as a limit cycle might be contemplated; this would be relevant in overcoming the friction of the surroundings. A further possibility to be contemplated is the excitation of solitons. It may be remembered that some nonlinear

THE BIOLOGICAL EFFECTS OF MICROWAVES

105

vibrating systems possess very stable dynamic excitations (solitons or solitary waves). Such excitations provide the possibility of nearly frictionless transport of energy. Theoretical work on this possibility is in 1980). progress based on Eq. (15) (Bilz P t d., In connection with our vibrational model it should first be remembered that the expected frequencies are 10'o-lO1l Hz for membranes, 1012-1014 Hz for proteins o r more general for certain bond-stretching groups, lo9 Hz for DNA or RNA molecules. Mode softening due to interactions may, however, open the range to much lower frequencies. Also frequencies of the order of Hz arising from oscillations of bound electrons cannot be excluded in principle. It must be mentioned in this context that stored energy is available in active biological systems in the form of "high-energy" chemical bonds, and electrically in the strong fields in membranes. To this we wish to add, tentatively, the energy of vibrations of polar modes, maintained during certain periods through energy supply, at a rate s, from various sources of metabolic energy. Suppose this rate s to be slightly smaller than so, then minimum energy supply required for strong excitation of a single mode [cf. (45)], so that the system is prepared for appropriate action by further supply of energy at a very low rate (>so - s). If the band of polar modes has frequencies in the microwave region, then external supply of energy by irradiation with microwaves will effect the coherent excitation and hence prematurely start the biological processes connected with it. From Section III,C it follows that the frequency of the actually excited coherent mode may differ from that of the incident microwave-it may be lower o r higher-and microwaves with quite a number of different frequencies may excite the same coherent mode and thus influence the same biological process. Actual experimental specification of the particular biological process will require application of the microwaves at specific instances of development of the biological system; whether in an overall measurementsay of the rate of growth-this leads to an increase or a decrease will depend on the particular type of event triggered by the microwaves. While experimental steps required for this specification may involve considerable difficulties, investigation of the dependence on intensity and on frequency is imperative and should be possible with the use of straightforward techniques. The main energy required for the various excitations must come from metabolic processes- biological pumping. Such processes are frequently connected with chemical activities such as protein synthesis. This invariably leads to displacement of ions, hence to electric signals seen by all polarizable regions, and hence to the possibility of energy exchange.

106

H. FROHLICH

B. Long-Range Interaction Static electric charges are screened by the ions of cell water at very short distances. Excitation of the highly polar state in a system, e.g., a protein, will therefore not lead to long-range interaction with another one when the systems are in cell water, although it will lead to effective interaction when the systems are placed within a membrane. In this latter case, due to the membrane field, the dipoles of the two systems are expected to be parallel in the direction of the field. The interaction is then repulsive. Formally, the interaction between such systems is governed by the dielectric constant of the medium, in the case of static charges in cell water by the appropriate longitudinal dielectric constant. As a consequence, the potential arising from a static point charge becomes a screened Coulomb potential. This is quite different for charges oscillating at sufficiently high frequencies when screening becomes only effective at distances considerably larger than a cell diameter. Dielectric loss must, however, also be taken into account, which it will be remembered is large in water in the 1Olo Hz region. Consider now the interaction of two systems at a distance R , sufficiently larger than their linear dimension L , capable of polar vibrations (Frohlich, 1972). On this condition interaction between these giant dipole vibrations only has to be considered as the fields due to higher poles decrease rapidly with distance. The band of polar modes of the combined system thus consists of the dipole, as well as of the higher pole vibrations. To calculate the interaction, at distance R , however, it is sufficient to select the modes with frequencies w+ and w- given in (3). This actually is a simplification assuming both systems to oscillate along one direction only, but this will not alter the basic results. Assume now the mode with frequency w- to be strongly excited to energy E-. If the vibration is (nearly) harmonic then this energy is proportion to WZ and to the square of the amplitude. We may consider this latter to remain unchanged on a virtual displacement of R . The force f between the two systems is then given by

where from (3) 2w2_/(wT

+ w:) = (A2 + R~/ERe)’”

(49)

THE BIOLOGICAL EFFECTS OF MICROWAVES

I07

The constant distance R , follows at once from (4), and we use, assuming w1

> w2, A =

(0:

- oi)/(w:

+ w;) > 0

(50)

Consider now the case that A' is large compared with the following term, so that

In the case of resonance, on the other hand, when w?/o? =

o1 = w2, i.e., A = 0,

1 - R$/e-R3

(52)

and the interaction becomes, assuming Ro/R > 1 ,

Owing to the pumping, E- is expected to be large compared with kT, and the interaction can therefore be considerable in the resonance case. It is of long range (1/R3)and attractive if E - > 0. In the absence of resonance (511, the interaction decreases rapidly with distance as l / R s . If we consider the case that mode W+ rather than w- is excited, then repulsion arises provided E+ > 0. Resonance interaction, o1= 02,is again of long range o:1/R3. Equation (3) for 0: is no longer valid when R is less than the linear dimension L of the subsystems. A further condition on the validity of the above is o2_> 0, which also imposes a limit on R . When R is much less than L , then roughly speaking the term l / R 3in p will be replaced by the smaller 1/L2R. In addition, however, nonlinear terms may be involved as discussed by Bhaumik et al. (1978). In pursuing further the quantitative properties of the interaction, it must be realized that the dielectric constant depends on frequency. Equation (3), therefore, represents an implicit equation for ocas has been realized by Genzel (1978), who solved .it by using the appropriate expression for the dielectric constant of water. It must also be pointed out here that in the resonance case, o1= w2, the large splitting o+ - W- may imply substantial differences between E+ and E-, and as a consequence lead to abnormally large interaction even if none of the modes is excited beyond thermal equilibrium. In this case, the interaction energy f is defined as the difference of the free energy at distance R from its value at R --.* 03. This yields I =

{

[<w+

+ w-) - (01 + wJ]h/2, kT log

w+o-/o~o~,

if ho % kT if h < k T

(54) (55)

I08

H. FROHLICH

Using the resonance case ( 5 2 ) , and similarly with W+

=

w+,

we find

w l ( l f R$/2e+R3),

if R3, e e?R3

(56)

””’(;-$), 4 R3

if i i w , > k T

(57)

and hence,

I=-

In the case of ( 5 3 , the factor tiol in (57) must be replaced by 2kT. Thus when E+ # E - , a long-range l / R 3 interaction arises even in thermal equilibrium. The case E+ = E - , when the I / R 3 interaction vanishes, leads to the well-known 1/R6 London interaction. The long-range interaction following from (53) may have considerable biological significance. Being frequency selective, it can lead to longrange recognition, and attraction if W- is excited. This might, for instance, hold for the attraction of an enzyme to a particular site, when the appropriate frequency on that site, interacting selectively with the particular enzyme, has been excited. Holland (1972) has applied this idea to the pairing of homologous chromosomes in meiosis. This must arise from a selective long-range attraction, which according to Watson (1970) has until now remained “a great mystery.” He also suggests that this interaction (he denotes it as dynamic specificity) might help to understand how RNA molecules, and proteins after their synthesis, get to their destinations in the cell. Excitation of w+, as we have seen, leads to selective long-range repulsion. We might conjecture this to be of relevance for the recognition of parts of a biological entity by the immune system. Each biological entity might have its own characteristic frequency or frequencies, which its immune system recognizes by being repelled from it. Long-range selective attraction will lead, of course, to close approach of the systems involved. At this stage, we have seen, mode softening of W- will take place. As a first consequence the combined system changes its long-range characteristics; the resultant oscillation may or may not be dipolar, depending on the angle between the oscillating dipoles of the two subsystems. Furthermore, the interaction with other representatives of the two subsystems will no longer be of the long-range type (53) because of the change of frequency. After the close approach of the two subsystems, short-range chemical processes of the usual type will be initiated. Thus, possibly such systems may exhibit both short- and long-range selectivity. The mode softening arising from the approach of an enzyme to its substrate will be counteracted to some extent by nonlinear terms that have been neglected in the calculation of w- in Eqs. (3) and (4). One possibility

THE BIOLOGICAL EFFECTS O F MICROWAVES

I09

of achieving this would be in terms of the model discussed in Section II1.B although this has not been carried out in detail. As a consequence we may expect a state with higher frequency and with strong polarization to arise, stabilized by mobile counterions that screen the arising dipole moment. It has been conjectured (cf. Frohlich, 1970) that the active states of enzymes always possess this high polarization, leading to strong internal electric fields. Independently, it has been pointed out by Green (1974) that these fields will be capable of reducing activation energies, and hence help understanding the enormous catalytic power of enzymes. It should also be emphasized again that the strong mode softening that arises at a relatively large distance R, [cf. ( 5 ) ] is a characteristic of large molecules possessing giant dipole vibrations, as we encounter them in biology. Thus a frequency of 1OI2 Hz with z = 30, using the proton mass, cm. yields R , -A further consequence of the nonlinear terms in (IS) arises from the possibility of the excitation of solitons (solitary waves) in biological systems such as enzymes (Bilz rt m l . , 1980). Solitons are localized excitations with great stability and thus are capable of transmitting energy nearly loss free when no chemical is transported. This may arise, e.g., in the action of muscles. Finally it should be pointed out here that the dielectric function of the medium between two interacting systems-as it arises in various expressions such as (57)-is the longitudinal one for the appropriate wavenumbers and frequencies ~ ( k w). , This may differ considerably from the transverse dielectric constant measured at this frequency.

C . Modcls f b r

Notitherriitil

Actions of’M i c r o w i w J

A microwave penetrating into a medium loses energy to it, which in the realm of linear response is proportional to the intensity of the radiation and whose magnitude and frequency dependence is governed by the complex dielectric constant of the medium. It must be understood (e.g.. Frohlich, 1958) that in a medium like water the energy loss arises through a subtle influence of the field of the microwave on the thermal motion of the electric dipoles of water. As a consequence this thermal motion is only very minutely perturbed, but an increase in temperature must arise so that under stationary conditions as much energy is removed by heat conduction as is supplied by the absorption of the microwave. Consequently we should not necessarily expect the occurrence of nonthermal effects in regions of high dielectric absorption. Effects are known in physics in which the supply of external energy is effected to a particular subsystem that is coupled weakly t o the rest of the

I10

H. FROHLICH

system. This subsystem then may still be near a thermal equilibrium corresponding to a temperature higher than that of the rest. Hot electrons in semiconductors is a well-known example, whereby the electrons receive energy from an external electric field. Their density must be sufficiently high to distribute through mutual collisions the energy they receive among themselves before passing it on to the lattice vibrations, which are treated as a heat bath at fixed temperature. In our model of coherent excitations (Section II1,C) external energy is supplied to the system of polar vibrations. They interact with a heat bath in two ways, either by exchanging quanta noj(6processes) or by a kind of phonon Raman effect by exchanging only the difference h(wi - oj) of the energy of two quanta (xprocesses). This latter effect is considered to be more prominent than the first. The constituents of the heat bath that interact strongly with the polar modes are unattached ions, mobile dipoles, and to some extent elastic vibrations. The interaction with unattached ions has a well-investigated analog in the interaction of nearly free electrons with the polar modes of an ionic crystal. Here emission of single quanta ho by a free electron is a rare event due to the difficulty of conserving energy and momentum, so that the principal scattering exists in double processes (emission + absorption). The same holds in our case as pointed out with respect to 4 processes in connection with (47). In addition to these processes, it has been assumed that processes through direct interaction of two polar vibrations are negligible compared with x processes. Under these circumstances it has been shown that x processes impose a distribution of excitation in the band of polar modes that is governed by the temperature T of the heat bath. In the approximation in which we consider supply of energy s and loss of energy 4 as slow processes, this implies that nj(l

+ nJeP@j = nl(l + nj)ePWi

(58)

or must hold, i.e., that in zero order the x terms of (23) must vanish. From this follows at once our approximative solution (43), and hence strong excitation of a single mode when the rate of supply of energy s exceeds a critical one so. In this approximation there exists a single "chemical potential" kTp and w , is the excited mode. The more refined model yielding a different pj for each wj [cf. (42)] does not permit the crude approximations made above. We now consider the quantities that determine the magnitude of so as follows from (35)or, in the simple approximation (431, from (44). Clearly

THE BIOLOGICAL EFFECTS OF MICROWAVES

111

p must increase as s grows, starting with p = 0 for s = 0. Strong excitation of w1 arises when w, - p

< w2

- 0 1

(60)

How sharp a transition in n, as a function of s at a certain so will be depends on the distribution of wj levels and cannot be answered in general. Such details are not very relevant for our present purposes. It is most irnportant, however, that Eq. (44) does not yield so, but rather the ratio so/+. Thus the smaller 4, the lower the energy transfer from the polar modes to the heat bath, the smaller is the critical rate so of energy supply at which the transition to strong excitation arises. Thus when s > so, then our system is capable of storing energy until the strong excitation of the mode wl, containing under stationary conditions the energy n h o l , is achieved. In principle, thus, very low r#~ will permit very small s > so to achieve strong excitation. Such storage is also characteristic for signal over noise systems. We consider now a biological process that is initiated by the consequences of strong excitation of a certain mode, leading to selective long-range attraction. This might, for instance, lead to an enzyme being attracted to an appropriate position in which it becomes active, or to another of the possibilities suggested above. Let t 1 be the time required for this process, which then is assumed to be followed by a chain of biological processes taking a time t z . The rate B of the total is thus B

= (1,

+

(61)

If tz does not involve long-range interaction, then B will depend on it through tl only. The first process then requires excitation of the coherent mode through energy supply satisfying s > so. The larger s - so, the shorter will be t l , and we approximate this by

where a is a constant and n

t,

= a / ( s - soy

2

1 a positive number. It follows that

(62)

If s < so then long-range attraction is absent so that the required transport can occur through diffusion only, making t l very large and B very small. Increased energy supply, on the other hand, will make f I very small so that, ultimately, the process described by tz determines the rate B , which becomes independent of s. Thus the function B(s) is steplike with the step at (s - so)'' = a / t z ; it is zero if s < so.

112

H. FROHLICH

Consider now s to be composed of a biological part sB and of s,, the rate at which energy is supplied by microwave irradiation, s

sB

+ s,

(64)

Then if sB < so, we find B = 0 for small s , until ,s = so - sB, when B rises with increasing s,, at first very slowly, and when s, reaches the value at which (s, + sB- so)'' = u / t z in a steplike manner, after which B no longer changes with increasing s,. The rate of the biological process described by B is thus either unchanged by microwave irradiation or increased, but never decreased. It must be pointed out, however, that this does not imply that biological processes of a kind different from that involved in B are not influenced. In fact, if the microwave initiates a process that at the particular time is not appropriate to the action of the biological system, then it may be expected to disturb the general development and in an overall observation, such as rate of growth, have a negative influence. Clearly it is desirable then t o test the influence of microwave radiation on a specific biological property, described in terms of B. It might be hoped, however, that even overall measurements will indicate the dependence of B ( s ) on s,.

01

I

A

'Sm

FIG. 1. Theoretical dependence of the rate of response B on the rate of energy supply S . The dependence of B on the rate of supply of radiation energy S, is indicated if the biological energy supply is at the rate SB.

THE BIOLOGICAL EFFECTS OF MICROWAVES

I13

Figure 1 shows B(s) as a function of s. For given sB, this also represents the dependence of B on the intensity of radiation s, if s, = 0 is placed at s = sB. Hence if sB > so + a / t 2 ,then the action of external radiation s, will be negligible. If, however, sB is less than so, then the action of the radiation again follows a steplike function of s,; it acts as a typical trigger effect if sB falls just below so. The actual value of s,, at which the biological effect is initiated may be very small, even if sB = 0, provided 4 is sufficiently small as discussed above. It should be pointed out, at this stage, that the nonlinear response to s, implies that pulsed radiation may yield a response different from continuous radiation of the same mean intensity. Thus, e.g., if the mean intensity is such that sB + ,s < so then continuous radiation will have zero response. The maxima of pulsed radiation may, however, reach above so and thus yield a response. It has been pointed out above that when s > so, radiation absorbed by any of the modes of the polar vibrational band will transfer its energy to the strongly excited mode. If this mode represents giant dipole vibrations, then one might hope to be able to detect it by absorption and reflection measurements. It must be realized, however, that these properties are largely dominated by cell water. The biological subsystems involved in a particular type of coherent vibrations might use a very small volume only, and thus contribute only little to the overall optical properties. It is difficult, at present, to predict whether such measurements could have a chance of success. D . Multicomponent Systems urid the Cuncer Problem

Consider an assembly of equal units capable of polar oscillations. In crystal dynamics it is shown that this gives rise to a band of polar normal modes (polarization waves) whose lowest frequency is different from zero. These modes can be divided into longitudinal and transverse modes: furthermore, three modes with zero wavenumber, i.e., giant dipole vibrations, exist whose frequencies depend on the macroscopic shape of the material (cf. Section 18 of Frohlich, 1958). This arises from the long range of the interaction between polar vibrations, as has also been discussed in Section III,A for the case of two units. A noncrystalline arrangement of the units does not basically change these conclusions although it influences the dependence of frequency on wavenumber. In general if all units have equal frequency o,then the band of normal modes ranges from frequencies lower than w to frequencies higher than w , just as in Section III,A w- is lower and w+ higher than the original frequency. It is of interest in this context that in w - , the two

114

H. FROHLICH

systems oscillate in phase when the line connecting the two systems is parallel to their direction of oscillation, while in the case that it is perpendicular they oscillate with opposite phase. In the first case then o- represents a giant dipole vibration, while in the second it does not. We can conclude that in large disordered systems no general prediction of the position of giant dipole vibrations within the band can be made. We now apply the considerations of Section II1,C to our band. To start with, we discuss the simple case in which the rate of supply of energy s is small, s < so, and neglect the nonlinear x terms in (23). We ask for the behavior of a single of our units, whose frequency in isolation we denote as o. This unit interacts with the (weak) excitations of various normal modes, frequencies wj, in a linear way so that a linear superposition of vibrations at various frequencies oj is excited. For a single normal mode then, the amplitude x of the oscillation of our single unit will be proportional to the amplitude Aj of the normal mode so that x = ajAj,

Aj

Ajo cos ojt

=

(65)

where Ajo is time independent and the parameter aj depends on the geometry of our system and on the wavenumber of the normal mode. Also then

x

+ w2x =

p4j

(66)

where the parameter pj also depends on the geometry of our system and on the wavenumber of the normal mode. The right-hand side is proportional to the force exerted by all the units on our particular one when the normal m o d e j is excited. From (65) thus x(w2

-

Wj")

=

pfij

(67)

and using (65) we find the frequency 0;

=

0 2

-

pj/aj

(68)

In the case of crystals, the parameters pj and ajcan easily be calculated and yield wj as a function of the wavenumber. At weak excitation, the oscillations of the various normal modes superimpose linearly, and correspondingly x becomes a linear superposition of the terms presented in (65). The realistic case of interaction with a heat bath implies introduction of a damping term and stochastic supply of thermal energy and results in a Planck distribution. Further supply of external energy to various normal modes leads to additional excitations, and if this supply does not exhibit any phase correlation, for the various frequencies, then x will be a linear superposition of contributions at the frequencies oj of all the modes, showing no phase correlations.

THE BIOLOGICAL EFFECTS OF MICROWAVES

115

Consider now the opposite extreme, the case that the energy supply is large, s > so and that the nonlinear x terms are important. As a result, a particular mode with frequency Wb, say, undergoes Bose condensation so that it is very strongly excited to the amplitude Ab,which we may assume to be so large that the temporal mean value of A; is large compared with the sum over the Af of all the other modes, so that we can disregard their excitation. As a consequence, the amplitude x of our particular unit will also be strongly excited, and we wish to investigate the stability of this excitation. For this purpose, introduction of the nonlinear x terms into the dynamic equations of the system would be required, a task that has not yet been carried out. We note, however, that when the x,l are very large, then they nearly entirely regulate the magnitude of the strongly excited mode; in other words, direct supply into and loss of energy from this mode through sb and +b are of minor importance. It should therefore be a good approximation to supplement Eq. (66) with nonlinear terms that enforce the required excitation, x = (YbAb

(69)

for given Ab.This can be done by extending (66) into the limit cycle equation .f -k

w'X

-k yX(X2 -

a2A;/4) = PA0

(70)

COS

where y is a positive constant, and, for simplicity, we have omitted a subscript b in a, p, and Ao.Solution of this well-known equation is, of course, no longer strictly harmonic. However, we deal with the first harmonic only, and disregard higher frequency terms. Clearly the y terms lead to damping when x" is large and to antidamping when this term is small, thus driving the system into a definite amplitude determined by Ao. In fact under stationary conditions when [cf. ( 6 5 ) ] x =

x0

cos

XO

Wbt,

= d

o

(71)

we find

.k(y - a2A;/4) =

- W&

Sin

Wbf(X$ COS Wbt

= -&&(x$

- a2A;) sin

-

Wbt

a2A$/4) = 0

(72)

if we disregard sin 3Wbt terms. Thus at the amplitude given by (71), and at this amplitude only, Eq. (70) reduces to (66) w i t h j = b. To investigate now the stability of our solution we consider x to deviate from it by (, i.e., replace (71) by x = d o cos

Wbt

-k

(73)

116

H. FROHLICH

Neglecting terms in [dO(-wb

sin

= &rAo)2i

wbr)

t2,Eq. (72) is now replaced by

+ k][(dO)'

+...

cos2 wbt - ( d 0 ) ' / 4

+ 2 d 0 5 cos w b f ] (74)

if we neglect terms with frequency 2wb. As a consequence we find from (70)

+ wz.$ +

ar(do)2i'

=

0

(75)

the equation of a damped oscillator whose effective damping constant is larger the higher the excitation of the Bose condensed mode. Thus any deviation 4 of the excitation of our unit from that required by the mode quickly dies out, except for higher frequency terms, which we neglect here. Similarly, additional energy has to be spent in order to cause a deviation 5 from the stationary x. It should be pointed out now that excitation of a normal mode wj also induces vibrations in systems whose frequencies in isolation differ from w ; in fact, the normal mode embraces all of these. The excitation of single regions of such systems will, however, be much smaller than those of our units unless their frequencies in isolation come very close to w . In general, therefore, the above considerations do not apply to such different regions. A more quantitative statement must, however, wait for a more detailed treatment. Two types of consequences arise from the strong excitation of a vibration of frequency wb in an assembly of (nearly) equal units, e.g., a tissue. First, the individual units obey the direction of the excited normal mode, i.e., they resist attempts at removing their oscillations from that directed by amplitude and phase of the normal mode. Second, in regions in which the electric field created by the normal mode is inhomogeneous, forces are exerted on oscillating individual units. This latter may be considered as a generalization of the case treated in Section IV,B where attraction or repulsion between two equal units was found depending on whether the combined frequency w- or w+ is excited. In this case a simple result arose when the distance between the two units is larger than their linear dimensions. For then only giant dipole oscillations of single units must be considered. In our present case the situation is much more complex if we are interested in the force between a selected single unit and all the others forming, e.g., a tissue. For the electric field due to the vibrating system of many units may be relatively strong at distances much larger than the size of a single unit even if the system as a whole does not carry out giant dipole oscillations-the latter would be prominent only at distances larger than the linear size of the whole system. Clearly we have to distinguish two types of forces: (1) those exerted by the whole system (whose wb mode

THE BIOLOGICAL EFFECTS OF MICROWAVES

I17

is strongly excited) on a single unit outside it at a distance larger than the linear size of a single unit; (2) forces acting within the whole system, which together with standard short-range forces determine the mean distance between units, and possibly also the macroscopic shape. In analogy with the results found in Section IV,B, we expect attraction when wb < w , i.e., in the case of mode softening. It should be mentioned in this context that since the band of polarization waves ranges from w1 < w to wz > 0, and since its width must increase as the mean distance between units decreases, wb is expected to decrease with decreasing mean distance when wb < w so that an attraction between units arises on excitation of wb. Hence a mean distance is established through conventional short-range interaction. One would also expect that, for similar reasons, individual units of the same kind are attracted to the bulk when they are separated from it. Such attractions may be strongly anisotropic if the excited normal mode possesses a highly anisotropic field. A crude example would be a narrow, long cylinder with a giant dipole oscillation along its excited axis. Relatively high fields, i.e., strong attraction, will then exist near its poles only. Something quite similar holds for a sheet of finite size, where all units oscillate in phase perpendicular to the main surface. If, on the other hand, neighboring units oscillate in opposite direction then their fields cancel to a first approximation. At the same time fields near the edges may be relatively strong. Clearly, much weaker forces are expected to be exerted on units whose frequency w' differs sufficiently from w , corresponding to the case of two units with different frequencies, discussed in Section IV,B. Considering the units as cells of a tissue it should be remembered that frequencies of greatly differing orders of magnitude can be expected as discussed in Sections III,A and IV,A. Modes with such different frequencies are based on different degrees of freedom and do not interact strongly. As a consequence it is feasible that quite a number of different frequencies are excited simultaneously in a cell. The second type of consequence from coherent excitation of a certain mode wb refers to the enforcement of the amplitude x in a single unit by the excited mode, as follows from Eq. (75). In principle this may have far-reaching influences on processes that are nonlinearly coupled to the x vibration. Consider, for instance, that this vibration is carried by the nucleus of cells and that initiation of certain processes preceding cell division requires reduction of x vibration, e.g., to thermal magnitudes. Then if a particular cell is a part of a tissue in which wb is strongly excited, so that x satisfies (70), the required reduction of amplitude must work against its stabilization, which follows from (75). In this model, the stabilization of the amplitude of single cells thus acts against the processes leading to cell

118

H. FROHLICH

division. A similar argument might hold for mutation. Clearly more explicit considerations can be developed; to be realistic, however, they require more detailed experimental knowledge than is available at present, but it should be mentioned that a very great number of possibilities exist, depending on the spatial structure of the particular normal mode. Thus if we consider a sheet with in-phase oscillations perpendicular to the surface but with a boundary condition of vanishing amplitude at the edges, then the inhibition of cell division would not hold for cells at the edges. Thus the two consequences of coherent excitation of certain modes in an extensive system such as a tissue may lead to (1) selective attraction or repulsion of individual units, and (2) stabilization of certain oscillations, which can be overcome only by a supply of sufficient energy. It must be stressed, at this point, that the coherent excitation also requires a supply of metabolic energy. A competition between this and the consequences of (2) may thus arise. To turn now to the cancer (Frohlich, 1977a, 1978) problem it must be mentioned first of all that in a normal tissue, cells are subject to a control with regard to cell division and to the occurrence of mutations. This control is absent in cancer, and the basic problem thus is to find the origin of the control in normal tissues. Now it has been shown above that a wide range of controls can be exerted by the excitation of coherent vibrations extending over certain regions of a tissue. This may lead to the attraction of cells with equal frequency to certain selected regions. Particular frequencies could thus be characteristic for particular cell differentiation, as first proposed by F. Frohlich (1973). The excitation may also lead to the inhibition of cell division, and of the occurrence of certain mutations, if these can occur only when the amplitude of the coherent vibration in a particular cell has been reduced. Since both establishment of the coherent vibration and of cell division with or without mutation require metabolic energy, it is a matter for detailed specification of a model to decide to what extent the control can be effective.

E . Brain Waves In recent years it has been found that electric fields at very low intensity in the region of 10-20 Hz as well as in the microwave region, appropriately modulated, can severely influence the electroencephalogram (EEG, brain waves) as well as calcium Ca2+efflux and other brain activities (as discussed by Adey and Bawin, 1977). It has also been reported by Elul ( 1974) that during certain periods large regions oscillate coherently.

THE BIOLOGICAL EFFECTS OF MICROWAVES

119

It is possible, in principle, to account for this on the basis of our general model of coherent excitations in terms of collective enzyme activities (Frohlich, 1977~). This possibility arises within the framework of the “greater membrane” of Schmitt and Samson (1969), which is shown to contain globular proteins that can act as enzymes. As pointed out in Section IV,B, it has been conjectured that the active state of enzymes possesses the high electrical polarization discussed in Section II,B. Thus consecutive excitation and deexcitation of enzymes will lead to electric polarization and depolarization, i.e., to an electric vibration whose frequency will be determined by the rate of the relevant chemical reactions. Consider now a system of enzymes and their substrates, excited through metabolic processes to our coherent vibrations, which as shown in Section IV,B may lead to selective long-range attraction. Let N be the number of excited, Z the number of nonexcited enzymes, and S the number of substrate molecules in a certain region. Then dN/dt = d Z S

- pN

dS/dt = - d Z S

+ yS

(77)

Here the 1y term describes the rat!: of increase of excited enzymes being proportional to Z, the number of nonexcited ones, and to NS,the rate of reactions. Each such process leads to the destruction of a substrate. The term pN describes the rate of spontaneous recombination of excited enzymes, and the term yS represents the rate of increase in the number of substrates due to our long-range dynamic attraction. Furthermore, we assume that the number 2 of unexcited enzymes is always in equilibrium, i.e., time independent; a,p, and y are constant parameters. The above equations then form the well-known Lotka-Volterra equations, which have oscillating solutions, i.e., we find the required oscillating chemical reactions. We note the time-independent solutions No, So, No =

so = PI&

(78)

so that with

we find L = yu

+ dwu,

ci = - p v

- dCrv

(80)

Thus if we can neglect the quadratic term u u then we find harmonic solutions with frequency (yP)’”.

120

H. FROHLICH

We assume now that the enzymes are arranged spatially in a crudely ordered fashion such that their polarizations, when in the excited state, are nearly parallel. The total polarization P of the region is then proportional to Y if we assume that the contribution of the time-independent part No is screened through mobile ions. Furthermore, the time-dependent polarization P induces an electric current whose resistance yields a negative contribution to P proportional to P. Also the interaction between excited enzymes may lead to a tendency toward a ferroelectric state and hence to a positive contribution to P, proportional to P and to a transition probability. We shall make the ad hoc assumption that this transition probability is governed by a (negative) activation energy proportional to - ( P k , - P), i.e., by a tendency to “fall” into the ferroelectric state whose polarization is Pmm.This implies that further terms i , have to be added to V, where il has the form il = (cze-r*~z - d 2 ) v

Here c2, d 2 , and

r2are positive constants. Thus i = y o + (c2e-Fvn- d 2 ) v + d u v

(81) (82)

We note that if we neglect the uv terms and develop the exponential up to P terms, then using the C? expression of (80) yields u = -pyv

+ [(CZ

-

d2)

- 3Pc2S]i

(83)

i.e., a limit cycle without external field [cf. (70)] provided c2 > d 2 . If on the other hand d2 > c2, then the oscillation is damped out through too large an electrical resistance. Thus in our model, excitation of coherent vibrations in enzymes and substrates leads to long-range interaction and hence to collective enzymatic processes that oscillate with frequency (py)1‘2,and, as a consequence, to coherent electric vibrations with the same frequency determined by the rate of spontaneous recombination of an activated enzyme (through p), and the rate of long-range attraction or substrates (through y). Neither value is known at present, but they might well yield a correct magnitude for brain waves, i.e., an order of 20 Hz.The coherent vibrations leading to the long-range interaction on the other hand should be in one of the regions discussed in Section III,A, i.e., probably between los and 1013 Hz, although lower frequencies are feasible since mode softening might be relevant. Apart from representing a model for EEG in terms of collective chemical processes, Eq. (82) has other far-reaching consequences, which have been discussed by Kaiser (1977a,b, 1978a,b) but are beyond the scope of this chapter.

THE BIOLOGICAL EFFECTS OF MICROWAVES

121

It would now be necessary, however, to extend the discussion to the case of more than one type of enzymatic processes. They all will then contribute to the total electric polarization P,which thus must yield an interaction between these processes, and it will have to be investigated whether or not they can coexist. It is feasible then that weak external fields at a frequency (py)1’2can have far reaching consequences on the selection of one or another limit cycle. In the present context it must be pointed out that this again would contribute a trigger effect, the main energy involved being available in the relevant collective chemical processes. In addition, radiation in a frequency region that influences the coherent electric vibrations resulting in long-range interaction (e.g., microwaves or millimeter waves) will interfere with this interaction and hence with the subsequent processes including the EEG.

V. EXPERIMENTS A . General

It is one of the most general biological features that energy supplied in terms of food, or of sunlight, is in part used to build up and maintain a very complex organization. A plant might well get warm under the influence of intense sunlight; yet no one would dream of suggesting that in this case the action of the sunlight is entirely thermal (photosynthesis!). This type of argument is, however, one that has a large following in the discussion of the biological effects of microwaves. It should be obvious, therefore, that it is quite impossible to classify biological effects of microwaves in terms of their intensities alone as has been suggested, e.g., in the “Conclusions” of the International Symposium at Warsaw in 1973; for the absorbed energy depends on the dielectric properties of the particular material, which varies with the frequency of the microwave and depends on the composition of the particular system; moreover as indicated above, nonthermal effects may well be accompanied by general heating. For a decision it would be necessary to heat the system by different means and compare the resultant effects with those found by microwave heating. Such a procedure might, however, give rise to misunderstandings, for not only could one imagine the occurrence of “hot spots” characterized by a subregion with high absorption in conjunction with low thermal conductivity, but also it might occur that certain degrees of freedom are only loosely coupled with the rest of the system. If these interact strongly with each other then they may be endowed with a tem-

122

H. FROHLICH

perature different from that of the rest of the system. As mentioned before, effects of this kind are well known in physics, e.g., hot electrons. We should agree, therefore, to define an effect as thermal when it can be produced by ordinary heating. We should also agree that it is impossible to establish a general intensity limit below which no biological effects occur. Such limits must depend on frequency and on the particular biological system. We may also discard here direct effects of the electric field of the microwave on the biological system, as this would require unrealistically high intensities. Any change of a system under the influence of electric fields leads beyond the realm of linear response. For most molecules this is well known to be beyond lo5 V/cm. Biological systems may, however, be very “soft” in this respect. It must be observed, however, that changes in the constitution of a system by an electric field must arise from a displacement of charges such that their potential energy changes by more than kT. We note that for the electronic charge e this implies a change of electric potential by V = k T / e = 3 x V. For a displacement by cm (thickness of a membrane), the corresponding electric field is E = 3 x 104 V/cm. Since the intensity of an electromagnetic wave in vacuum is Pc/47r, the above field is carried by a wave of 10s W/cm2. The field changes, of course, as the wave enters a dielectric medium with complex structure. We may mention in this context the estimate by Schwan (1974), who finds that in a biological membrane an alternating membrane potential of only 1.5 x lo-’ V is induced by a 3-GHz microwave of intensity 10 mW/cmz. To obtain the above-mentioned 3 x V thus requires an increase in intensity by (neglecting the dielectric constant) a factor (2 x 105)2leading close to the above estimate. From these considerations it seems fairly safe to conclude that microwave effects on biological systems that cannot be explained in terms of heating must arise from trigger effects as treated in Sections IV,C and IV,E. It may be remembered that in the models treated in these sections the principal energy required in the relevant processes is stored by the biological system; the role of the microwave consists in triggering the occurrence of the particular effect. A detailed mathematical treatment would require a time-dependent solution of Eq. (23) when the microwave supply of energy s, [cf. Eq. (64)] is switched on at a time at which the biological energy supply sB was below the critical so. It can be seen qualitatively, however, that as s, is switched on, the system will accumulate more energy (supplied by microwaves) than it loses, until after a period, which might be considerable, Bose condensation is achieved, provided s, > so - sB. Such systems, clearly, are subject to great fluctuations, and appropriate treatment must therefore incorporate these effects.

THE BIOLOGICAL EFFECTS OF MICROWAVES

123

According to this theory, as discussed in Section III,C, the microwave may be absorbed in any level of the relevant band as most of the absorbed energy will be channeled into the mode that is to be excited. One may therefore expect the same biological process to be triggered through a whole range of microwave frequencies. It may also be contemplated that the strongly excited mode undergoes a further transition, similar to that discussed in Section III,B. In the particular model discussed in Section IV,C it was assumed that the biological event observed to be triggered by microwaves consists of a whole chain of steps of which only the first one depends on the coherent excitation of the relevant level. This first step takes a time t l , which decreases with increasing excitation, i.e., with increasing rate s, of supply of microwave energy; all the other steps take a time tz independent of s,. As a consequence, the total time c1 + t z tends toward the s,-independent value f z as the microwave intensity increases. In this form this result, however, holds only if the microwave intensity is the same at all relevant systems. If, on the other hand, the relevant systems are distributed such that owing to absorption the microwave intensity differs, then under rather general circumstances a logarithmic increase with s, precedes the independence of it. Consider, for instance, a homogeneous distribution of systems in a layer of thickness L with the microwaves impending perpendicularly to the surface. The rate at which the biological process proceeds now depends on x through s,(x). Thus (63) using (64) must now be replaced by

if

= 0,

sm(x><

Here c = a / t z and A = so - sB > 0 are independent The observed mean rate 3 is then obtained as Jo

and it has been assumed that the biological rate of supply of energy, sB,is below the critical value so. We carry out the integration of (86) for the case n = 1, assuming s,(x) = sme-OZ= z

Define a value x

=

d by

H. FROHLICH

124

such that B(x) = 0 for x > d. Then

C zlz0+ c - A log-21 -log ZO c -A Z O Z ~+ c - A

where

z1 =

S,

> A,

zo = A,

if

L>d

(90)

so that B=

- [1 sm logaLt, A

and

C

A

+logC - A c -

B = 0,

C

+-log(1 C - A

if s,

+ -)]Sm

C - A

(91)

IA

Developing for small s,,, - A, clearly

whereas for large s,

If on the other hand L < d , then zo must be replaced by

zo = s,ePaL > A,

or

s,

> be*

(95)

yielding

which for sufficiently large s, tends toward 1/r2, independent of s,. Thus ultimately the r a t e 3 will become independent of s, even for thick layers. It must be realized, however, that large s, may lead to nonnegligible heating. If the biological effect on which the microwave acts depends on temperature then this may mask the original effect. The amount of heating is determined by the overall dielectric properties of the material and in contrast to our specific effects may be expected to vary only slowly with frequency. From the point of view of physics, it is thus imperative to investigate the dependence of a particular biological effect on both frequency and intensity of the microwave. Furthermore, on the basis of our model, the microwave has supple-

THE BIOLOGICAL EFFECTS OF MICROWAVES

125

mented the amount sB of biological pumping (i.e., rate of energy supply) by s, and thus has triggered a biological effect that, without the microwave, was due to occur at a later stage. In certain cases it might happen that the opportunity for this action occurs only at certain stages of biological development. Whether this retards or accelerates the overall biological development may be different for different cases. It is a most important experimental task to try to specify the particular biological event that is influenced nonthermally by microwaves in a certain frequency region. It must also be emphasized again that if the biological energy supply sB exceeds the critical so sufficiently, then no effect of microwave irradiation will occur. Biological developments usually lead to structural changes of systems (e.g., cell division o r formation of proteins) and thus are, from the point of view of physics, highly nonlinear effects. This also holds of the nontherma1 action of microwaves in our model. It would be wrong, however, to conclude that investigation of fractions of the system, e.g., particular molecules, would exhibit nonlinear response to microwaves, for only the whole active biological system shows such properties. It may also be tempting to find the frequency regions that show active biological response by measurement of the absorption of microwaves. While this cannot be excluded in principle, it must be realized that the relevant spatial regions might be very small such that the energy absorbed by them is negligible compared with the overall absorption. Experimental evidence on the frequency and intensity dependence of biological effects of microwaves is, at present, available in the millimeter wave region only and is discussed in Section V,B. This evidence does support the main principles of our model. Trigger action of microwaves is, of course, only one feature of this model, which predicts strong excitation of polar modes through biological pumping. Evidence for this in a higher-frequency region is now accumulating with the use of Raman effect and will be discussed in Section V,C. The very great number of investigations of the action of 2450-MHz microwaves on animals frequently are carried out at few intensities only, and, therefore, in the absence of frequency variation d o not permit, at present, analysis from our point of view. Certain of them show, however, effects at such low intensities that they do give evidence for nonthermal action. Thus a great number of obviously nonthermal effects are described in the book by Baranski and Czerski (1976). While in their present stage of development, most of these effects are beyond the scope of this chapter, the frequently observed difference between pulsed or modulated waves and continuous waves at equal mean intensity should be discussed briefly.

126

H . FROHLICH

An obvious reason may arise from the nonlinear reaction to microwaves, as illustrated in Fig. l, in conjunction with Eqs. (63) and (64). Thus, if the microwave energy supply s,, together with the biological supply sB, is less than the critical so, then no effect can be expected. For pulsed waves, however, the maximum s, will be larger than the mean and together with sB may exceed the critical so. This possibility may be tested by varying the intensity of the microwaves, or by varying the pulse shape and pulse interval. Another possibility exists, however, namely, that electric fields at the (low) pulse frequency cause an independent effect that acts jointly with effects of the microwave. Clearly it will be necessary then to investigate the effect of low-frequency electric fields alone. This, in fact, has been established in the case of the action of 147 and 450 MHz microwaves at intensities of 0.1 and 1 .O mW/cm2 on the brain. In a summary article by Bawin et al. (1978) the effects of extremely low frequency fields (ELF) at frequencies between 6 and 12 Hz and gradients in air of 0.1-0.5 V/cm on the efflux of calcium from cerebral tissue of chick and cat are described. The authors find decreases in the efflux of 12- 15% compared with the unirradiated control. The microwave alone showed no effect. Modulation of the 147-MHz wave with frequencies between 6 and 20 Hz, however, showed an increase of the efflux of up to IS%, and modulation of the 450-MHz wave with 16 Hz also showed an increase. Thus the microwave reverses the effect of the E L F fields although alone it exhibits no such effect. This need not mean that the microwave does not cause other effects. Thus on the basis of the model sketched in Section IV,E one could expect that microwaves in a certain frequency region affect the excitation yielding the long-range interaction between enzymes and substrates. This then led to the periodic chemical reactions presumed, in this model, to be the basis for the EEG. It would then have to be shown that the EEG is influenced by the microwave and that it is directly involved in the binding of calcium ions which thus could be affected by changes in the EEG. For it must be realized, in view of thermal fluctuations, that the binding energy of each single calcium ion must be larger than kT. The low magnitude of the applied field that can modify the efflux thus points to a collective effect in the binding. Concerning the influence of microwaves on the EEG, it should also be mentioned that investigations by Takashima et al. (1979) on the effect of 1 - 10 MHz irradiation modulated by 15 Hz on mammalian EEGs prove the existence of modifications in the case of chronic irradiation of nonthermal level. Acute irradiations, on the other hand, did not produce changes in the EEG. From the point of view of our theory, as mentioned above, it seems

THE BIOLOGICAL EFFECTS OF MICROWAVES

127

likely that the EEG is based on the existence of long-range interactions that can be modified by weak external fields. More experimental material will be required in order to make more specific connections. It can be stated with confidence, however, that collective effects must be prevalent in all phenomena that can be dealt with by our general theory, and that the majority of them will refer to collective vibrations. For this reason it seems desirable to support the existence of such vibrations directly by experimental work. Experiments in this direction have been devised for the case that involves protons in the vibrational mode, e.g., by Palma (1973), Aielloet al. (1973), and Vento et al. (1979). These authors emphasize the difference to be expected between independent and collective properties when protons involved in a collective mode are replaced by the twice as heavy deuterons. Their results so far support the existence of collective excitations in a water-agar system. This in turn touches on the possible properties of cell water (cf. Drost-Hansen and Clegg, 1979), assumed to exist in a number of modifications of ordinary water. The task thus exists of finding the relevant frequencies with the possibility of soft modes leading into the microwave regions.

B. Experiments with Millimeter Waves In the previous section it was noted that direct action of the electric field of microwaves would require unrealistically high intensities. Nonthermal action of microwaves, in particular at 2450 MHz, seems to be established beyond doubt. We must therefore take the attitude outlined in the preceding theoretical sections, although details of particular models may have to be revised in due course. The main general principle, however, should hold, namely, that the microwave acts as a trigger for biological processes. If this is to occur at very low intensities, then the biological system must be able to store the energy supplied by the microwaves. This, in turn, will involve both frequency and time-dependent processes. The region of millimeter waves is the only microwave region in which at least some of these requirements have been fulfilled and the results, in fact, seem to support the main features of the theory (cf. Frohlich, 1975b). In order to gain sufficient insight, these requirements must be extended to include biological specification, for quite likely the action of a microwave of given frequency -is restricted to certain periods in the development of biological systems. This may, in particular, be so for single cells or for growing tissue, while it need not hold for tissue control as presented in Section IV,D.

128

H. FROHLICH

I . Influence of Microwaves on E. coli

We first discuss the influence of microwaves in the 70-75 GHz region on the rate of growth of E . coli bacteria, carried out by Webb and Booth (1969) and by Berteaud er al. (1975). The latter use an intensity of 10 mW/mm2, probably much larger than the intensity used by Webb and Booth. The irradiation times were three and four hours, respectively. In Fig. 2, N 1 and N2are the respective numbers of viable bacteria with and without radiation, counted after a given period of irradiation. Berteaud et al. give the accuracy of the cell count as 5%, small compared with the observed effects. Both groups agree that at 70.5 and at 73 GHz the rate of growth is reduced by the irradiation. The difference in magnitude might be connected with the different intensities, for temperature increase in the region of 37"C, used in the experiments, will increase the rate of growth. The magnitude of the reduction of growth may thus have been reduced in the experiment by Berteaud et a / . through thermal effects. These authors also find from a number of further experiments that the radiation has no lethal effect on the bacteria and does not influence the

FIG.2. Growth of E . coli bacteria as a function of the frequency of the applied radiation. A', is the number of bacteria subjected to radiation, N2without radiation (control). 0, Results by Berteaud er (I/. (1975); A , by Webb and Booth (1969). From Berteaud ef a / . (1975).

THE BIOLOGICAL EFFECTS OF MICROWAVES

129

EXTINCTION

’

0.01 0

I

I

1

I

2

4

6

8

I

K l h

FIG.3. Optically measured growth of yeast cultures as function of time. The straight line represents exponential growth. Its slope is the rate of growth. From Grundler et al. (1977).

rate of mutations. From the latter, in particular, they conclude that the radiation does not act on DNA. This need not imply, however, that the millimeter waves do not influence dynamic processes involving DNA during growth or cell division. In fact, the large effect obtained by Webb and Booth (1969) at very low intensities definitely points toward a trigger effect of the nature described in Section IV,C, although its biological specification would require further investigation. Such investigation might be of the nature of the experiments carried out by Webb and Dodds (1968) at a different frequency, 136 GHz. The intensity in this case was only 50 pW/cm2. Growing bacteria show a “lag” phase before exponential growth sets in, similar to the case of yeast, illustrated in Fig. 3. The authors find that if the washed cells were immediately exposed for about four hours to microwaves before being incubated in the nutrient, then no cell division took place in a period in which the nonirradiated control multiplied by a factor 6. The radiation was not lethal, however, as the number of viable cells did not decrease. When, on the other hand, the cells were put into a nutrient for 90 min before being exposed to the radiation, then cell growth did take place, although at a very low rate compared with the control. Clearly it would be most desirable to integrate and extend the two types of experiment, and to measure the dependence of the various effects on intensity. 2 . Influence of Millimeter Waves on Yeast Cells The rate of growth of yeast, like that of bacteria, increases with increasing temperature in the region between 30 and 35°C. The reduction of the rate of growth, which as discussed below arises under the influence

I30

H. FROHLICH

t :.L0.I 3 Y . 31

32 33 3 4 %

0.5

~

TEMPERATURE

(a)

41.6

41.7

41.9 41.0 FREQUENCY

42D

GHz

(b)

FIG.4. (a) Temperature dependence of the rate of growth of yeast cultures in the absence of radiation. (b) Rate of growth of yeast cultures with radiation divided by the rate without radiation as a function of frequency.

of millimeter waves at certain frequencies, can therefore not be ascribed to thermal effects. Devyatkov (1974) finds decreases in total growth of 35,20, and 40% at 7.16,7.17, and 7.19 mm, respectively, and an increase of 30% at 7.18 mm. The much more extensive experiments by Grundler et al. (1977*; Grundler and Keilmann, 1978) cannot be compared directly with the above, as they use a different genus. The growth of yeast cultures was measured optically as demonstrated in Fig. 3. After a lag period of about three hours the growth becomes strictly exponential as seen in the logarithmic plot. The slope of this section represents the rate of growth, the final result of the measurements. Figure 4a shows the result in the absence of irradiation at various temperatures. The very high degree of reproducibility should be noted. Figure 4b gives the result in the presence of radiation between 41.4 and 41.9 GHz under otherwise identical circumstances. A remarkable set of narrow resonances quite outside the fluctuations seen in Fig. 4a will be observed. The intensity of the radiation was of the order of 2 mW/cm2. While this is unlikely to cause significant heating, clearly, as mentioned above, this would increase the rate of growth, whereas decreases have been observed at several frequencies. Dependence on intensity, unfortunately, has not been measured yet, nor have the biological conditions been varied further.

