Quasi-Optical Control of Intense Microwave Transmission

Quasi-Optical Control of Intense Microwave Transmission

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Series II: Mathematics, Physics and Chemistry – Vol. 203

Quasi-Optical Control of Intense Microwave Transmission edited by

Jay L. Hirshfield Yale University, New Haven, CT, U.S.A. and

Michael I. Petelin Institute of Applied Physics, Nizhny Novgorod, Russia

Published in cooperation with NATO Public Diplomacy Division

Proceedings of the NATO Advanced Research Workshop on Quasi-Optical Control of Intense Microwave Transmission Nizhny Novgorod, Russia 17- 20 February 2004 A C.I.P. Catalogue record for this book is available from the Library of Congress.

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CONTENTS

Preface ……………………………………………………………..……..…ix Acknowledgements …………………..………………...……………………xi

Chapter 1 Quasi-Optical Components – Theory and Experiments ……………………………………… 1 Measurement of Near-Megawatt Millimeter-Wave Beams ……...…..…. 3 V. I. Malygin, V. I. Belousov, A. V. Chirkov, G. G. Denisov, G. I. Kalynova, V. I. Ilin, L. G. Popov

Oversized Transmission Lines for Gyrotron-Based Technological Ovens and Plasma-Chemical Reactors …….…………….15 A. Bogdashov, G. Denisov, G. Kalynova

Development of Lumped and Distributed Models for Accurate Measurements of Q-Factors of Quasi-Optical Resonators ……………...25 B. Kapilevich

The Mode-Matching Technique and Fast Numerical Models of Arbitrary Coordinate Waveguide Objects ……………………...……. 41 A. A. Kirilenko, V. I. Tkachenko, L. A. Rud, D. Yu. Kulik

Electric Field Integral Equation Analysis and Advanced Optimization of Quasi-Optical Launchers used in High Power Gyrotrons …..……….55 J. Neilson

Comparison of Two Optimization Criteria for Quasi-Optical Power Transmission Lines ………..………...……………65 N. N. Voitovich, B. Z. Katsenelenbaum, O. V. Kusyi

A General Purpose Electromagnetic Code for Designing Microwave Components ...………………………….……...73 W. Bruns, H. Henke

v

vi

Contents

Chapter 2 Quasi-Optical Devices and Systems ………….....93 Amplification and Generation of High-Power Microwave by Relativistic Electron Beams in Sectioned Systems ……..…….………95 E. Abubakirov, N. Kovalev, V. Tulpakov

Microwave Devices with Helically Corrugated Waveguides …….…….105 V. L. Bratman, A.W. Cross, G. G. Denisov, A. D. R. Phelps, S.V. Samsonov

Quasi-Optical Transmission Lines at CIEMAT and at GPI …………..115 A. Fernández, K. Likin, G. Batanov, L. Kolik, A. Petrov, K. Sarksyan, N. Kharchev, W. Kasparek, R. Martín

Superradiance of Intense Electron Bunches ………….………………...131 N. Ginzburg, M. Yalandin, S. Korovin, V. Rostov, A. Phelps

Transmission Line Components for a Future Millimeter-Wave High-Gradient Linear Accelerator …………………..…...……………..147 J. L. Hirshfield, A. A. Bogdashov, A. V. Chirkov, G. G. Denisov, A. S. Fix, S. V. Kuzikov, M. A. LaPointe, A. G. Litvak, D. A. Lukovnikov, V. I. Malygin, O. A. Nezhevenko, M. I. Petelin,, Yu.V. Rodin, G.V. Serdobintsev, M.Y. Shmelyov, V.P. Yakovlev

Ferrite Phase Shifters for Ka Band Array Antennas ……...…………...165 Yu. B. Korchemkin, V. V. Denisenko, N. P. Milevsky, V. V. Fedorov

Propagation of Wave Trains of Finite Extent on Wide, Thin-Walled Electron Beams ….……………….………………………..177 E. Schamiloglu, N. Kovalev

Quasi-Optical Multiplexers for Space Communication and Radar with Synthesized Frequency Band ……...………...……………..185 M. Petelin, G. Caryotakis, Yu. Postoenko, G. Scheitrum, I. Turchin

Active Compression of Rf Pulses ……………………………….………..199 A. L. Vikharev, O. A. Ivanov, A. M. Gorbachev, S. V. Kuzikov, V. A. Isaev, V. A. Koldanov, M. A. Lobaev, J. L. Hirshfield, M. A. LaPointe, O. A. Nezhevenko, S. H. Gold, A. K. Kinkead

Control of Intense Millimeter Wave Propagation by Tailoring the Dispersive Properties of the Medium ……………………219 A. Yahalom, Y. Pinhasi

Contents

vii

High-Power Millimetre Wave Transmission Systems and Components for Electron Cyclotron Heating of Fusion Plasmas ………………….…241 W. Kasparek, G. Dammertz, V. Erckmann, G. Gantenbein, M. Grünert, E. Holzhauer, H. Kumric, H. P. Laqua, F. Leuterer, G. Michel, B. Plaum, K. Schwörer, D. Wagner, R. Wacker, M. Weissgerber

Space-Frequency Model of Ultra Wide-Band Interactions in Millimeter Wave Masers …………………………………..……….…253 Y. Pinhasi, Y. Lurie, A. Yahalom

Chapter 3 Applications of Quasi-Optical Systems ………….271 Bi-Static Forward-Scatter Radar with Space-Based Transmitte r .…... 273 A. B. Blyakhman

Analysis of Nanosecond Gigawatt Radar ………………………..……...283 A. Blyakhman, D. Clunie, G. Mesiats, R.W. Harris, M. Petelin, G. Postoenko, B Wardrop

High-Power Microwave Spectroscopy …...……………………...………297 G. Yu. Golubiatnikov

A Multipactor Threshold in Waveguides: Theory and Experiment …..305 J. Puech, L. Lapierre, J. Sombrin, V. Semenov, A. Sazontov, M. Buyanova, N. Vdovicheva, U. Jordan, R. Udiljak, D. Anderson, M. Lisak

Quasi-Optical Mode Converters in Advance High-Power Gyrotrons for Nuclear Fusion Plasma Heating ………..…325 M. Thumm, A. Arnold, O. Drumm, J. Jin, G. Michel, B. Piosczyk, T. Rzesnicki, D. Wagner, X. Yang

Radar and Communication Systems: Some Trends of Development …353 A. A. Tolkachev, E. N. Yegorov, A.V. Shishlov

On Antenna Systems for Space Applications ……………..…………….371 K. van’t Klooster

Intense Microwave Pulse Transmission through Electrically Controlled Ferrite Phase Shifters ……………..…………...393 N. Kolganov, N. Kovalov, V. Kashin, E. Danilov