* The experiments on the influence of millimeter waves on the rate of growth of yeast cells (cf. Fig. 4) are at present being repeated by W. Grundler (J.Col/ecr.Phenom.-Rev. in print and personal communication) with highly improved accuracy. So far two resonances have been obtained containing ten about equally spaced experimental points within a frequency range of 10 MHz, thus giving very strong support to the previous results. N o dependence on the intensity was found as required by the theory, and demonstrated in Fig. I .

THE BIOLOGICAL EFFECTS OF MICROWAVES

131

From the point of view of our theory, the resonance frequencies that show a decrease in the rate of growth ust be attributed to a band of vibrations, those that show an increase to another overlapping band. The spatial regions to which these two bands belong may, of course, be well separated. The sharpness of the resonances points toward regions sufficiently separated from cell water, because contact with it would yield considerable friction, i.e., line broadening, although this could be overcome by certain nonlinear excitation. According to our theory, the microwave energy supplied to each mode is channeled, through x processes, to the mode that is strongly excited. Also once this mode is strongly excited, it might undergo further transitions and then be stabilized in an “activated” state. The present investigations will have to be extended considerably in order to be able to investigate these possibilities experimentally.

3. Induction of Colicins Colicins are a class of proteins manufactured on certain occasions by many bacteria of the E. coli group (cf. Luria, 1975). They act as antibiotics that kill cells of bacterial strains related to the strains that makes them. There exist very many kinds of colicins; each is the product of an extrachromosonic gene. Smolyanskaya et af. (1974) have shown that the induction of colicin can be significantly influenced by millimeter wave irradiation. This is illustrated in Fig. 5 , where the appropriately defined ratio of

Xmm FIG.5. Induction coefficient K of colicin under the influence of radiation divided by the same without radiation as a function of wavelength. From Smolyanskaya and Vilenskaya (1 974).

132

H. FROHLICH

' 0.w

O.O!

0.1

4.0

P, mWIcm

FIG.6. Dependence of K on the intensity of the radiation. From Smolyanskaya and Vilenskaya (1974).

colicin induction with and without radiation is presented as a function of wave length. Figure 6 shows the depenence on intensity (probably at 6.5 mm). It will be noted that no effect is observed at an intensity of 1 pW/cm2, whereas the effect is independent of intensity between 10 pW/cm2 and 1 mW/cm2, i.e., over a range of a factor 100. This is exactly as required by theory (cf. Fig. 1). The logarithmic increase [cf. Eq. (93)]would have to be expected to take place between 1 and 10 pW/cm2 within which region no measurements have been performed. Should experiment provide, however, a very sharp transition within this region, then Eq. (63) would apply and it would have to be concluded that only a relatively thin layer, within which the microwave intensity does not change much, is responsive. Figure 5 again indicates resonance behavior although the experimental points are not sufficiently close to permit comparison of the width of the resonances with that observed in yeast (Fig. 4b). Again we may assume that the microwave energy, absorbed in the resonance region is channeled, through x processes, to the mode that is strongly excited. Its frequency is not necessarily among those used in the experiments. Again the possibility of a further transition of the excited mode arises. Such processes may, in principle, require considerable time, and the experiments on the dependence of the effect on time, presented in Fig. 7, are of particular interest in this connection. They do, in fact, exhibit the ability of the

THE BIOLOGICAL EFFECTS OF MICROWAVES

0.5

I irradiation

133

2

time, h

FIG.7. Dependence of K on the irradiation time, for 6.5 ( I ) , 5.8 (2), and 7.1 ( 3 ) mm. From Smolyanskaya and Vilenslkaya (1974).

system to store the supplied energy over considerable periods. Considering the low intensity required for the effect, the system must possess such storing capacity to overcome the appreciable noise. The required time should decrease with increasing intensity; experiments in this direction would be desirable. m

-I

-I

FIG. 8. Frequency dependence of the induction of lambda prophages. From Webb (1979).

H. FROHLICH

I34

Motzkin et al. (1979) have also been able to demonstrate an enhancement of colicin induction under irradiation at 5.8 mm. Related in certain ways to the induction of colicin is the induction of lambda prophages in E. coli bacteria. These bacteria frequently contain the DNA of a certain virus. Certain circumstances such as irradiation by X ray or ultraviolet light induce this prophage so that the virus is produced and finally destroys the cell. Webb (1979) has shown that the growth can also be induced by millimeter waves in a narrow frequency region near 70.5 GHz, but not outside it, as shown in Fig. 8. It will be seen that lo6 out of 10'- cells are induced whereas only 10 out of lo7 cells are induced without irradiation, or with irradiation but outside the active frequency region. The effect also depends on intensity as required by our theory as shown in Fig. 9, although the decrease at higher intensities has not yet been explained. It should be mentioned, in this context that the irradiated bacteria are used in a monocellular layer so that Eq. (82) can be applied. By investigation of synchronized cells it has been found that the microwave irradiation is effective only during a narrow period of cell development (cf. Fig. 10). These results clearly eliminate thermal induction, which would not be restricted to a narrow frequency region. It is further shown that the effect occurs only when certain nutrients are used; it might be, of course, that other nutrients show a similar effect outside the frequency range investigated so far. It should be pointed out at this stage that effects of the type described above depend on many parameters, some of which, in particular with

2- '01

100 200 300 LOO 500 600 700

pW/cm* AT 70.L GHz

FIG.9. Dependence of the inductions of lambda prophages on the intensity of radiation. From Webb (1979).

THE BIOLOGICAL EFFECTS OF MICROWAVES

k

f to'

135

k

10 20 30 40 50 60 70 TIME OF INCUBATION [MINUTES] AT WHICH IRRADIATION BEGAN FIG.10. Dependence of the induction of lambda prophages on the time of incubation of a cell. From Webb (1979).

regard to the biological properties, are not known at present. Thus it has been mentioned to the author at various instances that large effects of the type described above have been confirmed, but have at later stage disappeared. This might well arise from a change of biological specifications that so far have not been brought under control. 4 . Influence of Millimeter Waves on Protein Metabolism

An investigation on the influence of 7.2 and 7.6 mm waves on certain aspects of protein metabolism by Manoilov et al. (1974) might help toward specification of the action of millimeter waves. These authors have introduced certain fungi and bacteria into nutrient solution and after a certain period have investigated the free amino acid content for the unirradiated control, and the 7.2 and 7.7 mm irradiated case. The intensity was 4-5 mW/cm2, the irradiation time 3 hours. Figure 11 shows for the case of Staphylococcus the percentage change of the irradiated samples over or below the control. Clearly several amino acids have been strongly influenced by one of the two frequencies but not by the other. Thus, e.g., in aspartic acid, while the 7.6 mm wave has no influence, the 7.2 mm wave has increased the content by 72%. From the point of view of our theory we should conclude that the 7.6 mm but not the 7.2 mm frequency belong to a band containing a frequency that when excited is involved in the appropriate chemical processes. This might be

I36

H. FROHLICH Staphylococcus

aureui

Ruar hourJ of irradiation

h = 7.6mr 80

40

n 8

FIG. 11. Influence of radiation on the content of various amino acids in Staphylococcus. The percentage change over nonirradiated cases, for two wavelengths, is presented.

From Manoilov et ul. (1974).

connected directly with the action of an enzyme, as the authors suggest. It might, alternatively, be connected with membranes, or other cell constituents, involved in the process. From our discussion of frequencies in Section IV,A, we would be inclined to favor the latter, as enzymes are likely to possess higher frequencies. It must be realized, however, that this statement might have to be modified through the possibility of mode softening. It should also be mentioned in this context that Tuengler et al. (1979) have been unable to observe an influence of microwaves in the frequency region between 40 and I15 GHz (7.5-2.6 mm) on certain other enzymatic function in vitro. Another experiment concerning the influence of microwave irradiation on biosynthesis was carried out by Webb (1975). He investigated the synthesis of DNA and RNA in E. coli bacteria using a radioactive tracer method. In no case was the rate of synthesis increased by microwaves. Certain frequencies reduced the rate, however, to about 1/10 of the unirradiated one for DNA, notably 59, 66, 73, 129, 136, and 143 GHz if the cells were grown in a glucose-amino acid nutrient. None of these frequencies influenced RNA synthesis. In a glucose-NH: medium, however, the relevant frequencies are 61, 66, 71, 76, 126, 136, and 141 GHz. In terms of our theory, we should conclude that the synthesis is con-

137

THE BIOLOGICAL EFFECTS OF MICROWAVES

nected with certain vibrations whose frequencies depend on the nutrient. We would suggest that they are based to certain regions in or near membranes in conjunction with nutrient molecules in or near these regions.

5 . Influence of Microwaves on Bone Marrow Cells of Mice Finally in this section the experiments by Sevastyanova and Vilenskaya (1974) must be discussed as investigations on frequency, intensity, and time dependence have been reported. The investigations deal with the damage to the bone marrow of mice arising from exposure to X rays or from the use of certain chemicals. When prior irradiation with microwaves has taken place, then at certain frequencies and intensities the damage is vastly reduced. In Fig. 12 it is shown that while the number of nonirradiated bone marrow cells is reduced t o about one-half by exposure to X rays, prior irradiation by microwaves of certain selected frequencies reduces the damage such that about 80% survive. No effect exists, however, at other frequencies. Figure 13 demonstrates the dependence of this effect on intensity. The effect is absent below 9.9 mW/cm2, then steplike reaches its maximum at

4.0-

-- - - - - - - - -I

0 ,

0

-

0.8

E

L Y

. 0

z 0.6

z

1,,

6.6

a4

,"-,

---* , 7.0

,

,;

b--

2

7.4

FIG.12. Dependence of the relative number of bone marrow cells N / N o on the wavelength of the radiation. N , number of cells; N o , number of cells without radiation. I , control; 2, X-ray irradiated; 3, X-ray and millimeter-wave irradiated. From Sevastyanova and Vilenskaya (1974).

138

H. FROHLICH

10 mW/cm2, and remains unchanged up to 80 mW/cm2. Figure 14 shows the time dependence-it takes 75 min of irradiation to reach the full response. The authors report that about 70% of the microwave radiation is absorbed in a surface layer of the skin of about 3 x cm thickness. Thus for direct action on a deeper region only a very small fraction of the 10 mW/cm2 will penetrate. If we take the case of colicin as a guide, then the threshold for action might occur between and mW/cmZ (cf. Fig. 6) and a reasonable thickness for penetration could arise, especially if we admit the possibility of even lower thresholds. On the basis of our theory the sharp step in Fig. 13 then indicates that a very thin layer only, within which the microwave intensity does not change appreciably, is sensitive to microwaves. For then the local formula (63) can be used without the integration over space carried through in connection with Eqs. (93) and (96). The experimental result then also implies that the first step, which involves the influence of the microwave irradiation, proceeds fast compared with the following steps, i.e., in terms of Section IV,C, c1 4 t2. The frequency dependence presented in Fig. 12, according to our theory, then defines some of the frequencies of the band containing the mode, which will be strongly excited. x Processes then are responsible for

power f l u x density, m W / c m 2

FIG. 13. 1 , Control; 2, relative number of X-ray-irradiated bone marrow cells; 3, dependence of X-ray- and millimeter-wave-irradiated cases on the intensity of the millimeter waves; 4, change Af of skin temperature as function of millimeter wave intensity. From Sevastyanova and Vilenskaya (1974).

139

THE BIOLOGICAL EFFECTS OF MICROWAVES

0.41

0

I

I

30

I

I

I

I

50 90 i r r a d i a t i o n t i m e , rnin

I

I

420

FIG.14. Dependence of the number of bone marrow cells on the duration of millimeter wave irradiation. 1, Control; 2, X-ray irradiated; 3, X-ray and millimeter-wave irradiated. From Sevastyanova and Vilenskaya (1974).

the channeling of the absorbed energy with this mode. The time required for this follows from Fig. 13. We should expect that this time decreases with increasing intensity and experiments in this direction would shed further light on the above interpretation. 6 . Summary

The examples on the action of millimeter waves on biological systems presented in the present section leave no doubt that nonthermal action exists at very low intensities. They give support to the theory presented in previous sections, according to which strongly excited polar vibrational modes play a basic role in the dynamics of biological processes, and that such excitation can be triggered by microwaves. Measurements of the dependence of various effects on frequency, intensity, and duration of irradiation over an appropriate range are required and when carried out in conjunction with biological specification may lead to new insight. Thus measurement of the dependence on intensity alone, in the above case, led to the conclusion of the existence of a thin layer in which the relevant oscillations should take place. From the frequency dependence of the rate of growth of yeast we were able to conclude that two different processes must be involved. Measurements on synchronized cells might then help to further specify the relevant biological processes.

140

H. FROHLICH

Clearly considerable experimental difficulties must be overcome to be able to present a complete picture of the involvement of vibrations in biological processes. Success would, however, have far-reaching repercussions on the understanding of dynamic processes in biology. C . Ruman Effect

According to one of our concepts (Section II1,C) metabolic energy excites specific coherent electric vibrations in biological systems at certain stages of its development. The discussions of Section V,B give support to this proposal for frequencies in the millimeter wave region, i.e., near 10" Hz, for only thus is it possible to understand the relatively large biological effects initiated by electromagnetic irradiation in the millimeter region at relatively low intensities. To demonstrate the generality of our concept it is important to give evidence for the existence of relevant excitation in neighboring frequency regions as well. Higher-frequency regions can be reached by Raman effect. It must then be shown that the system possesses proper frequencies in this region, and that these are excited, beyond thermal level, at certain periods of development. For the latter purpose measurement of the intensity ratio of anti-Stokes to Stokes lines can be successful provided the Raman frequency v is so high that the intensity ratio in thermal equilibrium, exp( - h v / k T ) , is appreciably smaller than unity. This requires Raman frequencies of the order of 100 cm-I ( 3 X 1OI2 Hz)or higher. At lower frequencies, the ratio of anti-Stokes to Stokes intensities approaches unity already in thermal equilibrium and can thus not be used to demonstrate nonthermal excitation. Should the nonthermal excitation be very strong, however, then measurement of the order of magnitude of the Raman intensity may suffice to establish it. Systems endowed with proper frequencies in the relevant regions are likely to be based on large molecules, principally proteins, placed inside or outside membranes. In fact, Brown et ul. (1972) have shown that achymotrypsin, an enzyme, possesses Raman frequencies down to 25 cm-I. Genzel ct al. (1976) also observed at 25 cm-I a Raman frequency of lysozyme when it is crystallized. In solution this line disappeared, probably due to friction in the solution. It may be expected then that the appearance of frequencies of this order in biological systems will depend on the manner in which such molecules are contained in cells. Thus low friction may be expected when they are dissolved in membranes, high friction when floating in cell water. It is important, therefore, to note that Drissler (1980), has shown by Raman effect on algae that certain chlorophyll lines, in the region between 100 and 3000 cm-I are present at low

THE BIOLOGICAL EFFECTS OF MICROWAVES

141

temperature but disappear at room temperature. Drissler et al. (1978), on the other hand, show that lines in the region between 800 and 1500 cm-l, assigned to vibrations of carotenoid molecules (possibly resonating with some chlorophyll lines) are present in life algae. These molecules thus may be built into the cell in a manner characteristically different from that of chlorophyll molecules. Certain modes in higher-frequency regions have already been discussed in Section 111. Apart from this it should be emphasized that biomolecules possess a great number of osci!latory modes in regions above 1000 cm-I, and a great literature exists on this subject. These investigations are of importance for the investigation of structure but have so far not been used to investigate the possibility of collective excitations. Candidates for collective excitations have been discussed in Section 111, and we consider in further detail the results obtained by Biscar and Kollias (1973a,b). These authors show that after careful preparation of poly-L-glutamic acid, Stokes Raman shifts are observed that are an integer multiple of a basic frequency, namely, 950 cm-' when the molecular weight is 93,000 and 860 cm-' when it is 103,000. Shifts up to the sixth harmonic are observed. Since the length of such a molecule is proportional to its molecular weight, the basic frequency is inversely proportional to the length L for small changes of L. This behavior would hold for acoustic modes, but then the frequencies would have to be several orders of magnitudes lower. Electronic acoustic modes, which the authors suggest, i.e., acoustic plasmons, require at least two partly filled energy bands for electrons, a requirement probably not fulfilled in this material. Quasi-free

FIG.IS. Stokes Raman spectrum of a paste ofE. coli bacteria at 7 K . The inset is obtained at higher sensitivity. From Drissler and Webb (1980).

142

H. FROHLICH

I

I

400

cm-'

2 00

FIG. 16. Stokes Raman spectrum of resting cells of B megaterium bacteria. From Webb and Stoneham (1977).

electrons, which according to Kuhn (1949) exist in certain long-chain molecules, might explain the experiments. In this case the electronic energy levels are E = ( h 2 2 m * ) n 2 ~ 2 / L 2 , n = 1, 2 , 3, . .

.

(97)

The basic frequency would then arise from the transition from n = 1 to n = 3, as the transition n = 1 to n = 2 is probably prohibited in Raman effect. The harmonics would then correspond to simultaneous excitation of electrons in different molecules. On this assumption the empirical

THE BIOLOGICAL EFFECTS OF MICROWAVES

143

value of about lo3 cm-' for the transition yields a length of L = (m/m*)2x 5 x lo-' cm, which is not unreasonable (m* is the effective electronic mass, which would have to be smaller than the electronic mass m). Turning now to experiments on bacterial cells, Drissler and Webb (1980) find in a densely packed paste of E. coli bacteria (about 10" cells/cm3) at 7 K three broad bands in the regions 900, 1400, and 2000 cm-'. Each band has a width of about 400 cm-I. All three bands possess fine structures of very many lines of width of about 10 cm-' as shown in Fig. 15. This fine structure is well reproducible, and it can be noticed that thermal noise is absent at this temperature. According to our theory we would identify the broad bands with the bands of modes introduced in Section 111. Metabolic activity would then be expected to excite, in living cells, a single line at certain periods of the development of the cells. Each of the broad bands might represent an overlap of several bands of modes whose originating systems (proteins in or outside membranes) might be separated spatially. In living cells we

I

I

400

c m-'

200

FIG. 17. Same as Fig. 16 with added nutrient. From Webb and Stoneham (1977).

I44

H. FROHLICH

+

I 2 00

I

J

0

cm-'

FIG. 18. Raman spectrum of the nutrient. From Webb and Stoneham (1977).

should thus expect the appearance of single Raman lines, both Stokes and anti-Stokes, in the frequency regions of the bands observed at 7 K. In synchronized cells, the actual positions should change with the age of the cells, as does the cell activity. In fact, earlier measurements as reviewed by Webb (1980) support this picture. In these measurements, unfortunately, Stokes lines only were investigated. It should be observed, however, that the density of cells for in vivo measurement is lo7 cells/cm3 only, i.e., a factor lo4 below that used in the measurements at 7 K. It seems possible that in thermal equilibrium, the Raman intensity would be too small t o be measureable (excluding

THE BIOLOGICAL EFFECTS OF MICROWAVES

145

resonance Raman effect), and hence that a case for nonthermal excitation can be made although this would have to be supported by more quantitative arguments. It should be mentioned in this context that the intensities of Stokes and anti-Stokes lines are proportional to (1 + n) and n, respectively, where n represents the number of quanta by which a particular vibration is excited. In the frequency region of the bands, the thermal excitation nT 4 1. It follows that a nonthermal enhancement of the excitation to n quanta requires n s 1 in order to yield a significant increase of intensity for Stokes lines. For anti-Stokes lines it requires only n S nT. A much simpler picture arises in the case of life algae that were investigated by Drissler and MacFarlane (1978) in a flow system in which an individual cell spends a negligible time in the laser beam. This time is too short to set the photosynthetic process into action so that the results represent the spectral properties (already referred to above) of an in vivo cell in the absence of metabolism.

FIG. 19. Stokes and anti-Stokes Raman spectra of synchronized active cells of E . coli B bacteria, taken at 40 min after incubation. From Webb cf a / . (1977a).

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H. FROHLICH

Stoker

anti- Stoker

FIG.21. Stokes and anti-Stokes Raman spectra of synchronized active cells of E. coli B bacteria, taken at 60 min after incubation. From Webb et al. (1977a).

THE BIOLOGICAL EFFECTS OF MICROWAVES

147

Addition of white light must then yield the changes arising from the metabolism. In the region below 200 cm-1 measurement by Webb and Stoneham (1977) of Stokes lines on cell of B megaterium bacteria at a density of 5 x lo' cells/ml show a broad band only when the cells are resting, but at least two lines when the cells are active and synchronized, as shown in Figs. 16 and 17. The spectrum of the nutrient is shown in Fig. 18. Again aquantitative investigation of the intensities might show that activation beyond thermal excitation is required. The crucial experiment for anti-Stokes lines has been carried out more recently by Webb et af. (1977a) on synchronized active cells of E. coli B bacteria. Figures 19-21 show the spectra taken 40, 50, and 60 min, respectively, after incubation. We note that the line near 120 cm-I ranges between 118 and 125 cm-'. At these frequencies the ratio of the intensities anti-Stokes : Stokes = exp( - hu/kT) in thermal equilibrium lies between 0.55 and 0.57. Experimentally after

I00

zoo RAMAN SHIFT cm-'

FIG.22. Stokes Raman spectra of mammary tissue. (a) Normal; (b) "normal" rightside tissue; (c) left-side carcinoma. From Webb et a / . (197%). (Reprinted by permission of John Wiley & Sons, Inc.)

I48

H. FROHLICH

averaging over eight spectra one finds 1.01 ? 0.10, and 0.93 ? 0.13, respectively. It can be noted that in thermal equilibrium nT 2: 1, whereas at the lower limit 0.8 of this ratio,

+ n) = 0.8,

or n =4 (98) requires a considerable enhancement; using 0.9, this would lead to n = 9. A further set of interesting Stokes lines has been obtained by Webb er al. (1977b) from normal mammary tissue, and from tissue of mammary carcinoma, as shown in Fig. 22. Anti-Stokes lines unfortunately are not yet available. The splitting and broadening of the lines of the carcinoma might give support to the theoretical suggestions of Section IV,B, although much more experimental evidence than available now will have to be provided. Finally it should be emphasized again that certain Raman lines occur at particular stages of development of cells only as shown in the review article by Webb (1980). n/(l

VI. CONCLUSIONS From the experiments on millimeter waves discussed in Section V,B, it can be concluded with reasonable confidence that these waves cause biological effects that can be understood neither in terms of heating nor through direct action of the electric field of the waves. It follows that the electromagnetic wave acts as a trigger to events for which the biological system is already prepared. This implies that the biological system has the possibility of storing the energy of the microwaves until the trigger effect can occur, and in fact we have shown that considerable irradiation times may be required until the effect reaches its full strength. Such action clearly is of a highly nonlinear nature and therefore cannot be understood in terms of linear response of the system to the impending microwave, using properties of the dielectric function. This latter type of argument has frequently been presented (as, e.g., Stuchly (1979) where, as also seems to be the habit, properties of a dilute system of dipolar molecules only are considered), and it should be added that the frequently propounded idea that the microwave "rotates" dipolar groups is, mildly speaking, misleading. This would require the expression for the dielectric constant to depend on the moment of inertia, which it does not (e.g., Frohlich, 1958). I n addition, it would require quite unrealistically high intensities. The strongest evidence for the existence of such nonthermal, nonlinear effects arise from their dependence on frequency, intensity, and

THE BIOLOGICAL EFFECTS OF MICROWAVES

I49

time of irradiation. To this we may add the occurrence of large biological effects, in other frequency regions, at very low intensities, although without measurement of the dependence of such effects on frequency the nonthermal nature is not convincing. Thus “microwave hearing” has been found to be a very sensitive temperature effect (e.g., Lin, 1977). One can predict, therefore, that this effect is very insensitive to a variation of the frequency, contrary to the effects discussed in Section V,B. It follows that an understanding of the nonthermal effects must be based on a general theory of the importance of electric vibrations in biological systems. This theory has been presented in Section 111, and its consequences discussed in Section IV. The presentation has been given as general as feasible, consisting largely in the introduction of the concept of collective coherent electric vibrations, and of highly polar metastable states. Both can be excited through metabolic energy (biological pumping). Both can have €ar-reaching consequences on the dynamic properties of biological systems. It will be required by collaboration between theory and experiment to find the details of these excitations. Clearly microwaves are only one experimental tool in this respect. Others include Raman effects, as discussed in Section V,C. A new tool, microdielectrophoresis, has recently, in the hands of Pohl (l979), provided new evidence for the existence of electric vibrations of certain rapidly dividing cells. These vibrations occur at relatively low frequencies, and it is of considerable importance to specify the regions that carry out these vibrations. Solution of this problem, of course, is most essential in all frequency regions that have been discussed here. To this must be added the specification required to find a particular effect. Thus in the experiments by Webb (1979) on the induction of prophages discussed in Section V,B it has been shown that in the investigated frequency region, one particular nutrient only yields the effect, and this particularly strongly in the presence of free oxygen. Quite generally, insufficient knowledge of specification is likely to be the reason for the difficulty that is sometimes found in reproducing experiments. In this respect, the influence of relatively weak magnetic fields must be mentioned, which, although not understood at present, might have considerable influence on the performance of a number of processes. Thus Shaya and Smith (1977) warn against the use of magnetic stirrers, as treatments by magnetic fields were found to influence the activity of the enzyme lysozyme (in v i m ) . Ahmed et ril. (1980) also find unexpected effects of magnetic fields on the deposit of lysozyme on glass surfaces, in the presence of oxygen. A most important requirement arising from the theory is the need for

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experiments in vivo, for both the basic concepts are connected with excitations through metabolic energy. This does not mean that investigations of metabolically nonactive systems are without value. Thus Raman effects on bacteria at 7 K (cf. Fig. 15) have exhibited the existence of bands of modes that form the structural background of the theory. Metabolic energy will then, at certain stages of development, lead to the coherent excitation of single levels, and evidence for this is also available. A most important question, which in no case has been answered, refers to the molecular specification and placement to which various excitations are due. In previous sections we have tended to attribute excitations in the 1000 cm-’ region to enzymes, the millimeter wave region to sections in membranes, modified by dissolved proteins, and possibly to DNA. The possibility exists, however, that millimeter waves cause transitions between the levels of the band exhibited in Fig. 15. This would involve nonlinear effects and also a slight modification of the theory as such effects are not possible without prior excitation of these levels. Thus in conclusion it should be emphasized again that microwave experiments have indicated the existence of coherent electric vibrations in biological systems. To elucidate their role it is imperative to investigate the same systems with other techniques such as the Raman effect.

REFERENCES Adey, W. R.,and Bawin, M. (1977). Neuroscience Res. Program. Bull. 15. Ahmed, N. A. G., Norman, M., and Smith, C. W. (1980). J . Collect. Phenom. (in press). Aiello, G., Micciancio-Giammarinaro, M. S., Palma-Vittorelli, M. B., and Palma, M. U. (1973). In “Cooperative Phenomena” (H. Haken and M. Wagner, eds.), p. 395. Springer-Verlag, Berlin and New York. Baranski, S., and Czerski, P. (1976). “Biological Effects of Microwaves.” Dowden, Hutchinson & Ross, Inc., Stroudsburg, Pennsylvania. Bawin, S. M., Sheppard, A., and Adey, W. R. (1978). Biochem. Bioenerg. 5,67. Berteaud, A. J., Dardalhon, M., Rebeyrotte, N., and Averbeck, M.D. (1975). C . R. Hebd. Seunces Acad. Sci., Ser. D 281,843. Bhaumik, D., Bhaumik, K., and Dutta-Roy, B. (1976). Phys. Lett. A 59, 77. Bhaumik, D., Dutta-Roy, B., and Lahiri, A. (1978). Phys. Lett. A 68, 131. Biscar, J. P., and Kollias, N. (1973a). Phys. Lett. A 45, 189. Biscar, J. P., and Kollias, N. (1973b). Phys. Lett. 45A, 191. Bilz, H., Biittner, H., and Frohlich, H. (1980). Z. Naturjorsch. Teil C (in press). Brill, A. S. (1978). Biophys. J . 4, 139. Brown, K. G., Erfurth, S. C., Small, E. W., and Peticolas, W. L. (1972). Proc. Nutl. Acad. Sci. U.S.A. 69, 1467. Bullok, T. H. (1977). Neurosci. Res. Program, Bull. 15, 17. Careri, G. (1969). I n “Theoretical Physics and Biology” (M. Marois, ed.), p. 5 5 . NorthHolland Publ., Amsterdam.

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Careri, G. (1973). In “Cooperative Phenomena” (H. Haken and M. Wagner, eds.), p. 391. Springer-Verlag, Berlin and New York. Devyatkov, N. D. (1974). Sov. Phys.-Wsp. (Engl. Transl.) 16, 568. Drissler, F. (1980). Phys. Lett. A (in press). Drissler, F., and MacFarlane, R . M. (1978). Phys. Lett. A 69, 65. Drissler, F., and Webb, S. J . (1980). 2.Naturforsch. Teil C (in press). Drost-Hansen, W., and Clegg, J. (1979). “Cell Associated Water.” Academic Press, New York. Elul, R. (1974). Neuroscience R e s . Program, Bull. 12, 97. Frohlich, F. (1973). In “Cooperative Phenomena‘’ (H. Haken and M. Wagner, eds.), Vol. VII. Springer-Verlag, Berlin and New York. Frohlich, F. (1977) In “Synergetics” ( H . Haken, ed.), p. 267. Springer-Verlag, Berlin and New York. Frohlich, H . (1958). “Theory of Dielectrics,” 2nd ed. Oxford Univ. Press (Clarendon), Oxford. Frohlich, H. (1968). Int. J . Quantum Chern. 2, 641. Frohlich, H. (1969). In “Theoretical Physics and Biology” (M. Marois, ed.), p. 13. North-Holland Publ., Amsterdam. Frohlich, H. (1970). Nature (London) 228, 1093. Frohlich, H. (1972). Phys. Lett. A 39, 153. Frohlich, H. (1973a). Riv. Nuovo Cimenio 3, 490. Frohlich, H. (1973b). J. Collect. Phenom. 1, 101. Frohlich, H. (1975a). Proc. Nut/. Acad. Sci. U.S.A. 72, 4211. Frohlich, H. (197%). Phys. Lett. A 51, 21. Frohlich, H. (1977a). Riv. Nuovo Cimenio 7, 399. Frohlich, H. (1977b). BioSysterns 8, 193. Frohlich, H. (1977~).Neurosci. Res. Progrum, Bull. 15, 67. Frohlich, H . (1978). IEEE Truns. Microwave Theorv Tech. 26, 613. Genzel, L . , Keilmann, F., Martin, T. P., Winterling, G., Yacobi, Y., Frohlich, H., and Makinen. M. w. (1976). Biopolymers 15, 219. Genzel, L. (1978). Phys. Lett. A 65, 371. Green, D. E. (1974). A n n . N . Y . Acad. Sci. 227, 6. Grundler, W., and Keilmann, F. (1978). Z. Naturforsch., Teil C 33, 15. Grundler, W., Keilmann, F., and Frohlich, H. (1977). Phys. Lett. A 62, 463. Haken, H. (1973). In “Cooperative Phenomena” (H. Haken and M. Wagner. eds.). p. 363. Springer-Verlag, Berlin and New York. Holland, B. (1972). J. Theor. B i d . 35, 395. Kaiser, F. (1977a). Phys. Left. A 62, 63. Kaiser, F. (1977b). B i d . Cybernet. 27, 155. Kaiser, F. (1978a). Z. Nnturforsch., Teil A 33, 294. Kaiser, F. (1978b). 2. Naiurfursch., Teil A 33, 418. Koshland, D. E., and Neet, K. E. (1968). Annu. R e v . Biochem. 37, 359 and 380. Kuhn, H. (1949). J. Chem. Phys. 17, 1198. Lin, J. C. (1977). IEEE Truns. Micruwaiv Theory Tech. 25, 605. Livshits, M. A. (1977). Biofiziku 22, 743. Luria, E. I . (1975). Sci. A m . Dee.. p. 30. Manoilov, S. E., Chistyakova, E. N., Kondrateva, V. F., and Strelkova, M. A. (1974). Sov. Phys. -Wsp. (Engl. Transl.) 16, 573. Mills, R. E. (1979). Phys. Lett. A 74, 278. Monod, J. (1972). “Chance and Necessity“ (trans].), p. 95. Collins, London.

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Motzkin, S . , Birenbaum, L., Rosenthal, S., Rubenstein. C.. Davidow, S., Remily, R., and Melnick, R. (1979). Eioelectrornagn. Symp., 1979. Palma, M. U. (1973). In “From Theoretical Physics to Biology” (M. Marois, ed.), p. 21. Karger, Basel. Pethig, R. (1978). Int. J. Quantum Chem. 5 , 159. Pohl, H. A. (1979). Do cells in the reproductive state exhibit a Fermi-Pasta-Ulam resonance? Research Note 98. Quantum Theoretical Research Group, Oklahoma State University, Stillwater. Prohofsky, E. W., and Eyster, J. M. (1974). Phys. Lett. A 50, 329. Rose, A. (1970). Image Techno!. 12, 13. Schmitt, F. O., and Samson, F. E. (1969). Neurosci. Res. Program, BUN. 7, 247. Schwan, H. P. (1974). In ‘‘Biological Effects and Health Hazards of Microwave Radiation,” (P. Czerski, ed.), p. 156. Polish Medical Publishers, Warsaw. Sevastyavona, L. A., and Vilenskaya, R. L. (1974). Sov. Phys.-Usp. (Engl. Trans/.) 16, 570.

Shaya, S. Y.,and Smith, C. W. (1977). J. Collect. Phenom. 2, 215. Smolyanskaya, A. Z., and Vilenskaya, R. L. (1974). Trans. Sov. Phys. U s p . 16, 571. Stuchly, M. A. (1979). Radiat. Environ. Eiophys. 16, 1. Takashima, S., Onaral, B., and Schwan, H. P. (1979). Radiat. Environ. Biophys. 16, 25. Tuengler, P., Keilmann, F., and Genzel, L. (1979). Z. Naturforsch., Teil C 34, 60. Vento, G., Palma, M. U., and Indovina, P. (1979). J. Chem. Phys. 70, 2848. Watson, J. D. (1970). “Molecular Biology of the Gene,” p. 187. Benjamin, New York. Webb, S. J. (1975). Ann. N . Y . Acad. Sci. 247, 327. Webb, S. J. (1979). Phys. Lett. A 73, 145. Webb, S. J. (1980). Phys. Rep. (in press). Webb, S. J., and Booth, A. D. (1969). Nature (London) 222, 1199. Webb, S. J., and Dodds, D. E. (1968). Nuture (London) 218, 374. Webb, S. J., and Stoneham, M. E. (1977). Phys. Lett. A 60, 267. Webb, S. J., Stoneham, M. E., and Frohlich, H. (1977a). Phys. Lett. A 63, 407. Webb, S. J., Lee, K., and Stoneham, M. E. (197%). Int. J. Quantum Chem., Quant. Eiol. Symp. 4, 277. Wu, T. M., and Austin, S. (1977). Phys. L e u . A 64, 151. Wu, T. M., and Austin, S. (1978a). J. Theor. B i d . 71, 209. Wu, T. M., and Austin, S. (1978b). Phys. Lett. A 65, 74. Wu, T. M., and Austin, S. (1979). Phys. Lett. A 73, 266.

ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS, VOL.

53

Ion Optical Properties of Quadrupole Mass Filters P. H. DAWSON Division of Physics National Research CounciL of Canada Ottawa, Canada

I. 11. 111. IV. V. VI.

VII. VIII. IX. X. XI.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ Ion Motion in the Quadrupole ........................ Outline of Ion Optical Techniq Source Characterization. .................................... Methods of Calculat ............................. The Normal Quadru A. Data Compilation . B. Fields of Finite Length . . . . C. Fringing Fields-Three-Dim lations . . . . . . . D. Fringing Fields-Two-Dimensional Linear Approximation. . . . . . . . E. Modified Fringing Fields.. .................................... Distorted Quadrupole Fields. .. The Higher Zone of The RF-Only Quadrupole ......................................... Imaging Properties ....................... Conclusions . . . . . . . .................

.........................................

153 I55 161 165 166 173 174 178 181 183 191 193 201 202 205 206 207

I. INTRODUCTION It is over 25 years since the publication of the first paper on quadrupole mass spectrometry (Paul and Steinwedel, 1953). After the remarkable initial contributions of Paul’s group (Paul et al., 1958), there was a relatively slow development of the quadrupole mass filter but a continuous increase in its use and importance. Quadrupoles dominate the fields of low resolution (MIAM< 1000) mass spectrometry and have found very widespread application in combination with gas chromatographs (Story, 1976a). In the past few years, there have been improvements in manufacturing techniques, in automation, and in data handling, but there has been little change in the design of quadrupoles and their associated ion sources. IS3 Copyright 0 1980 by Academic Press, Inc. All rights of reproduction In any form reserved. ISBN 0-12-014653-3

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P. H. DAWSON

Any advances have been achieved empirically. Now there are increasing demands on performance arising from biochemical, medical, and environmental applications (e.g., real-time trace gas analysis), and these are encouraging a reexamination of the ion optics of quadrupoles and a reevaluation of the theory of quadrupole design. There is a new effort to ensure optimum ion source design for particular types of applications. The requirement for a better understanding of quadrupoles and the limitations to their performance comes at an opportune time. In the last five years, there has been a rapid adaptation to quadrupole mass spectrometry of the methods of phase-space dynamics, long in use in accelerator physics. The new design methods not only provide a cheaper and more efficient way of calculation of ion optical properties but, perhaps more significantly, provide a new insight into performance evaluation. This chapter concentrates on describing the new design approaches. It starts from some very elementary descriptions of phase-space dynamics and the use of matrix methods in ion optics. The adaptation to the quadrupole mass filter is described [but not the applications to the monopole or the quadrupole ion trap (Dawson, 1980a)l. Methods of calculation are discussed in some detail. For the mass filter in its normal mode of operation, a basic data collection has been compiled, so that the detailed calculations do not need to be continually repeated by others. The experimental evidence that suuports the validity of the design theory is summarized and the need for more measurements is outlined. The problems of quadrupole field distortions are also briefly discussed. Some of the alternative modes of operation of the mass filter are explored to further illustrate the utility of the new approaches to design theory. The objective of this chapter is to make available to anyone interested in quadrupole performance, for any type of application, the means with which to calculate the design details-that is, the optimum coupling of source to analyzer and the performance tradeoffs that inevitably occur. There are two important elements involved in the design theory. One is an appreciation of the importance of fringing fields. The other is the application of phase-space dynamics. Some indication of the former was evident in a chapter on quadrupole mass spectrometry (Dawson and Whetten, 1969a) written in this series more than ten years ago. There was then no suitable method to treat the fringing field as part of the design problem but its importance was clear from the work of Brubaker (1961). This aspect was further explored by Dawson (1971, 1972) through the calculation of typical ion trajectories by numerical integration. The advenf of phase-space dynamics came with a description by Baril and Septier (1974) of its application to the quadrupole ion trap (see also Sheretov and Kolotilin, 1975). A treatment on the mass filter (Dawson, 1974a) and then the

QUADRUPOLE MASS FILTERS

155

inclusion of fringing fields in the design analysis followed rapidly (Dawson, 1975a,b). The new approach was briefly included in a textbook on quadrupole mass spectrometry and its applications prepared for publication in 1976 (Dawson, 1976a). However, there has been no detailed systematic account of the techniques and how to apply them. Since there are now recent experimental measurements that confirm the utility of the theory, it seems worthwhile to attempt to lay the foundation for its more widespread application in problems of quadrupole design. 11. ION MOTION IN

THE

QUADRUPOLE

For details of the traditional treatment of the equations for ion motion in quadrupole fields, the reader is referred to the available textbook (Dawson, 1976a). Here, a brief outline is given of the part that is essential to understanding the rest of this chapter. The quadrupole mass filter is shown schematically in Fig. 1. A voltage (U-V cos ot) is applied between opposite pairs of rods. The y direction is conventionally defined as that toward the poles with a negative bias. The z direction is axial. In the perfect, infinitely long field with hyperbolic rods, there is no axial field and only the transverse motion need be considered. This may be no longer strictly correct in an imperfect field or in a fringing field as we see later. The perfect field has another useful property: the motions in the x and y transverse directions are mutually independent and we can consider them separately. They are linked only by having the phase of

I

I

,' Ions FIG.1. A schematic view of the four quadrupole rods of hyperbolic cross section. Opposing rods are interconnected and a voltage (U-V cos 0 2 ) is applied between the two pairs.

156

P. H. DAWSON

the field in common. In fact, both x and y motion is represented by the generalized Mathieu equation dU2/dp + {a, - 24, COS[2(5 -

[o)]}~

=

O

(1)

where a , = - a u = 4eU/mw2r&

qz = - q u

=

2eV/mw2ra

with 5 = wr/2, where w is the angular frequency of the applied field, tothe initial phase of the field when the ion first experiences it, and ro the radius of the instrument aperture (half the rod separation). U is the continuous voltage applied between opposite pairs of rods and V is the zero to peak R F voltage similarly applied. In the remainder of this chapter we discuss transverse displacement scaled according to ro, transverse velocity in terms of r0/( (radius units per radian of applied field), and length of the de-

FIG.2. The superimposed Mathieu stability diagrams for the x and y transverse oscillations showing several regions of simultaneous stability.

QUADRUPOLE MASS FILTERS

157

9 FIG.3. A detailed view of the lowest stability area used in the quadrupole mass filter. The iso-/3 lines connect operating points where the frequencies of ion oscillation are identical. The tip of the stability diagram near u = 0.23699, q = 0.706, is used for mass analysis.

vice in RF cycles, with the implicit assumption of the absence of longitudinal fields. This means that the results are expressed in universally applicable terms independent of the particular combination of size of device, axial ion energy, and R F frequency that may be chosen. A discussion of these choices is given elsewhere (Austin et al., 1976). The Mathieu equation has solutions that are mathematically stable ( u remains finite as 6 + m) or unstable depending only upon the values of the parameters a and q and not upon the initial conditions (u,,, li0 = du,/de, to)of the ion. For transmission through the quadrupole mass filter, we are, to a first approximation, restricted to operating conditions where both x and y trajectories are stable. These are illustrated in Fig. 2. There are a number of ( a , q )regions of simultaneous stability. The one in use in normal quadrupole operation is shown in detail in Fig. 3. The iso-p lines connect operating points where there are identical frequency components in the ion motion. The fundamental frequency of ion oscillation is p 4 2 . Other frequencies are ( 1 - p / 2 ) w , ( 1 p / 2 ) w , etc. A mass spectrum is scanned by varying the magnitude of U and V while maintaining a constant U / V ratio. Ions of different m / e are then strung out along an operating line of constant u / q in the stability diagram. If this a / q ratio is chosen so that the line passes near the tip of the stable region shown in Fig. 3, then there is only a narrow window for ion transmission and hence a selectivity or filtering according to m / e . A slight increase in the u / q ratio will increase the resolution by narrowing the “window.” In a practical instrument, a / q may be adjusted slightly as the mass is scanned, in order to obtain a higher resalution ( M I A M ) at higher masses than at lower masses.

+

158

P. H. DAWSON

X

4

2

-2

1-1.0

FIG.4. A typical x-direction ion oscillation plotted in the xx phase plane. The points represent transverse displacements and velocities after each +O of an RF cycle. At the same phase of the field the points fall on an ellipse, of which three are illustrated. The phase corresponding to (a) is termed the zero phase.

All the calculations presented here are for a stated 4 4 operating line or a given operating point ( a 4 ) on a line where the stable region has a known calculated width and hence a nominal mass resolution. Note that in the normal mode of operation of the quadrupole at high resolution pl, += 0 and pZ += 1. This is reflected in the typical types of ion trajectories that are found. Figures 4 and 5 show the x and y trajectories plotted in the uli plane for an ( a 4 )operating point (0.23342,0.706) near the center of the stability region for an operating line with a resolution of 55. The points represent the combinations of transverse velocity and transverse position after each 1/10 of an RF cycle. These plots illustrate ion motion in the phase planes. The trajectories in the phase-plane “spiral” outward and then return toward the center. The principal frequencies of ion motion are evident. If the points corresponding to a particular phase of the R F field are examined; then they are found to fall on a characteristically shaped and oriented ellipse. These ellipses connect all possible sets of conditions at the particular field phase that will eventually lead to the same maximum ion displacement, which is, in fact represented by the extrema of the el-

I59

QUADRUPOLE MASS FILTERS

lipse ( a ) , usually called the zero-phase ellipse. If the trajectory had been chosen so that this maximum was equal to the instrument aperture radius ro, then the ellipse would enclose all possible combinations of transverse position and transverse velocity, which could result in u < ro for an infinitely long device and which would result in ion transmission in the perfect quadrupole field. This is the heart of the phase-plane approach: the ability to deal collectively with the ions that will be transmitted. We consider later the problems of injecting ions from a source to match up with and take advantage of the available acceptance for ion transmission. It is evident from Fig. 4 that the acceptance of ions depends a great deal on the initial phase of the R F field. In fact, all the ellipses shown have identical areas but different shapes and orientations. The area of the ellipses depends upon the (a,q) value. As the operating point, approaches a stability boundary, the appropriate x or y area goes to zero. The ellipse area (when uMAXis scaled to equal ro) is a relative indication of transmissivity of the analyzer. The sensitivity of an instrument will depend upon the production of ions in the source, their transverse distribution in the emittance from the source, and how well this emittance can be matched

i -

-t-

-1.0

Y

1-

0.5

FIG.5. A typical y trajectory plotted in the yy phase plane.

160

P. H. DAWSON

to the acceptance of the analyzer. The existence of the acceptance ellipses was shown in the early work on quadrupoles (Fischer, 1959) but the extensive use of this concept is quite recent. The equations of the scaled ellipses are conventionally represented by the equation

ruz

+ 2AuU + BU2 = E

(2)

where the emittance E is equal to the ellipse area divided by measured in units of ro. One also has the relationship

P, and u

BT - A' = 1

is

(3)

Note that the ellipse corresponding to the maximum possible value of u, (the zero phase in the normal operating region) has A = 0. A negative value of A corresponds to the acceptance of a converging beam (negative velocity associated with positive position) and a positive value to a diverging beam. Since the motion is governed by a linear second-order differential equation, the position and velocity at any time t with respect to the initial conditions can be expressed by linear combinations ~t = auo

+ bUo,

Lit

= cuo

+ dU0

The transformation for one R F period is of particular interest and will be represented by

[:I,

=

4aI.