Index of Authors ………...………………………………...………………399

PREFACE

Between February 17 and 20, 2004, approximately fifty scientists from ten countries came together at the Institute of Applied Physics (IAP), Nizhny Novgorod, Russia to participate in a NATO-sponsored Advanced Research Workshop whose appellation is reflected in the title of this volume, namely Quasi-Optical Control of Intense Microwave Transmission. The fashionable label “quasi-optical” has come into use in recent decades to denote structures whose characteristic dimensions exceed (sometimes by large factors) the free-space radiation wavelength. Such structures were and are developed to replace the traditional single-eigenmode ones in situations when high frequencies (short wavelengths) are combined with high powers, a combination that could otherwise lead to RF breakdown and high Ohmic wall heating rates. Treatments of guided wave propagation in oversized structures is aimed at preserving the propagating field coherence and thus to provide efficient transmission of RF power to remote destinations such as antennas, microwave ovens, plasma-chemical reactors, nuclear fusion machines, and the like. For the participants, this Workshop provided an unusual opportunity to meet and exchange ideas with, and learn from, colleagues from many countries working in a rather diverse agglomeration of fields. The attendees found themselves to be coupled in the common goals of characterizing, designing, and building quasi-optical structures for the control and transmission of intense microwave power flows. A number of junior research staff and students from IAP were also able to participate as informal onlookers, to witness first-hand the exciting give-and-take typical of an open international scientific forum. The 27 original formal presentations at the Workshop that are collected as individual sections in this volume represent contributions by 116 authors, some to more than one of the sections. Papers are grouped— somewhat arbitrarily—into three chapters: Quasi-Optical Components— Theory and Experiments, Quasi-Optical Devices and Systems, and Applications of Quasi-Optical Systems. Applications of quasi-optics extend to use of high-power microwaves (including millimeter-waves) for radar and communications (especially deep space millimeter wave systems, space debris detection radar, and radar for detection of small targets moving over heavy clutter); particle accelerators (especially for a future high-accelerationgradient electron-positron collider); plasma research (especially for controlled nuclear fusion and waste decontamination); and material processing (in particular, ceramic sintering with millimeter waves, and coating of metal surfaces with protective dielectric films.). ix

Preface

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It is hoped that readers of this volume come to more deeply understand and appreciate the need and remarkable capability of quasi-optical structures, and their utility in this wide range of applications. J. L. Hirshfield and M. I. Petelin, Editors

ACKNOWLEDGMENTS

The Advanced Research Workshop on Quasi-Optical Control of Intense Microwave Transmissions was sponsored by the North Atlantic Treaty Organization (NATO) Public Diplomacy Division’s Collaborative Programmes Section on Physical and Engineering Science & Technology. NATO support provided for travel to Nizhny Novgorod for foreign and nonlocal Russian participants, and for costs incurred in organizing and sustaining the Workshop. Appreciation is extended by the Workshop co-chairmen to NATO for its selection of this Workshop as one of those deemed worthy of support during 2004, and for its far-sighted policy of supporting international conferences and workshops to foster close, productive collaborations between scientists in the former Soviet Union and those working in NATO-member and non-affiliated countries. Financial support for the Workshop was also contributed by Russian Academy of Sciences (RAS); Institute of Applied Physics (IAP), Nizhny Novgorod, Russia; and by the small research and development firm Omega-P, Inc., of New Haven, Connecticut, USA. Appreciation is extended for this support to Professor Gennady Mesyats, Vice-President of RAS; Professor Alexander Litvak, Director of IAP; and to Dr. George Trahan, Vice-President of Omega-P. Professor Litvak also deserves thanks for making available a new bright and attractive lecture hall within IAP where the sessions of the Workshop were held. Further individuals who were of inestimable help in dealing with the myriad logistical and organizational steps necessary to the success of such an endeavor include Mr. Vladislav Agaphonov, Deputy Director of IAP; Mr. Edward Abubakirov, Mr. Anatoly Turko, and Ms. Natalie Bondarenko, members of the Local Organizing Committee. Special thanks are due to Miss Enid Stanley of Omega-P, Inc., without whose persistent and indefatigable efforts neither the Workshop nor this volume could have come into being. Finally, appreciation is extended to the participants whose presence at the Workshop helped make it the success that it was; it is their contributions that this volume records. J. L. Hirshfield, and M. I. Petelin, Workshop Co-Chairmen

xi

CHAPTER 1

QUASI-OPTICAL COMPONENTS – THEORY AND EXPERIMENTS

MEASUREMENT OF NEAR-MEGAWATT MILLIMETER-WAVE BEAMS

V. I. Belousov1, V. I. Malygin 1, A.V. Chirkov1, G. G. Denisov1, G. I. Kalynova1, V.I. Ilin2, L. G. Popov3 1

Institute of Applied Physics of Russian Academy of Sciences; Institute of Nuclear Fusion RRC “Kurchatov Institute”; 3 Gycom Ltd. 2

Abstract:

To measure parameters of microwave beams produced by modern gyrotrons, a number of special devices have been developed: quasi-optical filters, bidirectional couplers, calorimetric loads, etc. The wave beam pattern is studied by measuring intensity distributions at several cross-sections, which is used to reconstruct the beam phase distribution and design proper matching mirrors.

Key words:

microwave beams; gyrotron; beam phase front; quasi-optical transmission line; matching quasi-optical filter; meter of transmitted and reflected power; calorimetric load.

1.

INTRODUCTION

Gyrotrons are the most advanced high-power sources of millimeter wavelength radiation. They have been used for many years in electroncyclotron-wave (ECW) systems of many existing fusion installations. For the next generation of fusion installations, such as ITER or W7-X, the ECW systems based on gyrotrons capable to produce 1 MW / CW radiation are considered. Modern megawatt power level CW gyrotrons imply the use of complicated internal quasi-optical converters. The required accuracy of manufacturing of these quasi-optical converters is comparable with the limiting accuracy of machine tools, and sometimes exceeds it. Also, manufacturing of a gyrotron as a whole is a very complicated process at which gyrotron is exposed to high temperatures. Hence, some distortions of the form of the quasi-optical converter inside gyrotron are possible and therefore, there is the necessity of measuring real gyrotron wave beam parameters. The problem of loss-minimization for the microwave energy, on 3 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 3–13. © 2005 Springer. Printed in the Netherlands.

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V. I. Belousov, et. al.

the way from a gyrotron to a fusion installation, indicates the need for knowledge of real wave beam parameters. Thermovision measurements are used as the method of measurement of a power distribution of a gyrotron microwave radiation at megawatt power level1. Measurement of power of a gyrotron wave beam and absorption of its energy at a megawatt power level in a continuous wave regime, is a very serious problem during the tests of gyrotrons. It is possible to use quasi-optical bi-directional couplers for measurement of a power of a gyrotron wave beam, and a calorimetric load made of stainless steel, for absorbing of all energy of a gyrotron wave beam.

2.

MEASUREMENTS AMPLITUDE AND PHASE DISTRIBUTION OF A GYROTRON WAVE BEAM

Measuring the intensity distribution of a gyrotron beam occurs as follows. The beam in free space passes a thin flat dielectric plate inserted along its propagation path This plate has a low loss of microwave radiation and small coefficient of heat conductivity, thus the main power of the gyrotron wave beam goes into a load. The wave beam passing through a plate heats it and the distribution of temperature to its surface is registered by means of the infrared camera. As the plate has small a coefficient of heat conductivity, the distribution of temperature to its surface will correspond to distribution of power in a transmitted wave beam. The scheme of measurements of a gyrotron wave beam power distribution is presented in Figure 1.

Figure 1. The scheme of measurements of a power distribution of a gyrotron wave beam.