=

The matrix for transformation from n to m + n cycles will be M m . These transformations take us from one point on an acceptance ellipse to another and therefore must involve both the ellipse parameters and the frequency of transformation around that ellipse. In fact (Baril and Septier, 1974),

M =

[

cosfrp) + A sin(.lrp) -r sin(.lrp)

]

B sin(.lrp) A sin(7rp)

COS(P~) -

(5)

For the ion displacement to remain finite as 6 increases, then ITr MI < 2. This gives us the stability limits for the lower stability area of 0 < p < 1 in agreement with Fig. 3. Note that for the phase leading to the maximum possible value of u (A = 0, U = 0 , B M A X = l p ) , we have & A X r = E . For The characteristic dimenthe scaled ellipses, uMAX = 1 and E = I/&](. sions of the acceptance ellipses are illustrated in Fig. 6. Having established the connection between the ion trajectories and the quadrupole acceptance, we consider some of the basics of the

QUADRUPOLE MASS FILTERS

161

FIG.6. An acceptance ellipse showing its characteristic dimensions in terms of B , and

r.

E.

phase-space approach to ion optical design and the use of matrix transformations for those not familiar with this topic. We also briefly describe how the emission of an ion source should be characterized. After this, the specific application to the mass filter and the methods of calculation are described. Section 11, therefore, serves largely to familiarize the reader with the nomenclature and general approach. 111. OUTLINEOF ION OPTICALTECHNIQUES

The discussion so far has been limited to one-dimensional ( x or y ) examples where only the phase plane need be considered. Whenever the quadrupole field is not perfect-whether in the fringing field region or because of a slightly distorted field-motion in the three coordinate directions can become coupled and the problem ought to be treated in a multi-

P. H. DAWSON

162

dimensional phase space. However, the simplicity of the phase-plane approximation is maintained in the discussion here and it is sufficiently valid (Dawson, 1975a) for most of the calculations of interest. In this linear approximation, any section of the field along the flight path of the instrument can be represented by a (2 X 2) matrix M. The efThe matrix M can fect of two sections linked together is given by M1M2. represent a part of the quadrupole field, a fringing field, a field-free drift space, or an ion lens. For example, a field free drift space of length 1 (in units of ro) is represented

where v, is the axial velocity, expressed in ro/sec. A thin lens of focal lengthf(in units of ro) is represented by the transformation

The matrix for a transformation through one cycle of a quadrupole field at a stable operating point has already been given [Eq. (S)]. At an operating point outside the stable region for the particular coordinate direction, the equivalent matrix is

=

cosh(.rrp) + A sinh(ap) B sinh(7rp) -r sinh(7rp) cosh(7rp) - A sinh(.rrp)

[

The equation linking equivalent points in the phase plane is again given by Eq. (2) but E is now negative and the trajectory points lie on a hyperbola instead of an ellipse. For a more rigorous account of phase-space dynamics, textbooks should be consulted (Steffan, 1965; Lichtenberg, 1969; Septier, 1967). The matrices we have illustrated above can be used to transform a set of conditions from one point in the flight path to another. The set of conditions might be a source emittance or an analyzer acceptance or the restrictions imposed by an aperture or series of apertures. The transformations are governed by Liouville’s theorem, which can be expressed (Steffan, 1965) as: “In the vicinity of a particle, the particle density in phase space is constant if the particles move in a general external field with forces which do not depend on the velocity.”

I63

QUADRUPOLE MASS FILTERS

The consequences of importance to the present problem might be summarized as: (1) The phase plane area occupied by a group of ions cannot change its size (E is constant; IMI = 1). Areas transform into equal areas. ( 2 ) Straight lines transform to other straight lines in the phase plane (e.g., transformation of aperture limitations). (3) Ellipses transform into other ellipses of equal area. (4) The emittance of a source may be restricted by the use of apertures. It cannot be increased. If the matrix to pass from time tl to time t2 is

and the acceptance ellipse is characterized by AIBlrl at tl, then it will evolve at t2 to an ellipse characterized by

- 2cs - CC' CS' + SC'

- SS'

]["rl1 A

transformation) (forward

(10)

Conversely, we have

Some combination of lenses and drift spaces can be used to transform an acceptance ellipse to an ellipse of another shape and orientation. This provides a means of optimizing the matching of an analyzer to an ion source. Since the acceptance of the quadrupole analyzer can be calculated from ion trajectories [Figs. 4 and 5 ; Eqs. (4) and ( S ) ] , this acceptance can then be transformed back through any fringing fields, drift spaces, or ion lenses [using Eq. ( I l ) ] to give the equivalent acceptance ellipse at the source. A comparison with the source emittance will then indicate which ions are transmitted. The properties of the complete system will depend on this crucial factor: how the source emittance matches the analyzer acceptance. It will influence not only overall sensitivity, but the resolution/sensitivity trade-off, the limiting resolution as a function of instrument length, and mass discrimination effects. There are two complementary approaches to instrument design. One is to calculate the ion acceptance for the quadrupole analyzer and transform it back toward the source as described above. The matrix transfor-

164

P. H. DAWSON

mations are calculated for each section of the flight path. Many illustrations are given later, for example, on transforming the acceptance ellipses to those appropriate at the beginning of the fringing fields. This approach is used when one is trying to specify what the desired ion source characteristics (or ion source + lens system) should be. The second approach is more useful when the source characteristics are fixed and it is then the evolution of the ion “bundle” along the flight path which is of interest. Assume that the source emittance is characterized by a phase-plane ellipse. It is often convenient (Steffan, 1965) to reexpress the ellipse characteristics in terms of the envelope function E and the maximum angular velocity A as shown in Fig. 7. The ellipse equation becomes A2u2 - 2EE’uQ + Pa2 = E2

(12)

where A2 = e2/F

+ Et2

The equation of motion can be reexpressed as

E”

+ {a, - 2q,

c0s[2(5 - ~,)I)E-

2 1 ~ = 3

o

(14)

allowing E(5) to be calculated by numerical integration. However, a more accurate method (especially where E becomes small) is to calculate two orthogonal trajectories u , ( t ) and u 2 ( D and use

EM) =

+ U2(t)2io.5,

AM

= [ ~ ~ ( t+ ) 2~i~(t)210.5

(15)

FIG.7. An acceptance ellipse showing its characteristic dimensions in terms of E , E ‘ , A , and

E.

QUADRUPOLE MASS FILTERS

I65

Convenient starting conditions at the source for the two trajectories calculated are (uo = Eo, t i o = EA) and (uo = 0, iio = e / E O ) .An example of a display of E vs. ( in a complex instrument is given in Fig. 16, p. 172. As long as E < 1, there is total ion transmission. IV. SOURCECHARACTERIZATION Even in highly developed commercial instrumentation with simple electron bombardment sources, the detailed ion source characteristics are not usually known. An obviously necessary first step in design evaluation is to characterize the source by calculation of its ion optical characteristics or, more readily, by the measurement of the distributions of ion positions and ion transverse velocities as they emerge from the source. Such efforts are currently underway in several laboratories. The ideal ion source would emit ions with a uniform brightness throughout an emittance ellipse in the phase plane and the ellipse area would be equal to the analyzer acceptance (the latter, however, is a function of the operating point). If the source emittance is much smaller than the analyzer acceptance but correctly coupled, the instrument will be source limited and insensitive to analyzer characteristics but it will be inefficient in that all the phase space is not utilized. If the emittance is large, the instrument will become analyzer limited and some ions will not be transmitted. For a given total beam intensity, uniform occupation of the phase plane area will minimize interactions within the beam (e.g., space charge effects). The ideal source would also have ions with a uniform axial velocity v,. In practice, a source will be characterized by a five-dimensional phase space ( x , i , y , j , v J , the surface of which defines the boundaries of the beam. The surface may be different for different masses since we have defined iand y in units of ro/( and a fixed source may tend to have an angular distribution that is mass independent. The distribution of ions within the x i and yy phase planes can often be approximated by a series of ellipses representing particle equidensity contours. In a linear beam transport system, the x i and yy phase planes can be considered separately. First-order departures from linearity may take the form of small additional matrix elements such as are introduced by faults in a quadrupole field (see p. 193) or by “thick” lenses. These can be thought of as spherical aberrations. Another type of aberration is chromatic, i.e., depending upon 0,. A factor of this kind is introduced in the fringing-field region. It is treated here by carrying out separate acceptance calculations for ions that spend different numbers of R F cycles in passing through the fringing fields.

166

P.

H. DAWSON

V. METHODSOF CALCULATION

Several methods of calculation have been described in the literature (Baril and Septier, 1974; Dawson, 1974a, 1975a, 1976a; Bonner et al., 1979). That presented here seems to be the simplest to implement. The first step is to calculate the matrix elements [Eqs. (8) and (9)] for one cycle of the full quadrupole field for several (usually 10-20) initial phases of the R F field. This is simply done by numerical integration of the Mathieu equation of ion motion for two trajectories, one beginning at u = 1, ic = 0 (which will give C and C')and one beginning at u = 0, ic = 1 (which will give S and S'). Any standard numerical integration routine can TABLE I MATRIXELEMENTS FOR THE TRANSFORMATIONS REPRESENTING FULLAND PARTIAL BEGINNING AT THE ZERO PHASEFOR THE OPERATING POINT CYCLES OF THE FIELD a = 0.2361, q = 0.706" ~~~~~

~

~

~

~

Acceptance parameters

Matrix elements Phase transformation (6 - 60)lP

ml1

m22

m12

B

A

y Direction

0-0.1 0-0.2 0-0.3 0-0.4 0-0.5 0-0.6 0-0.7 0-0.8 0-0.9 0-1.0 x

0.94472 0.80812 0.65466 0.54210 0.50142 0.54106 0.65244 0.80460 0.93999 0.99466

0.94907 0.87171 0.93215 1.27914 1.98801 2.99729 3.97402 4.25874 3.22481 0.99466

0.30852 0.59321 0.87066 1.20900 1.71253 2.49034 3.59353 4.9 1476 6.12827 6.81135

58.901 43.103 28.295 19.416 16.636 19.413 28.288 43.089 58.881 65.997

20.889 26.563 19.328 9.049 0.00 -9.027 - 19.301 -26.534 -20.86 1 0.00

0.92 193 0.72192 0.47212 0.22773 0.00083 -0.22586 - 0.47009 -0.7 1958 -0.91944 -0.99725

0.92626 0.78433 0.73782 0.9 1245 1.33189 1.88919 2.28430 2.05033 0.86598 -0.99725

0.30611 0.57452 0.80906 I .05922 1.40830 1.91342 2.57887 3.28223 3.76512 3.75285

43.035 26.393 11.298 2.648 0.039 2.655 11.319 26.428 43.081 50.630

22.265 27.588 19.242 8.604 0.00 -8.598 -19.256 -27.609 -22.272 0.00

Direction 0-0.1 0-0.2 0-0.3 0-0.4 0-0.5 0-0.6 0-0.7 0-0.8 0-0.9 0-1.0

a The acceptance parameters are derived by combining the elements for the full and partial cycles.

QUADRUPOLE MASS FILTERS

I67

FIG. 8. x-acceptance ellipses for ten different initial phases of the RF field for the operating point 0.2361,0.706.

be used. The data presented here were obtained using a fourth-order Runga-Kutta method with an integration step of 1/3000 of an RF cycle and using double precision. It is convenient to carry out the integration for the “zero” phase, which has A = 0 and C = S’.E is then readily obtained as l/BMMAX. If some of the intermediate values of position and velocity are retained during the trajectory calculations, one also has transformation matrices for going from the zero phase to 0.1, 0.2, etc., phases. Table I shows a typical set of matrix elements calculated in this way and the ellipse parameters derived when the zero phase ellipse is transformed using Eq. (10). Figures 8 and 9 show the x and y acceptance ellipses obtained for the operating point 0.2361, 0.706, which is on an operating line with a nominal resolution of 180. These are the acceptances when the perfect quadrupole field is infinitely long, which in practice means that it is longer than the (1/p, or 1/1 - pl) of the operating point. Two real modifications we must consider are finite-length quadrupole fields and fringing fields at the entrance. The fringing field is simple to deal with when a two-dimensional geometrical model can be used. The usual assumption is that the field at the

I

0.6

-0'6

t

FIG.9. y-acceptance ellipses for ten different initial field phases for the operating point 0.2361.0.706.

-0 L1

+ 1

FIG.10. The acceptance ellipses of Fig. 8 transformed back to the beginning of a linear fringing field that is two cycles long.

QUADRUPOLE MASS FILTERS

I69

-0.4 --

I

FIG.11. The acceptance ellipses of Fig. 9 transformed back to the beginning of a linear fringing field that is two cycles long.

entrance increases linearly as one approaches the quadrupole and that the x and y directions remain independent. This assumption is discussed in

the next section. Two trajectories are again calculated for the fringing field, but this time for the whole time spent there (since the field is nonrepetitive) and for every initial phase of interest. The ellipses for the full field are then transformed backward using Eq. (1 1) and the appropriate fringing-field matrix elements. Figures 10 and 11 show the ellipses of Figs. 8 and 9 transformed back through fringing fields two R F cycles long. The interpretation of these ellipses is considered later. The finite-field length requires a slightly different approach. As evident in Figs. 4 and 5 , there is always a local maximum in the ion displacement near one particular phase (the zero phase in the case of the lowest stability region). Therefore, in limiting the allowable amplitude of ion oscillation, the sets of rods act like a series of limiting apertures of radius ro situated one cycle apart. The restriction of entrance conditions for ion transmission through a field n cycles long will be indicated by the phase-plane area enclosed by the backward transformation to the entrance of the lines u = ro through n cycles, n - 1, n - 2, . . . , 1 RF cycles. The transformations are readily accomplished using the zerophase matrix elements. Examples are shown in Figs. 12 and 13 for the x

x 0 I5

, -~-

_c_

0.5

-1.5

1-6

-0.05

-0.15

FIG. 12. Transformation of the ?ro limits to oscillation in the x direction back to the quadrupole entrance for the indicated numbers of RF cycles. The operating point was 0.2334,0.706. The acceptance limits gradually delineate an ellipse as the field lengthens.

-

Y 0 I --

-0.1 --

FIG. 13. As for Fig. 12 but in the y direction. 170

I.5 I

X

FIG. 14. Transformation of the f r o limits to oscillation in the x direction back to the quadrupole entrance when the operating point (0.238,0.72) is outside the x stability boundary. The central trapezoidal area can still lead to ion transmission for a finite length field. 0.2

-

Y

I

0.1 .-

-0.1 -~

-02-

FIG. IS. Transformation of the f r o limits to oscillation in the y direction for the operating point 0.2281.0.69, which is outside the y stability boundary. 171

P. H. DAWSON

0.04 00

50.0

1000

150.0 2000

2500 3 0 0 0 3500 4000 450.0

5000

5500 6 0 0 0

6500

7 0 0 0 7 5 0 0 8000

TENTHS OF CYCLES

FIG.16. Illustration of the y envelope function calculation for ten different initial field phases for three quadrupoles in series allowing for appropriate fringing fields. The source had E = 0.2, E' = -0.025, and e = 0.0025. The quadrupoles had a = 0.2334, q = 0.706 in the end sections and a = 0, q = 0.2 in the central sections.

and y directions. The transformed limit lines are tangential to the acceptance ellipses. The ellipses are good approximations when n > 1/1 - pZ and n > l/py, respectively, and are identical in the infinite limit. If the field is short, ion transmission may occur even if the operating point is outside the stability region. This case can be treated in an exactly analogous fashion. Examples are shown for the x and y directions in Figs. 14 and 15 for the zero initial phase. The lines are tangential to hyperbolas. There is an area in the phase plane where transmission can occur if the field is not infinitely long (the central trapezoid). The area decreases the longer the field and decreases more rapidly the further the operating point

QUADRUPOLE MASS FILTERS

I73

is outside the stability boundary. The orientation of the trapezoidal area in the phase plane also departs more from that of the acceptance ellipse of the same initial phase the further one is from stability. The above discussions concern the transformation of the instrument acceptance back toward the source in order to compare with the source acceptance. However, evolution of the ion envelope from the source down the flight path can be considered using similar calculations. If the matrix elements for transformation from the source to some point in the analyzer are again C , S, C ' , and S ' , and the source is characterized by E,, A,, E;, and E (Fig. 7), then the envelope function E is given by

E = ( C E ; + 2CSE&;

+ SZA;)0.5

and A by

+

A = ( C f 2 E ; 2C'S'EJZA

+ S'2A30.5

Figure 16 shows the calculation of the envelope function for the y direction for ten different initial phases of the field when the source plus lens had the characteristics Eo = 0.2, EA = -0.025, and E = 0.0025 and the flight tube contained three quadrupoles in series with a = 0.23342, q = 0.706 in the two outer quadrupoles and a = 0 , q = 0.2 in the center one. Appropriate fringing fields were included at the entrances to each quadrupole. Such an arrangement might be utilized in experiments in photon-induced (McGilvery and Morrison, 1978) and collision-induced dissociation of ions (Yost and Enke, 1978).

VI. THE NORMALQUADRUPOLE MASS FILTER It was evident in some earlier work (Dawson and Meunier, 1979) that the matrix elements for one cycle of the quadrupole field have a systematic dependence on a and q in the small region near the stability tip. This instigated a search for practical relationships that might be used, so that in considering particular operating points, the trajectory calculations do not need to be repeated over and over again. These useful relationships (Dawson, 1980b) are presented in Section VI,A for normal quadrupole operation, including the full one-cycle field beginning at the zero phase, the partial cycle transformations to other phases, and transformations due to linear fringing fields of various lengths. This provides a basic data collection for quadrupole design work. The general consequences of this type of design calculation and the resulting performance predictions are then discussed, including comparisons with experimental results in Sections V1.B-E.

174

P. H. DAWSON

A . Data Compilation 1 . The Zero-Phase Full-Cycle Transformation

In the local region of the stability diagram, which is of interest in mass analysis with reasonable resolution, the stability boundaries and the related iso-p lines can be very well approximated by straight lines. The matrix elements m,,and m,,also have a linear dependence on q for each scan line of a given K ( = q / a ) . [Note that for the zero phase m,, = mZ2,and one

1.0

1.00

0.99

0.98

I

9 FIG. 17. The variation of the zero-phase matrix elements myl and -mf1 with q for operating lines, where K = q / a is: (a) 3.0246, (b) 2.9903, and (c) 2.9833.

I75

QUADRUPOLE MASS FILTERS

6.05

3 77

mr2

4 2

6.8C

3.76

6.7E

3.75

0.700

0 705

9

0.710

FIG. 18. The variation of the zero-phase matrix elements m t and mT2 with q for operating lines, where K = q / a is: (a) 3.0246, (b) 2.9903, and (c) 2.9833.

always has m2, = (m11m22- 1)/m12.] Some calculated values are shown in Figs. 17 and 18 for scan lines with K = 2.9833, 2.9903, and 3.0246. For the y direction, there is evidently a good approximation that mil = 1 (4 - q;)1.8947, where q’ is the 9 where m,,= 1. For the x direction mfl = - I (44 - q)3.7442. The values of q ’ depend, of course, on K as shown in Fig. 19. This is another way of representing the boundaries of the stability diagram. Its shows the nominal resolution-based on the width of the stability region-for any value of K.

+

P. H. DAWSON

176

3.C2

K

3.00

2.98

0.70

0.69

9‘

0.71

FIG. 19. The values of q when myl = 1 and rnfl = - 1 for operating lines of various K ( = q / u ) . This is another representation of the stability diagram.

For any of the matrix elements (m), it is found that rn = K ,

f

K2q f K,K

Values of K 1 ,K 2 , and K , are given in Table 11, so that it is no longer necessary to repeat the integrations for any operating point near the stability tip. The analysis can be pursued a little further, since for the zero phase p, + 0 and r n t = cos(irp) = 1 - rn2p2/2. Equating with the expression above for myl, one obtains p, = 0.61963(q - q;)0.5.However my2 = B sin (rnpu)= sin ( ? T ~ ~ ) /=E ‘~ T T ~ ~ / Since E ~ . my2 is almost constant in the region of interest (-6.801, then eU = 0.4628, = 0.2863(q - q;)0.5.One can similarly derive ez = 0.836(1 - pz) = 0.7307(qL - q)0.5.For an operating point at the center of a peak of nominal resolution R, q: - q = q - q; =

v Direction 0-0.1 0-0.2 0-0.3 0-0.4 0-0.5

0-0.6 0-0.7 0-0.8 0-0.9 0-1.0

1.01090 1.03858 1.08315 1.17375 1.36299 1.70147 2.20495 2.81943 3.40827 3.80222

-0.07767

-0.26478 -0.47378 -0.65844 -0.83000 - I .O 1978 - 1.24222 - 1.4851 1 - 1.72078 - 1.92022

-0.00379 -0.01455 -0.03143 -0.05573 -0.09215 -0.14729 -0.22589 -0.32315 -0.41916 -0.48600

1.01109 1.04141 1.10268 1.21983 1.37312 I .47887 1.52472 1.76419 2.56442 3.80222

-0.07 156 -0.17767 -0.09967 0.35889 1.37700 3.03189 4.86033 5.43378 3.10400 - 1.92022

-0.00382 -0.01475 -0.03341 -0.06475 -0.1 1921 -0.2076 I -0.32787 -0.44816 -0.51 175 -0.48600

0.31524 0.63719 0.97284 1.33601 1.74336 2.19365 2.66529 3.17126 3.83445 4.831 10

-0.00789 -0.04900 -0.10011 -0.07 167 0.86200 2.1 1111 3.78600 5.2 1422 5.44333

-0.00038 -0.00312 -0.01047 -0.02542 -0.05356 -0.10394 -0.18746 -0.31006 -0.46306 -0.62190

0.98749 0.94521 0.87398 0.80 138 0.77435 0.83400 0.98767 1.17378 1.25117 1.06855

-0.10889 -0.37589 -0.69278 - 1.01900 - 1.41089 - 1.96111 -2.70022 -3.48644 -3.97056 -3.7661 1

0.00379 0.01408 0.02918 0.04871 0.07443 Ci. 10857 0.15000 0.18994 0.21152 0.19816

0.98757 0.94799 0.89236 0.84398 0.78046 0.62597 0.37779 0.25194 0.52542 1.06855

-0.10278 -0.2921 1 -0.34967 -0.14489 0.36089 1.10233 1.69333 1.30100 -0.73222 -3.7661 1

0.00379 0.01429 0.03 108 0.05723 0.09942 0.16251 0.23816 0.29455 0.28679 0.19816

0.31300 0.61767 0.90672 1.17918 1.43582 1.65999 1.81838 1.90969 2.02014 2.26994

-0.01 133 -0.07400 -0.18056 -0.26589 -0.23989 -0.01344 0.43889 0.94733 1.07933 0.37756

0.00038 0.00306 0.01003 0.02359 0.04764 0.08825 0.15117 0.23595 0.32941 0.40743

0.18411

x Direction

0-0.1 0-0.2 0-0.3 0-0.4 0-0.5

0-0.6 0-0.7 0-0.8 0-0.9

0- 1 .o

~~

a

The matrix element for any (a,q)operating point is given by m

=

K, + K,q

+ K,(q/a).

178

P. H. DAWSON

0.706/2R2. The overall combined transmissivity is then TMAX = E,E~= 0.0738/R. This illustrates the origin of the inverse relationship between the total acceptance and the resolution assuming the acceptance can be wholly utilized. This assumption is not generally true and the effective acceptance may be much smaller (see below). In the case of full ellipse occupation with an ideally long quadrupole, at any other point on the peak = ( q - q;)0.5(q&- q)0.5 and one would obtain excellent peak T/T,,, shapes (half-width -7/8 of total width).

2. The Partial-Cycle Transformutions The matrix elements for the partial-cycle transformations, which are combined with the, zero-phase full-cycle values to give the acceptance ellipses at other initial phases, also have approximately linear dependencies on q and K . The appropriate constants are given in Table 11. 3 . Fringing Fields

As mentioned before, a two-dimensional linear model is assumed with independent motion in the x and y directions. These are the most laborious of the calculations but, as might be expected, the matrix elements also have linear dependences on q and K . Some examples are given in Table 111. It is also interesting to examine the matrix elements as a function of the time spent in the fringing field for a given operating point. An example for the y direction is given in Fig. 20 for ions arriving at the full field at the zero phase. The conditions for they direction during ion entry correspond to unstable (a,q) values and one obtains the approximately exponential increase in the matrix elements provided that the fringing field is more than about one RF cycle long. The values for nonintegral field lengths are slightly different especially for m,, and could lead to some fine structure on the axial velocity dependence as discussed on p. 185. The matrix elements for the x direction have a more irregular sinusoidallike dependence on the time spent in the fringing field. B. Fields of Finite Length

The general principles of the calculations for finite-length devices have been illustrated in Figs. 12-15. The field can be considered in the infinite approximation provided that n > l/pu and n > 1 / 1 - &. These conditions would be approximately true in the center of a peak provided that n > 2.1R0.5and n > 3.3R0-5,respectively (Dawson and Meunier, 1979). However, at the edges of the peaks, the approximation will not be valid

TABLE I11

y Direction

0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

4.8 1695 4.95824 4.75897 4.22 180 3.61610 3.25000 3.25038 3.56195 4.02627 4.47652

2.32500 1.86189 0.61 122 -0.49167 - 1AM267 - 1.08322 -0.92822 -0.46856 0.45589 1.64300

- 1.07370 - 1 ,07977 -0.94070 -0.74262 -0.57948 -0.49402 -0.49 198 -0.57292 -0.73125 -0.92778

6.66045 8.86824 11.36680 12.98770 12.50080 10.09280 7.12056 4.94562 4.28139 5.03521

3.74100 8.03289 6.61944 2.24456 - I .83144 -4.90433 -7.65489 -9.80722 -9.17078

0.78882 0.87934 0.61664 0.17448 -0.16679 -0.29408 -0.25324 -0.10570 0.13583 0.46720

-3 4 9 2 2

0.32335 0.31190 0.23271 0.13528 0.06516 0.03668 0.04638 0.09169 0.16997 0.26207

- 1.a4743 0.05357 2.30522 3.30989 2.53926 0.85668 -0.71955 -1.78144 -2.38608 -2.54763

1.51944 -2.65289 -8.15556 - 1 1.12490 -10.08890 -6.80222 -3.46656 -0.8951 1 1.11856 2.40256

-3.86300

- 1.03983

- 1.92501 - 1.22134 -0.65592 -0.32813 -0.40953

16.68810 17.69480 18.01410 17.32280 15.85590 14.33890 13.45020 13.46090 14.23590 15.42690

5.05533 5.56433 3.34567 -0.10322 -2.9001 1 -4.2641 1 -4.31200 -3.20633 -0.901 22 2.29700

-2.70469 -2.99102 -2.93455 -2.57743 -2.11 120 - 1.72426 - 1.52140 - 1.54274 - 1.79484 -2.23 122

-0.15604 0.31047 0.70262 0.79933 0.6 1770 0.31519 0.01160 -0.24954 -0.42825 -0.42778

5.09851 5.98626 6.17881 5.51402 4.42690 3.49347 3.00539 2.97386 3.33875 4.0805 I

- 10.15030 - 12.94220 - 14.10690 - 13.OO540 - 10.50310 -7.9431 1 -6.13878 -5.34078 -5.68178 -7.34911

1.09799 1.22749 1.18076 0.99023 0.75863 0.57697 0.48959 0.51128 0.64426 0.86528

-2.03770 -2.86050 -3.05292

-2.63 131

x Direction

0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

-3.78256 -3.10967 - 1.87589 -0.81867 -0.2%33 -0.273 11 -0.64300 - 1.38278 -2.43578

,. The matrix elements for a two-cycle-long fringing field starting at the given phase are m = K 1 + K,q + Ks(q/a).

P. H. DAWSON

180

50.0

my

/x

/

10.0

’/

//

x’;/

5.0

*/ x

O/

x

0

/ /

0

0

/

/

o

/ I .o

0

I

I

I .o

2.o

I

3.0 “f

Fic. 20. The matrix elements m y for transformation through fringing-field regions of various lengths nf in RF cycles.

and the ion acceptance will be enlarged. Ions will also be transmitted even for points outside the stability diagram and this will produce trailing edges on the peaks. Those on the low-mass side arise from undesired transmission in the y direction, those on the high-mass side in the x direction. The former will generally be more of a problem because of the angles at which the operating line cuts across the iso-p, and iso-p, lines. This is in accordance with experimental observation. The details of the peak shape will depend on exactly how the source being used matches the instrument acceptance in the x and y directions, particularly the acceptance for points just outside the stability boundary. An experimental rule-of-thumb gives the necessary length of the analyzer to obtain “good” peak shapes (Austin et a l . , 1976) as R = n 2 / h , where h is equal to about 25. No detailed comparisons of experimental performance for a source of known emittance have yet been made, although the

QUADRUPOLE MASS FILTERS

181

main features of the experimental observations are clearly predicted. Note that if the ion source emissivity was accidentally well matched to the acceptance at some point near the edge of a peak (with its different orientation in the phase plane as discussed earlier), then irregularities in peak shape could be produced. These would be progressively more important at high resolution. Low-level irregularities near the leading edge of peaks are frequently observed but this origin has not been experimentally confirmed. Various geometries might be suggested to reduce peak tailing. A central stop approximately placed in the lens system coupling the ion source to the analyzer might be used to eliminate the ions, which would be accepted at operating points near the edges of the peaks (Dawson and Redhead, 1977). In this regard, the elementary suggestion is often made that for quadrupoles, the source should have a small emittance with the ions focused on the central axis; this would indeed lead to high transmission but also to very broadened peaks for a given operating line. The trade-off between ion acceptance, resolution, peak shape, and instrument length is a very complex one. More measurements from well-characterized sources are required in order to compare with the detailed theoretical calculations that can now be easily carried out.

C . Fringing Fields -TlzretJ-Dirnrti.sionLi1Cukulutions At the entrance to and exit from any quadrupole, there is some fringing-field region where the R F and DC fields are varying with the ion's axial position. Normally, this fringing field might be expected to effectively extend over a distance of at least the order of the radius of the device. In the fringing-field region, x , y , and z motions become coupled and a highly complex situation arises. There has only been one study published (Dawson, 1975a) that takes account of this coupling. That study assumed a fringing field of the form @(x, y ,

Z) =

@o(x2 - Y"Z/V"o

(18)

which is particularly amenable to analysis since the resultant equations of ion motion are

d2X/dt2+

[U

d 2 y / d t 2-

[U -

d2z/d5'

+ [U

- 29

- 2q cos

2(5

- to)1.Z/ro = 0

(19)

t o ) ] y ~ /= ~ o0

(20)

cos 2 ( 5 - t0)](x2- y 2 ) / r o = 0

(21)

2q cos 2 ( 5

-

This is probably quite a good approximation for a field terminated by a grounded aperture plate. When x and y are both small, d z z / d p + 0, and

I82

P. H. DAWSON

the equations reduce to the linear two-dimensional fringing field approximation discussed in detail in Section VI,D. The analysis of the full three-dimensional fringing field is very incomplete. It has been used to calculate some typical ion trajectories and principally to judge the conditions under which the linear two-dimensional theory might be applied. It is found that at moderate to high resolution the effective acceptance (50%) averaged over all the initial phases of the field is small enough that the linear two-dimensional theory can be used. The presence of the fringing field has an important effect, which seems to be a general one, provided the ion spends more than about one R F cycle passing through it (Dawson, 1975a). There is a kind of induced synchronization of the ion motion with the field, which means that different initial field phases tend to have similar acceptances. In this sense, entrance fringing fields can be beneficial. This can be seen in the increased overlap of the ellipses in Figs. 10 and 11 compared with the ellipses for the full field only. However, if too long is spent in the fringing-field region, the y trajectories can become enlarged since the effective ( a , q )values in the fringing-field region [that is, (a,q). z / r o ] correspond to incipient instability in the y direction. This problem is examined in detail in Section IV,D. The principal point of interest to emerge from the three-dimensional fringing field calculations is the evidence of drastic modifications to the axial velocity. It is evident, of course, that there are likely to be inherent difficulties in introducing low-energy ions at points well removed from the axis when the rods have high continuous voltages (several hundred volts) applied between them and RF voltages several times larger. In the quadrants near the x poles, the ions are most likely to be repulsed. The three-dimensional trajectory calculations show that even the R F alone has a tendency to decrease the z velocity. Slow-moving ions approaching the normal quadrupole can be reflected by the fringing field, or they may remain trapped within the fringing field region for many R F cycles. The presence of trapped ions would be very undesirable. The effects of ion reflection would be most likely to be seen experimentally as a discrimination against high-mass ions (the slowest ions for a fixed ion energy) or low-energy ions when operating at low resolution with a source of large emissivity. There is some evidence for such effects in the transmissivity vs. resolution curves of Figs. 26 and 27. The exit fringing fields can also be important. Their influence has often been minimized when an electron multiplier detector is used by allowing the multiplier field to penetrate into the quadrupole structure. In the general case, ions tend to be accelerated out by the R F component of the field. In the y quadrants, the DC component acts to retain the ions. Again some ions may become trapped in the fringing-field region; others may

QUADRUPOLE MASS FILTERS

183

even be drawn back into the analyzer and retransmitted toward the source. Some particular examples have been illustrated elsewhere (Dawson, 1975a, 1980a). Such effects might be important when an electron multiplier is not used, or in multiple-stage quadrupole devices, or when the electron multiplier is offset from the quadrupole axis and the draw-out field becomes too small. The ions emerging from the quadrupole also tend to form diverging beams, but this can be discussed using the linear two-dimensional approximation. Few measurements of emergence of ions have been reported. The transverse displacements have been viewed using a microchannel plate (Weaver and Mathers, 1978; see also Birkinshaw et al., 1978) and some measurements of energy distributions have been made (Story, 1976b) with rather surprising results in some cases. D . Fringing Fields -Two-Dimensional Lineur Approximation

The linear fringing-field approximation was first proposed by Brubaker (1968) and extensively used by Dawson (1971, 1972, 1974a, 1975a). One can combine the appropriate matrices taken from Section VI,A in the manner described in Section V. Figures 10 and 11 have already been used to illustrate the acceptance for ten different initial field phases at the beginning of the fringing field when it is two cycles long with aY = 0.00398 T

1

FIG. 21. x-acceptance ellipses for ten different initial phases at the beginning of a fringing field two cycles long for an operating point that is inside the stability limit by 6” = -0.0124.

I84

P. H. DAWSON

T

I

FIG. 22. y-acceptance ellipses for ten different initial phases at the beginning of a fringing field two cycles long when the operating point is inside the stability limit by ijY= 0.001 14.

and 6” = -0.00106, where 6 = (q - q ’ ) / q ’ and q’ is the value at the stability boundary. Note that the acceptance near the stability tip depends largely on 6 rather than on the particular ( a , q ) value. Figures 21 and 22 show similar sets of acceptance ellipses when Sy = 0.00114 and 6= = - 0.0124. The orientations of the ellipses do not vary very much with 6 in the region of interest. Some results for fringing fields of different lengths = 0.00398. As the time spent in the are given in Figs. 23 and 24 for fringing field increases, the y ellipses become better aligned but also drawn out to y values where the full acceptance cannot be utilized. The overlap of the x ellipses also increases with fringing-field length but less dramatically (Dawson, 1976a). If one has a source of known emittance, it is simple to compare the emittance with the acceptance for many initial phases at a given operating point and to predict the average transmission. For a general assessment of quadrupole properties, some assumption about the source is required. For the prediction of general trends and for general quadrupole design work, it has been suggested (Dawson, 1975a) that the overlap area for 50% of the initial phases be designated as the “effective” overall acceptance. Using the generalization suggested above, the trends in transmissivity

QUADRUPOLE MASS FILTERS

185

(the product of x and y acceptances) and the variation with resolution and axial ion velocity can be explored. For example, choosing a fixed operating point, and plotting the “effective” transmissivity as a function of nf (the length of the fringing field), gives a result such as Fig. 25. The general shape of the curve does not depend very much on the exact operating point. As is evident in Fig. 20, there may be fine structure due to nonintegral length fields. In the normal quadrupole operation with a fixed ion energy, nf a ( ~ z / e ) Oso. ~that Fig. 25 becomes a mass discrimination effect (see the upper scale). Note that a short time spent in the fringing field is actually beneficial, since the acceptance ellipses are better aligned and it is easier to match a static source. For very slow ions, the x and y acceptances become very asymmetric. The elongation of the y ellipses is explained by the tendency of the y rods to attract the ions. For maximum transmissivity, the ions have to be injected as a converging beam at all initial phases, in order to counteract the defocusing field. Some commercially available quadrupoles operate with “programmed ion energy,” where the ion energy is varied during the mass scan in order to minimize mass discrimination. However, the ions must still remain in the full field sufficiently long that R < n 2 / h . Another commonly used modification is to operate the quadrupole T

-0‘1 -0 2

FIG.23. y-acceptance ellipses for Sy = 0.00398 at the beginning of a fringing field one cycle long.

186

P. H. DAWSON

I

1

FIG.24. y-acceptance ellipses for 8' cyctes long.

=

0.00398 at the beginning of a fringing field three

axis off-ground so that ions are decelerated as they pass through the fringing field. In this way, low-velocity ions can be injected into the quadrupole field, without spending too much time in the fringing field. Approximate modeling of this situation (Dawson, 1975a) shows that the ellipse overlap depends principally on the actual time spent in the fringing field rather than on the final axial velocity, and so the technique can be quite effective. However, experimentally there have been some measurements that indicate that the parameter h ( n 2 > Rh) may increase for the retarded ion entry (Dawson, 1976b). More data are required. As discussed earlier, if the acceptance ellipses could be perfectly matched at all phases, the transmissivity would decrease as 1/R. However, normally it will be the overlap of the ellipses for the different initial phases that is important and the effective transmissivity will decrease approximately as 1/R2. To summarize, detailed predictions of peak shapes, resolution as a function of n , transmission vs. resolution, etc. can readily be made for a source of known characteristics. The general trends can be predicted as follows: (1) At low resolution, the transmission may be source limited and will vary little with resolution. In this region, there is likely to be discrimination against slow ions because of reflection in the fringing fields.

I87

QUADRUPOLE MASS FILTERS

(2) At intermediate resolution, the transmission will be analyzer limited and transmissivity will decline as 1/R2. There will be velocity discrimination due to the problems of ellipse overlap as was illustrated in Fig. 25. (3) At higher resolution, a resolution limit will be reached set by the length of the analyzer and this will depend on the axial ion velocity (R = n2/h).At the limiting resolution, transmissivity will drop abruptly. There is experimental evidence supporting these statements. Figure 26 I

I

I

I

I

M/2

M

2M

4M

8M

r\

I I

I

h

0 X

\

I

wY w

\

I I

I

W 0

\ \@ \

I

z

I

2 a

\

I I

W

0 0

a

3

\

I

IC

v

W

3\

\

\

I I I

E

5W

LL I L

\

\

I I I

W

@\

\ \

I

\

\ \

2

4

I . 6

"f

FIG.25. The effective overall acceptance (50% transmission in x and y directions) as a function of the length of the fringing field in RF cycles. The mass scale above assumes a fixed axial ion energy. The operating point was 0.2334.0.706.

I88

P. H . DAWSON

\

\

F I G .26. Transmission vs. resolution (at 10%)of the peak height) for K+ ions of various axial velocities with an instrument with unmodified fringing fields. The axial velocities expressed as r,/cycle were: (i) 0.59, (ii) 0.51. (iii) 0.42, (iv) 0.32. (v) 0.27, and (vi) 0.19. The dashed line is the theoretically predicted relationship.

shows some transmission/resolution curves for potassium ions with various axial velocities emitted from a large source (Dawson, 1976b). The three regions are clearly evident. The dashed curve shows the predicted T cc 1/R2relationship. [This has been observed by other groups also (Wittmaack, 1977).] The limiting resolution Rlimobeys Rlim= n 2 / h up to some maximum value where it increases only very slowly with n . This

189

QUADRUPOLE MASS FILTERS

-----&-

A

(vi)

1

f

I

I 0.I

I

10

50

I

loo

I

mo

I loo0

RO.6

FIG.27. Transmission vs. resolution (at 50% of the peak height) for K+ ions of various velocities with an instrument with a lossy dielectric entrance aperture, which separates the RF and DC fringing fields. Axial velocities as in Fig. 26.

I90

P. H. DAWSON

maximum was found to be insensitive to ion input conditions or to modification of the fringing field and was attributed to intrinsic field imperfections of the particular quadrupole. The transmission of low-velocity ions was improved in the intermediate-resolution region by operating the quadrupole slightly above ground but the curves had a complex shape with transmission decreasing in two stages and this is not presently understood (Dawson, 1976b). The relative transmission of the ions of different axial velocities could be altered at intermediate resolutions by modification of the fringing fields (Fig. 27). The type of velocity (or mass) discrimination predicted in Fig. 25 has been observed experimentally for both electron-bombardment sources (Ehlert, 1971) and secondary ion sources (Dawson and Redhead, 1977). The most direct experimental verification of the design theory comes from measurement of ion acceptance using a movable highly collimated ion source (Hennequin and Inglebert, 1978, 1979). Figure 28 compares measurements of 50% acceptance ellipses (effective acceptance) with the earlier calculations for the center of a peak with resolution 55 when the fringing field is two cycles long. Figure 29 shows a similar example for R = 225. One problem of interpretation lies in choosing the axial position at which to make the comparison. The measurements do not yet extend to longer fringing fields but provide excellent confirmation of the usefulness of the design data. The effective acceptances were, as predicted, dependent on axial velocity and not directly on ion mass. The measurements also include acceptance contours for loo%, 25%, etc. transmission.

FIG. 28. Comparison of the theoretically predicted (lines) and experimentally measured effective acceptances for ions spending two cycles in the fringing fields for R = 50: X , 32-eV Csf ions; 0, 20-eV Rb+ ions.

QUADRUPOLE MASS FILTERS

191

FIG. 29. As for Fig. 28, but for resolution 225.

In most of the previous discussion we have been talking in terms of “transverse” matching of the source to the analyzer. There is also the possibility of “longitudinal” matching; that is, pulsing the source to match the acceptance at one particular phase or a narrow band of phases. This has been attempted using a “bunching” box interposed between the source and the analyzer (Lefaivre and Marmet, 1974) to which is applied a potential of the form V(t) = rnx2Vo/[rnx2+ 2eV0t2 - 4~t(ernV,/Z)~.~] where x is the thickness of the box and V , the potential through which the ion has been accelerated. In an experiment approximating V ( t ) with a linear potential variation for high-mass ions, a small gain in ion signal (-2) was found. The experiments were carried out on a rather unusual quadrupole (of 5 cm radius) and have not been more generally utilized. Another suggestion is that bunching to less than 1/10 of a cycle might be achieved merely by insertion of an electrode with a few volts of RF applied (Dawson, 1976a). In longitudinal bunching, one still has the quadrupole fringing field to take into account and much of the acceptance may be at too large a u value to be useful. However, there should be a gain in useful acceptance, particularly in the x direction and at high resolution. Some further exploration is warranted, and detailed acceptance measurements need to be made. E . Modijied Fringing Fields

Since the fringing fields are all important in determining ellipse overlap, modifications to improve that overlap are of great interest. Modified fringing fields have been used for some years. The pioneering work came from Brubaker (1968), who introduced the “delayed DC ramp.”

192

P. H . DAWSON

Short rod sections were added at the entrance to the quadrupole with only the RF connected to them, so that the ions experienced the increase in RF field before the DC field. A later version used four electrodes ahead of the quadrupole with the DC voltages reversed so as to delay the onset of the DC field. This arrangement may have more flexibility in empirically modifying the fringing fields. A more recent modification of the fringing field is the use of a cylinder at the quadrupole entrance, which is made from a lossy dielectric (Fite, 1976). This allows penetration by the R F field but not the DC field. The value of these techniques of entrance modification remained controversial for many years, probably because they were evaluated in a purely empirical fashion. Modifications to the acceptance are only useful if the source is such as to take advantage of the changes. There is a very great need for a more systematic evaluation, such as by the direct measurement of the acceptance ellipses. Considerable improvements in quadrupole performance may be possible by correctly "tailoring" the fringing fields. Figure 27 showed some transmission resolution measurements for a quadrupole with a lossy dielectric entrance aperture. The point to note in comparison with Fig. 26 for the normal quadrupole is the reversal in the transmission for low-velocity ions compared to highvelocity ions in the central region. The fine structure on these curves was shown to be due to incomplete ion collection by the offset electron multiplier under conditions where the ions were highly defocused at the ion exit. Some other measurements on a similar quadrupole have also been reported and an improved resolution was found (Dylla and Jarrell, 19761,

FIG.30. Approximate effective acceptances (50% of phases lead to transmission) calculated for a DC fringing field assumed to be delayed and shortened to half the length of the RF fringing field. The numbers indicate the length of the RF fringing field.

193

QUADRUPOLE MASS FILTERS TABLE IV COMPARISON OF EFFECTIVE ACCEFTANCE E ~ FOR E ~ LINEAR AND SEPARATED FRINGING FIELDSOF VARIOUS LENGTHS" Fringing field length (RF cycles) I 2 4 a

Resolution 55

Resolution 600

Lineai

Separated

Linear

Separated

1.2 x 10-4

5 . 5 x 10-5 1.2 x 10-4 1.2 x 10-4

5 . 8 x 10-7

3.2 x 10-7 6.5 x 4.5 x 10-8

1.0 x 10-4 3.5 x 10-5

2.5 x 6.3 x 10-7

q = 0.706.

but the limits to resolution of the instrument in Fig. 27 were very similar to those of the same instrument before modification. The theory for the modified fringing fields is not well developed. One problem is the choice of a suitable model. Improvements, particularly in the y direction, have been predicted using linearly increasing R F and DC fields with the DC delayed (and sometimes shortened). This is because the region of incipient instability in the y direction can be avoided. Some of the published calculations are in error (Dawson, 1977). Figure 30 gives some corrected results for effective acceptances. With the model used, the orientation of the y ellipses in the phase plane varies with axial velocity. There is a large gain in effective acceptance in the y direction. Overall effectiveness will obviously depend to a great extent on source matching. Table IV makes some comparisons at different resolutions assuming exact matching t o the effective acceptances. However, the validity of the model is much more in question than that for the normal quadrupole and detailed experimental measurements become that much more important.

FIELDS VII. DISTORTED QUADRUPOLE Distortions in quadrupole fields have long been acknowledged as limiting performance but there has been little quantitative information available. Austin et nl. (1976) made a compilation relating maximum attainable resolution to known mechanical tolerances in rod construction and assembly, which is shown in Fig. 31. Round rods are still the most widely used to create the quadrupole field because of the relative ease of precision manufacture and precision mounting. The rods are, in theory, best chosen to have a radius of r = 1.148ro to minimize field distortions (Dayton et a / ., 1954). The presence of a grounded cylindrical housing outside the rods may also influence the choice of rod radius (Denison, 1971).

194

P. H. DAWSON

lo-'

I

t x $ ,THIRD-ORDER * , THIRD-ORDEI F THEORY/ '\ \ *

(a)

W

'.

(b)

THEORY

a 0

K

a W

;1 0 - 2 0 z

U I 0 W

B

I0-3

10

I00

I

30

M A X I M U M RESOLUTION

FIG.31. Maximum attainable resolution as a function of the mechanical tolerance in rod manufacture and assembly. The experimental curve is adapted from Austin et al. (1976).

For analytical mass spectrometers, the quadrupole rods are said to be cm and to paralmanufactured to tolerances in radius of a few times lelism of cm. Recently there has been a commercial move toward the use of rods of hyperbolic cross section. The scientific value of this has not been experimentally proven in the published literature and recent theoretical studies (Dawson and Meunier, 1979) suggest the direct improvements may be small at today's level of performance. However, the correct positioning of the hyperbolic rods may be less critical, and commercially one is presently more interested in the percentage yield of quadrupoles that meet specifications after manufacture than in the theoretical limitations to performance. Direct comparisons of different quadrupoles are difficult to make since even identically manufactured quadrupoles tend to vary considerably in their properties. There is one published experimental study directly comparing round and hyperbolic rods (Brubaker, 1970), but direct measurements of acceptance would again be more interesting. Before considering field errors from the point-of-view of design theory, it is illuminating to list some of the possible types of distortions. For example: (a) misplacement of one or more rods with parallelism main-

I95

QUADRUPOLE MASS FILTERS

tained; (b) nonparallelism of rods, rod bending, and rod bowing; (c) local field distortions due to surface contamination; (d) rotation of one or more rods when hyperbolic rods are used; (e) the use of round rods; and (f) harmonics and subharmonics in the RF. Systematic errors such as (a), (d), (e), and (f) can be treated by modifying the equations of ion motion. Any geometric distortion leads to higher-order terms in the equations and also to a coupling of motion in the different coordinate directions. Borrowing from concepts developed for accelerator design (Halbach, 1969; K. Pocek, private communication, 1978), the misplacement of one or more rods can be represented by additional terms AB, in in the equation for the potential given in cylindrical coordinates as @ = @o(r)[(r/ro)2 cos 28

+ AB,(r/ro)" cos no]

Consider one or more rods displaced along their symmetry planes by a distance 6ro;then the additional terms are AB = Kn6, where for n = 1-6, K , is given as:

One rod misplaced Opposite rods in same direction Opposite rods moved outward All rods moved outward

1

2

3

4

5

6

0.149 0.298

0.214 0

0.192 0.384

0.116 0

0.043 0.086

0.010 0

0

0.418

0

0.232

0

0.020

0

0.836

0

0

0

0.040

Rods of circular cross section also give terms for n = 2 , 6 , 10, etc., but the magnitude of the term in n = 6 can be reduced to zero in the region of interest by correct choice of the rods positioning. Expressed in Cartesian coordinates, the various additional contributions become A&(2- 3xy)/r& AB4(x4 - 62y2 y4)/r40, ABe(xe 15x4y2+ 1 5 x 2 ~-~ys)/r& and so on. There is coupling between the x and y trajectories introduced by these terms. One effect of field distortions (von Busch and Paul, 1961; Dawson and Whetten, 1969a,b) is to produce nonlinear resonances at operating points where

+

( & / 2 ) K + (n - K)&,/2 = 1 where K can have values n, n - 2, n - 4, etc. Third-order resonances occur when pZ = 3 and pZ/2 + py = 1; fourth order occur when px = 0.5, py = 0.5, and px + pu= 1, and so on. The resonance lines are shown in Fig. 32. They have been extensively investigated experimentally and theoretically and ion transmission dips have been shown to result at these

P. H. DAWSON

196

0.2-

a

-0.2 -

1

0

I 0.2

I

I

0.6

0.4

I

1

I.o

0.8

q

FIG.32. Nonlinear resonances in the stability diagram due to the presence of third-, fourth-, and sixth-order distortions.

operating points. Their occurrence has also been directly related to electrode misplacement (Dawson and Whetten, 1969b). This is a gross effect of rod misplacement but one that has been shown to become more and more important at high resolution when operating near the tip of the stability diagram. However, the resonance dips are very narrow. A more general concern is the loss in transmissivity or the limit to resolution that might occur because of the presence of higher order terms. It is important to have even some approximate estimate of the importance of field distortions. A recent study adopted the simplification of considering only the y = 0 or x = 0 planes so that the two directions could still be considered independently (Dawson and Meunier, 1979). The 2 x 2 matrix for one full cycle of the field was extended in the presence of a small amount of a third-order (hexapole) distortion to 10 terms, viz., U li

0

QUADRUPOLE MASS FILTERS

197

To calculate the additional terms, three additional trajectories were considered. The additional terms were not very dependent on the chosen initial conditions. The matrix elements were then examined as a function of All3 and the (a,q) value. There are of course, two possible third-order distortions-in the x direction or in the y direction. The additional matrix elements were found to be independent of the a,q value in the region of interest but to depend linearly on A&. The effect of the distortion is to make the kind of straight-line transformations illustrated in Fig. 13 into curves because of the nonlinearity. Figures 33 and 34 show some results for the transformation of the ro limit for the y direction for the operating point 0.2345, 0.706 in the presence of AB3 = +0.0033 and A& = - 0.0033. The - y o limit will be influenced in the opposite way. The apparent increase in the acceptance ellipse beyond u = 1 in the one case is not likely to be useful and the main effect is the decrease in the acceptance ellipse in the case of the other limit. This phenomenon is important only in the y direction. In the x direction, where ions oscillate rapidly between

+

0

I0

0.0s

-0

0s

FIG.33. Transformation of the + r , limit to oscillation in the y direction back to the quadrupole entrance for the operating point 0.2334,0.706 in the presence of a third-order distortion AB, = 0.0033. Compare with Fig. 13.

P. H. DAWSON

198

T 0 . I0

+

FIG.34. As for Fig. 33 but with Ms= -0.0033.

positive and negative values, the odd-order distortions do not build up in importance to the same extent. The useful acceptance area decreases approximately linearly with A& at about the same rate for all operating points, and so the effect is most severe at high resolution. The limits to resolution were estimated by extrapolating the acceptance to zero with the result shown as curve (a) in Fig. 31. Of course, this kind of limit would only apply for a third-order distortion in the y direction. Reversal of the rod voltages would minimize the effect. There is a second, more general influence of distortions that applies to both x and y directions and to distortions of all orders. This involves nonlinear changes in the frequencies of ion oscillation and changes in the stability diagram dependent on the ion's initial transverse displacement and transverse velocity. It is found that the distortion of order n can be very well approximated by considering only two additional terms in an expanded matrix such as that given above. That is,

where for n

=

3, 4, 6 ,

199

QUADRUPOLE MASS FILTERS 3

m:, m Ys

-3.0

mB

mL

-0.84

4

6

-4.12 -4.12 2.43 -1.32

6.27 -1.59 -3.20 -2.12

The dependence of the transformation of the + r o limits on AB,,and on u8-I introduces a shift in the stability area (or a broadening of the limit of stability) depending upon which ion is considered. In effect, there is a horizontal movement of the stable region across the (a,q) diagram. This movement is proportional to AB,,and to u$-’. The “smearing” out of the stability diagram will limit attainable resolution. Setting the resolution limit as the value where the maximum shift in the stability diagram is equal to the nominal (undistorted) peak width, the following relationships are obtained:

(i)

=

(l/AB3)ra,

(ii) Rlim = (0.706/AB4)e

(iii) RIim= (O.4/AB6)rt where r, is the equivalent aperture effectively filled by the source (expressed in units of r,). The limit (i) for ra = r, is shown as curve (b) in Fig. 31. The effectively filled aperture will depend on source matching. These calculations give some indications of the limitations likely to be imposed by the presence of field distortions, and they may have important technological implications. There are several weaknesses in the calculations, such as the necessary approximations, the omission of x,y coupling, and the need to take into account the effects of fringing fields and the way they influence utilization of the available acceptance. However, the calculations are consistent with the empirical evidence that is so far available. The likely influence of distortions on peak shapes can be calculated and may be of diagnostic value. As measurements of acceptance become more widespread and as source emittances become better defined, it would be very useful to measure the limiting resolution as a function of how the acceptance is filled. Nominally identical quadrupoles often vary considerably in performance and this is known to be related to rod geometry. An evaluation of the field distortions present would be immensely valuable in tracking down the exact source of these variations. One type of measurement has recently been found (Holme et al., 1978; P. H. Dawson and M. Meunier, unpublished data,l978) where the presence of distortions is clearly demonstrated. The quadrupole is operated ’in the zero DC mode in the presence of a single gas with a retarding grid at the ion exit that only allows the pas-

200

P. H. DAWSON

FOURTH

ORDER

0.2

0.4

9

0.6

0.8

FIG.35. Transmitted argon ion current in a quadrupole operated with RF only and with a retarding grid interposed before the ion collector in order to accept only high-energy ions. The nonlinear resonances due to field distortions are identified.

sage of high-energy ions. The R F voltage is scanned. At positions of nonlinear resonance due to the presence of field distortions, ions have amplified trajectories and as they emerge from the exit fringing fields some of these ions acquire high energies. Figure 35 shows an example. The distortions are clearly evident and the transmitted signal has some intriguing characteristic line shapes. The measurements would, of course, require quantitation but even a simple comparison of quadrupoles of different performance might be revealing. The calculations show that the low-order distortions are more important than the higher-order ones since the dependence on l/rt-2 means that the sacrifice in instrument aperture in avoiding limitations to the resolution is so much greater. Correctly positioned round rods are said to reduce the n = 6 term to zero and to leave a B,, of about -2.4 x loe3 (K. Pocek, private communication, 1978). The latter’s limit to resolution could be avoided by a negligible sacrifice of instrument aperture (i.e., by proper source design). In this sense, hyperbolic rods may not be much superior to round rods. On the other hand, a 1% error in round-rod radius (Dayton el ul., 19541, which (or rod positioning) is likely to give B6 = would set the resolution limit at about 400. A 1% outward translation of all four hyperbolic rods gave only a resolution limit (for full aperture utilization) of about 1000. The positioning of hyperbolic rods, as might be expected, is not as critical as for round rods. The whole question of field distortions and limitations to performance has only just begun to be studied in a systematic way. It is highly complex but of considerable technological significance as the demands for improved instrumentation increase.

QUADRUPOLE MASS FILTERS

20 1

VIII. THEHIGHERZONE OF STABILITY It is possible to operate the mass filter using the higher zones of stability shown in Fig. 2. A deterrent is the high a,q values involved. However the iso-p lines are closer together in the higher zones and it is possible to attain the high a,q values by using lower RF frequencies since mass filtering should be possible with fewer RF cycles spent in the analyzer. There is one published theoretical study of the zone situated near a = 3.2, q = 3.2 (Dawson, 1974b). It considered only parallel entry of ions into the analyzer and ignored the effects of fringing fields at the entrance, which one would expect to be very important. Recently (Dawson, 1980b) the phase-plane acceptance has been calculated and fringing fields taken into account. The stability zone consists of an extension of the lower region in the y direction coupled with part of the second region in the x direction. An operating line that passes through the center of the zone will only give a resolution of about 33. It would have a large acceptance in the x direction but much smaller in the y direction. Higher resolutions are ob-

I I'

\\

FIG. 36. x-acceptance ellipses for ten different initial field phases for the operating point 3.1291, 3.2185 in the second stability zone. The ellipse oriented along the x axis is for the - 0 . 1 8 initial ~ phase.

202

P. H. DAWSON

tained by using an operating line that passes through one tip of the stability zone bounded by a y and an x boundary. The y calculation of acceptance and the incorporation of fringing fields is identical to that described earlier. The fringing fields involve a,q values giving rise to pronounced y instability and are very detrimental even if the number of RF cycles involved is limited by operating the analyzer at a reduced frequency. Calculations were carried out for an operating point a = 3.1291, q = 3.2185, which is near the center of a peak of nominal resolution 55. The effective y acceptance area (50% transmission) with a 0.5 cycle fringing field was about 15 times lower than for the normal quadrupole. The x direction calculations are a little different since p lies between 1 and 2 and admixtures of various frequencies in the ion trajectories are different. One result is that the zero phase no longer gives rise to the local maximum in the ion oscillation. Figure 36 shows some characteristic acceptance ellipses for ten different initial phases. The initial field phase for the ellipse oriented . initial transverse velocities can be tolalong the x axis was - 0 . 1 8 ~ Large erated in the x direction. For the center of the peak at resolution 55, the x effective acceptance area with a 0.5 cycle fringing field is about 60 times that in the y direction or 6.6 times that of the normal quadrupole under similar conditions. The overall combined x and y effective acceptance is therefore less than half that of the quadrupole operated in the usual manner. The acceptances are expressed in terms of transverse velocities given in ro/t, so that any drop in frequency required to maintain the short fringing field (and reasonable RF voltages for an adequate mass range) would also lead to a decrease in the ions accepted. The higher regions illustrate the usefulness of the design techniques in assessing potential new developments but, at the moment, mass filter operation in these regions remains a scientific curiosity.

IX. THE RF-ONLYQUADRUPOLE This modification of the mass filter has been arousing some interest recently because of its potential for high-mass transmission since it should avoid some of the fringing-field problems described earlier. The first experiments were reported by Brinkmann (1972). He operated the quadrupole in the RF-only mode (i.e., a = 0) so that it acted as a high-pass filter. The higher-mass ions having stable trajectories were then discriminated against by using a retarding field collector. Only ions having a q value close to the stability limit near 0.91 were able to reach the collector. This was presumably because they emerged from the quadrupole exit with large transverse displacements and acquired excess energy from the

203

QUADRUPOLE MASS FILTERS

fringing field. Good resolutions were obtained at high masses but the peaks were superimposed on large steps in the background. The geometry of this type of device was subsequently improved (Holme, 1976) and many of the problems with its performance were overcome. A detailed study has been published (Holme et al., 1978). Another simple R F only device uses the normal quadrupole geometry with differentiation of the transmitted signal (Weaver and Mathers, 1978). Recently, a different variation of the RF-only quadrupole has been developed (Dawson et al., 1979). This uses a gridded aperture between the quadrupole exit and the entrance to the electron multiplier collector. The aperture has a solid central stop. A negative voltage (for positive ions) of several hundred volts is applied to this electrode and draws the ions from the quadrupole exit. The more stable ions have smaller amplitudes of oscillation and are eliminated by the stop. We discuss this device in more detail than the retarding field device since design calculations have been made illustrating its performance. ,

I

,

,

,

,

,

I

,

60 -

0.71 , 0.50rc 0.35rc O.25rc 0900

0902

0904

0906

0908

q

FIG.37. Calculation describing the operation of an RF-only quadrupole with a stop at the ion exit to eliminate high-mass ions with stable trajectories. The dashed line shows the 100% acceptance area of the mass filter as a function of q . The solid curve represents the overlap area "blacked out" by the shadow of the ion stop transformed back to the ion entrance. The horizontal lines represent sources of various sizes.

149 I

XlO

FIG. 38. A spectrum obtained with an RF-only quadrupole showing how the resolution increases with n', where n is the number of cycles spent in the field. The ion energy was 5 eV; P = 4 X lo7 Tom.

205

QUADRUPOLE MASS FILTERS

Using the ion optical methods outlined earlier, the effective acceptance of the quadrupole was calculated for various values of q . The effective “shadow” cast by the ion stop at the entrance was also calculated using back transformations. Figure 37 compares the 100% (i.e., at all phases) overlap area as a function of q for the quadrupole of radius ro and for the stop of radius 0.71ro.When the latter is lower than the former there will be transmission provided that the source “effective radius” is large enough to fill the available acceptance. With a large source a multistructured peak is possible (and has been observed). However, a source of low emittance will give a single peak of narrow width. The calculation was carried out for ions spending 40 cycles in the full field and two cycles in the entrance fringing field. The peaks on the curve illustrating the overlap area for the shadow of the stop are caused by the special imaging properties of the quadrupole field (see Section X). Of course, in practice, taking account of all the available acceptance and real ion sources, the predicted peak structure would be considerably smoothed out. Experimentally, the significance of the size of the source emittance and the size of the ion stop has been confirmed. Figure 38 shows some experimental data taken using a 15-cm long quadrupole coupled to a conventional ion source. With a constant axial ion energy of 5 eV, the half-height resolution increases approximately according to n4 until it reaches some limiting value for each mass. The peak shapes are slightly asymmetric with tails on the low-mass side but this is minimized by appropriate source design. Ions formed by decomposition of parents traveling down the quadrupole tend to be broadened at the base. The high-mass characteristics and the limits to resolution are still under investigation.

X. IMAGING PROPERTIES Quadrupole fields have special imaging properties. The exact imaging has a precise dependence on the ( a , q ) value for a given scan line and so potentially provides the possibility of constructing high-resolution focusing instruments. The matrix for transformation through one cycle of the field was given in Eq. ( 5 ) . For n cycles of the field, the transformation is

M”=

) + A sin(mp) [c o s ( m p sin( mp) -

B sin(mp) cos(mp) - A sin(mp)

1

If p = p / n , where p is an odd integer, then an inverted image is found after n cycles for all initial phases. If p is an even integer, an upright image is formed.

206

P. H. DAWSON

The first suggestion (Lever, 1966) was to use simultaneous imaging in x and y directions in a focusing monopole. Such an instrument has been

built (Fock and Whitbourn, 1978) but the hoped-for high resolution was not achieved. Fringing fields present some problems for focusing quadrupoles but some novel geometries have been proposed (Carrico, 1976) to avoid these. There has also been a suggestion to inject ions tranversely into a quadrupole structure (Dawson, 1973), but obtaining a sufficiently large undistorted field would pose difficulties. One experimental realization of the use of the focusing properties was in a simultaneous mass and energy selector (presumably of low resolution) as part of an ion-molecule collision system (Teloy and Gerlich, 1974). The device has a series of offset apertures. Only ions of the chosen mass and energy have both the appropriate q value and the exact number of cycles between the apertures to be focused on the apertures and transmitted.

XI. CONCLUSIONS The emphasis in this review has been placed on the utilization of modern ion optical design techniques in quadrupole mass spectrometry in the belief that the increasing demands on performance posed by specialized biological, medical, and environmental applications are only likely to be met by a systematic diagnosis of present limitations rather than by a mere continuance of the empirical search for better instruments. Recent detailed measurements of instrument acceptance give considerable confidence in the usefulness of the theoretical approaches outlined. Better modeling of the fringing-field region would be helpful, but currently the greatest need is for more direct experimental measurements of ion acceptance, particularly when the fringing fields are modified in various ways. In principle, these could be combined with measurement of the acceptance at different field phases. Overall measurements of source-plusanalyzer performance are often of limited diagnostic -ialue. There is also a great need to better characterize the limitations to quadrupole performance imposed by imperfect geometry. This necessitates more study of field errors and a possible way of comparing these has been suggested. Peak shape problems, which arise quite often as performance is pushed to high levels, can only be usefully discussed if they are specified in terms of the stability diagram (e.g., plotting peak dips at different resolutions on the a,q diagram) and the number of cycles the ions spend in the RF field. Finally, a number of unconventional ways of using quadrupole fields are under investigation and the combination of detailed experimental

QUADRUPOLE MASS FILTERS

207

measurements with ion optical calculations presents us with a very useful diagnostic capability. The ion optical techniques described in this chapter are simple, easy to use, and readily accessible to anyone interested in advances in quadrupole mass spectrometer performance. ACKNOWLEDGMENTS The author thanks Prof. J. B. French and the graduate students at the Institute of Aerospace Studies of the University of Toronto for the opportunity to try out much of this material in a series of lectures. He is grateful to Dennis Hailer for help with some of the computations of the data base for the mass filter.

REFERENCES Austin, W. E., Holme, A. E., and Leck, J. H. (1976). In “Quadrupole Mass Spectrometry and Its Applications” (P. H. Dawson, ed.), p. 121. Elsevier, Amsterdam. Bani, M., and Septier, A. (1974). Rev. Phys. Appl. 9, 525. Birkinshaw, K., Hirst, D. M., and Jarrold, M. F. (1978). J. Phys. E 11, 1037. Bonner, R. F., Hamilton, G. F., and March, R. E. (1979). Int. J. Mass Spectrum. Ion Phys. 30, 365. Brinkmann, U. (1972). I n / . J. Mass Spectrum. Ion Phys. 22, I . Brubaker, W. M. (1961). Instrum. Meas.: C h e m . Anal., Electr. Quant., Nuclear. Process Control, Proc. Int. Instrum. Meas. Cot$> Sth, 1960. Brubaker, W. M. (1968). A d v . Muss Spectrum. 4, 293. Brubaker, W. M. (1970). NASA Tech. Rep. NASW 1298. Carrico, J. P. (1976). In ”Quadrupole Mass Spectrometry and its Applications” (P. H. Dawson, ed.), p. 225. Elsevier, Amsterdam. Dawson, P. H.’(1971).J. V u c . Sci. Technol. 8, 263. Dawson, P. H. (1972). J. Viic. Sci. Technol. 9, 487. Dawson, P. H. (1973). I t i t . J. Mass Spectrom. Ion Phys. 12, 53. Dawson, P. H. (1974a). I n t . J . Mus.s Spectrum. I o n Phys. 14, 317. Dawson, P. H. (1974b). J. V a r . Sci. Technol. 11, 1151. Dawson, P. H. (197%). I n / . J. Muss Spectrom. I o n Phvs. 17, 423. Dawson, P. H. (1975b). Int. J. Mass Spectrum. Ion Phys. 17, 447. Dawson, P. H. (1976a). I n “Quadrupole Mass Spectrometry and Its Applications” (P. H. Dawson, ed.), p. 9. Elsevier, Amsterdam. Dawson, P. H. (1976b). I n t . J. Mass Spectrom. Ion Phys. 21, 317. Dawson, P. H. (1977). I t i t . J. Muss Spectrom. Ion Phys. 25, 375, Dawson, P. H.(1980a). In “Applied Charged Particle Optics,” Suppl. 13B (A. Septier, ed.). Academic Press, New York. Dawson, P. H. (1980b). To be published. Dawson, P. H., and Meunier, M. (1979). In!. J. Muss Spectrum. Ion Phys. 29, 269. Dawson, P. H., and Redhead, P. A. (1977). Rev. Sci. Instrum. 48, 159. Dawson, P. H., and Whetten, N . R. (1969a). I n / . J. Mass Spectrom. Ion Phys. 2, 45. Dawson, P. H . , and Whetten, N. R. (1969b). Int. J. Mass Spectrom. /on Phys. 3, 1. Dawson, P. H., Meunier, M., and Tam, W.-C. (1980). Adv. Mass Specfrom. 8.

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Dayton, 1. E., Shoemaker, F. C., and Mozley, R. F. (1954). Rev. Sci. Instrum. 25, 485. Denison, D. R. (1971). J . V a c . Sci. Techno/. 8, 266. Dylla, H. F., and Jarrell, J. A. (1976). Rev. Sci. Instrum. 47, 331. Ehlert, T. C. (1971). J. Phys. E 3, 237. Fischer, E. (1959). Z. Phys. 156, 26. Fite, W. L . (1976). Rev. Sci. Instrum. 47, 326. Fock, W., and Whitbourn, W. A. (1978). I n t . J . M a s s Spectrom. Ion Phys. 26, 8. Halbach, K. (1969). Nucl. Instrum. & Methods 74, 147. Hennequin, J. F., and Inglebert, R.-L. (1978). I n t . J . Mass Specrrom. Ion Phys. 26, 131. Hennequin, J. F., and Inglebert, R.-L.(1979). Rev. Phys. Appl. 14, 275. Holme, A. E. (1976). I n t . J. Mass Spectrom. Ion Phys. 22, 1. Holme, A. E., Sayyid, S., and Leck, J. H. (1978). Int. J. Muss Spectrom. Ion Phys. 26, 191. Lefaivre, D., and Marmet, P. (1974). Rev. Sci. Instrum. 45, 1134. Lever, R. F. (1966). IBM J . Res. Dev. 10, 53. Lichtenberg, A. J. (1969). “Phase Space Dynamics of Particles.” Wiley, New York. McGilvery, D. C., and Morrison, J. D. (1978). Inr. J. Mass Spectrom. fon Phys. 28,81. Paul, W., and Steinwedel, H. (1953). Z. Naturforsch., Teif A 8, 448. Paul, W., Reinhard, H. P., and von Zahn, U. (1958). 2.Phys. 152, 143. Septier, A., ed. (1967). “Focusing of Charged Particles,” Vols. 1 and 2. Academic Press, New York. Sheretov, E. P., and Kolotilin, B. I. (1975). Sov. Phys.-Tech. Phys. (Engl. Trans/.) 20, 260. Steffan, K. G. (1965). “High Energy Beam Optics.” Wiley, New York. Story, M. S. (1976a). I n “Quadrupole Mass Spectrometry and Its Applications” (P. H. Dawson, ed.), p. 287. Elsevier, Amsterdam. Story, M. S. (1976b). Quoted by Austin et a/. (1976). Teloy, E., and Gerlich, D. (1974). C h e m . Phys. 4, 417. von Busch, F., and Paul, W. (1961). Z. Phys. 164, 581. Weaver, H. E., and Mathers, G. E. (1978).I n “Dynamic Mass Spectrometry” (D, Price and J. F. J. Todd, eds.), Vol. 5, p. 41. Heyden, London. Wittmaack, K. (1977). Proc. I n t . V u r . Congr., 7th, 1977 p. 2573. Yost, R. A , , and Enke, C. G. (1978). J . A m . C h e m . SOC. 100, 2274.

ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS, VOL.

53

Spread Spectrum Communication Systems P. W. BAIER

AND

M. PANDIT

Universiiai Kaiserslautern Fachbereich Elekiroiechnik Kaisersluuiern. Wesi Germany

1. Introduction.. ........................................................... 11. Basic Spread Spectrum Techniques . . .,. . . . . . . . . . . . . . . . . . . . A. Working Principle of Transmitter and Receiver. ..........................

...................

A. Generation of the Spreading Function g ( t ) . .

B. Spreading Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Message Modulation ........................

.....................

V. Limits of Spread Spectrum Techniques.. ................................... A. Limits on the Processing Gain. ..........

C . Limits on the Synchronizability VI. Examplas of Realized Spread Spect

...........................................

209 214 214 217 226 226 233 240 249 254 256 256 258 260 263 266

I. INTRODUCTION The basic structure of a wireless communication system is shown in Fig. 1. The message signal so&), which may be analog or digital, is modulated onto a carrier signal in the transmitter to obtain the modulated signal st(t). The signal st(t) is radiated by the transmitting antenna. Ideally, the antenna of the receiver receives the signal s,(t), which, apart from a delay and an attenuation, is identical with s t ( t ) . The signal s,(t) is demodulated in the receiver to obtain the signal sm(t),which is ideally a true replica of the message signal sot(t). The practical situation differs from the ideal one, above all because the received signal consists not only of the desired signal s,(t), but also of an unwanted interfering signal n ( t ) , which cannot be filtered away from s&). The interfering signal n ( t ) can arise from various sources, e.g., from atmo209 Copyright 0 1980 by Academic Press, Inc. All rights of reproduction in any farm reserved. ISBN 0-12-014653-3

210

P. W. BAIER AND M. PANDIT

FIG.1. Generic wireless communication system.

spheric noise or from other transmitters. The noise of the front-end amplifier of the receiver can also be looked upon as an interfering signal at the receiver input. The input interfering signal n(t) gives rise to an interfering signal no(t) at the receiver output. In order to judge the goodness of a communication system, the signals s,(t) and se(t) and the interfering signals n(t) and no(t)can be characterized Nin,and Nout,respectively. On the basis of these by their powers Pin,Pout, powers, the signal-to-noise ratio (SNR) y,n at the input of the receiver and the SNR youtat the output of the receiver are defined by

Youout = Pout/Nout

(2)

The output SNR youtof any receiver is a function of the input SNR yin, I.e., yout

= flyin)

(3)

holds. One of the objectives pursued in communication engineering is to suppress interfering signals as much as possible, i.e., to make youtas large as possible. There are two principally different ways of achieving this aim. First, one can make youtlarge by making yinlarge. In practice this is usually achieved by employing high-power transmitters and directional antennas. Such antennas constructed with advantage in the form of electronically steerable antenna arrays can be used to concentrate the radiated power in the direction of the receiver and to avoid interfering signals at the receiver. Second, one can achieve a large youtby employing special signaling techniques that inherently suppress interfering signals. By doing this, one is altering the functionfin Eq. (3) suitably. As a rule, a suitable combination of both the techniques yields the practical optimum. Signaling techniques that offer interference suppression owe their efficacy to the fact that, by utilizing a transmission bandwidth BRFthat is considerably larger than the bandwidth Bb of the message signal sot(t), redun-

SPREAD SPECTRUM COMMUNICATION SYSTEMS

21 1

dance is produced, and at the receiver this redundance can be exploited for interference suppression. A classical method of information transmission applicable for analog signals that employs such a bandspreading technique and thereby offers interference suppression is frequency modulation (FM). Various methods of coded transmission of digital signals that have been developed in the last three decades can also be looked upon today as classical bandspreading methods. Systems employing classical bandspreading techniques are dealt with in standard textbooks, e.g., Lucky et al. (1968) and Stein and Jones (1967). A common feature of the classical bandspreading methods mentioned above is that they make use of the available bandwidth BRFvery effectively. A 100% increase in B R F usually results in an increase of more than 3 dB in interference suppression, provided that the input SNR yinis above a certain minimum level. For FM systems this minimum level has a value of about 10 (see, e.g., Stein and Jones, 1967). Below yin= 10 the interference suppression decreases abruptly due to the FM threshold effect. Digital communication systems employing coding for bandspreading do not exhibit a distinct threshold effect. However, in cases where yin< 1, effective communication can be realized only by employing a large ensemble of long code words. This involves practical problems. Therefore, one can roughly say that interference suppression based on classical > 1 holds for bandspreading methods is feasible only if the condition y,Yin the receiver input SNR. Even though communication systems are often operated in environments in which yinis larger than the minimum level quoted above, there are situations in which this is not the case. For example, such a situation may occur if the interfering signal n ( t ) is not caused by a more or less casual source, but by a deliberate jammer who aims to disrupt the communication. This type of interference has to be taken into account especially when designing communication systems for military applications. Figure 2 illustrates a typical configuration of a communication system and a jammer. A ground station controls the movement of a missile by means of a radio command signal s,(t). A jammer located in the operational area of the missile sends an interfering signal n(t) whose power is, say, equal to the power of the transmitted signal st(t). Assuming that the transmitter, the jammer, and the missile have omnidirectional antennas, the SNR at the receiver input of the missile is as low as yin= 0.02. A conventional communication system, such as an FM system, would totally fail under these conditions. Fortunately, it is possible to achieve a satisfactory quality of communication even in such situations by employing so-called spread spectrum techniques.

An important feature common to conventional bandspreading com-

212

P. W. BAIER AND M. PANDIT y,,=002

0 MISSILE

v

70 k m

STATION

0 JAMMER

FIG.2. SNR 7," at the receiver input in a typical situation ofjammed communication.

munication systems as well as to spread spectrum communication systems is that the bandwidth B R F of the transmitted signal is considerably larger than the message bandwidth B,,. The difference between the two classes of systems, which is of interest to the user, lies in the minimum SNR -yin tolerable and in the effectiveness with which the available bandwidth B R F is exploited for interference suppression. In contrast to conventional bandspreading techniques, spread spectrum communication systems can function satisfactorily even if the input interfering power Nin is much larger than the input signal power Pin;on the other hand, the spectral effectiveness, i.e., the gain in SNR obtained by a certain bandwidth luxury, is smaller in the case of spread spectrum communication systems than in the case of conventional bandspreading systems. Because of the smaller spectral effectiveness and the conceptionally smaller values of yin, spread spectrum communication systems employ transmission bandwidths that may be many times the transmission bandwidth of conventional bandspreading communication systems. Spread spectrum techniques supply a method to cope with large interfering power Nin at the receiver input. From this property, it follows immediately that spread spectrum techniques are also advantageous if several communication links are to operate in the same area in a common frequency band and are thus delivering undesired signals of large power to one another. In the case of such a multiple-access operation, the undesired signals can be subjected to interference suppression and practically eliminated. In addition to interference suppression and multiple-access capability, spread spectrum techniques have further favorable features that have been summarized in Table I. These features are not only important in military applications, but may also be interesting in a nonmilitary context. However, it should also be mentioned that the capabilities summarized in Table I are conceptional and may sometimes be hard to realize in practice. The field of spread spectrum communication systems is relatively new, although one of the first spread spectrum systems cited in the litera-

SPREAD SPECTRUM COMMUNICATION SYSTEMS

213

ture (Dixon, 1976b)-the noise modulation and correlation system developed at MIT-dates back to the late 1940s. In this system, a large transmission bandwidth is obtained by rapid phase reversals of the signal to be transmitted. A spread spectrum communication system using a different process to spread the bandwidth, viz., the process of making the carrier frequency hop from one value to another in a prescribed manner, is reported to have been described by K. Gilmore (Dixon, 1976b). The development of high-speed transistors, integrated circuits, and surface acoustic-wave and charge-coupled devices has contributed to the implementation of spread spectrum communication systems with everincreasing capabilities and degrees of sophistication. An indicator of the capabilities of spread spectrum communication systems is the frequency of phase reversals or the hopping rate of the carrier frequency as the case may be. Over the years between the late 1950s to the present time, these parameters have experienced a spectacular rise, in the one case from a value of some hundreds of kilohertz to hundreds of megahertz and in the other from a few kilohertz to several hundred kilohertz. Furthermore, whereas an SNR gain of 20 d B at data rates of 4 kbits/sec was representative of the late 1950s, the corresponding figures for 1979 would be 30 dB and 5 Mbits/sec. Even though the subject of spread spectrum techniques is a relatively new area in communication engineering, there are numerous possibilities to study and work through the various aspects of this subject. A large number of papers, special issues of journals, books, manufacturers’ guides, course manuscripts, and patents are available. The authors’ choice of four of these publications would be A G A R D (19731, Nuval Symposium (1973), Dixon (1976a), and f E E E (1977). In view of the extensive literature the present review has the following goals: (1) Unified exposition of the fundamental principles of spread spectrum techniques. By this means, the reader is to be given an economical possibility to work through the whole area and prepare himself for the detailed literature.

TABLE I CAPABILITIES O F SPREADSPECTRUM C O M M U N I C A T SYSTEMS ION Interference suppression at low input SNR Multiple access and selective calling Ranging Suppression of indirect signals Message privacy

P. W. BAIER AND M. PANDIT

214

(2) Critical analysis of system capabilities, which can be achieved in practice by using spread spectrum techniques. This review should aid the reader to analyze his own problem of information transmission and consider whether he should resort to spread spectrum techniques. From these goals it follows that the present review is not directed to specialists in spread spectrum techniques, but to those who want to gain a survey of the principles and the state of the art of these techniques.

11. BASIC SPREAD SPECTRUM TECHNIQUES A . Working Principle of Transmitter and Receiver One may ask why conventional bandspreading communication systems need a SNR yinlarger than the lower limit of about 1 already mentioned. A plausible answer for this is that the form of the radiated broad-band signal st(t)is determined solely by the message signal sot(t).In the frequency modulator or in the channel encoder with subsequent carrier modulator, the analog or the digital signal s,&) acts upon the carrier and transforms it into the broad band signal s t ( t ) . As the transmitted message signal sot(t) is not known at the receiver, little apriori knowledge of the received broad-band signal s,(t) is available. Therefore, it is difficult to separate the desired signal sr(t)from an interfering signal n(t), if the powers of these signals are of the same order of magnitude, i.e., if yin 5 1 holds. The key to the spread spectrum principle lies in changing this situation. The a priori knowledge about s,(t) at the receiver is increased by separating the message modulation from the bandspreading modulation process. Then a function entirely independent of the message signal sot(t)

Fl I""'.:/

MESSAGE 5ot(t) SOURCE

-

MESSAGE

MODULATOR-

Y SJt) A,

SPREADING I

MODULATOR

GENERATOR

FIG.3. Generic spread spectrum transmitter.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

215

MESSAGE

SPREAD1NG

SINK

MODULATOR

FUNCTl ON

FIG.4. Generic spread spectrum receiver.

can be used to control the band-spreading process. This spreading function, denoted by g ( t ) , can be chosen in concurrence with the receiver. The receiver thus has knowledge of g ( t ) and, at least theoretically, the means to simply eliminate the bandspreading performed at the transmitter, even at low values of the receiver input SNR Y , ~ As . a consequence, the desired signal can be separated even from large interfering signals. The generic spread spectrum transmitter is shown in Fig. 3. The message signal sot(t) is first modulated onto a carrier A cos(2.rfOt) by means of a narrow-band conventional modulation process. Thereby, a signal s ; ( t ) is obtained with a bandwidth BfiFthat is of the same order of magnitude as the bandwidth Bb of the message signal sot(t). Subsequently, the spread spectrum modulation is performed by means of a spreading function generator and a spreading modulator. Spread spectrum modulation yields the signal st(t) to be transmitted, which has a bandwidth BRF%- Bb. The generic spread spectrum receiver is shown in Fig. 4. With the help of the known spreading function g(t)-or to be exact g(r - At), where At is the delay between transmitter and receiver-the spreading modulation is eliminated in the despreading modulator. Thereby the signal s,(t) with the bandwidth B , is transformed into the signal s:(t) with the bandwidth BAF. After spectral compression, message demodulation is performed. The bandpass following the despreading modulator is dimensioned in such a way that the spectrally compressed signal s#) just passes through it without experiencing any distortion, that is, the bandpass bandwidth is usually BAF. Of fundamental importance for the working of the receiver is the proper timing of g ( t ) . This has to be performed by a synchronizing circuit that uses only the interference-corrupted received signal as a reference. The inputs of the spreading function synchronizer shown in Fig. 4 are the received signal s,(t) + n(t) and the spreading function g ( t ) gen-

216

P. W. BAIER AND M. PANDIT

erated at the receiver. The output of the synchronizer controls the timing of the spreading function g(r). For the present, it is assumed that all problems concerning generation and synchronization of g ( t ) in the receiver have been solved. For achieving spread spectrum modulation, it is possible to choose the amplitude, frequency, or phase of the message-modulated signal ~ ; ( t= ) a(r) cos[2rfot

+ &)I

(4)

as the quantity to be influenced in the spreading modulator. The terms a(?) and V ( r ) in Eq. (4) represent the message modulation. Correspondingly, the expressions s t ( t ) = g ( t ) a ( t )cos[2rfor

+

&)I

(5)

s,(O = a(r>cos[2~f~or +

kp,g(t) +

st(r) = a(r) cos[2~for+

kFM

I

&)I

g ( t ) dr

( 6)

+

(7)

are obtained for the spread spectrum signal. The spectrum of the signal st(r) depends on the message-induced terms a(r) and cp(t), on the spreading function g(r), and on the modulation constants kFM and kpM,respectively. The bandwidth B,, of the signal st(r) increases with increasing bandwidth of the spreading function g(t) and increasing values of the constants kFM

and kpM, respectively. As described in detail later, in one scheme-the so-called frequency-hopping scheme-a relatively narrow-band spreading function g(r) is used and spectrum spreading achieved by making the constant kFM large, and in a second one-the so-called phase-hopping scheme-a function g(r) having a large bandwidth is used in conjunction with a moderately large modulation constant kpM. In order to spectrally compress the received signal s,(t) in the despreading modulator, it is necessary only to perform the process inverse to the spread spectrum modulation process given by Eqs. ( 3 4 7 ) . Besides the methods of spectrum spreading represented by Eqs. ( 3 4 7 1 , sometimes the time-hopping process is also referred to as a method of spectrum spreading (see, e.g., Dixon, 1976a). However, this is actually a pulse modulation method in which the transmitter and receiver are active for short intervals of time distributed pseudorandomly. Thus, time hopping is actually not a spread spectrum method in the sense of Figs. 3 and 4. However, the time-hopping principle is often used in conjunction with spread spectrum modulation based on frequency hopping (see, e.g., Smith, 1978).

SPREAD SPECTRUM COMMUNICATION SYSTEMS

217

B. Firndamental System Cupabilities The spreading and subsequent despreading processes applied to the message-modulated signal yield ultimately the signal s i f t ) , which again is only modulated by the message. Thus, the spread spectrum process has on the whole no effect on the transmitted signal. The situation is different in the case of a received interfering signal n(r). The signal n ( t ) is not subjected to the entire spread spectrum process, but only to the despreading process. Thereby, a modified interfering signal n’(t) is obtained at the input of the bandpass in Fig. 4.The corresponding interfering signal at the output of the bandpass is termed n * ( r ) . With respect to the interfering signal, the system in Fig. 5a is equivalent to the system in Fig. 4. In Fig. 5a, the receiver has different inputs for the desired signal and for the interfering signal. In this system the message-modulated signal is transmitted without being spread-spectrum processed and the interfering signal n(r) at the input of the message demodulator is obtained by subjecting the received interfering signal n(t) to despreading modulation and subsequent filtering. In a further step, the equivalent system in Fig. 5a can be replaced by the equivalent system in Fig. 5b. This system consists of a conventional transmitter and receiver for the desired signal, and a modified transmitter for the interfering signal. Figure 5b reveals that one can look upon a spread spectrum communication system as a system in which the desired signal is unaltered, but at the same time the interfering signal is forced to undergo an amplitude, frequency, o r phase modulation and subsequent filtering. The properties and applications of spread spectrum communication systems described in the next sections are partly based on this principle.

I . Interference Suppression In the spreading modulator the amplitude, frequency, o r phase of the message-modulated signal s;(t) is subjected to rapid and/or large changes. The inverse process is performed in the despreading modulator by effecting corresponding amplitude, frequency, or phase fluctuations. Therefore, also the despreading modulation can be looked upon as a broad-band modulation, which is, however, only effective for signals other than s&). By this modulation, narrow-band signals are spread over a bandwidth that is approximately equal to BRF. The idea of interference suppression in spread spectrum communication systems can be elucidated with reference to Fig. 5b: The interfering signal n(r) is spectrally spread in the despreading modulator and then strongly reduced in power by filtering it with the aid of a narrowband filter with bandwidth Bk,-this filter is therefore called interference

218

P. W. BAIER AND M . PANDIT

\I qt) 1r

MESSAGE

MESSAGE

--* SOURCE

\

SPREAD1NG FUNCTION GENERATTOR

dt)

4

$t)

c * -& u

n‘(t) +

DESPREADING

’

Tr

-

MODULATOR I

t

c

CARRIER

3

r

MESSAGE MESSAGE DE4

0 J SPREADING

GENERATOR

A h sJt)

MESSAGE SOURCE

+

MODULATOR

SINK

MESSAGE

MODULATOR L

CARR I ER SOURCE (bl

FIG. 5 . Equivalent configurations of a spread spectrum communication system: (a) Modification of the received interfering signal; (b) modification of the interfering transmitter.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

219

suppression bandpass. The effectiveness of this idea depends on the character of the interfering signal n(t).One decisive factor is the bandwidth BN of n(t). Depending on their bandwidth BN,interfering signals can be classified as:

(a) Narrow-band signals, (b) broad-band signals, (c) very broad-band signals,

BN BiF; BN BRF; BN + BRF.

The power density spectra of the three classes of interfering signals are represented schematically in Fig. 6. Also shown in Fig. 6 are the power density spectra of the interfering signals n’(r), which appear at the output of the despreading modulator. The bandwidth of n ’ ( t ) is denoted by BA. Narrow-band interfering signals are spread to a bandwidth of BE, = BRFin the despreading modulator. The interfering power N;, at the output of the interference suppression bandpass is thus smaller than the ’

SIGNAL n ( t )

fo

SIGNAL n ’ ( t )

f

FIG.6. Power density spectra (schematic) of narrow-band (a), broad-band (b), and very broad-band (c) interfering signals.

220

P. W . BAIER AND M. PANDIT

interfering power Nin at the bandpass input by a factor of the order of B&/BRF. Thus, for narrow-band interference, the SNR at the message demodulator input is $n

=

yin(BA/B&f

xn(BR,/Bi,),

BA

BRF

( 8)

The ratio B R F / B k F is often termed processing gain. Broad-band interfering signals are also spectrally spread by the despreading modulator over a bandwidth El; that is somewhat larger than the bandwidth BE, in the case of narrow-band interference, as the original bandwidth BN is larger. The SNR at the input of the message demodulator is once again approximately given by Eq. (8) with a somewhat larger gain in the SNR on account of the larger B;. If the interfering signal is a very broad band signal, the despreading modulator does not bring about any appreciable additional spectral spreading. Thus, B; is approximately equal to B,. The SNR at the message demodulator input is then approximately 3/:n

=

yin(BA/BkF)

Yin(BN/BkF)?

BE;

BN

(9)

From Eqs. (8) and (9) follows that the larger the bandwidth of the interfering signal and the smaller the bandwidth of the message-modulated signal, the stronger is the interference suppression. On the other hand, if the bandwidth of the interfering signal is a priori very large, the spread spectrum process yields no gain in SNR. In such cases a communication system without spectrum spreading according to Fig. 7 could be used instead of a spread spectrum system, and Eq. (9) would still hold. Thus, spread spectrum techniques are no measure against very broad-band interfering signals, for instance, against interfering thermal noise. Equation (8) also reveals that the gain in SNR increases linearly with the transmission bandwidth BRFutilized. The spectral effectiveness of spread spectrum communication systems is therefore smaller than that of classical interference suppression techniques (FM o r channel encoding). On the other hand, spread spectrum techniques make it theoretically possible to cope with arbitrarily low values of the SNR provided a sufficiently large transmission bandwidth BR, is available and the interfering signal does not have a very large bandwidth. It should be mentioned that the jam resistance of spread spectrum communication systems can be further increased by equipping them with so-called null steering antennas. By using such antennas, the interfering signal can be adaptively nullified (see, e.g., Compton, 1972). A condition for the validity of Eqs. (8) and (9) is that the power of the interfering signal n’(r) is evenly distributed over the bandwidth B;. If this is not fulfilled, an estimate of the degree of interference suppression can

22 1

SPREAD SPECTRUM COMMUNICATION SYSTEMS

MESSAGE SOURCE

--+

MESSAGE MODULATOR

-

1 ,

MODULATOR

SINK

FIG.7. Suppression of a very broad-band interfering signal without employing spread spectrum processing.

be obtained only by complicated calculations (see, e.g., Petit, 1977). However, the conclusions drawn from Eqs. (8) and (9) still hold. Hitherto, the conditions under which interfering signals are optimally suppressed have been considered. One can also reverse the question and ask oneself which classes of interfering signals are least suppressed by the spread spectrum process. From the point of view of the interferer, the optimum interfering signal is obtained by modulating a narrow-band signal with an exact replica of the spreading function g ( t ) , where g ( t ) is the spreading function contained in the received signal s,(t). Such an interfering signal is spectrally compressed perfectly by the despreading modulator, and can thus pass with its total power N,, through the interference suppression bandpass. 2. Multiple Access and Selective Culling

Often a communication system does not consist of a single transmitter and a single receiver. A simple extension is the use of a transmitter and a receiver at each of the stations, resulting in a two-way communication link. Multiuser systems consist of more than two transmitters and receivers. In such cases, it may be required to provide for selective calling and multiple-access facilities. In the case of selective calling (see Fig. 8) a transmitter T is able to selectively call any one of various receivers R, over a common channel, for instance, a communication satellite. In a multiple-access system, several communication links, each consisting of a transmitter T, and a receiver R,, operate over one and the same transmission channel as shown

222

P. W. BAIER AND M. PANDIT

FIG.8. Configuration of a communication system with selective calling capability.

in Fig. 9. It is thereby implied that the total available frequency band of the channel is restricted. The tasks described above may be accomplished classically by using frequency division multiplexing or time division multiplexing techniques. A different approach is the use of spread spectrum transmitters and receivers. If the transmitter T, is to selectively address the receiver R,, the two stations T, and R,, are allocated one and the same spreading function g ( t ) = g,(t). Other communicators active at the same time must make use of different spreading functions. In this way, a form of code division multiplexing is obtained. By an appropriate choice of the spreading functions, it can be achieved that every active link disturbs the other active links only to the extent of a signal that has been subjected to the interference suppression process. By interchanging the spreading functions suitably, the assignment of the receivers to the transmitters can be flexibly changed.