The measured distributions of amplitude of a field of a gyrotron wave beam "Vesuvius - 5" (170GHz / 1MW) at several distances from a gyrotron window are presented in Figure 2. Using an amplitude distribution of a field

Measurement of Wave Beams

5

in five sections, not including the distribution at the gyrotron flange, preliminary reconstruction is made of the phase front of a wave beam on the basis of a technique described by Chirkov 2.

Figure 2. Distribution of amplitude of a field of a gyrotron wave beam "Vesuvius - 5" at several distances from gyrotron window z (mm): 62, 312, 562, 812, 1062, 1412.

Because the gyrotron wave beam at the gyrotron flange also contains spurious radiation that sometimes reaches up to 15 %, this cross-section is excluded from procedure of reconstruction of a phase front of a wave beam. If the coupling coefficients in the procedure are rather high (K t 97%), then the infrared measurements of a wave beam are considered as suitable for further analysis, as shown in Figure 3.

Figure 3. Preliminary reconstruction of the phase front of a gyrotron wave beam at five sections (mm): 312, 562, 812, 1062, 1412. Coupling coefficients K(%): 97, 98, 98, 97, 97.

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Where K

º ª i « ³ A( x, y , z k ) ˜ A ( x, y , z k )ds » ¼ ¬s 2

2

2

,

i ³ ( A( x, y, zk )) ds ˜ ³ ( A ( x, y, zk )) ds s

s

A(x,y,zk) is an amplitude distribution measured at the z = zk cross section, and Ai(x,y,zk) is an amplitude distribution during the i-th iteration. Furthermore, on the basis of these intensity measurements, the wave beam phase front is retrieved more precisely on three sections as seen in Figure 4, corresponding with the method 2 that defines parameters of the wave beam.

Figure 4. Reconstruction of the phase front of a real gyrotron wave beam on three sections: 312 mm, 562 mm ɢ 812 mm.

Using the phase received as a result of reconstruction and real amplitude of a wave beam in section z = 312 mm, is possible to calculate amplitude and a phase distributions of the wave beam on the gyrotron output flange, as shown in Figure 5. For testing continuous megawatt power level gyrotrons, there are the objective difficulties connected, first, with absorption of such power, and second, with its measurement and control over time. The gyrotron wave beam consists of paraxial beam and spurious radiation. The share of parasitic radiation reaches from 5 % up to 15 % of a full gyrotron microwave power.

Measurement of Wave Beams

7

Therefore, it is necessary to filter and absorb parasitic radiation and to transform the paraxial beam to an optimum wave beam for a transmission line. This function can be carried out a two-mirror quasi-optical filter.

Figure 5. The reconstructed amplitude and a phase of a wave beam on a gyrotron flange. Gaussian contents: Șa(Șa,ph) = 94,3% (93.4%), rx = 16.0 ɦɦ, ry = 15.5 ɦɦ.

3.

TWO-MIRROR QUASI-OPTICAL FILTER

In order to reduce losses in the transmission line it is necessary to use shaped mirrors 3, 4, 5 based upon knowing the distributions of amplitude and phase of the gyrotron beam (see Figure 5). Quasi-optical filter consists of a metal box (aluminum or stainless steel) with input and output apertures for a wave beam. The absorber of parasitic microwave radiation is located on the inner walls of the filter. It is possible to use water flowing inside Teflon tubes or ceramics cooled by water, as an absorber. The cooling water flows at about 2 liters per second. Mirrors have a water cooling system for operating in a continuous regime. Subsequently, it is necessary to absorb and measure full microwave gyrotron power at the output of a quasi-optical filter, but it is a very difficult problem to combine both functions into one device. It is much easier to solve this problem by dividing these functions into two devices. One device is to simply absorb the full gyrotron microwave power into a load. The second device is to measure and control in time transmitted and reflected gyrotron power at the load.

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4.

V. I. Belousov, et. al.

BI-DIRECTIONAL COUPLER

Measurement of continuous microwave radiation at the megawatt power level is a very difficult problem. Therefore by means of a corrugated mirror, it is possible to derive a wave beam of low power, namely about 0.5 % that of the full wave beam6. If a sine corrugation on a mirror surface makes an angle of 45° to the incident plane of an initial wave beam, the coupled wave beam will be distributed in a plane perpendicular to the plane of the mirror in a direction at an angle of 45° to the incident plane of the initial wave beam (Figure 6). Transmitted and reflected coupling wave beams are distributed on the different sides corresponding to the incident plane of main wave beams and consequently, there is a good decoupling of the transmitted and reflected coupled channels. The period of sine wave corrugations of the mirror (d) in this case will be equal to a wavelength (O). y Pin

z

2l0

Pref

d

Pref −1 x

Figure 6. The corrugated coupling mirror.

The share of the coupled power (Pref-1) depends on depth of a corrugation (l0): Pref-1 a (k l0)2 Pin, where Pin – power in an initial wave beam. If an incident wave beam is large, then it is possible to corrugate only the central part of a mirror, and thus the depth of a corrugation has a Gaussian distribution (Figure 7). The shape of a corrugation of a mirror surface is described by the following formula: § § x2  y2 · · ¸ § ¨ ¨ ¸ ¹ ˜ ¨ 1  1 ·¸  x ˜ y ˜ §¨ 1  1 ·¸ ¸* ª1  cos§ 2ʌ x ·º Z(x,y)  l 0* exp¨  © ¨ ¸» « ¨ ¸ ¨ ¸ 2 © d ¹¼ ¨¨ © a 2 b2 ¹ © b 2 a 2 ¹ ¸¸ ¬ © ¹

Measurement of Wave Beams

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where l0 = 0.08 mm – amplitude of depth of a corrugation, a = 31.46 mm – semi axis an ellipse of a corrugation in a plane of a falling wave beam, and b = 47.16 mm – semi axis an ellipse of a corrugation in a perpendicular plane to a plane of incidence of the wave beam. X (mm) 0

10

20

30

40

50

Y

0.0

-0.4

X Z / lo

-0.8

-1.2

-1.6

-2.0

Figure 7. The coupling mirror with corrugation in the central part.

The schematic drawing of a measuring unit is represented in Figure 8. The coupled wave beam from the first corrugated mirror (Ʉcoup1 = 0.55 %) propagates to the second corrugated mirror and to a calorimeter. The calorimeter measures power in the coupled wave beam, and in view of a coupling coefficient (Ʉcoup1) full power in an incident wave beam. The coupled wave beam from the second corrugated mirror (Ʉcoup2 = 1.5 %) propagates to a taper with the detector on the end. The detector measures the power in an incident wave beam depending on time. In the reflected channel is established only the taper with the detector, as the reflected power should be about two orders of magnitude less than the transmitted power.

Figure 8. The meter of transmitted and reflected power: main channel and coupled wave beams.

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V. I. Belousov, et. al.

Thus, the meter measures transmitted and reflected power of the wave beam and controls changing of this power in time.

5.