FIG.9. Configuration of a communication system with multiple-access capability.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

223

There are two essential advantages of code division multiplexing based on spread spectrum techniques: A global timing of all transmitters and receivers is, in principle, unnecessary, and, in the case of a continuous increase in the number of active links, the system as a whole approaches saturation gradually and not abruptly, i.e., the degradation is “graceful” (Cooper et al., 1979). Spread spectrum multiple-access communications have also been discussed by Mohanty (1977), Yao (1977), Haber (1978), and Goodman et al. (1980). 3 . Ranging

In certain applications, the transmitter and receiver of a communication system move relative to each other and it is required to provide means for measuring the distance between them as well as their relative velocity and acceleration. The classical electrical engineering methods of measuring these quantities are offered by radar techniques. Under certain circumstances, spread spectrum communication systems can take over this task of ranging in addition to their primary task of message communication. Let the spread spectrum transmitter and spread spectrum receiver in Fig. 10 be in synchronism. Then the spreading function generated in the receiver lags with respect to the spreading function generated in the transmitter by the delay Ar. Let it be assumed that a highly stable time reference is available to the receiver and that the clock frequency of the spreading function generator at the transmitter is also very stable. By means of an initial synchronization of the time reference with the transmitted spreading function g(t), an exact knowledge of the instantaneous value of the spreading function g ( t ) contained in the transmitted signal s t ( t ) is made available to the receiver. Furthermore, since in a synchronized spread spectrum receiver, the spreading function g(t - At) con-

SPREADING FU NCTlON

SPREAD”G FUNCTION GENERATOR

DISTANCE

-*

MODULE

+

EXACT TIME

REFERENCE

224

P. W. BAIER AND M. PANDIT

tained in the received signal s,(t) is identical with the spreading function generated at the receiver at every instant, the spreading function g(t - Ar) is also known to the receiver. Thus, the receiver can determine the delay Af between the generation of the spreading function at the transmitter and its arrival at the receiver, and subsequently the distance between the two stations. If periodic spreading functions are employed, it has to be ensured that the period T is at least as long as the maximum expected value At,,,= of the delay between transmitter and receiver in order to eliminate ambiguity of the measured distance. The ranging principle described above functions only if the frequency stability of the spreading function generators at the transmitter and receiver is high, if exact initial timing is possible, and if a precise time reference is available at the receiver. Less stringent conditions are imposed on the frequency stability and timing precision if a two-way communication link is employed. Figure 11 shows such a system. The signal of a spread spectrum transmitter at station I is received by a spread spectrum receiver at station 11; the signal of a spread spectrum transmitter at station I1 is received by a spread spectrum receiver at station I. At station I1 only one spreading function generator is provided for receiver and transmitter. The signal transmitted from station I contains the spreading function g ( r ) ; the signal received at station I1 contains the spreading function g(t - Af). As, in the case of synchronism, the spreading function generated at station 11 is also g(t - At), the spreading function contained in the signal received at station I is g(t - 2 A t ) . A comparison of the spreading func-

SPREADING FUNCTION

+S

GENERATOR d

SPREAD ~

~

SPREAD ~

$

~

M

SPECTRUM

MITTER

RECEIVER

-

g(t-At)

MODULE

4

-

SPREADING

DISTANCE

*

g(t-2at)

v-3- \' Yr

SPREADING

SPREAD

FUNCTION 4 SPECTRUM GENERATOR

RECEIVER

-

AI

FUNCTION

GENERATOR

T

~

SPREAD SPEC T RUM TRANSMITTER

SPREAD SPECTRUM COMMUNICATION SYSTEMS

225

tions g ( t ) and g(t - 2 At) that can be performed at station I yields the delay Ar and consequently the distance between the two stations.

4. Suppression of Indirect Signals

In radio communication, the received signal consists sometimes not only of the desired direct signal, but also of indirect signals that are reflected versions of the transmitted signal. The reflections can be caused, e.g., by topographical formations or atmospheric layers. The indirect signals are without effect if their power is much smaller than the power of the direct signal. If, on the other hand, their power is of the same order of magnitude as that of the direct signal, considerable transmission disturbances will result. Let the delay of an indirect signal with respect to the direct signal be denoted by AT. If AT is small and is of the order of the period l/fo of the carrier, the indirect signal does not cause signal distortions, but only fluctuations of the total received power. If AT approaches or exceeds l/BRF, where B , denotes the transmission bandwidth, frequency-selective fading occurs. In the case of communication systems using conventional modulation, frequency-selective fading impairs the quality of the received message signal unless equalizing measures are taken. In contrast to this, spread spectrum communication systems have an inherent capability to suppress the detrimental effects of frequency-selective fading. If the receiver is synchronized to the direct signal and the delay time AT is sufficiently large, the indirect signals are treated as interfering signals and thus subjected to interference suppression (see, e.g., Baier and Grunberger, 1975). The minimum value of A7 for which this effect occurs depends on the spread spectrum modulation employed. The described mechanism of the suppression of indirect signals is, in principle, common to phase- and frequency-hopping spread spectrum communication systems. However, in the case of the latter the required minimum value of AT is larger than the actual time delays encountered in practical situations. On the other hand, frequency-hopping spread spectrum communication systems possess another characteristic due to which the effects of frequency-selective fading are reduced: The message is transmitted not over one but over several frequencies. An example of recent investigations dealing with the performance of spread spectrum communication systems possessing resistance against frequency-selective fading is the paper by Goodman et ml. (1980). If the receiver is not synchronized, the indirect signals can effectively impair the operation of initial synchronization. The influence of multipath propagation on the synchronization performance of the receiver has been considered, e.g., by Griinberger (1976).

P. W. BAIER AND M. PANDIT

226

5 . Message Privacy Messages transmitted in conventional radio transmission systems have practically no message privacy, i.e., security against eavesdropping. The eavesdropper has only to receive a sufficient amount of the radiated power with his antenna to get at the message. If message privacy is desired in conventional communication systems, one has to resort to additional encryption measures. In contrast to this, spread spectrum communication systems have to a certain extent an inherent resistance against eavesdroppers. The evaluation of a received spread spectrum signal by an unauthorized party is possible only if the proper spreading function g ( t ) is available at his receiver. This fact leads to a principal possibility of achieving message privacy if one assumes that the interceptor is not in a position to invest in an expensive receiver. On the other hand, the spreading functions used are, without exception, deterministic functions, as otherwise even the receiver that is supposed to receive the transmitted message would be unable to reproduce the spreading function. Therefore, one has to accept that an interceptor can determine the run of the spreading function by incurring sufficient ingenuity and expense, and subsequently evaluate the transmitted message. Even such a qualified interceptor has to overcome yet another hurdle. The spectral spreading of the transmitted signal s,(t) has the effect of bringing the spectral power density down to a very low value. Consequently, for the case of equal radiated power, the interceptor has much greater difficulty to discover a spread spectrum signal than a signal without spectrum spreading. OF SPREADSPECTRUM 111. IMPLEMENTATION COMMUNICATION SYSTEMS

A . Generation of the Spreading Function g ( t )

I . Requirements on the Spreading Function g ( t )

In principle, any function that transforms the narrow-band signal s ; ( t ) given by Eq. (4) into a broad-band signal st(r) given by Eqs. ( 3 4 7 ) is suitable to be used as a spreading function &). In order to achieve this bandspreading, in the case of Eq. (3,g ( t ) itself must exhibit rapid fluctuations, i.e., g ( t ) must have a large bandwidth. In the case of Eq. (7), even a narrow-band g ( t ) yields large bandspreading, if only the modulation constant kFMis made sufficiently large.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

227

The freedom one has in principle in choosing the spreading function g ( t ) narrows down if the practical implementation of spread spectrum communication systems and the reasons for their application are considered. First, g(t) must be a deterministic function, as otherwise it would be impossible to generate identical replicas of g ( t ) at the transmitter and receiver. Second, in order to prevent the spreading function generators from becoming too complicated, usually a periodic function with period T is employed as the spreading function g(t). Furthermore, the spreading function g ( t ) should possess a number of desirable properties, which are listed on the left-hand side of Fig. 12. Figure 12 also shows how these properties of g(t) are related to the desired properties of the spread spectrum communication system listed on the right-hand side of the figure. In what follows, Fig. 12 is discussed. An important requirement on the spreading function is the requirement of good autocorrelation behavior. This requirement means that g(t) and its time-displaced version g(t - T ) differ from each other significantly in an appropriate sense. In some cases, good autocorrelation behavior is given if the autocorrelation function

RANGING

GOOD AUTOCORRELATION BEHAVIOR SUPPRESSION OF INDIRECT SIGNALS MAKES POWER DENSITY SPECTRUN OF SPREAD SPECTRUM SIGNAL UN I FORM MESSAGE PRIVACY BELONGS TO A CODE FAMILY WITH GOOD CROSS-CORRELATION BEHAVIOR INTERFERENCE SUPPRESSION H A S APPROPRIATE PERIOD T SYNCHRONIZATION IS NOT EASY TO IMITATE

MULTIPLE-ACCESS CAPABILITY ( 0 )

(b)

FIG. 12. Requirements on the spreading function and related system properties: (a) Desired properties of g(r); (b) related system properties.

228

P. W. BAIER AND M. PANDIT

has a sharp peak at T = 0 mod T and is approximately zero elsewhere. By good autocorrelation behavior it is ensured that spectral compression of the received signal s,(t) occurs only if the spreading function contained in s,(r) and the local spreading function generated at the receiver have no time displacement with respect to each other. Good autocorrelation behavior makes it possible to discriminate sharply between the states “synchronism” and “no synchronism” of the receiver. Therefore, good autocorrelation behavior is especially important if the spread spectrum communication system is employed for ranging purposes or is expected to suppress indirect signals caused by multipath propagation. Furthermore, good autocorrelation properties are favorable with respect to receiver synchronization. Another requirement on the spreading function is that it should make the spectrum of the spread spectrum signals given by Eqs. (5)-(7)as uniform as possible. The power of the signals s t ( t ) and s,(t) should be distributed evenly over the available bandwidth BRF.If this is the case, there are no frequency regions that are predominantly occupied by the transmitted signal st(r). Therefore, an intentional interferer cannot increase his jamming efficiency by concentrating his power into certain regions of the transmission band. A power density spectrum that is flat over the total available bandwidth BRFimplies that the power density is low. Consequently, the presence of the signal is difficult to detect by an eavesdropper or by an interferer. If it is intended to exploit the selective calling and multiple-access capabilities of a spread spectrum communication system, one needs not just one spreading function g(t), but a family of spreading functions g,(t). The members of the family must be as dissimilar as possible to each other, so that the different communications disturb each other as little as possible. This is considered in Fig. 12 by the requirement that the spreading functions belong to a code family with good cross-correlation behavior. In certain cases, good cross-correlation behavior is ensured if the crosscorrelation functions of all pairs of spreading functions are zero. Another important point is the choice of the period T of the spreading function. Advantageous from the viewpoint of combating a jammer or an eavesdropper is the use of a spreading function g(r) with a very large period T . By doing this, the determination of the run of g ( t ) is made difficult for an unintended party. On the other hand, T must not be too large in order not to unduly complicate the initial synchronization of the receiver, which is considered in Section 111, C in more detail. If a jammer or an eavesdropper is to be prevented from making unauthorized use of the employed spreading function, it is not only important to choose the period T sufficiently large, but also to ensure that the

SPREAD SPECTRUM COMMUNICATION SYSTEMS

229

structural properties of g f t ) are such that g ( r ) is not easy to imitate. This can be achieved by employing spreading function generators with a sufficient degree of sophistication. Apart from the desired properties of g ( t ) shown in Fig. 12, g(t) can be principally an analog signal, a multilevel digital signal, or a binary signal. Of these possibilities, the first one is impractical on account of the difficulty of building two independent generators that generate identical analog signals of a rather complicated structure. Multilevel digital signals can be derived from binary signals. Binary signals themselves can be relatively easily generated. This is the reason why binary pseudonoise (PN) signals are extensively used as a basis for the spreading function g(t) (Drouilhet and Bernstein, 1969; Solomon, 1973). Such PN signals have similarity with true random binary signals, but are not really random (see, e.g., Berkowitz ef ul., 1965). Principally, a PN signal p ( t ) can be represented as W

c A d t - VTJ

p(t) = v=-m

-

dr - ( v +

1)TJ

( 1 1)

with d t ) = 1, t

2

0;

dt) =

0, t < 0

The coefficients c,, which take on the values 1 and - 1 corresponding to the binary states H and L, form a binary pseudorandom sequence with L elements per period. The quantity I/T, is the clock frequency ofp(t). The period ofp(f) is then T = LT,. If the spreading function is to be a binary signal, one can directly use the PN signal p ( t ) ;then g ( t ) = p ( t ) holds. If the spreading function is to be a multilevel signal, g(t) can be generated from the PN signal p ( t ) . For this purpose, u consecutive chips of p ( f )are looked upon as one binary u-bit

SHIFT

P N - SIGNAL

I

REGISTER

SELECTOR

SPREADING FUNCTION

1 OUT OF 2"

FIG. 13. Generation of a multilevel digital spreading function g ( t ) using a binary PN signal ~ ( 1 ) .

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P. W. BAIER AND M. PANDIT

word. By shifting the chips successively by one place, L words each of length v are obtained. Depending on the signal p ( t ) , the number of distinct words is equal to or less than 2". A one-to-one correspondence is established between the distinct v-bit words and the values taken on by the multilevel signal. The generator of a multilevel spreading function can be implemented according to the scheme shown in Fig. 13. This configuration uses a shift register and a selector. The duration of a single digital state of a binary spreading function g ( t ) will be termed chip width T,, and the period designated as T; 1/T, is the clock frequency or chip frequency of g ( t ) .

2 . m-Sequence PN-Signal Generators The so called m sequences are frequently used as sequences {c,} for PN signals p ( t ) . Often a PN signal that employs an m sequence is itself referred to as an m sequence. This nomenclature is adopted in the following sections. m Sequences can be generated easily, and yield spreading functions that in general fulfill the requirements in Fig. 12 relatively well. Shift registers with appropriate feedback connections supplemented either by mod-2 adders or by frequency dividers are used as generators of m sequences. Figure 14 shows three forms of m-sequence generators. Generators (b) and (c) can be operated at higher clock frequencies than generator (a), because in generator (a) the delays caused by the individual mod-2 adders accumulate. The theoretical and practical aspects of m-sequence generators have been exhaustively treated by various authors (see, e.g., Berkowitz et al., 1965; Golomb, 1967). The number of chips in a period, i.e., the length of an m sequence generated by a generator employing an m-stage shift register is L=2m-1

(12)

The period of the PN signal p ( t ) is then LT, = (2" - 1)T, Equation (13) shows that large periods can be achieved by using only a relatively small number m of stages. However, the length L = 2" - 1 is obtained only if the configuration of the feedback connections and/or the frequency dividers is appropriate. Various aspects of the correlation behavior, especially the autocorrelation and cross-correlation functions of sections of m sequences, have been investigated in detail (see, e.g., Gupta and Painter, 1966; Lindholm, 1968; Baier, 1976; Cartier, 1976). In keeping with the ease of generation, the algorithm according to which an m sequence is generated is simple. The structure of the m se-

SPREAD SPECTRUM COMMUNICATION SYSTEMS

23 1

CLOCK

P

I

1

CLOCK

I FIG.14. Different structures of rn sequence generators: (a) Mod-2 adders in the feedback network; (b) frequency dividers 1 : 2 between the stages; and (c) mod-2 adders between the stages.

quence used in a spread spectrum communication system can thus be deciphered by an unauthorized party with only moderate effort. Another consequence of the simplicity of the generating algorithm is that the number of possible m sequences of a given length L = 2‘“ - 1 is limited. Thus, for a ten-stage shift register, one has L = 1023, and the number of possible m sequences is as low as 60. 3. Other PN-Signul Generutors

If exclusively m sequences are used as PN signals, considerable limitations have to be tolerated with regard to the achievable decipherability resistance, correlation properties, and code family size. Therefore, it is necessary to envisage alternative classes of PN signals that do not have these limitations, but can be generated as easily as m sequences. Some of the possibilities of generating such PN signals are considered now. One possibility of obtaining a PN signal with a high resistance against deciphering is to set out from an m-sequence generator and subject two or more parallel outputs of the shift register stages to a nonlinear operation such as “and,” or “or” (see Ristenbatt and Daws, 1977). Figure 15 shows

232

P. W. BAIER AND M. PANDIT CLOCK

NONLINEAR F E E 0-F 0 RWARD

FIG.15. PN-signal generator with nonlinear feed-forward network

a typical configuration of such a PN-signal generator with a feed-forward network. By modifying this network, a multitude of PN signals can be generated that cannot be deciphered as easily as m sequences. A further possibility of generating alternative PN signals is obtained by combining m-sequence generators. The generator shown in Fig. 16 consists of two m-sequence generators that generate different m sequences of length L , or L2, respectively, and a mod-2 adder in which the two m sequences are added. If both m sequences have the same length, i.e., L , = L,, and are appropriately chosen, a so-called Gold sequence also of length L , is obtained (Gold, 1967). By changing the relative position of the m sequences with respect to one another, a whole family of Gold sequences with good cross-correlation behavior can be generated. If L, and L, are prime relative to one another, the resulting PN signal has the length L = L,L,. This fact offers the possibility to obtain long PN signals by simple means. The so-called JPL ranging codes are generated according to this principle. Their specialty is that they facilitate fast synchronization of the receiver PN-signal generator (Golomb et ul., 1964). One of the main reasons why m-sequence generators or spreading function generators based on m-sequence generators have been very attractive is that long sequences can be generated using limited hardware.

CLOCK

41

FIG.16. PN-signal generator consisting of two different m-sequence generators

SPREAD SPECTRUM COMMUNICATION SYSTEMS

233

CLOCK

*

.OAD

SHIFT REGISTER

FIG. 17. Programable PN-signal generator.

With the advent of large, compactly packaged digital memories (PRO , ROM), alternative configurations of PN-signal generators have become feasible, which are not only as compact as the m-sequence-oriented generators, but have no restrictions placed on them regarding the sequences they generate. Figure 17 shows the basic scheme of such a generator in which a relatively slow memory is used in conjunction with a fast shift register. The desired PN signal is programed into the PROM in the form of binary words each of which has a length equal to the number of shift register stages. The words are successively loaded in parallel into the shift register. After each loading, the shift register is clocked to obtain the individual bits of a word at the output of the last register stage. The addressing circuit of the memory and the shift register are controlled by a common clock signal. Generators of the structure shown in Fig. 17 have been designed and implemented, e.g., by Baier et al. (1979). The implementation of PN-signal generators of the types shown in Figs. 15-17 is not problematic. On the other hand, it is no simple task to find PN signals that satisfy the requirements shown in Fig. 12. Theoretical investigations of the correla.tion properties are difficult and one has to resort to laborious computer simulations. B . Spreciding Modulation

In this section it is shown which methods of spread spectrum modulation come into question for practical implementation. First, it can be stated that amplitude modulation given by Eq. ( 5 ) is practically unsuited due to the following reason: Generally, it is necessary to use a limiter o r an AGC circuit at the receiver front end, for instance, in order to suppress strong pulse jammers; in such a device, however, spread spectrum ampli-

234

P. W. BAIER AND M. PANDIT

tude modulation would also be-at least partially -suppressed. Another disadvantage of spread spectrum amplitude modulation is that the maximum power available at the transmitter would not be continuously used and that amplitude and phase nonlinearities of the system components would distort the spread spectrum signal. Thus, it is desirable that the transmitted signal be a constant envelope signal. It was found that only digital functions come into consideration as spreading functions. Therefore, digital phase modulation and digital frequency modulation remain as possible spread spectrum modulation schemes. On account of the abrupt phase o r frequency transitions, these modulation schemes can be termed phase or frequency hopping, respectively. Besides these two, hybrid modulation schemes can also be employed. 1. Phase Hopping

A variety of special spread spectrum modulation schemes can be thought of under the expression phase hopping. These differ from one another in the number and values of possible carrier phases. A readily implementable version of phase hopping often employed is the method of direct sequencing, whereby a binary spreading function g ( t ) is used. The carrier phase takes on the values 0 or 180" corresponding to the binary L and H states of the spreading function. The spreading modulator as well as the despreading modulator are easily implemented using a double-balanced mixer of the type shown in Fig. 18. Thanks to the simplicity of the modulation circuits, no problems are caused by signal delays, even if one chooses a relatively high chip frequency l/Tc; practical values of chip frequencies go up to some hundreds of megahertz. Thus, a large bandwidth BRFcan be obtained at relatively low cost by employing direct sequencing spread spectrum modulation. Besides the direct sequencing systems, phase-hopping spread spectrum communication

--g(t)

FIG.18. Balanced mixer as modulator for direct-sequencing spread spectrum modulation.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

235

FREQUENCY

2 I T,

FIG.19. Envelope of the spectral power density of a direct-sequencing spread spectrum signal.

systems in which the phase is made to pseudorandomly hop between the four values 0,90, 180, and 270" can also be designed. Such a quadriphase system has been described by Cahn ( 1973). In order to be able to specify the requirements on the amplifiers, the filters, the antennas, and other system components that are passed by the spread spectrum signals st(?) and s,(t), detailed knowledge about the spectrum of these signals is needed. As an example, the power density spectrum of a direct-sequencing spread spectrum signal is examined. The direct-sequencing spread spectrum modulation can be treated as DSB-AM with the pseudorandom modulating function g ( t ) E { - 1, l}. Therefore, in the case of narrow-band message modulation, the power density spectrum of the spread spectrum signal is equal to the power density spectrum of g ( t ) ,transposed into the transmission frequency band. If g ( t ) is an m sequence or some other noiselike binary signal, the envelope of the power density spectrum is of the form (sin x / x ) ~ ,which is shown in Fig. 19. The first zeros of the spectrum are a t a distance -+ 1/T, from the carrier frequency fo;theoretically, the width of the spectrum is infinite. Because of the periodicity of g ( t ) , the fine structure of the spectrum is discrete. The distance between the spectral lines is, however, only 1/T. Therefore, the spectrum can be mostly replaced by a continuous powerdensity spectrum in practical calculations provided T + T, holds. Spectra of P N signals have been dealt with, e.g., by Berkowitz el al. (1965). When phase-hopping spread spectrum communication systems are implemented, it is necessary to limit the transmission bandwidth B , to a reasonable value even if the theoretical bandwidth of the spread spectrum signal is infinite. Furthermore, certain amplitude and phase distortions due to nonideal system components are inevitable even within this limited pass band. Because of these reasons, it is not possible t o eliminate the

236

P. W. BAIER AND M . PANDIT

phase hops in the receiver completely. There remain minor amplitude breakdowns and phase fluctuations that entail a reduction of signal power and the generation of so-called self-noise. These system degradations have been investigated in numerous publications (see, e.g., Hopkins and Simpson, 1975; Baier and Meffert, 1977). General rules of thumb for the specification of components in phase-hopping spread spectrum communication systems are: ( 1 ) The transmission bandwidth should lie in the range l / T c 5 BRF. I2 / T c , (2) the deviation from linear phase should not exceed 1 rad within this bandwidth, and (3) the deviation from constant attenuation should not exceed 1 dB within this bandwidth. Except for the degradation described, nothing of the phase hops remains after the spread spectrum signal has been spectrally compressed. Therefore, phase-sensitive methods, e.g., analog FM or digital DPSK, can be employed for message modulation. In the phase-hopping systems, high clock rates I/T, of the spreading function g(t) are possible and usual. Therefore, such systems are especially suited for precise ranging and for the suppression of indirect signals with small time delay AT. As the power is relatively homogeneously spread over the available bandwidth B,,, phase-hopping spread spectrum communication systems have a high interference resistance.

2. Frequency Hopping If spread spectrum modulation is effected by frequency hopping, the carrier frequency is pseudorandomly changed in discrete steps. Parameters that are important while designing a frequency-hopping spread spectrum communication system are the number and values of the carrier frequency steps, and also the clocking frequency l / T c and the structure of the multilevel digital spreading function g(t). The key component of the spreading and despreading modulators in a frequency-hopping spread spectrum communication system is a frequency synthesizer. This is a sinusoidal signal source whose instantaneous frequency can be precisely controlled by an external digital signal. In the present context, this signal is the spreading function g(t). The output signal of a frequency synthesizer can be represented in the form Ssyn(2) =

co~(274.A+ g ( t ) Aflt)

(14)

In the following, let it be assumed that the distance between the individual levels of g ( t ) is 1. Then the spacing between adjacent frequencies of the signal sSyn(t)is equal to Af. In case g ( t ) is a zero mean function, as assumed in the following, f, is the center frequency of the signal sSy,(t). A frequency-controllable signal source that is easy to implement would be

SPREAD SPECTRUM COMMUNICATION SYSTEMS

237

the classical voltage-controlled oscillator (VCO). However, the instantaneous frequency of such a generator does not possess the high stability required in spread spectrum communication systems (see Section V,A). Frequency synthesizers for spread spectrum applications work either on the principle of direct synthesis or indirect synthesis. In the former case, a set of stable fixed-frequency oscillators is employed; the outputs of these oscillators are nonlinearly combined to generate the instantaneous frequency prescribed by g(t). In the case of indirect frequency synthesis, a stable fixed-frequency oscillator and a phase-locked loop (PLL) consisting of a phase discriminatx, a loop filter, a VCO, and a frequency divider with variable ratio Y are employed. In the PLL, the frequency divider is connected between the VCO and the phase discriminator. The PLL is locked onto the output signal of the stable reference oscillator. Then the output frequency of the VCO is exactly Y times the reference frequency. The divider ratio r , and consequently the instantaneous frequency of the VCO, can be controlled by the spreading function g ( t ) . Nossen (1974) has described the design of frequency synthesizers in detail. A novel method of generating frequency-hopped signals using a surface acoustic wave (SAW) filter has been given by Grant r t d.(1976). Figure 20 shows the basic frequency-hopping spread spectrum transmitter. This configuration is a special version of the generic spread spectrum transmitter shown in Fig. 3. The spreading modulator consists of a frequency synthesizer and a mixer. The input signals of the mixer are the signals s,'(t) given by Eq. (4) and S S y , ( t ) given by Eq. (14). If the upper side-

MESSAGE SOURCE

sot(t)

\/

SPREADING MODULATOR

r-------l I

I

MIXING

MESSAGE MODULATOR

s't(t)

[r I

SOURCE

AND FILTERING

I

5,(t) "

I -

1

THESIZER I

I

FU NCTl ON GENERATOR

FIG.20. Generic frequency-hopping spread spectrum transmitter.

P. W. BAIER AND M . PANDIT

238

I

DESPREAD1NG MODULATOR

r-----i

1-

MESSAGE

MESSAGE

SPR EADlNG FUNCTION

SYN CH RONIZER

-

-

DE SPREADING FUNCTION GENERATOR

band of the mixer output signal is used for transmission, the equation st(t) =

d f ) c 0 ~ { 2 & h + f, + g(r) AfIt + cp>

(15)

is obtained for the radiated spread spectrum signal. Figure 21 shows the basic frequency-hopping spread spectrum receiver. This configuration is a special version of the generic spread spectrum receiver shown in Fig. 4. The despreading modulator is similar to the spreading modulator; it consists also of a frequency synthesizer and a mixer. Let the output signal of this frequency synthesizer be again sSy,(t) as given by Eq. (14). If the lower sideband of the mixer output signal is taken, the spectrally compressed signal s:(r) = a(r) COS[27&

+ cp(t)]

(16)

is obtained. In order to avoid overlapping of spectra, the frequencies of the described system must be so chosen that max{g(r) Af} -G f, andf, e fo hold. The purpose of the frequency-hopping modulation is to spectrally spread the message signal over a large bandwidth BRF,for instance, over a bandwidth of many megahertz. Theoretically, this can be achieved in two different ways: First, the bandwidth of the individual constant frequency signal pulses can be made large by employing a spreading function g ( t )

SPREAD SPECTRUM COMMUNICATION SYSTEMS

239

that has a short chip width T,; second, one can choose T, large, which results in a small bandwidth of the constant frequency signal pulses, and simultaneously distribute the individual frequencies over a large band. In the first case, a few densely spaced frequencies suffice to spread the signal si(t) over a given bandwidth BRF.In the second case, more frequencies and/or a larger spacing Afare needed. In practice, the hopping rate of frequency synthesizers has an upper limit of a few hundred kilohertz. This limit is low in comparison with a desired bandwidth BRFof many megahertz. Therefore, practical broad-band frequency synthesizers function exclusively according to the second principle. They employ a large number of frequencies that are distributed over the desired spread spectrum bandwidth BRF.In contrast to the almost continuous power density spectrum of phase-hopping spread spectrum signals, the power density spectrum of such a frequency-hopping spread spectrum signal is distinctly discrete; the spectral lines indicate the individual hopping frequencies. This is shown in Fig. 22. An aggravating property of frequency-hopping spread spectrum communication systems not shared by phase-hopping systems is due to the behavior of practically all frequency synthesizers available today: Every frequency hop is accompanied by a phase jump of unpredictable magnitude, an effect that has not been incorporated in Eq. (14). As a consequence, the zero phase angles of the constant frequency signal pulses can take on any value between 0 and 360". Because of this, the spectrally compressed signal s:( t ) also contains phase jumps of unpredictable magnitude at the instants corresponding to the frequency hops of the signal s,(t). These phase jumps unduly alter the message modulation if phase-sensitive message modulation schemes are employed. Therefore, at higher hopping rates, only phase-insensitive message modulation schemes such as frequency shift keying (FSK) come into question. In the case

FREOUENCY

FIG.22. Spectral power density of a frequency-hopping spread spectrum signal

240

P. W. BAIER AND M. PANDIT

of FSK it is desirable that the frequency jumps induced by the message signal occur simultaneously with the potential frequency hops of the signal ssy,,(f). Then the FSK signal s:(t) obtained after the despreading modulation would not exhibit any parasitic phase jumps. In frequency-hopping spread spectrum communication systems, T, is usually not below 10 psec. Therefore, such spread spectrum communication systems are not as suitable for precise ranging applications as are phase-hopping spread spectrum communication systems. Due to the relatively large T,, the transmitted signal of a frequency-hopping spread spectrum communication system can also be relatively easily detected and processed by an unintended receiver. The achievable interference suppression depends on the type of jammers. For instance, a sinusoidal interfering signal that does not coincide spectrally with one of the lines of the frequency-hopping spread spectrum signal is entirely suppressed. Due to this property, frequency-hopping spread spectrum communication is suited for multiple-access systems in which the near-far problem has to be taken into account. This problem arises if the receiver R, wishes to receive a message from a transmitter T, situated much farther away than a neighboring transmitter T,, and T, and T, radiate signals having equal power. If frequency hopping is used, apart from the instants at which T, and T, casually radiate the same frequency, communication between T, and R, is not disturbed byT,. Furthermore, by employing appropriate message encoding, even the errors arising from the casual coincidence of the frequencies of T, and T, are largely reduced. If a phase-hopping spread spectrum communication system were employed in the same situation, communication between T, and R, could be totally blocked by the dominating signal of transmitter T,. 3 . Hybrid Techniques

It can be advantageous to combine different spread spectrum modulation schemes. For instance, a relatively narrow-b:.nd direct-sequencing spread spectrum signal can be spread to a considerable bandwidth by additional frequency hops with a large Af. Practical systems sometimes do employ such hybrid techniques. In the system deocribed by Smith (1978), frequency hopping and direct sequencing techniques are combined with a time-hopping scheme. C . Receiver Synchronizution

A vital operation to be performed at a spread spectrum receiver is the synchronization of the locally generated spreading function with the spreading function contained in the received signal s,(t). In the foregoing

SPREAD SPECTRUM COMMUNICATION SYSTEMS

24 1

sections, synchronism of the two digital spreading functions was assumed; now the problems of bringing about synchronism and maintaining it are considered. Synchronization has to be achieved by locking the local spreading function generator onto the reference spreading function contained in the received signal sr(t).This is a difficult task because the synchronization has to be accurate up to a fraction of the chip width T, even if the received signal s,(r) is contaminated by interfering signals. A simple method of synchronization is possible if the clock frequencies of the reference and local spreading function generators are exactly equal: The two generators are brought to synchronism only at the beginning of the transmission and are then allowed to run freely. This method is indeed of practical interest for systems that communicate in short bursts. If communication is not limited to burst transmission of information, synchronization by initial timing only is purely of theoretical interest. This is mainly because the frequency stability of real spreading function generators does not suffice for a synchronous free run of long duration. Furthermore, even if the generators were stable enough, they would run out of synchronism due to variations in the transmission delay At, which are caused by changes in the atmospheric conditions or by relative movement of transmitter and receiver. In the following, first the elementary operations performed in synchronization systems and the implementation of these operations in the form of system components are described. Next, examples of synchronizing systems obtained by combining such components are given. 1 . Elementary Operations Performed in Synchronization Systems

When dealing with synchronization quantitatively, it is useful to introduce the concept “epoch.” As long as the reference and local spreading functions are synchronous, they are identical and can both be denoted by g ( t ) . On the other hand, when synchronous as well as asynchronous conditions are to be dealt with on a common basis, it is appropriate to represent the reference spreading function by the expression g ( r - E,) and the local spreading function by the expression g ( t - e l ) . The instantaneous arguments t - er and t - of the spreading functions g ( t - E ~ and ) g(t E ! ) are termed their instantaneous epochs. The quantities and are thereby the zero epochs and the quantity E = is the relative epoch of g ( t - el) with respect to g ( t - E , ) . In the case of synchronism, E = 0 holds and otherwise E # 0. Because of the periodicity of the spreading functions, any value of E in the range -m < E < can be reduced to a value of E lying in the range 0 5 E 5 T . The zero epoch of the reference spreading function g(t - E,) is a quantity that cannot be in-

242

P. W. BAIER AND M. PANDIT

fluenced at the receiver. The zero epoch el of the local spreading function g ( t - el) is known at the receiver and can be controlled. The purpose of receiver synchronization operations is to identify er and make equal to 4. Every practical synchronization scheme is based on at least some of the following elementary operations, which can be performed by corresponding hardware: (1) Recognizing whether the spreading functions g(t - E,) and g ( t el) are in synchronism or not (synchronism detector); (2) detection of the instant at which the instantaneous epoch t - E, of the reference spreading function g(t - E ~ )contained in the received signal s,(t) takes on a predetermined value Ef (fixed-epoch detector); (3) determination of the instantaneous epoch t - E, of the reference spreading function (instantaneous-epoch detector); (4) determination of the relative epoch E (relative-epoch discriminator); ( 5 ) setting the local spreading function generator to a predetermined initial state (settable spreading function generator); and (6) speeding up or slowing down the local spreading function generator and thus making its zero epoch a function of time (controllable spreading function generator).

While designing circuits for performing these elementary operations, it has to be borne in mind that the received signal s,(t) can be corrupted by SYNCHRONISM YESIN0

COMPARATOR

I SPREADING MODULATOR

n SPREADING FUNCTION GENERATOR

FIG.23. Synchronism detector.

I

SPREAD SPECTRUM COMMUNICATION SYSTEMS

[

FILTER

1 1 *I

FIG.24.

243

HOLD

Fixed-epoch detector.

an interfering signal n(t) and, as a consequence, the circuits performing epoch determination are prone to errors. An obvious criterion for the decision whether or not synchronism prevails, i.e., whether e = 0 or E # 0, respectively, is based on finding out whether the received signal sr(t)is spectrally compressed or not. If E = 0 holds, the power of the signal at the output of the interference suppression bandpass is large: if E # 0 holds, the power is small. Thus, in a synchronism detector the bandpass output power has to be compared with a reference level. The practical determination of the appropriate reference level is not without problems, since the bandpass output power depends not only on the relative epoch E , but also on the actual received powers Pinand Nin.One possibility of alleviating this difficulty is to take the bandpass input power as the reference. Figure 23 shows the principle of a synchronism detector. The task of a fixed-epoch detector is to determine the instant of time at which the argument t - E , of the spreading function contained in the received signal s,(t) takes on the value ef. This task can be solved by observing the signal s,(t) and recognizing the instant t = T at which the section of the spreading function contained in s,(t), T - TM 5 t 5 T, is identical with the section of the spreading function g ( r ) , ef - TM 5 t IEf. Fixed-epoch detectors can be conveniently implemented by using filters that are matched to the corresponding signal sections. At the instants at which the instantaneous epoch of the incoming spreading function g ( t 4 ) takes on the value ef, correlation peaks appear at the matched-filter output. Note that this application of the matched filter differs from the classical matched-filter application (see, e.g., Stein and Jones, 1967). Whereas classically the matched filter serves to signal the presence or absence of a known signal embedded in noise at a predetermined instant of time, in the current case it is used to signal the instant of time at which the signal appears. A fixed-epoch detector based on matched filtering is shown in Fig. 24. At the output of this circuit, periodic correlation peaks occur with a frequency of 1/ T . Matched filters for phase-hopping spread spectrum signals can be readily implemented by employing surface acoustic wave

P. W. BAIER AND M. PANDIT

244

and charged-coupled devices (see, e.g., Bell et al., 1973; Buss rt a / . , 1973; Milstein and Das, 1977). Fixed-epoch detectors for frequency-hopping spread spectrum signals can consist of a bandpass, a rectifier, and an integrate and dump circuit as described by Cole (1973). In order to avoid degradation that could be caused by the message modulation contained in sr(r),this modulation should be switched off or at least not be very broad band during the signal section chosen for fixed-epoch detection. To determine the instantaneous epoch t - E , of the reference spreading function g ( t - er), one has to observe the received signal s,(t) over a certain number q of chips. If, as in some frequency-hopping spread spectrum communication systems, g ( t ) is a multilevel digital function that takes on each of the allowed levels once and only once within the period T , it is theoretically sufficient to observe s,(r) over a time interval of duration one chip width T, (i.e., q = 1). If g ( t ) is a binary signal, the observation of s,(t) over a time interval of duration one chip width T, is not sufficient. In case g(r) is a known m sequence, the observation interval has to be at least m times the chip width T, ( q = m ) . Various versions of instantaneous epoch detectors have been suggested, e.g., by Ward (1963, Kilgus (1973), Ramsey (1973), and Ward and Kai (1977). All these are based on the structure shown in Fig. 25. In the single-chip decision device, the values of the successive individual chips of the reference spreading function g ( t - E,) are estimated. For this purpose, circuits consisting of matched filters and threshold devices are used. In the component labeled instantaneous-epoch calculator, the instantaneous epoch is estimated from the estimated values of the individual chips. For the proper functioning of the instantaneous-epoch detector it is necessary to know the clock signal of the reference spreading function g(t - E,). If an instantaneous-epoch detector is available, one could determine the relative epoch c = E~ - E, at any instant from the estimated value E ,

Y SINGLE

EPOCH

CLOCK OF g(t-&,)

FIG.25.

Instantaneous-epoch detector.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

DE-

245

BRF

FIG.26. Relative-epoch discriminator.

and the known value eI. However, this indirect method is rather cumbersome. A direct method is obtained by observing the output power of the interference suppression bandpass using a circuit of the type shown in Fig. 26. As has already been noted, the power P;, + Ni', at the output of the bandpass is large for E = 0 and small otherwise. The transition from large to small powers is continuous. For instance, a relation P,',+ N{,, = f l ~ )of the form graphically shown in Fig. 26 can be obtained. Therefore, the power at the bandpass output is a measure of the absolute value [el of E . The sign ambiguity of the relative epoch measurement can be resolved by despreading the incoming signal s,(t) with an early and a late version of the local spreading function in two separate despreading modulators and comparing the powers at the outputs of these circuits. In the special case of g(r) being an m sequence generated by one of the configurations shown in Fig. 14, one can use the output signals of adjacent stages of the shift register (Gill, 1966; Hartmann, 1974) as early and late versions of the local spreading function. The power Pi, + N;, quickly approaches a small value for I E ~ + T, and is independant of E for I E ( > T,. Consequently, the operating range of a relative-epoch discriminator is confined to a small region given by 1. ~ 1 < E,,, with emax== T,. The digital spreading functions are generated with the aid of digital circuits such as shift registers, counters, and frequency dividers. These circuits can be easily set to a prescribed initial state by external signals. This facilitates the construction of settable spreading function generators. One form of such a generator with good clock frequency stability has been described by Baier et ul. (1979). Controllable spreading function generators, i.e., generators of spreading functions whose zero epoch is continu-

246

P. W. BAIER AND M. PANDIT

FUNCTION DIVIDER

-ADVANCE/

FIG.27. Digitally controllable spreading function generator.

ously controllable can be obtained by employing a voltage-controlled oscillator (VCO) as the source of the clock signal. As VCOs are prone to a considerable frequency instability, the clock stability of the corresponding spreading functions is poor. A controllable spreading function generator with high clock stability can be implemented using a digital circuit of the form shown in Fig. 27. In this case, a stable clock source generates a clock signal of frequency n/T,, where n is an integer, e.g., n = 10. The clock signal is fed to a controllable frequency divider with the dividing ratio n . Thus, the output signal of the frequency divider has a frequency l / T c . In case an epoch-advance command appears, in the frequency divider one additional impulse is added to the pulses coming from the clock generator; if on the other hand, an epoch-retard command appears, one clock impulse of the clock generator is suppressed. By these means, the effective clock signal can be advanced or retarded in steps of Tcln. 2 . Synchronization Schemes Based on the elementary operations and their hardware implementations described in the foregoing section, two main concepts for receiver synchronization are possible. In the one concept, a controllable spreading function generator and a relative epoch discriminator are connected together to obtain a control loop as shown in Fig. 28; Any deviations of the relative epoch E from zero are sensed by the relative-epoch discriminator and made to disappear by automatically adjusting the zero epoch of the local spreading function appropriately. A frequently used practical implementation of the control loops according to Fig. 28 is the so-called delay-locked loop (see, e.g., Gill, 1966). It has already been mentioned that the relative-epoch discrimi-

SPREAD SPECTRUM COMMUNICATION SYSTEMS

\/

247

SYNCHRON ISM

i r s <(t)+n(t)

DETECTOR

4

g(t-El)

-

f

RELATIVE EPOCH DI SCR IMINATOR

--_

I\

YES

NO

SEARCH 0

VOLTAGE

% I

CONTROLLABLE SPREADING FUNCTION

CHRONISM DETECTOR

EPOCH DISCRIMI-

SETTABLE AND EPOCH DETECTOR

GENE RATOR

Ib)

FIG.28. Synchronization of the local spreading function generator by means of a control loop and (a) acquisition by serial search, (b) acquisition by fixed-epoch detection.

nator operates satisfactorily only for values of the relative epoch .. . , , . .. - _ . . . ,.. E for which I E ~ < emaxholds. For thls reason, means nave to De proviaea [or me initial synchronization and also for the resynchronization that has to be performed if synchronism is lost. To carry out these processes generally referred to as acquisition and reacquisition, a synchronism detector that signals “out-of-lock” if exceeds emaxis needed. In the scheme shown in Fig. 28a (see, e.g., Dixon, 1976a), an out-of-lock signal opens the control loop and at the same time actuates the control input of the spreading func.I

24 8

P. W. BAIER AND M. PANDIT

tion generator. The effect of this actuation is to vary the zero epoch of the local spreading function generator monotonically until the state I E ~ < emaxis reached. As soon as this state is sensed by the synchronism detector, the control loop is closed. Figure 28b shows how a synchronism detector, a fixed-epoch detector, a relative-epoch discriminator, and a controllable and settable spreading function generator can be combined to yield a synchronization system. This system employs a fixed-epoch detector for acquisition and a control loop for tracking (see, e.g., Cahn, 1973). If synchronism is not present, i.e., > E,,, is sensed, the switch connecting the output of the fixed-epoch detector and the spreading function generator is closed. As soon as the instantaneous epoch of the incoming spreading function takes on the predetermined value programmed into the fixed-epoch detector, a peak appears at the output of this detector. The peak is the actuating signal that sets the spreading function generator to the appropriate initial state. At the instant at which this is performed, the state I E ~ < emaxis achieved and the control loop can take over the task of maintaining the condition E = 0, i.e., the task of tracking. An alternative synchronization scheme is illustrated in Fig. 29. In this system all that is used is a fixed-epoch detector and a settable spreading function generator clocked with a stable frequency equal to the clock frequency of the reference spreading function g(t - E , ) . The instants at which the instantaneous epoch of the reference spreading function takes on a prescribed value E~ are marked by peaks at the output of the fixedepoch detector. These peaks are fed to the set input of the spreading function generator. In this way, the instantaneous epoch of the local spreading function is periodically set to the appropriate value. In the time intervals between consecutive peaks, the local spreading function generator runs autonomously. The accuracy of the clock frequencies, the varations of the clock frequency of g(r - E,) due to the Doppler effect, and the period

IE~

t

--EPOCH

FUNCTION

FIG. 29. Synchronization of the local spreading function generator by means of a fixed-epoch detector.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

249

T of the spreading functions are the main factors that determine the feasibility of the scheme shown in Fig. 29. Baier et al. (1977b) have described a practical implementation. D . Messuge Modulation Theoretically, any type of modulation process can be envisaged for message modulation [see Eq. (4)].The only restriction is that the bandwidth B;tF of the message modulated signal s;(t) must be much smaller than the transmission bandwidth BRF.In practice, one is not quite so free regarding the choice of the message modulation method. This is because the statement that message modulation and spread spectrum modulation are two entirely independent processes (see Section I1,A) is true only in principle. In practical systems, these processes interact. Therefore, it is necessary to look upon them from a common viewpoint. On the one hand, message modulation tends to degrade the performance of the spread spectrum components of a system, and on the other, the signal at the input of the message demodulator can differ from the desired form as a result of the foregoing spread spectrum processing. It is now considered which methods of message modulation are suitable for the two spread spectrum modulation schemes, viz., phase hopping and frequency hopping, and what is to be noted by the application of these message modulation schemes. Without further deliberation, it can be stated that amplitude modulation does not come into consideration because it would be impaired, or even suppressed, by the AGC or limiter circuits generally employed at the receiver input. I . Messuge Modulation Schemes for Phase-Hopping Spread Spectrum Communication Systems

In a phase-hopping spread spectrum communication system, ideally the input signal of the message demodulator does not contain any residual modulation that can be traced back to the spread spectrum process. Therefore, no detrimental effects of the spread spectrum process have to be considered while choosing the message modulation scheme. Frequency modulation (FM) is suitable in the case of an analog message signal sot(t) (see, e.g., Baier, 1975). However, it is important to note that FM in conjunction with direct-sequencing spread spectrum modulation yields a spread spectrum signal that can be easily processed by an eavesdropper to win the message: Just by squaring the spread spectrum signal he can obtain the despread FM signal, although with doubled modulation index. Frequency shift keying (FSK) and phase shift keying (PSK) are

250

P. W. BAIER A N D M. PANDIT

T

ENTIAL SOURCE

ENCODER

i I I I

L---

SYNLH-

---

t SPREAD1NG

BALANCED

A cos i2n tot1 CARRIER

FUNCTION

GENERATOR

SOURCE

FIG. 30. Direct-sequencing spread spectrum transmitter with binary DPSK message modulation.

suitable as binary or M a r y modulation schemes (Stein and Jones, 1967) for digital message signals. Binary phase shift keying offers a simple method of combining the message modulation with the spread spectrum modulation. This possibility is illustrated in Fig. 30, which shows a transmitter incorporating direct-sequencing spread spectrum modulation and so-called differential phase shift keying (DPSK) as message modulation. In contrast to straightforward phase shift keying in which the binary L and H states are assigned, e.g., to the absolute phases 0 and 180" of the carrier, in DPSK L corresponds to "0" phase transition of carrier" and H corresponds to 180" phase transition of carrier." In the DPSK scheme, it is not necessary to know the absolute carrier phase at the receiver-a knowledge that generally would be difficult to obtain. In the system shown in Fig. 30, the binary message signal sot(t) is first differentially encoded and subsequently added mod 2 to the binary spreading function g ( t ) . The resulting binary bit stream modulates the carrier in the double-balanced mixer by causing phase hops of 180". It has already been mentioned that message modulation deteriorates the performance of various components of spread spectrum communication systems. This applies above all to the detectors of synchronism, fixed epoch, and instantaneous epoch, and to the relative-epoch discriminator at the receiver. Considering the case of the synchronism detector, it is noted that due to the message modulation the power of the spectrally compressed signal s:(t) at the input of the interference suppression bandpass is distributed over the bandwidth B&. To ensure that as little signal power as possible is "

SPREAD SPECTRUM COMMUNICATION SYSTEMS

25 1

lost, the bandwidth of the interference suppression bandpass has to be made larger now than in the case of no message modulation being present. This leads to an increase of the interfering power at the output of the bandpass and to a greater uncertainty of the decision whether synchronism is present or not. Therefore, one has to endeavor to make BAF as small as possible. Now the influence of message modulation on the performance of a fixed-epoch detector is considered. Such circuits usually contain filters that are matched to certain sections of the direct-sequencing spread spectrum signal s,(t). Perfect matching is possible only to a spread spectrum signal not containing message modulation because otherwise the exact run of s,(t) would not be known at the receiver. Consequently, the performance of fixed-epoch detectors is degraded if their input signals s,(t) contain message modulation. The detectors may fail completely if message-induced phase or frequency hops occur within the sections of the received signal that have been programmed into the matched filters. In systems using analog FM as message modulation, the detector performance is degraded if the instantaneous carrier frequency differs appreciably from the nominal carrier frequency for which the detector has been designed. One method of circumventing the difficulties caused by message modulation is to switch off the message during the intervals in which the signal sections programmed into the matched filters are transmitted. In the case of a digital message signal sot(?), another remedy is sometimes available: The signal sot(t) can be synchronized with the spreading function g ( t - E,) in such a way that sot(?) has no effect upon the transmitted signal st(t) during the critical signal sections. This synchronization measure is indicated by a dotted line in Fig. 30. By this means it can also be achieved that potential phase hops induced by the spreading function on the one hand and by the message signal on the other occur simultaneously. In this way, the separation of the message signal and spreading function by a third party is made more difficult. What has been said above concerning the degradation caused by the message modulation not only holds for the synchronism detector and the fixed-epoch detector but also, with certain modifications, for the instant-epoch detector and the relative-epoch discriminator. 2 . Messuge Modulation Schemes j b r Frequency-Hopping Spread Spectrum Communication Systems As already mentioned in Section 111,B,2, phase-sensitive message modulation schemes are generally unsuitable for frequency-hopping

252

P. W. BAIER AND M . PANDIT

spread spectrum communication systems. Consequently, analog signal transmission by frequency modulation is not readily feasible. For the transmission of digital signals, the method of frequency shift keying (FSK) is to be preferred (see, e.g., Drouilhet and Bernstein, 1969). If this modulation scheme is employed, it is necessary to synchronize the data bit stream with the spreading function clock signal. In slow frequencyhopping systems, i.e., systems in which two or more message bits are transmitted in an interval one chip width T, long, it is also possible to implement differential phase shift keying (Huth, 1977). However, slow frequency-hopping systems suffer the disadvantage of being rather vulnerable against jammers and eavesdroppers. The general concept of the transmitter of a frequency-hopping spread spectrum communication system is shown in Fig. 20. The complexity of this transmitter structure can be reduced if binary FSK is used as message modulation. For this purpose, the digital spreading function is suitably modified by the digital message signal sot(z). Instead of g ( t ) the modified spreading function gmd(t)is fed to the frequency synthesizer. This leads

I I I I

-

L-

-1-

gmod(t)

SPREADING FUNCT 10 N MODIFlCATlO N

SPREADIK

L -SYNCH - - - FUNCTION

GENERATOR

253

SPREAD SPECTRUM COMMUNICATION SYSTEMS

H - CHANNEL

" s,(t)

DESPREADING MODUL AT OR

' II

FILTERING

t

FREQUENCY

I

SYN-

FIG.32. ulation.

-

fo

-

+

'

I

'

COMPARATOR

MESSAGE

4

I

I

I---* I

THESIZER

i- -f-

4*

I.)

I I I

i

-

I

MIXING AND

d&

rxl ru

I 1

SINK '*

S

b

A

*

t

+ I I

fo+Af

I

I

L - CHANNEL

II

1 _I

I

Frequency-hopping spread spectrum receiver with binary FSK message mod-

to the transmitter configuration shown in Fig. 3 1 . The dotted line indicates the mutual synchronization of spreading function generator and message source. The modification of g ( t ) can be effected for instance according to the rule gmod(f) = g ( i ) if

sOt(f)

=

H,

grnod(t) = g ( t )

+

1 if

sOt(t) =

L

In this case, the transmitted instantaneous frequency has its original value

fo + g ( t ) Af when the message signal is H, and its original value plus 4f when the message signal is L. By adapting the general receiver configuration shown in Fig. 21 to the transmitter shown in Fig. 31, the receiver shown in Fig. 32 is obtained. Two interference suppression bandpasses have been provided at the output of the despreading modulator, one with center frequency fo (H channel) and one with center frequencyf, + 4 f ( L channel). The message signal is won by rectifying the bandpass outputs and taking the higher of the two values. Up to now, the message modulation has been dealt with from the point of view that the message remains unimpaired by the spread spectrum process. It has yet to be considered how the FSK modulation impairs the performance of the spread spectrum components. In phase-hopping spread spectrum communication systems, the message modulation affects

254

P. W. BAIER AND M. PANDIT

the synchronization of the local spreading function generator as shown in Section III,D, 1. This is also the main detrimental effect of message modulation in frequency-hopping spread spectrum communication systems. As a n example, the system shown in Figs. 31 and 32 is considered. Due to message modulation, every level of the synchronized spreading function in the receiver corresponds not to one, but to two frequencies separated Therefore, in each of the detectors for synchronism, instant epoch, by and fixed epoch and in the relative-epoch discriminator two channels similar to those shown in Fig. 32 must be employed. As both channels are active all the time, it is necessary to contend not with the interfering signal from only one channel, as would be the case in a system in which no message is to be transmitted, but from two channels. This leads to a degradation of the performance of the synchronization components. Besides the necessity to provide for parallel channels, message modulation entails a further complication. As already mentioned in Section III,C,I, in the case of frequency-hopping spread spectrum signals in which every particular frequency occurs once and only once within the period T , fixed- and instant-epoch detection can be based on the observation of a single chip. Now, more than one chip has to be correctly identified to determine the epoch of the reference spreading function g ( t - E ~ ) .

u.

IV. AN ALTERNATIVE APPROACH TO SPREAD SPECTRUM SIGNALING In the spread spectrum communication systems considered hitherto, the message modulation/demodulation and the spread spectrum modulation/demodulation have been processes that are-apart from the interactions dealt with in Section II1,D-independent of one another. In the case of a digital message signal, an alternative spread spectrum signaling principle can be obtained by combining the two modulation processes. This can be done by assigning a specific waveform belonging to a set of orthogonal spread spectrum waveforms to every possible value (or word) of the digital message signal so&). In this case, the transmitted signal consists of a series of such waveforms, thus still being a spread spectrum signal of the type given by Eqs. ( 9 4 7 ) . In the receiver of a communication system based on this signaling principle, it is advantageous to use matched filters for the identification of the received orthogonal spread spectrum waveforms. The main factor that determines the degree of interference suppression is the time -bandwidth product of the waveforms and of the corresponding matched filters. With the advent of surface acoustic wave (SAW) devices and charge-coupled devices (CCD), time -band-

SPREAD SPECTRUM COMMUNICATION SYSTEMS

MESSAGE

FILTER

SOURCE

DRIVER

255

U-lJ

SAW FILTER

FIG.33. Spread spectrum transmitter employing S A W filters for signal generation.

width products exceeding 1000 have become feasible at high data rates. The degree of interference suppression that can be obtained with the aid of such devices is comparable to that attainable with conventional phase- or frequency-hopping spread spectrum communication systems. Furthermore, the variety of spread spectrum waveforms is no longer restricted to the forms described in Section III,B, which can be easily generated and processed using more conventional means. For instance, chirp signals with additional pseudorandom phase hops can be employed (Federhen, 1975). Such more intricate waveforms are advantageous with respect to message privacy, interference suppression, and other desirable system properties shown in Fig. 12. An example of a spread spectrum communication system in which SAW filters are used in the transmitter and receiver is shown in Figs. 33 and 34. This system is designed to transmit a binary message signal sot(t). The impulse responses of the SAW filters are spread spectrum waveforms. The filter driver contained in the transmitter converts the binary message signal into narrow impulses. Depending on the instantaneous value of the message, the impulses are fed either to the SAW filter H o r SAW filter L. Every impulse causes the corresponding filter to generate a spread spectrum waveform of duration Tb at its output. The transmitted spread spectrum signal st(?) is obtained by combining the output signals of the two filters. The receiver is also provided with two SAW filters, which are matched to the waveforms generated at the transmitter. The output signals of the matched filters are rectified and compared at the appropriate instants in the comparator. A synchronization circuit is necessary to determine these instants. In spread spectrum communication systems based on the configura-

256

P. W. BAIER AND M. PANDIT

Y

s,(thr

MATCHED

+

FILTER

4

*

-

H

T COMPARATOR

L-0

MATCHED

--C

FILTER

+

-H-

+

MESSAGE

T

L

tions shown in Figs. 3 and 4, interference suppression at the receiver is achieved by spectral compression of the desired signal s,(t) and filtering away the spectrally spread undesired signals. In the receiver shown in Fig. 34, the received signal s,(t) is compressed not in the frequency domain but (bitwise) in the time domain, whereas interfering signals remain uncompressed. Interference suppression is achieved in this case by observing the broad-band output signals of the two matched filters at certain instants of time at which the SNR attains a maximum value and not by observing a certain spectral domain given by the passband of the interference suppression bandpass.

v.

LIMITSOF

SPREAD SPECTUM

TECHNIQUES

A . Limits on th" Processing Guin

Equation (8) reads in words: The improvement in the SNR due to the spread spectrum process, i.e., the processing gain B R F / B k F , increases with increasing bandwidth BRFof the spread spectrum signal and with decreasing bandwidth of the message-modulated signal. Theoretically,

SPREAD SPECTRUM COMMUNICATION SYSTEMS

25 7

one could make the processing gain arbitrarily large by choosing the bandwidths B R F and BAF appropriately. Practical limits on BRFare given by the maximum realizable chip frequencies in phase-hopping spread spectrum communication systems and by the maximum realizable number of frequencies in frequency-hopping spread spectrum communication systems. Spreading function generators can be built with chip frequencies up to several hundred megahertz. Considering frequency synthesizers for frequency-hopping spread spectrum communication systems, a maximum number of about 5000 different frequencies and a maximum hopping rate of a few hundred kilohertz become feasible by employing modem technologies. As a consequence, the bandwidth B R F of phase-hopping as well as frequency-hopping spread spectrum communication systems can reach a maximum value of some hundred megahertz. Apart from the technological grounds given above, there are other reasons why BRFcannot be made arbitrarily large. A value of B R F of hundreds of megahertz makes it necessary for various system components, e.g., filters, mixers, duplexers, amplifiers, and antennas, to be very broad-banded in the sense that they do not cause appreciable amplitude and phase distortions. Therefore, the difficulties encountered while developing system components increase with increasing bandwidth B R F . The center frequencies of the spread spectrum signals appearing in the transmitter and in the receiver must be larger than half the spread spectrum bandwidth BRF,in order that the spectral domains of the negative and positive frequencies remain clearly separated from each other. This requirement must be fulfilled in all IF stages of a system. Therefore, too large a value of BRFleads to IF frequencies that cannot be handled easily. Also with respect to frequency allocation to various services, it is difficult to reserve excessively large bandwidths for spread spectrum communication systems. It is appropriate to mention a further fact on account of which it is pointless to increase B E , beyond a certain limit. As described in Section I I , B , l , spread spectrum techniques do not offer any SNR advantage if the bandwidth of the interfering signal is a priori very large [see Eq. (911. Examples of such very broad-band interfering signals that originate from natural sources are the atmospheric noise picked up by the receiving antenna and the noise of the front-end amplifier of the receiver. If a received intentional interfering signal n ( t ) is spectrally spread to such an extent in the despreading modulator that the spectral power density of the spread signal n ' ( r ) is of the same order of magnitude as the spectral power density of the "natural" interfering signals, a further increase in the degree of spectrum spreading, i.e., in the bandwidth BRF,does not yield any notice-

258

P. W. BAIER A N D M. PANDIT

able gain in the total SNR. To elucidate this point, consider the following situation: Let the only natural source of interference be the receiver input stage, which has a noise figure F = 3, and let the intentional interfering signal n ( t ) be a narrow-band signal with the power N,, = W. In this case, it is of no avail to choose the spread spectrum bandwidth much larger than B R F = Ni,/(FkTo) = 8.34 MHz ( k is Boltzmann's constant, To = 290 K). The minimum possible value of BkF is determined by the message bandwidth B b . Both bandwidths are of the same order, with BAF being more or less larger than B b depending on the employed message modulation scheme. It is possible to make B b , and simultaneously BAF, small by avoiding unnecessary redundance in the message signal. However, Bb cannot be reduced below a certain minimum value if the communication link is to serve its purpose. This problem has been dealt with, e.g., by Meffert (1977). A lower limit on the bandwidth of the interference suppression bandpass-which usually is chosen equal to the bandwidth BLFof the message-modulated signal -is given by the frequency deviations due to instabilities of the oscillators incorporated in the communication system and to the Doppler effect. In a receiver equipped with a very narrow interference suppression bandpass, such frequency deviations would cause the signal s:(t) to lie spectrally more or less outside the passband. As a consequence, part of the signal power Pi,would be lost. As an example, consider a communication system with an RF offo = 20 GHz and a bandwidth of the message-modulated signal of BAF = 10 kHz. In order to avoid a noticeable degradation due to frequency instabilities and Doppler effect, the relative frequency deviation of the RF oscillators has and the relative velocity ure1of to be kept well below BAF/f0= 0.5 x the transmitter with respect to the receiver must be considerably smaller = 150 m/sec (c, = 3 x lo8 m/sec). If the quoted conditions than c&p/fo concerning frequency stability and relative velocity are not fulfilled, the bandwidth of the interference suppression bandpass must be chosen larger than B;(F = 10 kHz. As a consequence, the processing gain would decrease. B . Limits on the Suppression of Undesired Signals

The degree of suppression of undesired signals is not only determined by the attainable processing gain BRF/B;(F, but also by the nature of the interfering signal. Certain signal forms can cause a high interference at the message demodulator input, even though the communication system has a high processing gain. An unfriendly party radiating interfering signals would endeavor to

SPREAD SPECTRUM COMMUNICATION SYSTEMS

259

make the most of its available power in order to jam the communication. Easily generatable (so-called unintelligent) interfering signals such as continuous sinusoidal or continuous noise signals are not optimum from the point of view of a deliberate jammer. A very effective jamming signal is a spread spectrum signal that contains the spreading function g(t) present also in the signals s,(t) and st(t). If, in this case, the jammer succeeds in making his spreading function take on the correct value of the zero epoch, the jamming signal will be despread at the receiver, and the interfering power will pass through the interference suppression bandpass undiminished, i.e., N,', = Ni,. When trying to generate a spread spectrum interfering signal of this type, the enemy encounters two difficult tasks. First, he has to find out the run of the employed spreading function g ( t ) ,and second, he has to time his signal correctly. In principle, g ( r ) , usually a periodic function, can be found out by observing the transmitted signal s,(t) over a sufficiently long time interval. Proper timing can be achieved by the opponent if he knows the location of the transmitter and receiver relative to his own position. Another effective jamming strategy is possible if the communication system is of the push-to-talk type. In such a system, transmission takes place in the form of bursts followed by periods of no transmission, with the receiver being in a standby mode all the time. If the opponent intercepts and stores burst trains of the transmitted signal, he can block the receiver by retransmitting the bursts. A further example of effective jamming is the frequency-follower type, which can be used against certain frequency-hopping spread spectrum communication systems. If the hopping rate is sufficiently low, the opponent can determine the instantaneous transmission frequency and use this knowledge t o radiate a signal whose frequency follows the frequency of the transmitted signal s t ( t ) . Such a signal is not subjected to interference suppression and may impair the process of message demodulation. Intelligent jammers based on the principle of observing the transmitted signal and radiating closely adapted interfering signals as described above are powerful, though not easily implementable. Besides these, there are other types of effective jammers that can be implemented more readily. Pulse jammers can be effectively employed against phase-hopping spread spectrum communication systems. During the pulse-on intervals, the communication can be totally disrupted and, furthermore, the synchronism of the receiver can be broken. Against frequency-hopping spread spectrum communication systems, a multitone interfering signal that consists of a set of frequencies occupying a certain fraction of the bandwidth BRF is an effective means of jamming (see, e.g., Houston, 1975). Such a jammer causes the message data to be received incorrectly during definite periodic intervals of time. Convolutional and Reed-

260

P. W. BAIER AND M . PANDIT

Solomon coding are suitable countermeasures against this type of jammers (Drouilhet and Bernstein, 1969; Huth, 1977). Undesired signals can also be caused within the system itself due to multipath propagation and multiple-access operation. It was already discussed in Section II,B,4 to what degree indirect signals can be suppressed by the spread spectrum process. Interfering signals caused by other active participants in a multiple-access system can be kept low only by employing a spreading function family having good cross-correlation behavior. The determination of sets of spreading functions suited for frequency-hopping spread spectrum communication systems has been dealt with, e.g., by Solomon (1973). Results regarding suitable families of spreading functions for direct sequencing spread spectrum communication systems are also available (Gold, 1967). Even if sets of such optimum spreading functions are employed, active transmitters cause interfering signals in neighboring channels. This implies that there is an upper limit to the number of system users. In this connection it can be noted that of the 1770 possible pairs of m sequences of length L = 1023, 30 pairs have conspicuously bad cross-correlation behavior. If these pairs are considered, the cross-correlation function attains peak values of more than 30% of the peak value of the corresponding autocorrelation function (Baier et ul., 1977a).

C . Limits on the Synchronizubility The term synchronization as applied with reference to spread spectrum receivers generally implies the acquisition and the tracking processes. A criterion for judging the acquisition capability of a spread spectrum communication system is the mean acquisition time T A .This is the mean value of the time that elapses between the instant at which acquisition is initiated and the instant at which synchronism is achieved. Under ideal conditions, i.e., if no interfering signal is present, TA attains a minimum value Tmin, which will be approximately calculated for the synchronization schemes shown in Fig. 28. The bandpasses in the synchronism detectors of these configurations have the bandwidth & (see Fig. 23). Consequently, the response time of the synchronism detector is of the order of I/&,. If a synchronization scheme according to Fig. 28a is used, the zero epoch el of the local spreading function g ( t - el) is varied until the synchronism detector signals “synchronism.” During this search process, every value of el should be maintained for a period of time approximately equal to the response time of the synchronism detector.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

26 1

The spreading function has L chips. Therefore, on an average L / 2 values of Q have to be tried before achieving synchronism. Consequently, T,, would be L/2B;,. In contradistinction to this, the minimum mean acquisition time Tminof an acquisition system incorporating a fixed-epoch detector (see Fig. 28b) would be equal to half the period of g ( t ) , i.e., Tmin= T/2. The mean acquisition times achieved in practice are larger than T,,,,, because interfering signals give rise to detection losses and false alarms in the synchronism and fixed-epoch detectors. A number of investigations pertaining to the influence of interfering signals on the acquisition time have been published (see, e.g., Sage, 1964; Pandit, 1977; Holmes and Chen, 1977; McCallaand Weber, 1978). In the following, afew considerations are given that can be used to obtain a rough estimate of TA.These considerations are intended to impart an idea of the principles of calculation and of the attainable values. If the effects of interfering signals are to be kept sufficiently low, the available signal energy E with respect to the spectral power density Noof the interfering signal should reach a certain value before a yes/no decision is made by the synchronism detector. A reasonable value for the ratio E / N , would be 50. With this value of EIN,, a decision with an error probability of about can be made (see, e.g., Lucky et al., 1968). Setting out from this nominal value of E/No = 50, estimates of the acquisition performance of various synchronization configurations can be obtained. If a train of the signal s , ( t ) is to have the energy E , the duration TE of the signal train is given by the equation

As the interfering signal n'(t) at the output of the despreading modulator has a bandwidth of approximately BRF, the spectral power density is approximately given by = Nin/BRF

NO

(18)

Equations (17) and (18) along with Eq. (1) yield

TE =

(E/NO)(YinBRF)-'

(1%

By setting E / N o = 50 in Eq. (19), =

is obtained.

50/YinBRF

(20)

262

P. W . BAIER AND M . PANDIT

Equation (20) can be applied to the synchronization scheme shown in Fig. 28a. Each of the L/2 different values of el must be examined for a time interval of duration TEgiven by Eq. (20). Therefore, the mean acquisition time would be

L TA =--

50 YinBRF

Consider a direct-sequencing spread spectrum communication system in which L = 1023, yin = lo+, and B R F = 50 MHz holds. Then Eq. (21) yields TA = 50 msec for the mean acquisition time. Equation (20) can also be used to investigate the synchronization scheme involving a fixed-epoch detector as shown in Fig. 28b. In this case let it be required to find the minimum admissible value of the input SNR yinfor which the minimum value Tminof the mean acquisition time given above is attained. A maximum time-bandwidth product of about 1000 (see, e.g., Bell et al., 1973) is assumed for the matched filter incorporated in the fixed-epoch detector. Consequently, the product TEBRF can be set equal to 1000. By substituting this value in Eq. (20),the minimum allowable SNR at the receiver input yinmin= 50/TEBRF= 50/103 = 0.05

(22)

is obtained. This lower limit for xnholds approximately for the synchronization configuration shown in Fig. 29 as well, since this configuration also incorporates a matched filter. From what has been said above, it is apparent that an interfering signal impairs the acquisition process. Under certain circumstances, the interference can completely block the acquisition. As an example, consider a spread spectrum receiver in the acquisition mode, receiving an interfering spread spectrum signal that carries the same spreading modulation as the transmitted signal s t ( t ) . In such a situation, the receiver is liable to lock onto the interfering signal n ( t ) and not onto sr(r). After acquisition has been completed, the tracking phase is initiated in the synchronization systems shown in Fig. 28 by closing the control loop. Tracking is a process that is not as critical as acquisition. Nevertheless, an interfering signal leads also here to malfunctions. These manifest themselves as an imperfect control of the local spreading function generator, resulting in a jitter of the relative epoch about its desired value E = 0 (see, e.g., Davies, 1973). The jitter can be countered by narrowing the loop bandwidth. This, however, results in sluggish loop dynamics so that problems may arise if the transmitter and receiver experience relative acceleration with respect to one other.

263

SPREAD SPECTRUM COMMUNICATION SYSTEMS

VI. EXAMPLESOF REALIZEDS P R E A D S P E C T R U M COMMUNICATION SYSTEMS Spread spectrum communication systems are primarily built for military applications. Consequently, particulars of projected or implemented systems are mostly classified. However, some information can be obtained from unclassified literature and from material published by manufacturers. A selection of implemented or projected spread spectrum communication systems is shown in Table 11. For a more detailed chronology of the development of the spread spectrum communication systems, the reader is referred to La Rue (1975) and Dixon (1976b). In what follows, two spread spectrum communication systems are considered in more detail, namely the SIECON system (Siemens, 1977) and an experimental communication modem that has been developed and built by Dostert (1980). SIECON is a universally applicable spread spectrum communication system with multiuser capability and a built-in ranging device. It is suitable for the transmission of relatively broad-band analog message signals, e.g., TV or infrared sensor signals, and also for the transmission of digital TABLE I1

IMPLEMENTEDOR PROJECTED SPREADSPECTRUM COMMUNICATION SYSTEMS Approximate date 1948 1950 I960 1961

1969 I97 1/74 I977 1977

1978 I978

System NOMAC (noise modulation and correlation system) Phantom system AN-ARC-50 RACEP (random access and correlation for extended performance) TATS (tactical transmission system) AN-USC-28 NAVSTAR Global Positioning System SIECON (Siemens ECMresistant communication and navigation) MX-170C voice modem JTIDS (joint tactical information distribution system)

Developed at

Source

MIT, Lexington

Dixon (1976b)

General Electric Sylvania Magnavox Martin

Dixon (1976b) La Rue ( 1975) Cornetto (1961)

Magnavox

Siemens

Magnavox

Drouilhet and Bernstein (1969) La Rue (1975) Cahn and Martin (1977) Siemens (1977)

Sundaram (1978) Smith (1978)

FIG. 35. SIECON transmitter module. (Reprinted with permission of Siemens AG, Munich.)

FIG. 36. SIECON receiver module. (Reprinted with permission of Siemens AG, Munich.I

SPREAD SPECTRUM COMMUNICATION SYSTEMS

265

message signals. As an example, it can be employed for communication between remotely piloted vehicles and control stations or for controlling guided missiles. SIECON employs direct-sequencing spread spectrum modulation. The message modulation schemes are digital DPSK and analog FM. Transmission occurs in the Ku band. Figures 35 and 36 show a command transmitter and a command receiver belonging to the SIECON program. The modules have an unusual external form because they are intended to be built into airborne objects. In the experimental communication modem mentioned, the objectives of achieving miniaturization and a short acquisition time have been taken into account by employing SAW tapped delay lines. The receiver synchronization is performed according to the principle illustrated in Fig. 29. The spreading function generators have the configuration shown in Fig. 17. The modem is suitable for the transmission of analog message signals with a bandwidth of Bb = 3 kHz (e.g., speech) and of digital message signals with a bit rate of 200 kbits/sec. F M is used for analog message modulation and FSK for digital message modulation. The spectral spreading to a bandwidth of B,, = 20 MHz is effected by means of direct sequencing. The length of the PN signal that is not an m sequence is L = 1278. In the receiver either a 127-tap o r a 255-tap SAW device manufactured by Siemens or alternatively a 255-tap SAW device manufactured by

FIG.37. Transmitter and receiver of the experimental modem.

266

P. W. BAIER AND M. PANDIT

Hazeltine can be used. The mean acquisition time TA of the receiver is about 0.5 msec. In the case of analog message signals, an SNR of yin= 0.01 at the receiver input is increased to an SNR of yout= 10 at the message sink input. In the case of digital message signals, an SNR of yin= 0.2 at the receiver input gives rise to a bit error probability of only Pb = Figure 37 shows the transmitter and the receiver of the experimental modem. ACKNOWLEDGMENT The authors wish to express their thanks to Dr. G. Griinberger, Mr. H. Grammiiller, and Dr. H. Sepp of Siemens AG, Munich, for their helpful suggestions and for providing the photographs in Figs. 35 and 36.

REFERENCES AGARD (1973). AGARD-NATO Lect. Ser. No. 58. Baier, P. W. (1975). Siemens Forsch.-Entwicklungsher.4, 61 -67. Baier, P. W. (1976). IEEE Trans. Commun. Technol. 24, 1143-1148. Baier, P. W., and Griinberger, G. K. (1975). Nachrichtentech. 2. 28, 349-353. Baier, P. W., and Meffert, K. (1977). Freyuenz 31,243-246. Baier, P. W., Heiser, S., and Sepp, H . (1977a). Proc. Theorie Anwendung Diskreter Signale Kolioy. 1977 pp. 47-50. Baier, P. W., Grammiiller, H., and Pandit, M. (1977b). AGARD Con$ Proc. 230, Ref. 5.9. Baier, P. W., Dostert, K., and Pandit, M. (1979). West German Patent Application (in prep.). Bell, D. T., Holmes, J. D., and Ridings, R. V. (1973). IEEE Trans. Microwave Theory Tech. 21, 263-271. Berkowitz, R. S. el a / . (1965). “Modern Radar.” Wiley, New York. Buss, D. D., Collins, D. R., Bailey, W. H., and Reeves, C. R. (1973). IEEE J . Solid-State Circuits 8, 138-146. Cahn, C. R. (1973). AGARD-NATO Lect. Ser. No. 58, Ref. 5. Cahn, C. R., and Martin, E. H. (1977). Proc. Int. Conf. Electron. Syst. Navig. Aids, 1977. Cartier, D. E . (1976). IEEE Trans. Commun. 24, 898-903. Cole, R., Jr. (1973). Proc. Symp. Spread Spectrum Commun. N a v . Electron. Lab. Cent.. 1973 pp. 43-49. Compton, R. T. (1972). Off. N a v . R e s . (U.S.), Final Rep. No. 3098-2. Cooper, G. R., Nettleton, R. W., and Grybos, D. P. (1979). IEEE Commun. Mag. March, pp. 17-23. Cornetto, A. (1961). Electron. Des. June 21, pp. 8-11. Davies, N. G. (1973). AGARD-NATO Lect. Ser. No. 58, Ref. 4. Dixon, R. C. (1976a). “Spread Spectrum Systems.” Wiley, New York. Dixon, R. C. (1976b). In “Spread Spectrum Techniques” (R. C. Dixon, ed.), pp. 1-14. IEEE Press, New York. Dostert, K. (1980). Doctoral Dissertation, Fachbereich Elektrotechnik, Universitat Kaiserslautern. Drouilhet, P. R., and Bemstein, S. L. (1969). IEEEElectron. Aerosp. Syst. Conv. Rec. pp. 126-132.

SPREAD SPECTRUM COMMUNICATION SYSTEMS

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Federhen, H. M. (1975). Signal August, pp. 64-67. Gill, W. J. (1966). IEEE Trans. Aerosp. Electron. Syst. 2, 415-424. Gold, R. (1%7). IEEE Trans. lnf. Theory 13, 619-621. Golomb, S. W. (1967). "Shift Register Sequences." Holden-Day, San Francisco, California. Golomb, S. W., Baumert, L. D., Easterling, M. F., Stifiler, J. J., and Viterbi, A. J. (1964). "Digital Communications with Space Applications." Prentice-Hall, Englewood Cliffs, New Jersey. Goodman, D. T., Paul, S. H., and Prabhu, V. K. (1980). Proc. Zuerich Semin. Digital Commun., 1980 Ref. A S . Grant, P. M., Morgan, D. P., and Collins, J. H. (1976). Proc. IEEE 64, 826-828. Gninberger, G. K. (1976). Arch. Elektr. Uebertragung 30, 1-8. Gupta, S. C., and Painter, J. H. (1966). IEEE Trans. Commun. Technol. 14, 796-801. Haber, F. (1978). NATO Adv. Study Insr., Ser. E. 25, 55-64. Hartmann, H. P. (1974). 1EEE Trans. Aerosp. Electron. Syst. 10, 2-9. Holmes, J . K., and Chen, C. C. (1977). IEEE Trans. Commun. 25, 778-784. Hopkins, P. M., and Simpson, S . S. (1975). IEEE Trans. Commun. 23, 467-472. Houston, S. W. (1975). Proc. IEEE Natl. Aerosp. Electron. Conf., 1975 pp. 51-58. Huth, G. K. (1977). IEEE Trans. Commun. 25, 763-770. IEEE (1977). lEEE Trans. Commun. 25, Spec. Issue, 745-869. Kilgus. C. C. (1973). IEEE Trans. Commun. 21, 772-774. La Rue, G. C. (1975). Signal August, pp. 72-75. Lindholm, J. H. (1968). IEEE Truns. lnf. Theory 14, 569-576. Lucky, R. W., Salz, J., and Weldon, E . J., Jr., (1968). "Principles of Data Communication." McGraw-Hill, New York. McCalla, E., and Weber, C. (1978). Int. Conf. Commun., 1978 16.5.1-16.5.5. Meffert, K. H. (1977). Doctoral Dissertation, Fachbereich Elektrotechnik, Universitat Kaiserslautern. Milstein, L. B., and Das, P. K. (1977). IEEE Trans. Commun. 25, 841-847. Mohanty, N. C. (1977). IEEE Trans. Commun. 25, 810-815. Naval Symposium (1973). Proc. Symp. Spread Spectrum Commun. N a v . Electron. Lab. Cent., 1973. Nossen, E. J. (1974). RCA Eng. 19, 81-85. Pandit, M. (1977). Habilitation Dissertation, Fachbereich Elektrotechnik, Universitat Kaiserslautern. Petit, R. (1977). Proc. 15. Reg. Three Cunf. (Southeast Con '77) pp. 185-188. Ramsey, J. L. (1973). Pruc. Symp. Spread Spectrum Commun. Nav. Electron. Lab. Cent., 1973 pp. 11-16. Ristenbatt, M. P., and Daws, T. L., Jr. (1977). IEEE Trans. Commun. 25, 756-762. Sage, G. F. (1964). IEEE Trans. Commun. Technol. 12, 123-127. Siemens (1977). Broschure SIECON-System, Order no. A42040335-A 1-1-7629. Smith, E. G. (1978). AESS Newsl. March, pp. 25-29. Solomon, G. (1973). Proc. Symp. Spread Spectrum Commun. N a v . Electron. Lab. Cent., 1973 pp. 33-36. Stein, S., and Jones, J. J . (1967). "Modern Communication Principles." McGraw-Hill, New York. Sundaram, G. (1978). In!. Defence Rev. N o . 3. Ward, R. B. (1965). IEEE Trans. Commun. Technol. 13, 475-483. Ward, R. B., and Kai, P. Y.(1977). IEEE Trans. Commun. 25, 784-794. Yao, K. (1977). IEEE Trans. Commun. 25, 281-287.

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A D V A N C E S IN ELECTRONICS A N D ELECTRON PHYSICS, V O L .

53

Electron Interference MING CHIANG LI Depurtment of Physics Virginiu Polytechnic Institute and Stare University Blackshurl:. Virginiu

I. Introduction.. ..........................

................... ...................... ................... kground . . . . . . . . . . . . . . B. Electron B e a m . . .................... 111. Crystal Diffraction . . . . . . . . . . . . . .................................... A. Fraunhofer Diffraction .................... ................. B. Fresnel Diffraction ......................................... IV. Two-Beam interference. ........................... .............. A. Wave Function and Beam Splitting.. .......... . . . . . . . . . . . . . . . . . . . . . . . . B. Wave Front Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................. C. Amplitude Interference. ........................ V . Interference Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Mollenstedt- Diiker Interferometer. . . . . . . . . . . . .............. B. Marton Interferometer ....................................... ................... VI. Proposed Experiments. ......................... A. Modified Marton Interferometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Cross-Beam Experiment, .................... ................... C. Intensity Correlation Exp ......... ................... VII. Discussion . . . . . . . . . . . . . . . . ........... ............. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .............

269 27 I 27 1 273 274 275 279 281 282 285 286 289 290 292 294 295 297 301 303 304

I. INTRODUCTION In de Broglie’s (1924) theory, the electron is described by a wave packet, which is a spatially localized wave. This offered an explanation of the electron’s semiclassical orbit in a Bohm atom in terms of a confined wave. On the basis of the above theory, Schrodinger (1926) introduced his famous wave equation upon which the essential tool of modern physics, quantum mechanics, is based. The wave-particle duality of light was well established by then. The de Broglie theory placed the corpuscular electron in the same category as 269 Copyright @ 1980 by Academic Press, Inc. All rights of reproduction in any form reserved ISBN 0-12-014653-3

270

MING CHIANG LI

light, and bridged the wave-particle difference through the construction of a wave packet. This is the concept that later was to be used to resolve a good many theoretical difficulties in quantum mechanics. Experimentally, the de Broglie wave of electrons was directly verified through crystal diffraction in 1927. Actually, with the triumph of Schrodinger's wave mechanics in 1926, no one had any doubt concerning the wave nature of electrons. A characteristic phenomenon of a wave is its ability to interfere. Yet, any progress in interference experiments of electrons was rather slow. Between 1930 and 1950, there was no intentionally planned experiment in electron interference. The findings of the Fresnel diffraction fringes of electrons in 1940 was an incidental achievement in the development of the high-resolution electron microscope. Beginning in 1950, electron microscopists were actively involved in deliberate efforts to carry out direct interference experiments of electrons. Finally in 1954, the first electron interferometers were successfully demonstrated: but during the next few years, experimental activities in electron interference proceeded rather slowly. From 1960 to 1962 after the Bohm- Aharonov (1959) experiment became known, things began to change. A number of interesting interference experiments, including the Bohm- Aharonov experiment, were performed. This renewed interest reached a new peak, which was comparable to the early 1950s. After 1963, very little was done in the area of interference, especially since the group in the National Bureau of Standards left the field. About this time Tubingen became the only center for electron interference. From 1970 interest arose on work associated with the electron interference microscope. Meanwhile, success with the neutron interferometer also stimulated further experiments in electron interference. The slow pace of experimentation in electron interference may be attributed to several reasonc. The triumph of quantum mechanics has suppressed the need for experiments that exclusively exhibit the wave characters of electrons: the stringent requirements of these interference experiments have discouraged many experimenter5 and numerous preconceived ideas have kept physicists away from these experiments. Thus, many important interference experiments of electron interference slipped by unnoticed. Young's experiment on diffraction of electrons was done in 1961 by a Tiibingen group. For decades, the experiment had been considered a thought-experiment (Gednnken experiment). It is pedagogically clean and can be used to illustrate many of the concepts and apparent paradoxes of quantum physics. However, the experiment did not catch the attention of textbook writers and classroom teachers. This situation continued for more than a decade. In 1974 an editorial comment in the Ameri-

ELECTRON INTERFERENCE

27 1

can Journal of Physics finally called attention to the existing experiment of multiple-slit diffraction by electrons (French and Taylor, 1974). The present chapter includes a description of de Broglie’s wave packet and a wave packet relating to crystal diffraction of electrons. A theoretical explanation of beam splitting and coherence detection mechanisms in electron interference experiments is presented along with a historical review on these experiments. Several proposed new interference experiments are mentioned. Finally, an attempt is made to assess the achievements and need for further efforts in the area of electron interference.

11. ELECTRON WAVE A . Theoretical Background

A beam of electrons with momentum q, is described by a quantummechanical state Iso).In actual space-time, it represents a wave

(r, riao) = (2.1r)-3/2expri(l6.r - wet)]

(1)

whose wave vector k,, is related to the momentum qo, 90 = hko

and the circular frequency

ooto

(2)

the kinetic energy Qo of electrons

Qo = firno

(3)

where fi is Planck’s constant. However, electrons are also particles. The wave and particle are two different concepts in classical physics. To bridge such a difference in quantum mechanics, de Broglie (1924) introduced the concept of wave packet J$J. In other words, a beam of electrons may be considered a collection of wave packets. The wave packet is a pure state in quantum mechanics; it has a continuous momentum spread Aq. The average momentum of the electron packet represents the actual momentum of the electron. Quantum mechanics does not provide a concrete description of the profile of the wave packet. For the sake of theoretical discussion, one usually chooses a simple profile. For example, a normalized Gaussian packet is a common choice:

where the subscript a denotes the rectangular components of the corre-

272

MING CHIANG LI

sponding vectors. In actual space-time, the Gaussian packet has the form (r, tlJa> =

j-(r, rlq>~q(ql$,,)

where m is the mass of electrons and r = ( X I ,X,, X 3 ) . Equation (5) denotes a localized wave, which is peaked at r = qt/m. This packet represents a moving electron in the beam. However, its spatial spread Ar,

varies with time. As time increases, the width of the spatial spread also increases. This is called the dispersion of a wave packet (Schiff, 1968). It happens even in free space. Eventually, the wave packet is no longer localized and itself disappears. The dispersion of a wave packet is the main obstacle in de Broglie’s wave theory of matter. However, there are mathematical models (Ignatovich, 1978) in which the wave packet does not disperse. Whether these mathematical wave packets represent real physical packets requires further investigation. It is experimentally impossible to have a beam of electrons all having the same velocity. Within a beam, some of the electrons move faster and others slower. These electrons have a certain momentum distribution $b(qo - q b ; Aqb), where q b denotes the average momentum of electrons in the beam. Aqb is the average momentum deviation of electrons with respect to the average momentum q b . In terms of quantum-mechanical description, wave packets differ within a beam. Hence, a beam is a collection of various wave packets, and can be described by a density matrix $b(qO

- q b ; Aqb)I$p

’dq0

$PI

(7)

Hence, one needs two types of functions to describe a beam: the profile function JlP(q - q o ; Aq) and the distribution function $b(qg - q b ; Aq,). The former is coherent in nature and the latter incoherent. Henceforth, Aq is referred to as the coherent spread and Aqb the incoherent spread of the beam. The concept of a wave packet is deeply embedded in the formalism of

ELECTRON INTERFERENCE

273

modern physics. Quantum theories based on monoenergetic plane waves have encountered various difficulties, whereby wave packets are often called upon to circumvent them. Although the idea of wave packets has been repeatedly used in many quantum theories, its characteristic feature cannot be traced from any measurable quantities as predicted by these theories. For example, in the potential scattering theory of a wave packet (Low, 1959), where the packet characters play dominant roles, the measurable differential cross section does not provide any information on this packet. So far, no one knows the wave packet profile of a given particle beam and the mechanism by which the wave packet is formed. However, the wave packet can reveal itself in direct interference experiments. This is the subject of the present review.

B . Electron Becim Electrons, as generally encountered in electron interference experiments, have eaergies mostly in the range above 20 keV and wavelengths less than 0.08 A. The electron source size has a diameter of a few micrometers for heated pointed filaments and as little as 20-50 A for field emission tips. When combined with electron lenses, these sources can give well-collimated beams. A divergence of lod6or less can be achieved fairly readily. In the 100-keV range, the voltage supplies may have a stability of better than giving sufficient chromatic coherence. The fundamental reason for using electrons with energy above 20 keV in the interference experiments is in obtaining reasonable penetration into the diffractor and freedom from perturbation caused by stray laboratory magnetic fields and space charges. Interference is a wave phenomenon. In describing electron interference, one uses exclusively the language of wave theory. The wave packet is replaced by wave train and momentum by wave vector. The wave vector spreads Ak = Aq/h and Akb = Aqb/h are usually divided according to their relationship with respect to the mean wave vector kb = qb/h. The spreads parallel to kb are referred to as the longitudinal spreads Akl , Akbland that perpendicular as the transverse spreads Ak, , Akbtwith Ak = Akl Akb = Akbl

+ Akt + Akbt

( 8)

(9)

The breadth across the face of a wave train is inversely proportional to the coherent transverse spread Akt and the length to the coherent longitudinal spread Akl. In a partially coherent beam, wave trains can differ in length

274

MING CHIANG LI

and breadth as well as velocity. There is no proper coordination among these trains, and the destructive interference makes their apparent length and breadth shorter. * Theoretical interest concerning the length and breadth of the electron wave train began as early as 1930, and has persisted to the present. However, these quantities are not sensitive to the interference experiments. The present view toward the breadth is (Cowley, 1975): Electrons are emitted from the region of high electron density surrounding an atom. The region is sufficiently small in comparison with all other dimensions in the interference experiment and is treated as a point. Within a given source there are a number of independently emitting regions. This view asserted that each electron wave train, which is from a point, can be well collimated through a lens and have a large breadth. Since each train might be originated from different and independent regions, the size of a given source would give an indication of the transverse wave spread Akbt. With respect to the train length, the view is that the emitting region is not considered as essentially different from a p emitter and the length is often limited only by the thermal energy spread of the source (Gabor, 1956). The emitting region is not a fully defined physical entity, and the coherent spread Ak is not calculable. In the existing interference experiment of electrons, one cannot isolate the coherent spread Ak from the incoherent spread Akb. To obtain more information about the emitting region, further experiments are required. The aforementioned views have not been quantitatively verified at the present. 111. CRYSTAL DIFFRACTION

For the interference of light, one begins with conceptually simple and pedagogically clear experiments such as Young’s double slits and Fresnel’s biprism experiments. The short electron wavelength makes the source slits difficult to manufacture and stability hard to maintain. However, nature has readily provided a closely spaced and periodic diffractor, namely crystal, which makes the stringent requirements less strenuous. The first electron interference experiment is on crystal diffraction and demonstrated by Davisson and Germer (1 927) and by Thomson and Reid (1927). Their experiments provided evidence of the correctness of the de Broglie relationship, relating the wavelength to momentum, as well as to the essential wave nature of the electron. Since then crystal diffraction of * If the profile and distribution functions both are Gaussian, the apparent train breadth is inversely proportional to [(Ak,)* + (Akk,,)2]1’2 and the apparent train length to [(Akl)2 + (Ak,l)2]”2.

ELECTRON INTERFERENCE

275

electron has been an important tool for crystal structure analysis (Cowley, 1975). Usually, diffraction processes were classified as Fresnel and Fraunhofer diffractions, depending on the distance between the observation point and the diffracting system. Points that are many wavelengths away from the diffracting system, but still near the system in terms of its own dimensions, lie in the Fresnel zone. Points that are further away at distances large compared to both the dimensions of the diffracting system and the wavelength are in the Fraunhofer zone. The diffraction patterns in the Fresnel and Fraunhofer zones show characteristic differences. Distinction between these two also exists for crystal diffraction. It was noted by Li (1978a) that for an incident plane wave, the diffracted wave is a plane wave in Fresnel diffraction and a spherical wave in Fraunhofer diffraction. The observation of such a difference is specially important in the construction of electron interferometers based on crystal diffraction (Li, 1978a). In the following discussion, these two types of diffraction are treated separately. A . Fraunhofer Diffruction

Let rj = ( x j l ,xj2, x j 3 ) denote the position vector of a unit cell in the crystal and k, the wave vector of the monochromatic incident electron beam (See Fig. I). The wave function of a diffracted beam, under the kinematical approximation, has the form N

-

flk,; n) exp(ik, rl

+ ik(r - rjI-iQt/h)

(10)

j= 1

wheref(b; n) is the atomic scattering amplitude of a unit cell in the direction n, N the total number of cells in the crystal, and Q the kinetic energy

Y

FIG. I . An incident beam k( is diffracted by a crystal C with its center located in the origin of the coordinate system.

276

MING CHIANG LI

of the incident electron beam with

Q

=

ti2k2/2m

with

k2 = ki ki

(11)

For Fraunhofer diffraction, the approximation

-

/r - rjl = r - (rj * r/r) = r - rj n is made in handling phase factors of Eq. (lo), which becomes

(12)

where k = kn = kr/r

(14)

is the wave factor of a diffracted beam. It is explicitly expressed in Eq. (13) that the outgoing diffracted wave is spherical. The objective here is to exhibit the spread effect of an electron beam in crystal diffraction and to study the coherence of diffracted beams. It would be helpful to choose a simple experimental arrangement in order to avoid unnecessary complication. Let us choose an ideal crystal with the shape of a parallelepipedom, whose sides are parallel to cell edges and to axes of the reference frame. The three fundamental lattice vectors are a, = ( a l , 0, 0 )

(15)

a2 = (0, a 2 , 0 )

a3 = ( 0 , 0, a d The summation in Eq. (12) can be carried out:

where N , is the number of unit cells along the edge a, with N = N l N 2 N 3 , and the subscript a is used to denote components of wave vectors. To eliminate irrelevant phase factors, it is assumed in Eq. (18) that the center of the crystal coincides with the origin of the reference frame. For a large number N , , one can use the approximation

where K is a reciprocal lattice vector of the crystal.