CW CALORIMETRIC LOAD FOR MEGAWATT POWER LEVELS

The basic problem of a load for continuous microwave radiation megawatt power level is the overheating of an absorber causing its breakdown and destruction. For resolution of this problem, it is necessary to reduce the density of power on absorbing parts of a load, and to more uniformly distribute this power on the absorbing surface. The design of a load in many respects depends on the material of the absorber. If the absorber absorbs at normal incidence about several percents from the incident power, (stainless steel, for example) then design of a load would require a wave beam to fall repeatedly on the absorber. Such a load-type is represented in Figure 9. In this load, the absorber consists of stainless steel tubes where cooling water is flowing. The wave beam, formed by two mirrors, and a quasi-optical filter inserted ahead of the load, enters into the load through a narrow aperture (‡ = 63.5 mm) and propagates to the defocusing mirror located at the bottom of the load. The scattered wave beam is distributed on stainless steel tubes, dissipates and partly absorbed in them. Repeated absorption of a wave beam in the load is thus reached. Power distribution at the wall of the load after the defocusing mirror is presented in Figure 9. The area of the absorbing surface of the load is much greater than the area of the entrance aperture of the load, therefore the share of the reflected power is small and reaches for the load that was tested not more than 5 %. Thickness of stainless steel tubes is about 1 mm. The flow of cooling water should be about 5 – 7 liters per second for absorption of 1 MW continuous microwave power. To obtain power distribution uniformity on the wall of the load in an azimuth plane, the linear polarization of a wave beam was converted to circular by help of a polarizer. The parabolic mirror installed before the load is very good for this purpose.

Measurement of Wave Beams

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Figure 9. The load with a two-mirror quasi-optical filter and distribution of the power at the wall of the load after defocusing mirror.

6.

SET-UP FOR TESTING GYROTRONS OF MEGAWATT POWER LEVEL

The real scheme of a set-up for power measurement is diagrammed in Figure 10. This transmission line has shielding to contain stray microwave radiation. The diffraction losses in this transmission line are about 5%.

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V. I. Belousov, et. al.

Figure 10. The scheme of a set-up for test of a gyrotron « Vesuvius -5 » 170 GHz / 1 MW / CW at INF RRC « Kurchatov institute ».

In experiments during the test of a gyrotron « Vesuvius - 5 » at a power level of about 900 kW, microwave radiation was obtained in pulses of 20 seconds; and at power levels of about 700 kW, in pulse durations of 40 seconds. The limitation of pulse duration is basically connected to breakdowns in the load. Apparently, the density of power on some parts of the load exceeded allowable values that resulted in overheating of the surface and as consequence, breakdowns. For absorbing 1 MW continuous microwave power, it is necessary to increase the area of an absorbing surface of the load.

7.

CONCLUSION

Methods of measurements of parameters of gyrotron wave beams, described in this article, allow one to carrying out tests of powerful continuous wave gyrotrons in real regimes. The Thermovision method of measurement of parameters of a real gyrotron wave beam allows production optimum mirrors of the quasi-optical filter to minimize losses of power in transport of the microwave energy of a gyrotron up to calorimetric load. A quasi-optical bi-directional coupler, used in a transmission line, allows measurement of the microwave radiation power during gyrotron operation, and a calorimetric load on the end of a transmission line allows absorbing all microwave energy of a gyrotron.

Measurement of Wave Beams

8.

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REFERENCES 1.

2.

3. 4. 5.

6.

Kuznetsov S.O. and Malygin V.I., Determination of gyrotron wave beam parameters, International Journal of Infrared and Millimeter Waves, 12, (11), 1991, pp 1241-1252. Chirkov A.V., Denisov G.G., Aleksandrov N.L. 3D wave beam field reconstruction from intensity measurements in a few cross sections. Optics Communications. Vol. 115 (1995), pp. 449-452. L.B. Tartakovsky, V.K. Tikhonova. Synthesis of linear array with given amplitude distribution. Journal of radiotechnics & electronics, 12, pp. 2016-2019, 1959. B.Z. Katsenelenbaum, V.V. Semenov. Synthesis of the phase correctors forming a given field, Journal of radiotechnics & electronics, 2, pp. 244-252, 1967. Bogdashov A.A., Chirkov A.V., Denisov G.G., Vinogradov D.V., Kuftin A.N., Malygin V.I., Zapevalov V.E. Mirror synthesis for gyrotron quasi-optical mode converters. International Journal of Infrared and Millimeter Waves, Vol. 16, No. 4, 1995, pp. 735-744. Belousov V.I. at all. Coll. Pap. “Gyrotron”, Ed. Flyagin V.A., Inst. Appl. Phys., USSR, Gorky, 1989, 155 - 160.

OVERSIZED TRANSMISSION LINES FOR GYROTRON-BASED TECHNOLOGICAL OVENS AND PLASMA-CHEMICAL REACTORS

A. Bogdashov, G. Denisov, G. Kalynova Institute of Applied Physics (IAP RAS) 46, Ulyanov str., Nizhny Novgorod - 603950 ,Russia Abstract:

High-power millimeter-wave gyrotrons are used in a number of technologies: ceramics sintering and joining (including nanoceramics), functionally graded coatings, rapid annealing of semiconductors, microwave plasma assisted chemical vapor deposition, and multiply charged ion production are among the most advanced developments. The paper presents the status and examples of transmission line developments for such gyrotron-based systems.

Key words:

microwave transmission lines, gyrotron, mode converter, mode filter.

1.

INTRODUCTION

A growing demand of the nuclear fusion community in the millimeterwave power sources resulted in the development of gyrotrons capable of producing about 1 MW in practically continuous wave (CW) regime at frequencies of up to 170 GHz [1]. Electron cyclotron plasma heating is a unique area of gyrotron application to this date. However, it has become evident during the last decade that many microwave energy applications might greatly benefit from an increase in the frequency of radiation. High temperature processing of materials, e.g. advanced ceramic sintering, was one of the first fields where the advantages of the millimeter-wave (mmwave) heating as compared with conventionally-used power of 2.45 GHz have been demonstrated [2]. The capability of efficient volumetric heating of low-loss ceramic materials and rapid uniform sintering oflarge size specimens and batches of samples is of great importance for the successful development of processes of industrial interest. Very high uniformity of the mm-wave heating is of paramount importance for the annealing of silicon wafers of

15 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 15–23. © 2005 Springer. Printed in the Netherlands.

A. Bogdashov, G. Denisov, G. Kalynova

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large diameter (• 300 mm), a necessary step in the manufacturing of ultra large integrated circuits [3]. Significant improvement of performance characteristics of the electron cyclotron resonance ion sources can be achieved with an increase in the frequency of the applied microwave power [4]. The microwave-assisted chemical vapor deposition of diamond films is another process which gains drastically in the rate of deposition if the plasma is sustained by the mm-wave power [5]. The application of the mm-wave beams for surface treatment of materials is a promising method which in many cases is competitive with the surface heating by other concentrated energy flows, such as laser, ion or electron beams, plasma flow [6]. Awareness of the potential of the mm-wave power use in technology initiated in the beginning of 1990’s, the development of the first gyrotronbased system purposely designed for research in material science [6]. Since then, several types of gyrotron systems of different power, operating at various frequencies, have been developed.

2.

EXPERIMENTAL FACILITIES

The general concept of the gyrotron system architecture remains invariable despite the differences in the technical specifications of the gyrotrons that are used and the nature of applications (Fig. 1). A gyrotron system is made up as a standard computer-controlled device to which the feedback loop is applied. The gyrotron systems do not differ from microwave sources of other frequencies in terms of control. However, the difference in the operating frequency results in a drastic dissimilarity of all major components. The gyrotron systems are designed as an integrated set of the following principal components: x a gyrotron, the source of the mm-wave power, x transmission line for transport of mm-wave power to an applicator, x an applicator, x diagnostic subsystem and PC controller for automatic/manual processing. The specific design of these components is flexible and depends on a particular application. The output power of gyrotrons can be smoothly regulated from about 5% to 100% of the full power by variation of the electron beam voltage. All CW gyrotrons can operate in pulse regime with the same or slightly higher output power Typical operating voltage of these gyrotrons is in the range of (15-30) kV, and the electron beam current is (1-2.5) A. An efficiency of the standard .

Oversized Transmission Line

17

gyrotrons operating in frequency range of (20-80) GHz is about 0.3–0.4, and about 0.60-0.65 in the gyrotrons with a depressed collector [7].

High Voltage Power Supply

Gyrotron

Transmission Line

Applicator

Solenoid Power Supply

Power Meter

Process Parameters

PC - based Control System T

3.

Figure 1. Block diagram of the gyrotron system. T

TRANSMISSION LINES

Microwaves leave a gyrotron via a waveguide, which is oversized as compared to the wavelength of radiation. Various transmission lines (TL) can be designed for the transport of microwaves from the gyrotron to an applicator. The design of these TL depends mostly on what one would like to have at the input of the applicator in terms of the electromagnetic field pattern and polarization. At frequencies above 20 GHz, a TL can be built either as an oversized waveguide, a set of quasioptical mirrors, or can be of a mixed type.

3.1

The 28 GHz 10 kW CW Transmission Line for Electron Cyclotron Resonance Ion Source

A schematic drawing of the waveguide TL of the 28 GHz gyrotron system designed for powering the electron cyclotron resonance ion source is shown in Fig.2. The structure of this TL is based on waveguide components. However, it should be realized that at a high frequency the TL is composed of multi-mode components. Therefore, the design and principle of operation of these components usually differ greatly from those used at lower frequencies. The transmission line includes the following components: x a bi-directional coupler,

A. Bogdashov, G. Denisov, G. Kalynova

18

x a 90° quasioptical mirror bend. This section can be also used for measuring the absolute value of microwave power produced by gyrotron. For this purpose, the bend is cooled with water and furnished with a set of temperature sensors, x a mode convertor, which transforms the operating mode of the gyrotron, TE 02 , into the TE 01 mode, x a mode filter, which serves to protect a gyrotron against the microwave power reflected back from the ion source. Operation of the filter is based on selective absorption of power of non-symmetrical modes, x a launcher, which produces the required electromagnetic field pattern at the input of the ion source, x additionally, the line is equipped with an arc detector, which serves to shut off the power if, by some reason, arcing occurs in the transmission line. An efficiency of the mm-wave power transport through the entire TL is over 97%. B

B

B

T

B

Figure 2. 28 GHz gyroton-based system for ion source. T

Oversized Transmission Line

19

gyrotron, mode TE02

fiber to Arc-detector

attenuator

to amplifier diode

compensator

mode converter TE02 o TE01

water in out to meter of transmitted power

out

out

compensator

waveguide bend water in

mode filter

in vacuum proof window

Figure 3. 28 GHz 10kW transmission line for ECR ion source.

T

T

3.2 24 GHz, 3 kW Transmission Line for Ceramics Sintering One of the promising areas of mm-wave industrial applications is high temperature processing of materials, such as sintering and joining of advanced ceramics, annealing of semiconductors, etc. Most of the gyrotrons systems designed to this date are furnished with a microwave furnace, which comprises a large cavity resonator, that can be evaculated and backfilled to operate over a wide pressure range (10 -4 -2 bars). High uniformity of the microwave energy distribution in the furnace is an essential prerequisite for the processing of large size specimens and for reproducible heating of many specimens processed simultaneously in one batch. The approaches to attaining a distribution of high spatial uniformity are different for the multimode applicators fed with the mm-wave (L >> O) and microwave (L t P

P

A. Bogdashov, G. Denisov, G. Kalynova

20

O) radiation (where L is the size of applicator and O is the wavelength of radiation). The mm-wave radiation usually enters the furnace as a wave beam (see, for example, Fig. 3) or through an opening in the multimode waveguide. High uniformity of the microwave energy distribution in the furnace is achieved as the result of superposition of the electromagnetic fields of hundreds simultaneously exited modes.

3

4

5

2

6 1

T

Figure 4. 24 GHz 3 kW transmission line for ceramics sintering. T

The 24 GHz, 3 kW gyrotron system shown in Fig. 4 features an unparalleled capability of both volumetric heating of specimens by the mmwave energy uniformly distributed over the whole volume of the cavity, and local heating by a focused wave beam [10]. This is achieved by the use of two types of mirrors alternatively directing the wave beam entering the applicator to the stirrer or to a specimen. Transmission line consists of following components (referred to Fig.4): 1 – TE11 mode polarizer, 2 – waveguide bend (>99% TE11 mode efficiency), 3 – mode filter serves to protect a gyrotron against the microwave power reflected back from the sintering oven, 4 – mode converter creates Gaussian wave beam at the microwave oven (see Fig.5), 5 – barrier ceramic window, 6 – sintering oven. Measured power transmission coefficient is 97r1%.

Oversized Transmission Line

T

21

a) b) Figure 5. Thermo-paper images of microwave intensity a)TE11 mode with vertical polarization, b)Gaussian wave beam. T

3.3 The 30 GHz, 15kW Transmission Line for CVD Diamond Growing Microwave system for CVD diamond growing is very attractive branch of material processing. Total time of polycrystalline diamond growing strongly depends on plasma density and radiation frequency. To investigate respective plasma-chemical reactions, gyrotron-based system was developed at Institute of Applied Physics [5]. Transmission line is shown in the Fig. 6. It includes following microwave components: 1,2 – beam forming quasi-optical mirrors, 3 – plane mirrors of power splitter, 4 – square corrugated waveguide for microwave power splitting, 5 – reaction position (discharge region), 6 – wavebeam waist in the discharge region, 7 – circular corrugated waveguides, 8 – low-loss HE11 mode miter bend, 9 – 30GHz / 15kW gyrotron, 10, 11 – TE02 – Gaussian wavebeam mode converter and focusing mirrors with special profiles,

A. Bogdashov, G. Denisov, G. Kalynova

22

T

Figure 6. 30GHz 15kW transmission line for CVD diamond reactor. T

Preliminary tests show a relatively low power transmission coefficient of 86%. Further development of the TL includes some additional improvements of microwave components: TE02 – Gaussian wave beam mode converter, HE11 miter bend and power splitting system. Nevertheless, the gyrotron system demonstrates stable operation in CW regime. It’s very useful for CVD reaction experiments.

4.

CONCLUSIONS

Wave transmission and control systems used in technological applications of gyrotrons are simple, reliable and have over 95% transmission efficiency.