ELECTRON INTERFERENCE

277

The preceding discussion is based on crystal diffraction by a monoenergetic plane wave and is adopted by all textbooks on crystal diffraction. In 1959, Low put forward a detailed description on potential scattering by a wave train. The Fraunhofer diffraction of a crystal is a special case of potential scattering. According to his description, the diffracted wave train has the form

N

1

dk,F(ki, k)4(k, - ko; Ak)f(k,; n) exp[i(kr - Qt/fi>]

(20)

where Although legitimately one cannot ask for any more detailed description of an electron beam and its wave trains beyond what has been said in Section 11, it would be very helpful to specify a convenient functional form to the profile function 4(ki - k,,; Ak) for the purpose of displaying the coherent effects. In Section 11, a Gaussian form was chosen for the purpose of displaying the dispersion effect of a wave train. Here the chosen profile is not entirely a Gaussian:

This form represents an infinitely long wave train with a finite breadth. The function in Eq. (22) is sharply peaked and the atomic scattering amplitudef(kt; n) is a gradually varying function. To a good approximation, one can write Eq. (20) as

To perform integrations in Eq. (23), one makes a linear approximation Now Eq. (23) is proportional to

To avoid unnecessary complication, it is further assumed that the crystal is thin and terms depending on its thickness N3a3 in Eq. (25) have been neglected. Equation (25) denotes a spherical wave train with its angle

278

MING CHIANG LI

spread depending on the breadth of the incident wave train as well as the crystal cross section. The diffraction has altered the shape and character of the wave train. For an arbitrary wave train, the alteration would be more complicated than that in Eq. (25). Due to the incoherence among different wave trains in a quasimonoenergetic electron beam, the experimentally measured intensity of a Fraunhofer diffraction, according to Low (1959), is proportional to

N2

J-:

dt

1

dko&b(ko - kb; Akd

li

dkiF(kt, k)

x +(ki - k,; Ak)f(ki; n) exp[i(kr - Qt/fi)]12

(26)

where +b(kO

- kb;

Akb)

&(Qo

-

Qb;

Aq,)

If the wave train alteration from the crystal can be neglected, as a basic assumption of the standard crystal analysis, then Eq. (26) becomes

1

N 2 dG&(ko - kt,; A16))ffko; n)F(ko, k)/'

The factor in the last line of Eq. (27) can be eliminated by a proper normalization. Hence, the trace of the incident wave train, which is deeply embedded in the theory, completely disappears. The diffracted wave has a larger wave vector spread than the incident wave. The extra amount is an added uncertainty induced by the spatial extent of the diffracting crystal. From the familiar Laue condition, diffracted beams are separated by reciprocal vectors. To observe the diffraction process experimentally, the diffracted wave spread should be less than the lowest reciprocal lattice vector. Hence, there is a requirement on the monochromaticity of the incident electron beams. The requirement is less severe as compared to that for later electron interference experiments. In the first crystal electron diffraction experiment of Thomson and Reid (1927), the source of electrons was a low-pressure gas discharge, which is known to be heterogeneous in energy with a large spread compared to a thermionic cathode, and the stability of the 10-keV accelerating voltage was quite poor. Since the crystal diffraction process alters the wave train characters of the incident wave, one can in principle obtain the wave train information through crystal diffraction. However, it does require a very careful measurement as well as a well-defined theory on the mechanism by which the wave train is formed.

279

ELECTRON INTERFERENCE

B . Fresnel Diffraction For Fresnel diffraction, the observation point is closer to the diffracting crystal than that for Fraunhofer diffraction. One usually replaces the approximations in Eq. ( 1 2 ) by

where vectors r and rj have components ( X , , X , , X 3 ) and (xjl, x j 2 , xj3), respectively. The diffracted wave function in Eq. (10) can be written as G(ki, r)f(k,; n) exp(- iQtlti)

(29)

where N

G(ki, r) =

exp iki * rj + ik(X3 - xj3)

1=1

To sum the above quantity, one utilizes its Fourier transformation &,

X3;q l ,

v 2 )=

dX, dXzG(ki,r) exp[ - i ( q l X 1 + q 2 X 2 ) ]

N

x

2 exp[i(ki - k')

rj]

j=1

where k ' = ( q l , qz,k ) . The summation in Eq. (31) is similar to that in Eq. (13). After summing the series, one has

(32)

The phase in the last large parentheses may be linearly approximated,

- I. x -3v ; 2k

= -

i-

x3 ( k h + K,)' 2k

x3

t ik (ki,

+ K,)(ki,

-

77,

+ K,)

(33)

After the Fourier transformation of the previous function and using Eq.

280

MING CHIANG LI

(33), one arrives at

where k;

=

{kil

+ K1, k,z + K z , k

-

(2k-')[(ki1 + K1)'

+ (kiz + KZ)'])

(35)

As expressed in Eq. (34), the outgoing diffracted wave in a Fresnel diffraction is a plane wave, while in a Fraunhofer diffraction, one observes a spherically diffracted wave. In conventional crystal diffraction of a single electron beam, only the diffracted beam intensity is observed; whether the diffracted beam is in a plane- or a spherical-wave state is immaterial. Authors (Azaroff, 1968) of most textbooks on crystal diffraction seldom point out the distinctions between Fresnel and Fraunhofer diffractions. It is quite common to consider the diffracted beam as in a plane-wave state, when Bragg and Laue diffraction conditions are being discussed, or as in a spherical-wave state when the wave function of the diffracted beam is expl icitly written. The diffracted wave train of a Fresnel diffraction has the form

To see the effect of a Fresnel diffraction on a wave train, one follows the same discussion as in the case of the Fraunhofer diffraction. The profile function is taken from Eq. (22) and a linear approximation is made to the wave vector in Eq. (35). One writes

kI = k; with

+ Ak;

(37)

ELECTRON INTERFERENCE

28 I

After integration, Eq. (36) is proportional to

-

Nf(ko; n) exp[i(kh r - Q t / h ) ]

Terms depending o n N3a3are neglected in Eq. (40).The breadth of the diffraction wave train depends not only on the breadth of the incident wave train and the crystal cross section, but also on the location of the wave train. The latter dependence is a dispersion effect. The phase in the square bracket of Eq. (40) is the phase delay resulting from the crystal diffraction. IV. TWO-BEAMINTERFERENCE Since the successful demonstration of electron diffraction from a crystal, experimenters have been duplicating the classic experiments of Young, Fresnel, and others upon which the wave optics of light was founded. A common feature of these experiments is that two distinct beams interfere with each other. In the early 1950s two types of two-beam interference experiments of electron had been successfully carried out. Now they are referred to as Mollenstedt-Duker (1954) and Marton (1952) electron interferometers. There are two stages involved in these experiments: (1) the creation of

FILAMENT

I I 1

POSITION FOR OBSERVATION

FIG.2.

Mollenstedt -Duker interferometer.

282

FIG.3.

MING CHIANG LI

Fresnel diffraction is used to split coherent beams. It is an amplitude division.

two coherent beams, and (2) the detection of coherence among these beams. Coherent beams are obtained through the splitting of a primary beam. In the Mollenstedt-Duker interferometer the coherent beams are produced by macroscopic electric fields as shown in Fig. 2. The electrons are deflected by a filament about 1 p n in diameter charged with a voltage of several volts with respect to the earthed electrodes at the sides. The coherent beams come from different portions of the primary beam. This is a wave front division, which was used in Young’s experiments. In a Marton interferometer, the coherent beams are produced through a crystal diffraction as shown in Fig. 3. They come from the same portion of the primary beam. This is an amplitude division. For the detection of coherence, two coherent beams are brought to intersect, and the resulting coherence can be detected using either of two methods. One is to observe the interference pattern of two coherent beams having different wave fronts. This type of interference is referred to as wave front interference. The other is to initiate a Fraunhofer diffraction by these two beams (Li, 1978a). Then the amplitude of the diffracted spherical wave contains the coherent information and the coherence can be detected from it. The latter type of interference has been referred to as amplitude interference. A . Wave Function and Beam Splitting

Coherent beams are obtained through the splitting of a primary beam. The wave function for describing the coherent beams depends on the manner in which the primary beam in split. Let us first consider a wave front division. In the Mollenstedt -Duker interferometer, the coherent beams are produced by the macroscopic electric field with a spatial separation. To give a full description of the Mollenstedt-Duker splitting mechanism, one has to develop a wave packet theory for scattering by a localized electric field. Since a wave packet theory for describing crystal diffraction was established in Section 111, it would be more convenient to

283

ELECTRON INTERFERENCE

utilize such a theory to give an illustration on a wave packet description of the wave front division. Two crystals having the same orientation, but separated by a distance b, are shown in Fig. 4. One of them is located on the origin of the reference system. In other words, two macroscopic electric fields in the Mollenstedt-Diiker interferometer are replaced by two crystals. An incident electron beam, through Fresnel diffraction by these two crystals, produces two coherent beams. In Fig. 4, irrelevant diffracted beams have been omitted. In the discussion of Section 111, the center of the crystal is located on the origin of the reference systems, and the incident wave has the form exp(iki r). The discussion can be extended to the crystal located at b and the incident wave exp(ikl * r). For a plane wave, Eq. (34) is replaced by q(ki, k; ; b) exp[ik,

b

+ ik;

(r

- b) -

iQf/ti]

(41)

where

For an infinitely long wave train with a finite width as given in Eq. ( 2 2 ) , one can replace Eq. (40) by qp(ko,k;; b) exp[ik,

b

+ ik,

9

(r

-

b) - iQt/h]

X

I

FIG. 4. Wave front division by the spatially separated crystals.

(43)

284

MING CHIANG L1

where

In Eqs. (42) and (44), terms depending on N3a3 are neglected by the assumption of a thin crystal. The wave train represented by the profile in Eq. ( 2 2 ) has the form

fi exp [- ( A k ) 2 (X,- 4 X 3 ) ] 2

exp[i(k;

*

r

-

Qf/ti)]

0

a=l

(45)

where

kb: = [ k o i , kozr ko

-

(2ko)-'(Gi + k&)l

(46)

For a plane incident wave, the wave function for coherent beams produced in the experimental setup of Fig. 4 can be written as q ( k i , k,; b) exp[ik, b + i k , (r - b) - iQr/fi] + q(ki, k,; 0) exp[zkz r - iQt/fi]

(47)

The relative phase between two terms in Eq. (47) is (kl - kl) b + (k1 - k2) * r + arglf(kl; n l f * ( k z ;n ) ]

(48)

This phase is due to the path length difference between two coherent beams and to the phase difference between atomic scattering amplitude. For an incident wave train as in Eq. ( 4 9 , the wave function for coherent beams produced in the experimental setup of Fig. 4 can be written as qp(b, klo; b) exp[iko * b + i k I o .(r - b) - i Q f / h ] + qp(k,, kzo; 0)exp[ikzo r - iQf/til

(49)

where k l o , kzo, and ko are the average wave vectors of the diffracted and incident beams. The wave train of the upper beam klo in Fig. 4 is described by the functions qp(k,,, klo; b). According to Eq. (44), the central axis of this wave train is determined by

285

ELECTRON INTERFERENCE

X , - b, - (k;h/kO)(X3- b3)= 0,

for

(Y

= 1,

2

(50)

As the separation b increases, the amplitude of the upper beam along the train axis decreases as

In the experimental arrangement of Fig. 4 , the incident wave train of Eq. (45) is aimed at the lower crystal; thus the upper crystal is off the axis of

the incident train by a distance b. Because of this finite train breadth, off the axis the coherence reduces, as the ability of the wave train to initiate the upper coherent beam decreases. In the wave front division, to offset such decrease the breadth of the incident wave train should be wider than the separation of the two crystals. A wider effective breadth requires a smaller source of electrons. The phase arg[qp(b, klo; b)] resulting from the dispersion is nonzero off the train axis. Then the relative phase between the terms in Eq. (49) has a term depending on the dispersion. Now let us turn to the amplitude division. The experimental arrangement is depicted in Fig. 3. The Fresnel diffraction of a crystal is used to split the primary beam kj. Irrelevant diffracted beams are also omitted in Fig. 3. For a plane incident wave, the wave function for coherent beams is

-

q k , kl; 0) exp(ik, r

- iQt/h)

+ q(ki, k2; 0) exp(ik2- r - iQr/h)

(52)

For an incident wave train, the corresponding wave function is q,(k,, klo; 0)exp(iklo r - iQt/W + qp(ko.kzo; 0) exp(ikzo r - iQt/h)

(53)

In the amplitude division, the dependence on the spatial separation has been eliminated. There is no restriction on the train breadth, hence one can use a larger source of electrons. B . Wave Front Interference A common method for observing the coherence of two coherent beams is through wave front interference, which is employed in both the Marton and Mollenstedt-Duker interferometers. For the convenience of our discussion, the state of coherent beams as described in Eq. (47)is simply written as

exp(ik,

r)

+ a exp(ik,

r)

(54)

where n denotes the relative phase and amplitude of these two beams.

286

MING CHIANG LI

In a wave front interference, one observes the interference pattern ) e i k l *+r aeiIrz*r(z = 1 + 2[a[cos[(k, - k,) * r + arg(a)] (55)

+

The fringe spacing d of the interference pattern satisfies the relation d = A/[2 sin($+)]

(56)

where A = 27r/k in the wavelength of electron beams and Cp is their intersecting angle. The electron beams used in electron interferometers have a wavelength about 0.05 A. Experimental requirements in obtaining an interference pattern from short-wavelength coherent beams are stringent. First the intersecting angle between the coherent beams must be small so that the fringe spacing is greater than the resolving power of the observing instrument; hence a very precise alignment is required. Second, the same angle must be sufficiently large in order to offset the inherent mechanical instability of the instrument for the purpose of obtaining a steady interference pattern. In a successful experiment, the intersecting angle is about rad. To study the spread effects on the interference pattern, one should consider the detailed mechanism on beam splitting and bending. For the experimental setup of Fig. 4, the interference variation in Eq. (49) produced by a wave train is

.

cos{(k, - klo) b + k0 - kzo) r

+ arg[q,(ko, klO;b)ll

(57)

Since beams are split and bent through crystal diffractions, wave vector differences in Eq. (57) can be expressed in terms of reciprocal lattice vectors k, - klo = Klo and klo - kzo

=

Kzo - Kio

(58)

The phase factor arg[q,(k,, klo; b)] is due to the dispersion of the wave train from the crystal diffraction. The presence of this phase factor would alter the fringe spacing given by Eq. (56). For an electron beam with a wide train breadth, it will be a small factor. If this factor can be neglected, the fringe variation in Eq. (57) becomes independent of individual wave vectors, but dependent on reciprocal lattice vectors. Hence, the incoherent beam spread will not alter the fringe spacing and the interference pattern is stable with respect to the external disturbing force, which tends to bend electron beams. Thus, incoherent and coherent spreads of an electron beam affect only the envelope of the interference pattern. C . Amplitiide Interference

In some direct interference experiments, the change of the relative phase factor arg a is of special interest. For example, in the famous

287

ELECTRON INTERFERENCE

Bohm-Aharonov experiment, one studies the relative phase change due to the alteration of the magnetic flux passing between two coherent electron beams, even though the beams themselves pass only through a magnetic-field-free region. In the measurement of the mean inner potential of thin film, the object is to measure the relative phase change due to the mean inner potential. Experimentally, it often relies on the observation of an interference fringe shift to demonstrate the changing of the relative phase factor arg a. However, to observe the relative phase change, it is not always necessary to rely on the interference pattern. This can be illustrated by considering a scattering process initiated by two coherent electron beams of Eq. (54). The scattered wave function satisfies the Schrodinger equation

+ (2rn/h2)V(r) +(r) = k2+(r)

- V2+(r)

-

(59)

and the asymptotic condition

J/(r)

r-=

+

+

efkIar ueikr'r F ( k l , k2; n)e'"/r

(60)

where V(r) is the potential of a fixed center, and n is the direction of the scattered wave, which comes from the disturbance of incident waves by the scattering center. The Schrodinger equation (59) and incident waves in Eq. (54) are both linear. The coherent scattering amplitude may be expressed as F ( k l , k 2 ; n)

= f(k, ; n)

+ uf(k2; n)

(61)

wheref(ki; n) for i = 1 , 2 is the conventional scattering amplitude of a single incident beam. Thus the scattered wave in Eq. (60) can be expressed as [f(kl; n) + af(k2; n)]efkr/r

(62)

The scattered wave has only a common spherical wave front, but its amplitude contains the coherent information a of the two beams in Eq. (54). Amplitude F ( k l , k,; n) is a macroscopic quantity and is related to the experimentally observed differential cross section

dX,(k,, k2; n) = (1 +

1 F ( k l , k2; n)I2 d o ,

(63)

where dR, is the solid angle. The conventional differential cross section for a single incident beam has the form dv(k,; n) = If(ki; n)I2 d R n ,

for i

=

1, 2

(64)

From Eqs. (63) and (64), one can write

dC(kl, k,; n)

=

(1

+ laI2)-' { d d k l ; n) +

d 4 k 2 ; n) + arg(a)]}

+ 21~1[a&: n)a(k2;II)]''~ cos[Q,

(65)

MING CHIANG L1

288

where @ = arg[f*fkl; n>f(kz;n>l

(66)

The differential cross sections in Eq. (65) can be measured macroscopically. Hence there is no need to rely on the interference pattern to observe the relative phase factor arg a. In the illustration the fixed scattering center plays the role of analyzer, which changes a microscopic quantity into a macroscopic one. This is accomplished by converting two separate incident waves into a single spherical wave. Since the coherence information of two incident waves is not contained in the wave part of the spherical wave, but rather in the amplitude, the interference has been referred to as amplitude interference. Besides a fixed center, amplitude interference can also be accomplished through Fraunhofer diffraction by a crystal. In Fraunhofer diffraction, the crystal converts an incident plane wave into spherical waves as in Fig. 5 . For two coherent incident waves in Eq. (54), the diffracted spherical wave can be written as 1 2N ; {f(kl ; n) exp[i(kl - k) j= 1

+ uf(k,;

rrl

-

n) exp[i(kz - k) r,]} exp(ikr - iQt/h)

(67)

As it is in fixed-center scattering, the coherence information of two inci-

dent waves is contained in the amplitude and not in the wave front of the diffracted spherical wave (see Fig. 6). From Eqs. (131, (181, and (191, summations in Eq. (67) can be carried out:

+ uf(k2; n)

n [ 2

exp

-

(k,

-

k

+ K ) : ] } exp[i(kr - Qr/h)]

168)

lY=l

where K and K' are reciprocal-lattice vectors. If the incident waves have

FIG.5 . The Fraunhofer diffraction of a crystal, which converts a plane incident wave into spherically diffracted waves.

ELECTRON INTERFERENCE

289

FIG.6. Amplitude interference through Fraunhofer diffraction.

wave vector spreads as in Eq. (22), from Eq. ( 2 3 , the diffracted wave has the form

x exp[i(kr - Q ' t / h ) ]

(69)

where klo and kzo are average moments of incident wave trains. The diffracted wave train in Eq. (69) has a wider angle spread than that in Eq. (68) because the spreads of incident waves make the angle spread of the diffracted wave wider. To observe amplitude interference in diffracted waves of Eqs. (68) and (69), one has to overlay a diffracted wave from one of the coherent incident waves to that from another. The experimental alignment procedure is to make these peaked functions in Eqs. (68) and (69) overlapping. Since the diffracted wave from an incident wave with a spread has a wider angle spread than that from a well-collimated incident wave, then the amplitude interference is easier to observe for the coherent electron beams with a wider coherent spread Ak. On the other hand, to observe the wave front interference, the coherent electron beams should have a narrower coherent spread bk.

V. INTERFERENCE EXPERIMENTS The interference experiments of electrons is a by-product in the development of electron microscope. By 1940, Boersch (1940) and Hillier (1940) observed contour fringes around opaque or semiopaque boundaries in out-of-focus pictures. A number of authors (Ruska, 1943; Boersch, 1943) assigned them to be Fresnel diffraction fringes. In 1947, Hillier and

290

MING CHIANG LI

Ramberg showed that the contour patterns could be fitted rather well to Fresnel's formula. The Fresnel fringes are well known to modern microscopists and are commonly used in electron microscopy as a focusing device. In 1951 Uyeda and collaborators (see Mitsuishi er d.,1951) observed equidistant dark bands running across an electron microscope image. These bands were interpreted as interference fringes produced by the wedge-shaped flakes off the lamellar crystals. In 1953, Rang observed interference fringes from a blister. The direct interferences experiments of two beams were successfully realized by Marton et a / . in 1953, and by Mollenstedt and Diiker in 1954. Instruments of two-beam interference experiments are referred to as interferometers. The success in constructing electron interferometers has led to the development of new instruments. In 1957 (Mollenstedt and Buhl, 1957), an electron interferometer was combined with an electron microscope to produce an electron interference microscope that makes phase modulation by the object visible. In 1959 (Jonssen and Mollenstedt, 1959; Jonssen, 1961), Young's experiment of electrons was realized. The Michelson interferometer of electrons appeared in 1972 (Lichte er a / . , 1972). A Young-Fresnel double-mirror interferometer was constructed in 1978 (Mollenstedt and Lichte, 1978). For understanding interference phenomena of electrons, the Mollenstedt -Duker and Marton interferometers are particularly important and deserve special attention. A . Mollenstedt -Diiker Interjerometer

This instrument, schematically illustrated in Fig. 2, is an electronoptical analog of Fresnel's biprism. By varying the filament voltage within several volts, the intersecting angle between coherent electron beams can be varied in a wide range, producing the biprism interference pattern with different spacings. The fundamental difficulty in the electron interference experiment of an interferometer is the unavoidable stray magnetic fields found in most laboratories. A change of magnetic flux through the enclosed area of coherent electron beams will cause a relative phase shift between these two beams; this, in turn, results in a loss of coherence by AC magnetic flux. The general success of the Mollenstedt-Duker over the Marton interferometer rests mainly in the compactness of the area enclosed by coherent electron beams. The Mollenstedt -Diiker interferometer has been used to measure the mean inner potential (Keller, 1961) of thin films, the quantized magnetic flux in super conductors (Doll and Nabauer, 1961; Deaver and Fairbank, 1961), the beats produced by the microbetatron (Bayh, 1962), the contact

29 I

ELECTRON INTERFERENCE

potential (Krimmel, 1964), the width of an electron source (Braun, 1972), and the Doppler shift of electron waves (Lichte and Mollenstedt, 1978). A detailed review on the above-mentioned experiments may be found in a recent talk by Mollenstedt and Lichte (1979). In 1959, The Bohm-Aharonov effect became known. Experimenters with access to electron interferometers were actively involved in observing such an effect, which deals with the significance of the vector potential in quantum mechanics. It states that even for electrons moving in regions without any magnetic field, the relative phase between two coherent electron beams is shifted by A4, if the magnetic flux enclosed by them is present; then

A4

=

-e/hc

I-

A dl = - ( e / h c ) B S

(70)

The experiment is depicted in Fig. 7, in which the magnetic field B is confined in the shaded region S. The Bohm-Aharonov effect created a controversy in quantum mechanics. It is considered by many that the effect has been convincingly confirmed noticeably by the whisker experiment of Chambers (1960) and the three-biprism experiment of Mollenstedt and Bayh (1962). However, in the analysis of Fowler et al. (1961) the fringe tilt in Chamber’s experiment could have resulted from the leak field. In Boyer’s analysis (1973), for both of the above experiments one can not rule out an interpretation based upon a classical electromagnetic lag effect. More recently, Bocchieri and Loinger (1978) showed that the Bohm-Aharonov effect is a consequence of an improper choice of initial conditions and experimental observations of this effect are not conclusive. The theoretical controversy over the Bohm-Aharonov effect is centered on the fundamental nature of the electromagnetic potentials V and A vs. that of the fields E and B in quantum mechanics. DeWitt (1962) and Belinfante (1962) pointed out that the quantum theory of interaction

I

SPLITTER

OBSERVATION

FIG.7. Bohrn- Aharonov experiment.

292

MING CHIANG LI

between charged particles and electromagnetic field can be reformulated solely in terms of the field strengths. Aharonov, Bohm, and others assert that potentials are more essential. At present, the Bohm- Aharonov effect has been studied for its consistency with the uncertainty principle (Furry and Ramsey, 19601, classical limit (Peshkin e t al., 1961), singlevaluedness, and momentum conservation (Boyer, 1972). With recent theoretical explorations in magnetic monopole and non-Abelian gauge fields (Wu and Yang, 1975), interest in the Bohm-Aharonov experiment has been reinforced.

B . Marton Interferometer The instrument illustrated in Fig. 8 is a rough equivalent of an optical interferometer of the Mach-Zehnder type. The electron beam traverses in succession three thin equally spaced crystalline laminae. During each traverse, the electron beam undergoes a Fresnel diffraction. Irrelevant diffracted beams are omitted in the figure. The first crystal is a beam splitter. It is an amplitude division. The remaining two crystals are used as benders of the electron beams, with the third one having particular importance in making the angle between the two interfering beams less than rad. This is necessary so that the beams could be accommodated by the aperture of a conventional electron microscope lens, used to enlarge the fringe spacing to a given size, a t which the fringe could be resolved by a photographic plate. The advantages and disadvantages of a Marton interferometer are all accounted for by the relatively large separations (- 1 mm) between coherent beams. Marton and his collaborators achieved fringe observation on the order of 5800. This sets a lower limit for the length of the apparent electron wave trains of about 28 nm and was the first direct experimental determination of this quantity. On the other hand, the apparent coherent

FIG. 8. A Marton interferometer. A well-collimated electron beam traverses three equally spaced thin crystalline laminae S,E l , and Ez in succession. On an actual scale, the rad and the distance between crystal laminae is intersecting angle 4 is about 2.5 x about 4 cm.

ELECTRON INTERFERENCE

293

length of the electron wave trains measured by a Mollenstedt-Duker interferometer (Keller, 1961), which has a much smaller beam separation, is about 14 nm. The presence of stray 60 Hz fields in almost all laboratories and the inherent small mechanical vibrations of the apparatus have made the task of stabilizing the interference fringe for such a large beam separation very difficult. Since 1954, the Marton interferometer has not been used. Although it does not enjoy the same kind of success as the Mollenstedt-Duker interferometer, it did influence the new generation of interferometers. The design of the three-biprism interferometer (Bayh, 1962) is one example. Instead of crystals, three filaments are used in the three-biprism interferometer. The first filament is negatively charged and plays the role of a beam splitter; the second filament is positively charged and is used as a bender; while the third filament is negatively charged and is used to create a small intersecting angle of two coherent beams in the plane of observation. These three filaments have the same roles as the three crystals in a Marton interferometer. With such an arrangement, the beam separation in the three-biprism interferometer is greatly increased in comparison with that of the original Mollenstedt-Duker interferometer. Furthermore, the X-ray interferometer of Bonse and Hart (1965) and the neutron interferometer of Rauch er a / . (1974)are actually variations of the Marton interferometer. In these interferometers, three parallel and equally spaced crystals are cut from a giant-sized crystal. The alignment difficulties of the Marton interferometer have been avoided. Atlhough the Marton interferometer has not been utilized in the past 25 years, interest in such an interferometer is very much alive. When the Bohm-Aharonov (1959) effect became known, it immediately brought to mind the Marton interferometer. It has since been suggested that, because of the large beam separation and stray magnetic field, the BohmAharonov effect is either not in existence or has blurred out Marton's fringes. Finally, Werner and Brill (1960) explicitly showed that, to the lowest order, the Bohm-Aharonov effect from the stray magnetic field exactly cancels the phase shift due to the magnetic field through the beam path, and the cancellation makes the interference pattern stable with respect to the stray magnetic field. So Marton's experiment, instead of proving the inconsistency of the Bohm-Aharonov effect, demonstrated the need for it. Now, with the appearance of the neutron gravity interference experiment of Colella er a / . (1973, one refers to the Marton interferometer again. In their experiment, the gravitational field plays the same role as the stray magnetic field in Marton's experiment. If the original Werner and Brill analysis were correct, then Colella er a / . should not have seen

294

MING CHIANG LI

the fringe shift caused by the gravitational field. This definitely conflicts with the actual experiment. Consequently, the Marton experiment has to be reinterpreted. According to the reinterpretation by Greenberg and Overhauser (1979), three effects cause the phase shift. However, only two effects were noted by Werner and Brill. The extra effect is the sliding of the electron beam along the plane of observation. As a result, bending and sliding effects cancel each other. Therefore, only the Bohm- Aharonov effect remains to cause the Marton’s fringes to shift. Greenberg and Overhauser’s analysis can be understood very simply. If the dispersion effect is neglected, the fringe variation in Eq. (47) of the Marton interferometer depends on the reciprocal lattice vectors and not individual wave vectors of coherent electron beams. The stray magnetic field changes wave vectors of electron beams, but not reciprocal lattice vectors. Thus the Marton interference fringes are stable with respect to the magnetic field through beam paths. One may wonder how it was possible for Marton to see any fringes at all. According to Greenberger and Overhause, it would happen as follows. The Bohm-Aharonov effect of the stray magnetic field causes a sinusoidal oscillation of interference fringes. These fringes spend most of their time at the extreme endpoints of their oscillations, and their major effect is a dimming of the pattern, rather than a total obliteration of it.

VI. PROPOSEDEXPERIMENTS Traditionally, electron interference experiments have been designed according to the guidelines set by the wave optics of light and in a manner similar to the classic experiments of Young, Fresnel, and others. However, there are fundamental differences between electron and light. For the latter, there are good optical media, clean mirrors, and no perturbing fields. In the case of electrons, there are no good media, no mirrors, and yet strong perturbing fields, especially stray magnetic fields. To overcome these obstacles, electron interference experiments are usually carried out with energetic electron beams that have a wavelength much shorter than that of light. The main objective of the classic experiments of light is to observe the interference pattern; this is not difficult for light with its longer wavelength, but with electrons, having much shorter wavelength, observation of the interference pattern becomes extremely difficult. MOIlenstedt and Diiker had chosen a geometry with a small coherent beam loop in order to avoid stray magnetic fields and mechanical instability. Marton’s interferometer, on the other hand, has a much larger coherent beam loop.

ELECTRON INTERFERENCE

295

Most of the difficulties encountered in the development of electron interference experiments were associated with the observation of the interference pattern. To minimize such difficulties, one probably needs to seek new interference experiments, which do not resemble those of optics and are not based on the observation of the interference pattern. The proposed interference experiments represent new efforts toward such a direction. A . Modijied Marton Interferometer

The modified Marton interferometer (Li, 1978a) is depicted in Fig. 9. Three identical crystal laminae are arranged in the same way as those in Fig. 8 and irrelevant diffracted beams have been omitted. Now the incident electron beam is a convergent beam. With the symmetric arrangement, diffracted beams in Fig. 9 are focused after passing through bender B. The diffraction areas (T on beam splitter S and analyzer A are equal. D is a solid-state detector, which is mounted far from the interferometer. In the modified Marton interferometer, two coherent beams are obtained from successive Fresnel diffractions by splitter S and bender B . To achieve a Fraunhofer diffraction of two coherent beams at analyzer A , the linear dimension of the diffraction area (T should be less than AL, where L is the distance between the interferometer and detector D.By taking L = 1 m and A = 0.05 A, the upper limit of the diffraction area o-is about 5 x 10-l2m2. Applying experimental techniques used in the electron microscope, an electron beam with an angle spread A k , / k = Atlo = low4rad can be focused onto an area with that dimension. The convergent beam has a larger-angle spread. From the uncertainty principle, the angle spread of an electron beam is nearly equal to the ratio of its wavelength to the radius of its emission gun tip. A typical value of a tungsten tip in an electron gun is about 500 A. For an electron beam with wavelength 0.05 A the corresponding angle spread Atlo is about lop4rad. It has been reported by Saxon (1972) that an effective electron gun tip can be as small as 5 A. It has been shown in Eqs. (25) and (40) that in both

FIG.9. The modified Marton interferometer as proposed

296

MING CHIANG LI

Fraunhofer and Fresnel diffractions, the diffracted beam has a widerangle spread than that of an incident beam. In the experiment of Marton, Simpson, and Suddeth, the best alignment is about E = rad, which yields a lower limit of the achievable mechanical stability. Hence, for E < he, the alignment of the modified Marton interferometer can be realized experimentally. There are a number of advantages in the modified Marton interferometer. In the original Marton interferometer, the experimental objective was to measure the interference pattern; hence a differential measurement had to be performed. That is to say, the detector should be able to resolve the small fringe spacing. Generally a photographic plate with the aid of a conventional microscope was used as a detector. However, photographic plates have poor temporal resolution. In order to be photographed, the interference fringes should be kept steady for a relatively long period of time. In their experiment Marton, Simpson, and Suddeth exposed the photographic plate for about 6 min. The presence of stray 60 Hz fields and other inherited small mechanical vibrations of the apparatus has made the task of stabilizing the interference fringes for such a long period of time very difficult. In the modified Marton interferometer, the experimental objective is to measure the total intensity of a diffracted beam. An integrated measurement can be performed. A solid-state device, which has an excellent temporal resolution, can be employed as a detector. The solid-state device can be made sensitive enough to count electrons with kinetic energy as small as 20 keV. The device’s efficiency in registering electrons transversing the sensitive region is nearly 100%. The fast risetime of the pulses, on the order of 1 nsec sec), permits the device to be used at high counting rates. Hence with the aid of the fast electronics, the solid-state device can sort out the effects of stray 60 Hz field and small mechanical vibrations of the apparatus. The stringent stability requirement over a long period of time is no longer necessary. In the original Marton interferometer, the coherent factor a had to be obtained through the observation of the interference pattern. The pattern, has a sensitive dependence with respect to a change of the misalignment. In the modified Marton interferometer, the coherent factor a can be obtained through measurements of the differential cross sections. These cross sections, for a convergent incident beam, have comparatively less-sensitive dependence with respect to a change of the misalignment. Consequently the modified Marton interferometer is more suitable for studying the variation of the coherent factor a than the original Marton interferometer. This can be shown as follows. A varying coherent factor a will induce a variation of the diffracted beam intensity. The period of the variation, which is independent of the misalignment, determines the rela-

ELECTRON INTERFERENCE

297

tive change of the coherent factor a , while in the original Marton interferometer, variation of the coherent factor a created the same shift effect on the interference pattern as that of stray 60-Hz fields. These shifts are difficult to be resolved utilizing any photographic method (Chamber, 1960). There is a well-known phase problem in crystallography: For lack of direct experimental phase information of the structure factorf(kl ; n), the electron density of a crystal inside a unit cell cannot be deduced directly (Beurger, 1960)from the experiment. In the absence of direct phase information, only certain crystal structures can be determined in an indirect way. It has been expressed that if there were some direct way of determining the phases, it would be a routine matter to find the arrangement of atoms in any given crystal no matter how complicated it may be. It was shown theoretically that through the diffraction of two coherent beams, one is able to measure the phase of the structure factor directly (Li, 1974, 1975, 1976). The modified Marton interferometer is basically the crystal diffraction of two coherent beams. A n y success in the proposed experiment means that we are steps closer in solving the phase problem of crystallography. The famous Bohm- Aharonov experiment is a diffraction experiment of two coherent electron beams. In the past, such experiments were performed with the use of a Mollenstedt-Duker interferometer. In our modified interferometer, coherent electron beams have a much wider spatial separation. The Bohm-Aharonov experiment can be carried out on a much larger scale (Li, 1978b). B. Crossed-Beam Experiment

In the crossed-beam experiment (Li, 1979), an electron beam is scattered by two coherent laser beams. The experiment is depicted in Fig. 10. Let us consider only the scattering for the time being. The monochromatic electron has energy-momentum ( Q , q ) and ( Q ’ ,9 ’ ) before and after scattering. The corresponding quantities for the photon are ( E , p) and ( E ’ , p’). The transition amplitude has the form

where ( E ’ , p’; Q ‘ , q’ltlE, p; Q , q ) is the reduced transition amplitude. In the above discussion, the photon before scattering is in a pure momentum state IE, p). In two coherent laser beams, the photon is in the

298

MING CHIANG LI

FIG. 10. The crossed-beam experiment as proposed: SM is the laser beam splitter; M denotes reflecting mirrors; W is a wedge that can be used to vary the relative phase between coherent laser beams.

Due to momentum conservation, the cross term in Eq. (74) does not exist. Hence for an electron in the monochromatic state, the coherent effect can not be observed. In reality, the electron is described by a wave packet. For the purpose of simplifying the discussion, instead of Eq. (74), the packet is chosen as

299

ELECTRON INTERFERENCE

where qo is the average momentum and Aq the momentum spread of the packet. The transition amplitude for the scattering by a wave packet in Eq. (75) can now be expressed as

( E ’ , p’; Q ’ , q’ITIE, P I , &(a);Jlp) =

J [ ( E ’ , p’; Q ‘ , q’lt(E, pr: Q, q> 6(E’ + X X

Q’ - E - Q )

+ q’ - pi - 9) + a(E’,P’;Q ’ , q’ltlE, PZ; Q, q > HE’ + Q’ - E - Q) Np’ + q’ - p2 - q)] (qlJlp) dq (76) 6(p‘

The transition probability is proportional to

I(E’, P’;Q ’ , q’ITIE, pi,

p~(a): Jlp)l2

(77)

By using Eq. ( 7 9 , and performing the integration with respect to the momentum q, one may rewrite Eq. (76) as I(E’9 P’;Q ’ , q’lTJE,P I , p ~ ( ~ r )$; + . , ) I 2 = (2~)-~[2.rr(Aq)’]-~” T’ 6(E’ Q’ - E - Q )

+

X

[l(E’. P’;Q’, q’ltlE, pl: Q , p’ + q’ (P‘ + q 2(Aq)’ ‘ - p1 - qo)2)

x h p

(-

-

pl)Iz

where T‘ is the long period of time in which and during which the transition process takes place. To obtain the experimentally observed transition probability, one has to carry out the integration with respect to the incoherent distribution of an electron beam.

300

MING CHIANG LI

where

( A ~ B ) ’= (Aq)’

-t

(ASb)’

(82)

is the intensity spread of the incident electron beam. Equation (81) contains a very important result. If IPi - k12< 8(Aq)’

(83)

the proposed experiment is a coherent process. It means that changing the relative phase between coherent laser beams will induce an intensity variation of the scattered beams. On the other hand, if Ipi - p ~ l ’ > 8(AqI2

(84)

the experiment is incoherent. Hence by changing the relative momentum of two coherent laser beams, one can measure the coherent spread of the electron wave packet. As we can see from Eqs. (78) and (79), the measurement is independent of the incoherent spread of an electron beam. In the discussion, the wave packet has been assumed to have a Gaussian shape. If the wave packet has any other shape, then Eq. (81) would contain the profile information of the wave packet. It is very interesting to examine the experimental feasibility of the proposed experiment. In a conventional crossed-beam experiment, the number of particles scattered per second can be written as

R = unlnzvV

(85)

where u is the corresponding cross section, and u and V are the relative velocity and intersecting volume of two incident beams. The beam densities are denoted by n , and n 2 . For laser-initiated fusion reactions and electron-cooling experiments, high-intensity lasers and powerful electron

30 1

ELECTRON INTERFERENCE

guns have been developed. To give an estimate, consider a pulsed laser with a power of lo6 Wand a beamwidth of 1 mmz, a 20-keV electron beam with pulsed current 10 A and beam width 1 mmz, and a cross section u = 47rr,"

(86)

where re is the classical electron radius. From this information, one can find the counting rate =

6 x 10"

(87)

sec-'

which is a measurable quantity. C . Intensity Correlation Experiment

In 1954, Hanbury-Brown and Twiss showed that observation of the intensity correlations of light from a star in separate receivers could be used to determine stellar diameters. The analysis of Brown and Twiss was based on classical wave interference. Later Glauber (1963) provided a quantum-mechanical interpretation in terms of normally ordered, photon operations. Since then, the Hanbury-Brown and Twiss experiment has initiated a whole new field of experimentation known as quantum optics (Loudon, 1973). In a paper by Goldberger et ul. (1963),they show that the intensity correlation measurement can be applied to particles obeying Fermi -Dirac statistics. An intensity correlation experiment is depicted in Fig. 1 1 . An electron beam is split by a crystal through Fraunhofer diffraction. The counting

+ CORRELATOR

FIG.11. The intensity correlation experiment as proposed.

302

MING CHIANG LI

rates from two separated detectors are multiplied in the correlator, which registers if both detectors count in coincidence. For an incident wave train, the counting rate in the correlator from Eq. (20) can be written as

I II

R = N

x (N

dktF(ki, k)

+(kl

-

b;Ak)f(k,; n) exp[i(kr

-

Qt/h)l

(1

/2

dkiF(ki, k’) +(k, - 16; Ak)f(ki; n’) exp[i(kr’ - Qr’/h)]

(88)

where k’ = kn‘ = kr’/r’

(89)

The detectors are mounted at positions r and r’. The rates for each detector are counted at different instants t and t’ with a time delay ~ = f ’ - t

(90)

Due to incoherence among different wave trains in a quasimonoenergetic electron beam, the experimentally measured counting rate in the correlator is proportional to

In the discussion of Section 111, the chosen wave train in Eq. (22) is infinitely long. Here the considered wave train has a finite length +(ki - ko; Ak)

=

[2~(Ak):]-1’2[2~(Ak)f]-1’4

Then the equation that corresponds to Eq. (25) is proportional to

x exp{i(k,r - Qot/h) - (Ak)?[r - (hko/rn)t]2}

(93)

If the distribution &(k,, - kb ; Akb) is also Gaussian, then integrations in Eq. (91) can be carried out. The experimentally measured counting rate in the correlator depends on the time delay T as

Through Eq. (941, the coherent length of electron wave trains can be mea-

ELECTRON INTERFERENCE

303

sured in the intensity correlation experiment. The success of the experiment is determined by the ability of the correlator, if it is able to resolve the time delay of 1 psec. The lower limit for which the coherent length can be measured is about 100 pm, or even less for slower moving electrons. Hence, one can lower the limit by inserting a decelerating electric field between the splitting crystal and detecting counters.

VII. DISCUSSION Despite the success in various electron interference experiments the wave packet or the coherent spread of an electron beam still remains hidden. Experimentally, electron beams can be made more coherent by reducing the size of the electron source, increasing the stability of accelerating voltage, etc., all these leading to a reduction of the incoherent spreads, and concomitantly, an increase in the apparent coherent spreads (Simpson, 1956). As long as the incoherent spreads cannot be entirely eliminated, the apparent coherent spreads will never become the true coherent spreads. Of course, numerous attempts had been made to estimate the coherent length of an electron beam. For example, Pendry (1974) only considered incoherent contributions. In some way his estimated length is an apparent length for which its true coherent length is infinitely long. Take Gabor’s estimation (1956), in which he only included the incoherent thermal spread. The apparent coherent length of the electron beam used in Marton et al. (1954) experiment from Gabor’s estimation was about 1300 nm, which was quite different from the experimentally observed value of 28 nm. The general attitude toward the wave packet or the coherent spread varies. A common view is that it does not contain any real physical information. At the present time no actual experimental attempt has been made for observing the wave packet. The wave packet has played a very important role in resolving wave-particle duality, bridging the gap between classical and quantum physics, overcoming theoretical difficulties in quantum mechanics, making a particle coherent, and so forth. Consequently, every effort should be made in search of such a fundamental physical entity. Quantum mechanics is a mechanics of coherence. Similarly, superconducting, lasering, Mossbauer effect, and Josephson effect are all phenomena of coherence. Yet, the disputes over the foundation of quantum mechanics, hidden variable theory, Bohm- Aharonov effect, etc. resulted from a lack of understanding of various phases in coherence.

3 04

MING CHIANG LI

Experiments in electron interference have treated coherence as the main experimental objective. Within the past 20 years, even these types of experiments have been rather limited in scope, with only a few experimental groups involved. In fact, some important and interesting experiments, such as multiple-slit diffraction of electrons slipped by unnoticed for more than ten years. The experiment of Marton, Simpson, and Suddeth created a theoretical disturbance at various times, but it was not repeated for more than 25 years. At the present, experimenters in electron interference are still mainly guided by light-optics analogs. As shown in Eq. (571, the existence of coherent spreads can effect the fringe spacing. Such an effect can not be accounted for in terms of light optics. A more active research in the electron interference could cure a number of irritations in modern physics. A basic quantity in quantum mechanics is the wave function, such that any experimentally measured quantity is the probability that is the magnitude squared of the wave function, whose phase can not be measured by conventional, sophisticated experiments at the present. Yet, phases are important in various physical processes. A number of elegantly designed indirect methods have been used to recover the lost phases. The success of indirect methods is limited since not every phase can be obtained through indirect methods. Although quantum mechanics is a mechanics of coherence, its coherent character has not been fully utilized. In coherent experiments, the various phases become directly measurable. It is expressed in Section VI that, through crystal diffraction of two coherent beams, direct phase determination in crystallography can be accomplished. To achieve such a direct measurement, one has to wait for a wider acceptance of electron interference experiments. None of the popular indirect methods can ever be a real substitute for a direct one. REFERENCES Azaroff, L. V. (1968). “Elements of X-Ray Crystallography.” McGraw-Hill, New York. Bayh, W. (1962). Z. Phys. 169,492. Belinfante, F. J . (1962). Phys. Rev. 128, 2832. Beurger, M. J. (1960). “Crystal Structure Analysis.” Wiley, New York. Bocchieri, P., and Loinger, A . (1978). Nuovo Cimento A 47, 475. Boersch, H. (1940). Naturwissenschaften 28, 71 1 . Boersch, H. (1943). Phys. 2. 44, 202. Bohrn, D., and Aharonov, Y. (1959). Phys. Rev. 115,485. Bonse, U . , and Hart, M. (1965). Appl. Phys. L e f t . 6, 155. Boyer, T. H. (1972). Am. J . Phys. 40, 56. Boyer, T. H. (1973). Phys. Rev. D 8, 1679. Braun, K . J. (1972). Diplomarbeit Tiibingen.