Oversized Transmission Line

23

5. REFERENCES 1. G.Denisov, Development of 1MW output power level gyrotrons for fusion systems, in Proc. 4 th Intern. Workshop "Strong microwaves in plasmas", Nizhny Novgorod, Russia, August 2000, pp. 967-986. 2. M. Janney and H. Kimrey, Diffusion-Controlled Processes in Microwave-Fired Oxide Ceramics, in Mat. Res. Soc. Symp. Proc., v. 189, Pittsburgh, PA, 1990, pp.215-227. 3. Yu. Bykov, A. Eremeev, V. Holoptsev, I. Plotnikov, and N. Zharova, Spike annealing of silicon wafer using millimeter-wave power, in Proc. 9 th Int. Conf. on Advanced Thermal Processing of Semiconductors - RTP 2001, Anchorage, Alaska, September 2001, pp.232239. 4. R. Geller, B. Jacquot, and P. Sortais, The upgrading of multiplied charge heavy-ion source MINIMAFIOS, Nucl. Instrum. Methods Phys. Rev A.. 243, 1986, p. 244-254. 5. A. Vikharev, A. Gorbachev, A. Litvak, Y. Bykov, G. Denisov, O. Ivanov, V. Koldanov, RU patent application, #2002125807 dated 30.09.2002. P

P

P

P

DEVELOPMENT OF LUMPED AND DISTRIBUTED MODELS FOR ACCURATE MEASUREMENTS OF Q-FACTORS OF QUASIOPTICAL RESONATORS B. Kapilevich Dept. of Electrical and Electronic Engineering, the College of Judea and Samaria, Ariel, Israel – 44837

1. INTRODUCTION Power mm-wave sources based on relativistic electron beams require high-Q resonators for a single-frequency and single-mode operation. Such a resonator can be formed on the basis of quasi-optical waveguides. A critical point in the practical study of these resonators is an accurate measurement of unloaded and loaded Q-factors. This is necessary for estimating the electron beam parameters required for reaching lasing threshold and mm-wave generation. The elements used for an excitation of quasi-optical resonators may cause additional diffraction losses. As a result, an amplitude response of a resonator is considerably deformed causing problems in accurate Q-factors measurements and preventing application of conventional measuring techniques. In this paper, several models of quasi-optical resonators excited by polarized grid couplers are developed for measurement of Q-factors using a scalar mm-wave HP-Network Analyser. Three models are considered below: 1. Lumped model: In this model, both a resonator and coupler are represented by its equivalent R-L-C parameters and a section of lossy line is introduced for simulating diffraction losses; 2. Mixed model: In this model, a resonator is represented by its equivalent short-circuited transmission line and coupling element which is replaced by an equivalent inductor loading this line; 3. Distributed model: In this model a distributed network circuit in terms of transmission matrix describes both resonator and coupler.

25 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 25–39. © 2005 Springer. Printed in the Netherlands.

26

Kapilevich

By using the models suggested, the equation determining the condition of critical coupling of a resonator with feeding waveguide was derived. This was used to estimate the unloaded Q-factor of the quasi-optical resonator of the Israeli Free Electron Maser (FEM) that recently generated output power of approximately 1 KW at W-band. Examples of Q-factor measurements using the models considered are discussed.

2. CONFIGURATION OF EXPERIMENTAL SETUP Figure 1 demonstrates a configuration of a quasi-optical resonator used in millimeter-wave FEM of Tel Aviv University [1]. The resonator is composed of a parallel curved plate waveguide (PCPW) section [2] shorted at the end. The polarising grid coupler is illuminated by a free space Gaussian beam formed by means of mode exciter and mirror as described in [3]. HP-8757D Network Analyser, is employed for measurement of a reflection coefficient. However, critical problems in characterization of quasi-optical resonator is a good matching of coupler and mirror with guiding system. Bad matching may lead to considerable return loss causing problems in accurate Q-factors measurements and preventing application of conventional measuring techniques. To solve the problem, different calibration procedures have been suggested to take into consideration coupling losses [4-8]. However, they don’t take into account diffraction losses playing important an role in the characterization of quasi-optical resonators. Mirror Transmission line

Reflecting grids of a variable coupler

Mode exciter

Shorted-line resonator

To network analyzer

Electron beam

Figure 1. Experimental setup used in measurements of a quasi-optical resonator excited by mode exciter and focusing mirror.

Development of Models

27

3. LUMPED MODEL OF A QUASI-OPTICAL RESONATOR Following [6] we can introduce a virtual line whose characteristic impedance is known, but the propagation constant may be unknown. The latter is reconstructed further from measured values of return loss. The virtual line is loaded by equivalent resonator’s circuit consisting of lumped elements R0, L0, and C0 representing its interior parameters [9], Fig.2. Hence, the input resonator’s impedance can be written as: § 1 1 Z in Z ¨¨ jZC 0   jZL0 R0 ©

· ¸ ¸ ¹

1

(1)

Figure 2. Lumped Model of a Quasi-Optical Resonator.

The input impedance ZCSin(Z) of the coupling line loaded by a resonator is calculated as follows:

Z inCS (Z) Z virt (Z) ˜

Z in (Z)  jZvirt (Z) tan[(E  jD )Leff ) Z virt (Z)  jZin (Z) tan[(E  jD )Leff )

(2)

where Zvirt(Z) is the impedance of virtual line, E - jD is the complex propagation constant, Leff is the effective length of virtual line, Z is angular frequency. A return loss (RL) measured by scalar the Network Analyser can be written now in the form:

RL(Z )

20 log S11

20 log

Z inCS (Z )  Z 0 Z inCS (Z )  Z 0

(3)

28

Kapilevich

where | S11| is a reflection coefficient, Z0 is a system impedance of the Network Analyser’s input waveguide. The expression (3) can be used for direct reconstruction of the interior parameters of a quasi-optical resonator from measured data employing curve fitting procedure [10]. The reference level of return loss RLref, in a vicinity of resonance frequency corresponding to a shorted regime of the virtual transmission line must be determined on the basis of real measurements. Figure 3 shows the results of measurements of equivalent FEM resonator parameters for the mode resonating at the frequency 99.999GHz in PCPW resonator of the length l=1.56m.

RL dB

Figure 3. Comparison modeling (solid line) and measured (dotted line) results. The dashed line corresponds to the reference level: R0 =19.5 Ohm, C0=1.0394E-9 F, L0 =2.4375E-15 H, Qload =12800.

Development of Models

29

4. MIXED MODEL OF A QUASI-OPTICAL RESONATOR A drawback of the technique based on lumped model is the difficulty in separating external coupling elements from internal resonating elements. In order to carry out such a separation, the model of a FEM resonator based on shorted-line representation is preferable. Such a model provides some advantages: x A possibility to simulate all longitudinal modes resonating within a specified frequency range; x Elements responsible for resonance or coupling effects can be easily separated; x A possibility to estimate frequency dispersion effects of the FEM resonator. The FEM resonator can be presented by the equivalent schematic shown in Fig.4, [11]. It consists of a shorted-line section of the length l corresponding to the physical length of the FEM resonator

Figure 4. The equivalent schematic of inductively coupled shorted-line resonator [11].