ELECTRON INTERFERENCE

305

Chambers, R. G. (1960). Phys. Rev. Lett. 5, 3. Colella, R . , Overhauser, A. W., and Werner, S. A. (1975). Phys. Rev. Lett. 34, 1472. Cowley, J . M. (1975). “Diffraction Physics.” North-Holland F’ubl., Amsterdam. Davisson, C. J., and Germer, L. H. (1927). Nature (London) 119, 558. Deaver, B. S ., and Fairbank, W. M. (1961). Phys. Rev. Lett. 7,43. de Broglie, L. (1924). Philos. Mag. [6] 47, 466. DeWitt, B. S. (1%2). Phys. Rev. 105, 2189. Doll, R., and Nabauer, M. (1961). Phys. Rev. Lett. 7 , 51. Fowler, H., Marton, L., Simpson, J. A., and Suddeth, J. A. (1961). Phys. Rev. 32, 1153. French, A. P., and Taylor, E. T. (1974). A m . J . Phys. 42, 3. Furry, W. H., and Ramsey, N. F. (1960). Phys. Rev. 118, 623. Gabor, D. (1956). Rev. Mud. Phys. 28, 260. Glauber, R. J. (1963). Phys. Rev. Letr. 10, 84. Goldberger, M. L., Lewis, H. W., and Watson, K. M. (1963). Phys. R e v . 132, 2764. Greenberger, D. M., and Overhauser, A. W. (1979). Rev. Mod. Phys. 51, 43. Hanbury-Brown, R., and Twiss, R. Q. (1954). Philus. Mag. [7] 45, 663. Hillier, J. (1940).Phys. Rev. 58, 842. Hillier, J., and Ramberg, E. G. (1947). J . Appl. Phys. 18, 46. Ignatovich, V. K . (1978). Found. Phys. 8, 565. Jonssen, C. (1961). Z. Phys. 161, 454. Jonssen, C., and Mollenstedt, G. (1959). Z. Phys. 155, 472. Keller, M. (1961). Z. Phys. 164, 274. Krimmel, E. (1964). Appl. Phys. Lett. 10, 209. Li, M. C. (1974). Phys. Rev. A 10, 781. Li, M. C. (1975). Phys. Rev. B 12, 3150. Li, M. C. (1976). Phys. Rev. B 14, 5529. Li, M. C. (1978a). Z. Phys. B 29, 161. Li, M. C. (1978b). Phys. Rev. A 18, 773. Li, M. C. (1979). Comments Atom. Mul. Phys. 5, 173. Lichte, H., and Mollenstedt, G. (1978). Electron Mirrosc., Proc. lnt. Congr., 9th, 1978 Vol. 1, p. 178. Lichte, H., Mollenstedt, G., and Wahl. H . (1972). Z. Phys. 249, 456. Loudon, R. (1973). “The Quantum Theory of Light.” Oxford Univ. Press (Clarendon), London and New York. Low, F. E . (1959). In “Lecture Notes of Brandeis University,” p. 3. Brandeis University, Waltham, Massachusetts. Marton, L. (1952). Phys. Rev. 85, 1057. Marton, L., Simpson, J. A., and Suddeth, J. A. (1954). Rev. Sci. Instrum. 25, 1099. Mitsuishi, T., Nagasaki, H., and Uyeda, R. (1951). Pruc. Jpn. Acad. 27 (2). 86. Mollenstedt, G., and Bayh, W. (1962). Naturwissenschafren 49, 81. Mollenstedt, G., and Bulh, R. (1957). Phys. Bl. 13, 357. Mollenstedt, G., and Duker, H. (1954). Naturwissenschafren 42 (2). 41. Mollenstedt, G., and Lichte, H. (1978). Optik 51, 423. Mollenstedt, G., and Lichte, H . (1979).In “Proceedings of the First International Workshop on Neutron Interferometry” (U. Bonse, ed.). Oxford Univ. Press, London and New York. Pendry, J. B. (1974). “Low Energy Electron Diffraction.” Academic Press, New York. Peshkin, M., Talmi, I., and Tassie, L. J . (1961). Ann. Phys. ( N . Y . ) 12, 426. Rang, 0. (1953). Z. Phys. 136, 465. Rauch, H., Treimer, W., and Bonse, U. (1974). Phys. Lett. A 47, 369.

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Ruska, E. (1943). Kulloid-2. 105, 43. Saxon, G. (1972). Optik 35, 195. Schiff, L. I. (1%8). “Quantum Mechanics.” McGraw-Hill, New York. Schrodinger, E. (1926). Ann. Phys. (Leipzig) [4] 79, 361. Simpson, J. A. (1956). Rev. Mod. Phys. 28, 254. Thornson, C. P., and Reid, A. (1927). Nature (London) 119, 890. Werner, F. G . , and Brill, D. R. (1960). Phys. Rev. Lett. 4, 344. Wu, T. T., and Yang, C. N . (1975). Phys. Rev. D 12, 3843 (1975).

Author Index Numbers in italics refer to the pages on which the complete references are listed. Beurger, M. J., 297,304 Bhaumik, D., 102, 107, I50 Bhaumik, K., 102, I50 Bilz, H., 105, 109, I50 Birenbaum, L., 134,152 Birkinshaw, K., 183,207 Biscar, J. P., 94, 141, I50 Blaugrund, A. E., 31,43 Bocchieri, P.,291,304 Boersch, H., 289,304 Bogolyubskii, S. L., 38,43 Bohm, D., 270, 287, 291,292, 293, 294, 297, 303,304 Bonner, R. F., 166,207 Bonse, U., 293,304, 305 Booth, A. D., 128, 129, 152 Boyer, T. H., 291, 292,304 Braun, K. J., 291,304 Brill, A. S., 93, 150 Brill, D. R., 293, 294,306 Brinkmann, U., 202,207 Brown, K. G., 140,150 Brubaker, W. M., 154, 183, 191. 194,207 Bruno, C., 41,43 Bulh, R.,290,305 Bullok, T. H., 88, I50 Bums, E. J. T., 39, 40, 41,44 Busby, K., 52,84 Buss, D. D., 244,266 Biittner, H., 105, 109, 150 Buzzi, 1. M., 49.82

A Adey, W. R., 118, 126, I50 Afonin, I. P., 33,43 Aharonov, Y., 270, 287, 291, 292, 293, 294. 297, 303,304 Ahmed, N. A. G., 149, 150 Aiello, G., 127, I50 Alfven, H., 37,43 Anderson, R. E., 27, 28,44 Austin, S., 102, 103, 104, 152 Austin, W. E., 157, 180, 193, 194,207 Averbeck, M. D., 128, I50 Azaroff, L. V., 280,304

B Babykin, M. V., 33,41,43 Baev, B. V., 33.43 Baier, P. W., 230, 233, 236, 245, 249, 260, 266 Baigarin, K. A., 33, 41,43 Bailey, W. H., 244,266 Baker, L., 7,43, 50, 52, 53.84 Bangerter, R. O., 4, 7 , 4 3 , 4 4 Baranski, S., 125, I50 B a i l , M., 154, 160. 166,207 Bartov, A. Y., 33, 41,43 Bawin, S. M., 118. 126, I50 Bayh, W., 290, 291, 293,304, 305 Belinfante, F. I., 291,304 Bell, D. T., 244, 262,266 Bergeron, K. D., 23, 24, 25,43,44 Bergstrom, N., 35.44 Berkowitz, R. S., 229, 230, 235,266 Bernstein, B., 8 , 4 3 Bemstein, I. A., 53,82 Bernstein, S. L., 229, 252, 260, 263,266 Berteaud, A. J., 128, I50

C

Cahn, C. R.,235, 248, 263,266 Careri, G., 93, 150. I51 Carmel, Y., 58,82 Canico, J. P., 206,207 Cartier, D. E., 230,266 Chaffin, R. J., 71,83 307

308

AUTHOR INDEX

Chambers, R. G., 291, 297,305 Chang, J., 7,43 Chen, C. C., 267 Chetvertkov, V. I., 9, 10,44 Chistyakova, E. N., 135, 136, I51 Chuang, S. S . , 80,83 Clauser, M. J., 2, 4, 35, 38, 39, 40,43,44, 45 Clegg, J., 127, I51 Cohen, D. R., 48,83 Cole, R., Jr., 244,266 Colella, R., 293,305 Collins, D. R., 244,266 Collins, J . H., 237,267 Colombant, D. G., 36, 42,44 Colson, W. B., 51, 60,63, 64,83,84 Compton, R. T., 220,266 Cooper, G. R., 223,266 Cooper, R. S., 6,44 Cooperstein, G., 31, 35, 36, 42,43,44 Copeland, D. A., 64,84 Cornetto, A., 263,266 Cortella, J., 41,43 Cowley, J. M., 274, 275,305 Creedon, J., 30,43 Creedon, J. M., 23, 28, 29, 34, 35,43,44 Cremer, C. C., 6,44 Czerski, P., 125, 150

D Danko, S. A., 41,43 Dardalhon, M., 128, IS0 Das, P. K., 244,267 Davidow, S., 134, 152 Davidson, R. C., 57, 58,83 Davies, N . G., 262,266 Davisson, C. J., 274,305 Daws, T. L., Jr., 231,267 Dawson, J. M., 53, 68, 73,83,84 Dawson, P. H., 154, 155, 162, 166, 173, 178, 181, 182, 183, 184, 186, 188, 190, 191, 193, 194, 195, 1%, 199, 201, 203, 206,207 Dayton, I. E., 193, 200,208 Deacon, D. A. G., 51, 64,83 Deaver, B. S., 290,305 de Broglie, L., 269, 270, 271, 274,305

Degan, I. J., 81,83 Delvaux, T., 41,43 Denison, D. R., 193,208 DeTemple, T. A., 48,83 Devin, A., 41,43 Devyatkov, N. D., 130,151 DeWitt, B. S., 291,305 Di Capua, M. S., 25, 30.43 Dirac, P. A. M., 50,83 Dixon, R. C., 213, 216, 247, 263,266 Dodds, D. E., 129, 152 Doll, R., 290, 305 Dostert, K., 233, 245, 263,266 Doucet, H. J., 49,82 Drissler, F., 140, 141, 143, 145, 151 Drobot, A. T., 53, 58, 63, 65,84 Drost-Hansen, W., 127, I51 Drouilhet, P. R., 229, 252, 260, 263, 266 Duborgel, B., 41,43 Duker, H., 281, 282, 283, 285, 290, 293, 294, 297,305 Duncan, C. V., 27, 28,44 Dutta-Roy, B., 102, 107, 150 Dylla, H. F., 192,208

E Efthimion, P. E., 51, 71,83, 84 Ehlert, T. C., 190,208 Einstein, A., 49.83 Elias, L. R., 51, 64,83 EM, R., 118, 151 Enke, C . G., 173,208 Erfurth, S. C., 140, I50 Etlicher, B., 49, 82 Evans, D. E., 48,83 Eyster, J. M., 93, 152

F Fairbank, W. M., 51,64,83,84, 290,305 Farnsworth, A. V., 7, 39, 40, 41,43, 44 Federhen, H. M., 255,266 Fedotoff, M., 41,43 Felch, K., 52,84 Fite, W. L., 192,208

3 09

AUTHOR INDEX Fock, W., 206,208 Fowler, H., 291,305 Freeman, J. R., 2, 29, 33, 35, 38,43,44, 45 French, A. P., 271,305 Friedman, M.,50.83 Frohlich, F.,89, 118, 151 Frohlich, H., 91,92,94, 95,97,99,105, 106, 109, 113, 118, 119, 127, 129, 130, 140, 142, 147, 148,150, 151, 152 Furry, W. H., 292,305

G

Gabor, D., 274,303,305 Gamo, H., 80,83 Gavrin, P. P., 33, 41,43 Genzel, L.,107, 136, 140, 151, 152 Gerasimov, B. P.,38.43 Gerlich, D., 206,208 Germer, L. H., 274,305 Gilgenbach, R. M.,52, 69,71, 73, 75,83, 84 Gill, W. J., 245,246,266 Glauber, R. J., 301,305 Glukhiky, V. A., 9, 10,44 Gold, R., 232, 260,266 Goldberger, M. L.,301,305 Goldstein, S. A., 29, 30, 31, 35, 36, 39, 40, 41,42,43,44 Golomb, S. W., 230, 232,266 Goodman, D. T., 223, 225,267 Gorbulin, Y. M.,41.43 Gouard, P.,41.43 Gover, A., 53, 81,83 Grammiiller, H., 249,266 Granatstein, V. L.,47,48,49,50,52, 53, 68,69,75.83,84 Grant, P.M.,237,267 Green, D. E.,109,I51 Greenberger, D. M.,2!h, 305 Griinberger, G. K.,225,266,267 Grundler, W.,129, 130,I51 Grybos, D.P., 223,266 Gubarev, A . V.,41,43 Gupta, S.C.,230,267 Gusev, 0.A., 9, 10,44

H Haber, F., 223,267 Hacker, M. P.,48,83 Haken, H., 98, 101,151 Halbach, K.,195,208 Halbleib, J. A., 39,44 Haldenwang, P., 49,82 Hamilton, G. F., 166,207 Hanbury-Brown, R.,301,305 Hart, M.,293,304 Hartmann, H . P.,245,267 Hasegawa, A., 53, 63,65,69.83 Heiser, S., 260,266 Hennequin, J. F., 190,208 Herndon, M., 49, 50,83 Hillier, J., 289,305 Hirschfield, J. L.,48, 53,82,83 Hirst, D. M.,183,207 Holland, B., 108,151 Holme, A. E., 157, 180, 193, 194, 199,203, 207,208 Holmes, J. D., 244, 262,266 Holmes, J. K.,267 Hopkins, P. M.,236,267 Houston, S. W.,259,267 Huetz, A., 49,82 Huff, R., 30,43 Huth, G. K.,252, 260,267

I Ignatovich, V. K., 272,305 lmasaki, K.,39,43 Indovina, P.,127, 152 Inglebert, R.-L., 190,208 Isobe, K.,48,83 Ivanov, V. S.,51,84

J James, B. W., 48,83 Jarboe, T . R., 7,44 Jarrell, J. A., 192,208 Jarrold, M.F.,183,207 Johnson, D. J., 30,43 Johnson, D. L.,9,44

310

AUTHOR INDEX

Jones, J. J., 211, 243, 250,267 Jonssen, C., 290,305

K Kai. P. Y., 244,267 Kaiser, F., 120, 151 Kalinin, Y. G., 41,43 Kapitza, P. L., 50.83 Kapitza, S. P., 82,83 Keilmann, F., 129, 130, 136, 140, 151, 152 Keller, M.. 290, 293, 305 Kidder, R. E., 2, 4,43 Kilgus, C. C., 244,267 Kirkpatrick, R. C., 4, 5, 6,43,44 Kiselev, V. N., 41,43 Kollias, N., 94, 141, 150 Kolotilin, B. I., 154, 208 Kondrateva, V. F., 135, 136, I51 Korop, E. D., 33,43 Koshland, D. E., 89, 151 Krimmel, E., 291,305 Krokhin, 0. N., 2,44 Kroll, N. A., 53,83 Kuhn, H . , 142, I51 Kwan, T., 53,83

L Lahiri, A,, 107, I50 Lamain, H., 49.82 Landecker, K., 49,83 La Rue, G. C., 263,267 Latmanizova, G. M., 9, 10,44 Law, J., 64,84 Lawson, J. D., 37.44, 58,83 Layman, R. W., 52,84 Leck, J. H.,157, 180, 193, 194, 199, 203, 207, 208 Lee, K., 147, 148, 152 Lee, R., 29, 30, 35.43 Leeper, R. J., 7,43 Lefaivre, D., 191,208 Lever, R. F., 206,208 Lewis, H. W., 301,305 Li, M. C., 275, 282, 295, 297,305 Lichte, H., 290, 291,305

Lichtenberg, A. J., 162, 208 Liksonov, V. I., 33,38,43,44 Lin, A. T . , 53, 68, 73,83,84 Lin, J. C., 149, / 5 / Lindemuth, I. R., 7.44 Lindholm, J. H., 230,267 Lindl, J. D., 4.44 Livshitz, M. A., 103, I51 Loewen, E. G., 70,84 Loinger, A . , 291,304 Loudon, R., 301,305 Louisell, W. H., 64.84 Lovelace, R. V., 22,44 Low, F. E., 273, 277, 278,305 Lucky, R. W., 211, 261,267 Luna, E. I., 131, / 5 /

M McCalla, E., 261,267 McDaniel, D. H., 9, 21, 23,44 McDermott, D. B., 47, 51, 52, 59, 69, 71, 75.78,83,84 MacFarlane, R. M., 141, 145, IS/ McGilvery, D. C., 173,208 McMullin, W. A., 53,83 Madey, J. M. J., 51, 64,83,84 Madsen, L. E., 6,44 Makinen, M. W., 140, 151 Manheimer, W. M., 51, 53, 68,84 Manoilov, S. E., 135, 136, IS/ March, R. E., 166,207 Marmet, P., 191,208 Marshall, T. C., 47, 51, 52, 59, 69, 71, 73, 75, 78.83.84 Martin, E. H., 263,266 Martin, J. C., 9, 15, 44 Martin, T. H., 9,44 Martin, T. P., 140, 151 Marton, L., 281, 282, 285, 290, 291, 292, 293, 294, 295, 2%, 297, 303, 304,305 Mathers, G. E., 183, 203,208 Maystre, D., 70,84 Mead, W. C., 4,44 Meeker, D. J., 7,43 Meffert, K., 236, 258,266,267 Melekhin, V. N., 82,83

31 1

AUTHOR INDEX

Melnick, R., 134, 152 Mendel, S. A., Jr., 39, 40,41,44 Meunier, M., 173, 178, 194, 1%. 199, 203, 207, 208 Micciancio-Giammarinaro, M.S., 127, 150 Miller, P. A., 33, 44 Mills, R. E., 102, I51 Milstein, L. B., 244,267 Mima, K., 69,83 Mitsuishi, T., 290, 305 Mix, L. P., 33, 39, 40,43 Mizchirutskii, V. E., 33,43 Miziritsky, V. I . , 41,43 Mohanty, N. C., 223.267 Mollenstedt, G., 281, 282, 283, 285, 290, 291, 293, 294, 297,305 Monod, J., 89, 152 Morgan, D. P., 237,267 Morrison, J. D., 173,208 Mosher, D., 35, 36,42,43,44 Motz, H.,50,84 Motzkin, S., 134, 152 Mozley, R. F., 193, 200,208

N Nabauer, M., 290,305 Nagasaki, H.,290,305 Nakai, S., 39,43 Nardi, E., 39,45 Nation, J. A., 29,44, 57, 58,82, 84 Nedoseev, S. L., 9, lo,# Neet, K. E., 89, 151 Nettleton, R. W., 223,266 Neviere, M., 70, 84 Nicolas, A., 41.43 Norman, M., 149, 150 Nossen, E. J., 237,267 Nuckolls, J. H., 3, 4,44

Onaral, B., 126, 152 Ostrem, J. S., 80,83 Ott, E., 22,44, 51,84 Ottinger, P. F., 36, 4 2 , 4 Ovchinnikov, 0. B., 9, 10,44 Overhauser, A. W., 293, 294,305

P Painter, J. H., 230,267 Palma, M. U., 121, 127, 150, I52 Palma-Vittorelli, M. B., 127, I50 Pan, Y.L., 4,44 Pandit, M., 233, 245, 249, 261,266, 267 Parker, R. K., 27, 28,44, 47, 49, 50, 52, 75,83,84 Pasechnikov, A. M., 9, 10, 33,43 Pasour, J., 49,83 Pasour, J. A., 49, 50, 70,83,84 Patou, C., 41,43 Paul, S. H., 223, 225,267 Paul, W.,153, 195,208 Pecherskii, 0. P., 9, l o , # Peebles, W. A., 48.83 Peleg, E., 39,45 Pellinen, D. G., 25,43 Pendry, J. B., 303,305 Peshkin, M., 292,305 Pethig, R., 93, 152 Peticolas, W. L., 140, 150 Petit, R., 221,267 Peugnet, C., 41,43 Phillips, R. N., 50.84 Pohl, H. A., 149,152 Popov, V. P., 38,43 Poukey, J. W., 2, 23, 24, 25, 29, 33, 35, 38, 39, 40,43,44,45 Prabhu, V. K., 223, 225,267 Prestwich, K. R., 2,29, 38.45 Prevender, T. S., 7,43 Prohofsky, E. W., 93,152 Prono, D. S., 34, 35,43,44

0

Oliphant, W. F., 30,43 Olsen, J. N., 7,43

Q Quintenz, J. P., 39, 40, 41,43, #

312

AUTHOR INDEX

R Rabinovich, M. S., 51,84 Raizer, M. D., 51,84 Ramain, G. J., 51, 64,83 Ramberg, E. G., 290,305 Ramsey, J. L., 244,267 Ramsey, N. F., 292,305 Rang, O., 290,305 Rauch, H., 293,305 Read, M. E., 29,44 Rebeyrotte, N., 128, I50 Redhead, P. A , , 181, 190,207 Reed, M., 57,84 Reeves, C. R., 244,266 Reid, A., 274, 278,306 Reinhard, H. P., 153, 208 Remily, R., 134, 152 Ridings, R. V., 244, 262,266 Ristenbatt, M. P., 231,267 Roche, M.,41.43 Rogers, H. H., 6 , 4 4 Rose, A., 88, I52 Rosenthal, S., 134, 152 Rouille, C., 49, 82 Rozdowicz, Z., 48.83 Rubenstein, C., 134, 152 Ruchadze, A. A., 51,84 Rudakov, L. I., 2, 9, 10, 33, 38, 41,43,44 Ruska, E., 289,306

S Sage, G. F., 261,267 Salz, J., 211, 261,267 Samarsky, A. A., 2, 38,43, 44 Samson, F. E., 119, 152 Sandel, F. L., 36, 42,44, 52,84 Saxon, G., 295,306 Sayyid, S., 199, 203,208 Schiff, L. I., 272,306 Schlesinger, S. P., 47, 49, 50, 51, 52, 70, 71, 73, 75, 78,83,84 Schmitt, F. O., 119, 152 Schneider, S . . 52,84 Schrodinger, E., 269, 287,306 Schwan, H.P., 122, 126, 152

Schwettman, H. A., 51, 64,83,84 Seftor, J. L., 49,83 Sepp, H., 260,266 Septier, A., 154, 160, 162, 166,207, 208 Sevastyavona, L. A., 137, 138, 139, I52 Sharp, L. E., 48,83 Shaya, S. Y.,149,152 Sheppard, A., 126, I50 Sheretov, E. P., 154,208 Shestakov, Y.I., 41,43 Shoemaker, F. C., 193, 200,208 Shope, S., 23,44 Sidorov, Y.L., 33.44 Simpson, J. A., 290, 291, 2%, 303, 304, 305, 306 Simpson, S. S., 236,267 Skoryupin, V. A., 41.43 Sloan, M. L., 58,84 Small, E. W., 140, I50 Smirnov, V. P., 9, 10, 33, 38,43,44 Smith, C. W., 149, 150, 152 Smith, E. G., 216, 240, 263,267 Smith, I. D., 8, 9, 15, 34, 35,43,44 Smith, P. R., 71,83 Smith, P. W., 81,84 Smith, R. A., 50, 53, 68,84 Smith, T. I., 51, 64,83 Smith, T. L., 51, 64.83 Smolyanskaya, A. Z., 131, 132, 133, 152 Solomon, G., 229, 260,267 Spitzer, R., 52, 84 Sprangle, P., 49, 50, 52, 53, 63, 65, 68, 69, 83,84 Stauffer, F. J., 70.84 Steffan, K . G., 162, 164,208 Stein, S., 211, 243, 250, 267 Steinwedel, H., 153,208 Stephanakis, S. J., 35, 36, 42,43,44 Stoneham, M. E., 142, 143, 144, 145, 147, 148, I52 Story, M. S., 153, 183,208 Strelkova, M. A., 135, 136, 151 Stuchly, M. A., 148, I52 Suddeth, J. A., 290, 291, 2%. 303, 304, 305 Sukhatme, V. P., 51,84 Sundaram, G., 263,267 Svin’in, M. B., 9, 10.44 Sweeney, M. A., 4,44 Szu, H. H., 69,83

3 13

AUTHOR INDEX

T Takashima, S., 126, 152 Talmadge, S., 51.84 Talmi, I., 292, 305 Tam, W.-C., 203,207 Tang, C . M.,53, 68,84 Tassie, L. J., 292,305 Taylor, E. T., 271,305 Taylor, G., 48,83 Teloy, E., 206,208 Tempkin, R. J., 48,83 Thiessen, A., 3 , 4 4 Thompson, J. R., 58, 84 Thomson, C. P., 274, 278,306 Toepfer, A. J., 2, 8, 9, 23, 38, 39, 40.43, 44,45 Treimer, W., 293,305 Tuengler, P., 136, 152 Twiss, R. Q., 301,305

U

Uhm, H. S., 58,83 Urutskoev, L. I., 38,43 Urv, M.,52.84 Uyeda, R.,290,305

V Van Devender, J. P., 21, 23, 25, 26.44 Velikhov, E. P., 9, 10,44 Vento, G., 127, 152 Vilenskaya, R. L., 131, 132, 133, 137, 138, 139, 152 von Busch, F., 195,208 von Zahn, U., 153,208

Ward, R. B., 244,267 Watson, J. D., 108, 152 Watson, K. M.,301,305 Weaver, H. E., 183, 203,208 Webb, S. J., 128, 129, 133, 134, 135, 136, 142, 143, 144, 145, 147, 148, 149, 151, 152 Weber, C., 261,267 Weldon, E. J., Jr., 211, 261,267 Werner, F. G., 293, 294,306 Werner, S. A., 293,305 Whetten, N. R., 154, 195, 196,207 Whitbourn, W. A,, 206,208 Widner, M. M., 7, 39, 40, 41,43,44 Winterberg, F., 2, 22,44,45 Winterling, G., 140, 151 Wittmaack, K., 188,208 Wolff, G., 41,43 Wolff, P. W., 51,84 Wong, H. V., 58,84 Wood, L., 3,44 Wu, T. M., 102, 103, 104, 152 Wu, T. T., 292,306

Y Yacobi, Y., 140, 151 Yamanaka, C., 39,43 Yang, C. N., 292,306 Yao, K., 223,267 Yariv, A,, 53,83 Yonas, G., 2, 6, 7, 8, 9, 29, 34, 35, 38.44, 45 Yost, R. A., 173,208 Young, F. C., 36, 42,44

W Wahl, H., 290,305 Walsh, J. E., 52, 84

Zhukov, P. G., 51,84 Zimmerman, G., 3,44 Zinamon, Z., 39.45

Subject Index

A

Bandwidth and interference suppression, 210, 212 of interfering signals, 219-221 phase-hopping spread spectrum system, 235-236 and processing gain in spread spectrum system, 256-258 Beam energy, in FEL system, 77-79 Beam-foil interaction, 38-44 Beam splitting, 282-285 Bennett pinch relation, 38 Binary frequency shift keying, 252 Binary phase shift keying, 250 Binary pseudonoise signal, as spreading function, 229 Binary signal, in communication systems, 229-230, 234, 244, 255 Biological materials and systems effects of microwaves on, 85-152 trigger effects, 98-104, 122-125 excitation of coherent vibrations, 98- 104 frequencies, 105, 140 metastable highly polar states, 95-98 stored energy, 105 Biological membrane, 92-93 electric potential difference, 88 membrane potential, 122 Blumlein principle, of modular accelerator, 14- 18 Body scattering, from relativistic electron beams, 49-54 Bohm-Aharonov effect, 270, 287, 291294, 297 Bone marrow cell, influence of microwaves on, 137-139 Bose condensation, 99, 101-104 Boundary current on axis of diode, 29 of power flow in vacuum, 22-25 Brain wave, 118-121 Bremsstrahlung, from pinched electron beam, 31

Accelerator, see also specific accelerators high-current electron beam generators, 8-9 light ion beam ignition systems, 42 Algae, Raman effect, 140-141, 145 Amino acid, 88-90 influence of millimeter waves on, 135’ 136 Amplitude interference, 282, 286-289 Amplitude modulation, of spread spectrum systems, 233-234 Analog signal, in communication systems, 21 1, 229 ANGARA-V accelerator, 9-24, 30, 3233, 42-43 Anode and ion flow in magnetically insulated diode, 34 in reflex triode, 35-36 and pinch collapse velocity, 31 Plasma formed at, 28-29, 31 Anti-Stokes scattering, 78-79 in biological materials, 140, 144- 147 Areal pinch collapse velocity, 31 AURORA accelerator, 8

B Backscattering, from relativistic electron beams, 48-49, 53, 59 Backward-wave oscillator, scattering experiments, 51 Bacteria, effect of microwaves on, 128129, 131-137, 143-147, 150 Bandspreading frequency- hopping modulation, 238-239 for interference suppression, 210-212 phase-hopping spread spectrum system, 234 spreading function, 226-233 3 14

SUBJECT INDEX Broad-band frequency synthesizer, 239 Broad-band interfering signal, 219-220

315

Cyclotron wave idler, 72-73 Cylindrical diode, 28

C

CAMEL accelerator, 33 Cancer, 118 Capacitor bank, in pulsed-power devices, 58-59 Carotenoid molecule, Raman effect, 141 Cathode electron emission from, 21-22, 26 for emission of relativistic electron beams, 58-59 and ion flow, in magnetically insulated diode, 34 plasma formed at, 22, 28-30, 33 CCD, see Charge-coupled device Cell division, 117- 118 Cell membrane, see Biological membrane Cerenkov-Raman maser, 52 Charge-coupled device, for spread spectrum communication system, 254 Chemical bond, high-energy, in biological systems, 105 Child-Langmuir law, 28 Chlorophyll, 140- 141 Chromatic aberration, in quadrupole mass filter, 165 a-Chymotrysin, 140 Code division multiplexing, 222-223 Coherent electric vibrations, in biological systems, 98-104, 110-111, 119-121, 149 Coherent electron beam, 282, 303-304 Coherent radiation generation, 68 and line-narrowing, 79-81 with quasi -optical Fabry -Perot cavity , 75-77 Cold beam, gain processes, 60-66, 79 Cold-cathode emission, of relativistic electron beams, 58 Colicin, influence of millimeter waves on induction of, 131-135 Compton scattering, 55-56 Crossed-beam experiment, 297-301 Crystal diffracton, 270, 274-281, 304 Cyclotron maser, scattering experiments, 50

D de Broglie’s wave theory, 269-272 Deformation, of biological material, 95 Dense target, interaction of electron beams with, 37-41 Despreading modulation, in spread spectrum communication system, 217-220, 238 Detector, for free-electron laser, 71 Dielectric vacuum flashover, in modular accelerator, 21 Differential phase shift keying, 250 Digital signal, in communication systems interference suppression, 21 1 as spreading function, 229, 245-246 in frequency-hopping spread spectrum system, 236 Diode, see also Reflex triode electron beam and ICF interactions, 3941 impedance, 30, 35 ion flow in, 31 magnetically insulated, 33-34 of modular accelerator, 20-21 for particle beam fusion, 26-37 perveance, 27-28 time-dependent phenomena, 30-3 1 Directional antenna, 210 Direct-sequencing spread spectrum system, 234-235, 250, 265 acquisition time, 262 Dispersion of wave packet, 272 Distributed resistive feedback, 81 DNA molecule frequencies, 105 influence of millimeter waves on synthesis of, 136 Doppler-shifted backscattering, 48-49, 53-54 DPSK, see Differential phase shift keying DT gas compression, 3-6 energy release through fusion reaction, 2-3 inertial confinement fusion, 1-2

3 16

SUBJECT INDEX E

EEG, see Electroencephalogram Electric field of microwaves, effect on biological system, 122, 126 Electric vibration, of biological material, 92-95 Electroencephalogram, effect of microwaves on, 118-121, 126-127 Electromagnetic undulator, 69 Electron beam, 273-274, 303 and ICF target interaction, 37-41 momentum, 272 Electron beam focusing, 28, 30, 33, 42 Electron beam transport, 33 Electron current density on accelerators, 32-33 in reflex triode, 35 Electron diffraction, 270-271; see o h Crystal diffraction Electron-driven target, for inertial confinement fusion, 6-8 Electron flow in reflex triode, 34 suppression, in high-current diodes, 3334 Electron interference, 269-306 crystal diffraction, 274-281 experiments, 289-303 historical background, 269-27 1 two-beam interference, 281-289 Electron interference microscope, 290 Electron microscope, 289-290 Electron sheath, for power flow in vacuum,22-24 Electron wave, 271-274 Electron wave packet, 269-273, 282-283, 303 Electron wave train, 273-274 Fraunhofer diffraction, 277-278 Fresnel diffraction, 280-281 intensity correlation experiment, 302 Energy requirements, for inertial confinement fusion, 2-8 Energy supply and excitation of coherent vibrations, 98-104

by microwaves, 105 and order of system, 90-92 stored energy of biological systems, 105

Enzyme, 88-90, 108- 109, 149- 150 excitation, 119- 121 frequencies, 140 Escherichia coli, influence of microwaves on, 128-129, 131-136, 143-146

F Fabry-Perot interferometer, 70, 75, 79-81 Feedback effect on coherence and linewidth, 8081 in superradiant system,, 75 FEL, see Free-electron laser Field ripple devices, 69-70 Filter, for spread spectrum communication system, 217, 219, 243,255-256 Fish, sensitivity to electric signals, 88 Fixed-epoch detector, 243-244, 247-248 acquisition time, 261 influence of message modulation on, 251, 254 synchronization scheme, 262 Flashover, in modular accelerator, 2 1 FM, see Frequency modulation Focusing monopole, 206 Foil target, electron beam interactions with, 38-41 Fraunhofer diffraction, 275-278, 282, 288289 intensity correlation experiment, 301 in modified Marton interferometer, 295296 Free-electron laser, 47-84 experimental methods, 67-82 future work,81-82 pulsed intense relativistic electron beams, 57-59 scattering from relativistic electron beams, 48-56 stimulated scattering, theory of, 59-67 Frequency, and biological effects of microwaves, 86, 93-95, 97-98, 105, 125, 140- 142 Frequency division multiplexing, 222 Frequency-hopping scheme, in spread spectrum communication systems, 216, 225, 236-240 bandwidths, 257 fixed-epoch detector, 244

3 17

SUBJECT INDEX jamming, 259 limits on processing gain, 257 message modulation, 251-254 Frequency modulation, 211, 265 phase-hopping spread spectrum system, 249 Frequency-selective fading, in communication systems, 225 Frequency shift keying, 239-240, 265 frequency- hopping spread spectrum system, 252 phase-hopping spread spectrum system, 249 Frequency synthesizer, in frequency-hopping spread spectrum system, 236239, 257 Fresnel diffraction, 275, 279-283 fringes, 289-290 in modified Marton interferometer, 295296 Fringing field quadrupole mass filter, 154-155, 167169, 178-193, 206 of finite length, 178- 181 modified, 191-193 three-dimensional calculations, 181183 two-dimensional linear approximation, 183-191 Front scattering, from relativistic electron beams, 49 FSK, see Frequency shift keying Fungi, influence of millimeter waves on metabolism of, 135 G

Gain cold beam formula, 60-66, 79 FEL with quasi-optical cavity, 76-77 warm beam formula, 66-67 Gain-scattering, 53 GAMBLE accelerator, 3 1 , 35 Gas switch, of modular accelerator, 15- 16, 18 Gaussian wave packet, 271-272 Geometric focusing, of ion beam, 35-36 Gold-foil target, and electron beam interactions, 38 Graphite, as cathode material, 58

Graphite pyramid calorimeter, 71 Gyratron, 48

H High -aspect -ratio diode, 29 -30 ion flow, 33 High-current diode, 28-29 High-gain free-electron laser, 76, 80 High-gain scattering process, 53 High-voltage pulse technology, 8

I ICF, see Inertial confinement fusion Idler wave in laser mode, 77-78 and noise, 65, 77 trapping potential, 64-65 Immune system, 108 Impedance diode, 28, 30, 35 of magnetically insulated transmission line, 26 Indirect signal, in radio communication, 225 Inertial confinement fusion, 1-2 beam interaction with ICF targets, 3741 particle beam generators, 8-21 power flow and energy requirement, 2-8 Instantaneous-epoch detector, 244, 251, 254 Intense electron beam interaction with ICF targets, 37-41 propagation of, and conductivity of medium, 38 Intense relativistic electron beam, 57-59 Intensity correlation experiment, 301-303 Interfering signal, of communication system, 209-210 bandwidths, 219, 257 influence on acquisition time, 261-262 influence on tracking, 262 suppression, 210-212, 217-221, 240, 254-256 limits on, 258-260 Interference, see Electron interference; Interfering signal

3 18

SUBJECT INDEX

Interference suppression bandpass, 217, 219, 221, 251, 253 bandwidth limits, 258 Interferometer, 270, 290; see also specific interferometers Ion beam, production and focusing, 35-37, 42 Ion current density, in reflex triode, 35 Ion-driven target, for inertial confinement fusion, 6-8 Ion flow, in diode, 31, 33-34 Ion optics, 154 calculation methods, 166- 173 distorted quadrupole fields, 193-200 fringing fields, 178-193 higher stability zones of mass filter, 201202 imaging properties of quadrupole fields, 205-206 ion motion in quadrupole, 155-161 normal quadrupole mass filter, 173- 193 RF-only quadrupole, 202-205 source characterization, 165 techniques, 161-165 Isentropic compression of fuel, in inertial confinement fusion, 3-4, 7-8

J Jamming of communication system, 21 1212, 220, 228, 240, 259 Jitter, of modular accelerator, 13, 15-16, 18 JPL ranging code, 232

L

Lambda prophage, effect of millimeter waves on induction of, 134 Laser, 47-48; see nlso Free-electron laser crossed-beam experiment, 297-301 Laser amplifier, 67 Laser oscillator, 67, 75-81 Light ion beam, 33-37 ignition systems, 42 Linear accelerator, scattering experiments, 51 Linear beam transport system, in quadrupole mass spectrometry, 165

Low-gain scattering process, 53 Lysozyme, 140, 149

M Magnetically insulated diode, 33-35 Magnetically insulated target, for inertial confinement fusion, 5-8 Magnetically insulated transmission, of modular accelerator, 19, 22-26 Magnetic field effect on experiments with biological materials, 149 ripple devices, 69-70 Magnetic field undulator, scattering experiments, 51-52 Mammary tissue, Stokes Raman spectra, 147-148 Marton electron interferometer, 28 1-282, 285, 292-294 modified, 295-297 Marx capacitor bank, 59 Marx generator, for modular accelerator, 10-15, 18 Mass spectrometry, quadrupole mass filters, 153-208 Matched filter, for spread spectrum communication system, 243, 254-256 Matrix transformation, in ion optical design, 162-164, 166 Meiosis, 108 Membrane, biological, see Biological membrane Message modulation, in spread spectrum communication system, 249-254 Metabolic activity, and biological effects of microwaves, 105, 135-137, 143, I50 Metastable states, of biological materials, 95-98, 149 Michelson interferometer, 290 Microdielectrophoresis, 149 Microwaves, biological effects of, 85- 152 on bone marrow cells, 137-139 brain waves, 118-121 cancer problem, 118 on colicin induction, 131- 135 on E. coli, 128-129, 136 experiments, 121-148 long-range interactions, 106- 109 multicomponent systems, 113-1 18

3 19

SUBJECT INDEX nonthermal actions, 109- 113 on protein metabolism, 135- 137 Raman effect, 140- 148 trigger effect, 148 on yeast cells, 129-131 Millimeter waves, biological effects of, 127-140, 148, 150 MITE, see Magnetically insulated transmission Mixer, for frequency-hopping spread spectrum system, 237-238 Modulation, spreading, 233-240 frequency hopping, 236-240 phase hopping, 234-236 Molecule, biological, 91, 96, I41 - 143 Mollenstedt -Duker electron interferometer, 281-283, 285, 290-292 Monte Carlo code, for beam-foil interactions, 38-41 M-sequence pseudonoise signal generator, 230-233 Multilevel digital signal, as speading function, 229-230, 244 Multiple-access communication system, 221-223, 228 Multitone interfering signal, 259 Mutation, 118, 129

N Narrow-band interfering signal, 219-221 Negative entropy, in biological organization, 90 Neutron interferometer, 293 Nickel shell target, and electron beam interactions, 40 Noise, see also Signal-to-noise ratio amplification, 68 in communication system, 210 and superradiance, 65, 77-78 Nonthermal effects of microwaves, on biological systems, 86, 91, 109-113, 121, 148- 149 Null steering antenna, 220

0 Optically-pumped gas laser, 48 Oscillating two-stream instability, in strong pump regime, 62-63

P Parapotential theory of magnetically insulated transmission lines, 23-26 pinched electron flow, 28-29 time-dependent pinching phenomena in diodes, 30 Parasitic three-wave interaction, 78 Particle accelerator, see Accelerator Particle beam fusion, 1-45 beam formation and focusing, 26-33 beam-ICF target interaction, 37-41 light ion beam, 33-37 particle beam generators, 8-21 power flow and energy requirements, 28 power flow in vacuum, 21-26 Particle beam generator, for inertial confinement fusion, 8-21 Particle code, for magnetically insulated transmission lines, 24-26 Particle-in-cell code, for beam-foil interactions, 39 Particle motion, in relativistic electron beam, 58 PBFA accelertor, 9-13, 15-19, 21, 23-26, 30, 32-33, 42 Perveance, diode, 27-28 PFL, see Pulse-forming line PFN, see Pulse-forming network Phase-hopping scheme, in spread spectrum communication systems, 216, 225, 234-236 bandwidths, 257 jamming, 259 limits on processing gain, 257 matched filters, 243 message modulation, 249-251, 253 Phase shift keying, phase-hopping spread spectrum system, 249 Phase-space dynamics, in quadrupole mass spectrometry, 154, 161-162 Pinch effect, 57 collapse velocity, 3 1 in diodes, 29-31, 33 Planar diode, 28 Plasma anode, 28-29, 31 cathode, 22, 28-30, 33 pinched flow, 29

320

SUBJECT INDEX

Plasma frequency, of biological materials, 93 Plasma target, interaction with electron beams, 38 Platinum-foil target, and electron beam interactions, 38 PN signal, see Pseudonoise signal Polarization, of biological material, 92-93, 95-98 Poly-~-glutamic acid, 141 Power density spectrum frequency- hopping spread spectrum system, 239 phase-hopping spread spectrum system, 235 Prophage, effect of microwaves on, 134, 149 Protein, 88-91, 143, 150 excitation, 106 frequencies, 105, 140 influence of millimeter waves on metabolism of, 135-137 metastable state, % oscillations, 93 PROTO-I accelerator, 32, 34 Proton current, in reflex pinch diode, 35 Pseudonoise signal, 229 generators, 231-233 m-sequence, 230-231 PSK, see Phase shift keying Pulsed-power technology for inertial confinement fusion, 1-2 intense relativistic electron beams, 5759 Pulse-forming line, of modular accelerator, 13, 15-16 Pulse-forming network, of modular accelerator, 13, 15-16, 18 Pulse jammer, 259 Pulse modulation, by time-hopping process, 216 Push-to-talk communication system, 259 Pyroelectric detector, 71

Q Quadrupole mass filter, 153-208 calculation methods, 166- 173 distorted quadrupole fields, 193-200 fringing fields, 178- 193

higher stability zones, 201-202 imaging properties, 205-206 ion motion in quadrupole, 155- 161 ion optical techniques, 161- 165 ion source characteristics, 165 normal, 173- 193 RF-only quadrupole, 202-205 Quantum mechanics, 269-270, 303-304 Quantum optics, 301 Quasi-optical Fabry-Perot etalon, 70, 7576

R Raman free-electron laser, 52 Raman scattering, 50-52, 55-56, 64-66 in biological materials, 140- 148, 150 Ranging, by spread spectrum system, 223225 Receiver for frequency- hopping spread spectrum system, 238 in multiple-access communication system, 221 in selective-calling communication system, 222 signal-to-noise ratio, 210 in spread spectrum communication system, 214-216, 223-224, 254-256, 264-266 synchronization, 240-249, 260-262 Reflection mesh, for wavelength measurements, 70 Reflex pinch diode, 35-36 Reflex triode, 34-35 Relative-epoch discriminator, 245-248 influence of message modulation on, 251, 254 Relativistic electron beam propagation of intense beams, 57-59 scattering, 48-56, 59-67 RNA molecul~s frequencies, 105 influence of millimeter waves on synthesis of, 136 5

Saturated parapotential theory, of magnetically insulated transmission lines, 23

32 1

SUBJECT INDEX SAW device, see Surface acoustic wave device Scattering, from relativistic electron beam, 48-56 Schottky barrier diode, 71 Selective calling, in communication systems, 221-222, 228 Self-pinched electron flow, in high-current diodes, 28-29 SIECON spread spectrum communication system, 263-266 Signaling techniques, for interference suppression, 210-211 Signal-to-noise ratio, 210-212, 266 and bandwidth of interfering signal, 220 Signal wave in laser mode, 77-78 and noise, 65, 77 SNR, see Signal-to-noise ratio Solid insulator, of modular accelerator, 19 Soliton, excitation of, 104-105, 109 Space charge, of relativistic electron beam, 57-59 Space charge wave idler process, 73 Spark gap switch, of Marx generator, 10, 12-13 Spectral resolution, in free-electron laser, 70 Spectrometer, for millimeter-submillimeter measurements, 70 Spectrometry, quadrupole mass filters, 153-208 Spherical aberration, in quadrupole mass filters, 165 Spreading function, of spread spectrum communication system, 215 generation of, 226-233 for jamming of system, 259-260 synchronization, 240-249 Spread spectrum communication system, 209-267 capabilities, 2 12-2 13, 2 17-226 acquisition capability, 260 interference suppression, 212, 217-221 message privacy, 226, 228 multiple access, 221-223, 228 ranging, 223-225 selective calling, 221-222, 228 suppression of indirect system, 225 examples of realized systems, 263-266

implementation, 226-254 generation of spreading function, 226233 message modulation, 249-254 receiver synchronization, 240-249 spreading modulation, 233-240 limits of, 256-262 on processing gain, 256-258 on suppression of undesired signals, 258-260 on synchronization, 260-262 SAW devices in. 254-256 transmitter and receiver, 214-216 Staphylococcus, influence of millimeter waves on metabolism of, 135-136 Stimulated scattering, 50-53, 59-67 Stokes scattering, 78 in biological materials, 140- 148 Strong-pump scattering process, 50, 6264 Superradiance experiments, 71-81 and trapping effects, 65 Superradiant amplifier, 67-68, 75 Surface acoustic wave device, for spread spectrum communication systems, 254-256, 265 Synchronism detector, 242-243, 247-248 acquisition time, 260-261 influence of message modulation on, 250-25 I, 254

T Thermal effects of microwaves, on biological systems, 85-86, 99- 104, 109- 110, 121-122 Thermonuclear neutrons, electron-beam produced, 38 Thick target, and electron beam interactions, 40 Thin foil target, and electron beam interactions, 38-41 Three-biprism interferometer, 293 Three-wave scattering process, 50-51, 54-55, 77-78 trapping effects, 65 Time division multiplexing, 222 Time-hopping process, in spread spectrum communication systems, 216

322

SUBJECT INDEX

Transmission line for intense relativistic electron beams, 59 of modular accelerator, 15-19, 21-26 Transmitter, in spread spectrum communication system, 214-216, 223-224, 255, 264-265 for frequency -hopping spread spectrum system, 237 in multiple-access communication system, 221 in selective-calling communication system, 222 Trapping effect, in stimulated scattering, 64-65 Traveling-wave amplifier system, 68, 75 TRITON accelerator, 33 beam-foil interactions, 38 Two-dimensional electromagnetic particle code, for magnetically insulated transmission lines, 24 Two-wave scattering process, 50-51, 53 trapping effects, 64 Two-way spread spectrum communication system, ranging, 224

U Ubitron, 50

Vlasov theory, gain formula for warm beam, 66-67 Voltage-controlled oscillator, 237, 246

W Warm electron beam. gain formula for, 66-67 Water-soluble protein, 91 Water switch, of modular accelerator, 1516 Water transmission line for intense relativistic electron beams, 59 of modular accelerator, 18- 19 Wave front interference, 282, 285-286 Wave function, 282-285, 304 Wave mechanics, 269-271 Weak-pump scattering process, 50, 5253, 64-66 Wireless communication system, basic structure, 209-210

X X-ray interferometer, 293

Y V

Vacuum, power Row in, 21-26 VCO, see Voltage-controlled oscillator VEBA accelerator, 52, 75 Very broad-band interfering signal, 2 1922 I , 257 Virus, influence of millimeter waves on production of, 134 Visual system, human, quantum efficiency, 88

Yeast, effect of millimeter waves on, 129131 Young- Fresnel double- mirror interferometer, 290 Young’s electron diffraction experiment, 270

2 Zero-frequency pump, 51, 72, 75 Zero-phase ellipse, 159