The equivalent inductor L corresponding to the polarizing grids coupler shunts its input. The model allows extracting Q factors in a relatively easy way. The formulation can be done using the inductively coupled shortedline resonator model [11]. As a result, the following expression can be derived for the magnitude of input reflection coefficient S11(Į,L,Ȧ)

Z jZL  1) 01 tanh[(D  jE )l ]  Z0 Z0 Z jZL (  1) 01 tanh[(D  jE )l ]  Z0 Z0 (

S11 (D , L, Z )

jZL Z0 jZL Z0

(4)

30

Kapilevich

where: L is the inductance; Z0 and Z01 are the system impedance of both the network analyser waveguide and of the resonator waveguide mode, D is the attenuation constant. Figure 5 demonstrates behaviour of the magnitude of S11 in the space of {D,L}. This shows a presence of global minimum corresponding to a near critical coupling condition at the resonance frequency f = 99.99 GHz. The following parameters of the resonator were used in calculation l = 1.56 m, Z0 = 467 Ohms, Z01 = 377 Ohms.

Figure 5. Behavior of the magnitude of S11 in a space of {D,L} near resonance frequency f0 = 99.99 GHz.

To formulate the algorithm for reconstructing D and L, one must take two measurements of S11 magnitude: first, at the resonance frequency f0 and second, at the frequency near resonance, f1. Assuming that their magnitudes are A0 and A1, respectively, the system of two non linear equations can be written for D and L:

S11(D,L,Z0 ) = A0 S11(D,L,Z1 ) = A1

(5)

The system (5) can be solved numerically by iterations. When solving equations numerically, it is necessary to define values from which the solver

Development of Models

31

should start its search for a solution. The details of this process can be found in [12]. The unloaded Qun and external Qe factors are calculated using formulas (9.23) and (9.28) from [11]:

Qun = E /2D Qe = [BL +I(1+BL2)]Z0/2Z01

(6) (7)

where BL = Z01/2S f0 L, I = 2S f0 l/c The example below illustrates Q-factor measurements obtained for the resonator excited in under-coupled regime, Qe > Qu. Weak coupling of the resonator can be realized by setting small angles between the inner polarizing grid and the external ones (about 10 – 15 deg.). The measured magnitudes of S11 at the resonance frequency f0 and at the frequency near the resonance f1, are given in the Table 1. The solution of the system (5) is found using preliminary determined guess values of D and L. Based on values of D and L determined from solution of the system (5), we can reconstruct frequency dependencies of S11 for Q-factors given in Table 1 (see Fig. 6) Agreement between these data is observed in a vicinity of the resonance frequency. Table 1. Results of measurements and reconstructing Q-factors for under-coupled regime

f0 = 99.99 GHz S11 =0.9099 f1 = 99.985 GHz S11 =0.96039 Guess values D = 0.05(1/m), L = 0.1 (nH) Solutions of the system (2.4) D =0.0844(1/m),L = 0.053(nH) Q – factors Qun = 12393 Qe = 261883 Qload = 11833

32

Kapilevich

Fig.6 Reconstructed and measured behavior of S11 as a function of frequency.

5. DISTRIBUTED MODEL OF A QUASI-OPTICAL RESONATOR In order to arrive at the maximum power delivery-point of the maser, the quasi-CWFEMwaveguide resonator’s output coupler is an important element in its operation. The ability to adjust, in real time, its out-coupling coefficient, the ability to continuously adjust the resonant frequencies of the resonator in order to allow fine tuning (between longitudinal modes) of the FEM lasing

Development of Models

33

frequency, and take full advantage of the high coherence and wide range tuneability of this maser, are highly desirable. In order to predict basic characteristics of such a resonator, a distributed model of a quasi-optical resonator is preferable. The coupler (shown schematically in Fig. 7), consists of three polarizing wire grids illuminated by a free-space Gaussian beam propagating along the z-axis. The electrical lengths between grids are (I Sfd) are I1 and I2. The wires of the external grids are perpendicular to the incident electric field. The inner grid orientation angle T with respect to the external one can be varied so that the total system transmittance is adjustable from 0 to 1. When such a coupler is placed at the output of the quasi-optical resonator, an optimisation of the output coupling conditions can be obtained by rotating the inner grid within the range T = 0 to 900. In addition, the fine frequency tuning of the quasi-optical waveguide resonator can be obtained by judicious displacement of the entire grid assembly along the resonator axis relative to the resonator output plane. These two degrees of freedom have been realized using remotely controlled stepping motors to provide the rotary and linear motions [13].

θ

E

φ1

φ2

Figure7. Scheme of 3 grids tunable coupler.

Calculationof the 3 grid system parameters can be done using a transmittance matrix approach. According to [14], a system consisting of 3 grids can be

34

Kapilevich

fully characterized in terms of the electrical lengths I1, I2 and inner angleT. The total transmission matrix of the 3 grid system was determined and power transmission coefficient can be written as follows: 4z4 (8) T 2 2 2 2 y1(z  x2 ) y2 (z  x1 ) 2 x2(z2  x12) x1(z2  x22) 2   [2x1x2  ] [x1y2  x2 y1  ] y2 y1 y1 y2

where z = cosT , x1 = sin)1, x2 = sin)2, y1 = cos)1, y2 = cos)2 For example, Fig.8 illustrates the angular behavior of the power transmittance of a 3 grid system calculated from (8) for equidistant ()1 = )2 = 450) and non-equidistant ()1 = 450 and )2 = 830) grid’s spacing as a function ofT. In both cases, the change of power transmittance lies within the interval 0 < T < 1 however, the equidistant configuration displays symmetry relative to lines T = 0.5 and T = 450 and preferable in practice.

(a)

(b)

ș Figure 8. Calculated power transmission coefficient T for equidistant (a) and non-equidistant (b) grids.

Assuming I1 I2 = 450 the following expression for the magnitude of reflection coefficient S11 as function of T can be derived:

S11

(sin 2 T  i cos 2T ) tanh Jl  i  sin 2 T (sin 2 T  i cos 2T ) tanh Jl  i  sin 2 T

(9)

Development of Models

35

Figure 9 illustrates the input reflectance |S11| dB of the quasi-optical resonator calculated from (9) for unloaded Q = 2E/D = 10470, ) = 450 , l = 1.532m and different angles of the inner grid T varying within the range 30 – 55 degrees. It is clearly observed that a gradual transition from undercoupled (T < 450 ) toward critically coupled (T = 450 ) and then to overcoupled (T > 450 ) regimes of the resonator considered with increasing T .

6. THE ANGLE OF CRITICAL COUPLING According to (9) two basic factors determine reflectance of the resonator loaded by grid’s coupler as a function of frequency-angular position of inner grid T and unloaded Q = 2E /D of quasi-optical resonator itself for a fixed resonator length. The exact value of the angle corresponding to zero reflectance, S11 = 0 (critical coupling of the resonator with a guide), can be determined from (9) as a solution of the following equation:

(sin 2 T  i cos 2T ) tanh Jl  i  sin 2 T

0

(10)

Figure 9. Input reflectance of the FEM resonator with 3 equidistant grids coupler for angles of the inner grid: ƑƑƑ T = 600, + + + T = 550, o o o T = 500, T = 450, ¸ ¸ ¸ T = 350different.

36

Kapilevich

Equation (10) is equivalent to a nonlinear system of two equations for two unknown parameters T and f: ­sinh 2Dl sin 2 T  sin 2 El cos 2T  2(sinh 2 Dl  cos 2 El ) sin 2 T 0 ® 2 2 2 ¯ sin T sin 2 El  cos 2T sinh 2Dl  2(sinh Dl  cos El ) 0

(11)

There are infinite numbers of roots satisfying system (11). Table 2 presents some of them calculated in the vicinity of resonance frequency near 100GHz for the same resonator’s dimensions as used in Fig.9 Table 2. The values of critical angle coupling Tc calculated from (11) for different Q

Qun-factor Grid’s angle, Resonance frequency f [GHz] Tc [grad] 5000 28.350 100.021 10470 38.760 100.025 21000 46.20 100.029 42000 52.260 100.032 To avoid wrong roots that can appear in a process of numerical solution of (11), a validation of data shown in Table 2 must be carried out. True critical coupling must reveal a zero reflectance at resonance frequencies for critical angle and to increase reflectance with any changing inner grid's angle. To validate the theoretical data the experiments have been done with the tunable 3-grid coupler to provide both angular adjusting of the inner grid and longitudinal shift of coupler itself [13]. The HP-8757D network analyzer was used to measure reflectance (transmittance) of the 3-grid coupler and the quasi-optical resonator. Figure 10 shows measured power transmittance of the 3-grid coupler in a free space. The spacing between grids is Ȝ/8 = 0.375mm (Ȝ = 3mm). The measurements were done at frequencies 95, 100 and 105 GHz. The curve corresponding to 105 GHz demonstrates almost symmetrical behavior respectively axis Tpower = 0.5 and ș = 45 deg that is closed to the theoretical prediction. The measured reflectivity of the FEM's resonator with 3 grid coupler is depicted in Fig.11. The curves are similar to the theoretical ones depicted in Fig.9 demonstrating under-coupled, critical and over-coupled conditions. Critical coupling corresponds to T near 45o (marked by circles). According to the Table 2 and the Q-factor corresponding with this angle, it is about 20000. This is in a good agreement with independent measurements using other techniques.

Development of Models

37

1

Tpower 0.8

T_95

0.6

T_100 T_105

0.4

0.2

0

0

20

40

60

80

100

θ Angle of inner grid, degrees

Figure. 10 The angular behavior of a power transmittance of the 3 grids coupler at frequencies 95, 100 and 105 GHz.

Frequency, GHz Figure 11. Measuredreflectivity of the of quasi-optical resonator with3 grids tunable couplerin a single mode operation for different T. The critical angle is Tc= 45o and marked by circles.

38

Kapilevich

7. CONCLUSION Both lumped and distributed models have demonstrated reliable results, and can be used for measurements and characterization of quasi-optical resonators. However, the distributed model is preferable since it provides direct links between angular-longitudinal coupler configurations and the resonator's properties.

8. ACKNOWLEDGEMENTS Author would like to thank: Prof. A.Gover, Prof. Y.Pinhasi and Dr. A.Yaholom for useful discussions concerning both models considered and measurements, Dr. A.Abramovich for development of LabView interfaces, MS students A.Faingersh and A.Eliran for assistance in arrangement of experimental setups. This work was done in the Israeli FEL Knowledge Center with partial support of the Israeli Ministry of Science.

9. REFERENCES 1.

I.Yakover, Y.Pinhasi, and A.Gover, Resonator Design and Characterization for the Israeli Electrostatic FEL Project, Nuclear Instr.& Methods in Physics Research, Section A.358, 1995, pp.323-326. 2. Nakahara and N. Kurauchi, Guided Beam Waves Between Parallel Concave Reflectors, 1967 Trans. MTT, vol.15, no.2, pp.66-71, 1967. 3. M.A.Shapiro and S.N.Vlasov, Study of a Combined Millimeter-Wave Resonator, IEEE Trans. MTT, nol.45, no.6, pp.1000-1002. 4. E-Y. Sun and S.-H.Chao, Unloaded Q Measurement the Critical-Points Methods. IEEE Trans. MTT, vol. 41, no.8, 1995, pp.1983-1986. 5. R.S.Kwok and J-F.Liang, Characteristics of High-Q Resonators for Microwave Filter Applications, IEEE Trans. MTT, vol. 47, no.1, 1999, pp.111-114. 6. H.Heuermann, Calibration Procedures with Series Impedance and Unknown Lines Simplifies on-Wafer Measurements, IEEE Trans. MTT, vol. 47, no.1, 1999, , pp.15. 7. D.Kajifez, S.Chebolu, M.R..Abdul-Gaffoor, and A.A.Kishk, Uncertainty Analysis of the Transmission-Type Measurement of Q-factor, IEEE Trans. MTT, vol. 47, no.5, 2001, pp.998-1000. 8. A.J.Lord, Comparing On-Wafer Calibration Techniques to 100GHz, Microwaves & Rf, vol.39, no.1, 2000, pp.114-118. 9. R.K.Mongia and R.K.Arora, Equivalent Circuit Parameters of an Aperture Coupled Open Resonator Cavity, IEEE Trans. MTT, vol. 41, no.8, 1993, pp.1245-1250. 10. D.Kajfez, Linear Fractional Curve Fitting for Measurement of High Q factors, IEEE Trans. MTT, vol. 42, no.7, 1994, pp.1149-1153 11. P.A.Rizzi, Microwave Engineering, Prentice Hall, 1988. 12. B. Kapilevich, A. Faingersh, A. Gover, Accurate determination of Q factors of a quasioptical resonator, Microwave and Optical Technology Letters, Volume 36, Issue 4, pp. 303-306, 2003

Development of Models 13. B.Kapilevich, A. Faingersh, A. Gover Modelling and Measurements of the Parameters of a Quasi-optical mm-Wave Resonator by Means of a Tunable Grid Coupler, European Microwave Week, 33 European Microwave Conf. – 2003, Germany, pp.85-88 14. A.A.M. Saleh, An adjustable quasi-optical bandpass filter – part 1: theory and design formulas, IEEE Trans. MTT, vol. 22, no.7, pp.728-734, 1974.

39

THE MODE-MATCHING TECHNIQUE AND FAST NUMERICAL MODELS OF ARBITRARY COORDINATE WAVEGUIDE OBJECTS

Anatoly A. Kirilenko, Vladimir I. Tkachenko, Leonid A. Rud, Dmitrij Yu. Kulik Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Proskura St., Kharkov, 61085

Abstract:

A new algorithm based on two versions of mode-matching (MMT) approaches is proposed for solving the boundary value problems associated with arbitrary waveguides or cavities having piece-wise coordinate surfaces. The solutions are initially based on a pre-processing procedure aimed for automatic recognition of an object’s structure and forming the matrix operators taking part in the mode bases search, or in the calculation of step junction S-matrixes. The new code has been tested by the relatively simple objects considered earlier, and by new objects that were not previously considered for MMT modelling because of the laboriousness of an algorithm elaboration. It was shown that the new MMT electromagnetic solver was also applicable in the cases of smooth boundary objects at step-wise approximated surfaces.

Key words:

complicated waveguides, mode-matching technique, automatic recognition, coordinate boundaries, arbitrary structures.

1.

INTRODUCTION

The mode-matching technique (MMT) continues to be a very powerful tool for the analysis, design and optimization of the microwave devices among several numerical methods of computational electromagnetics. Due to its simple nature, it appeared at the early stages of microwave technique development and provided exact solution of many boundary value problems in the analysis of the waveguides, resonant cavities and gratings. This power modelling technology remains the tool for the solution of actual problems of microwave communication technique1, power microwave transmission lines2, etc.

41 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 41–53. © 2005 Springer. Printed in the Netherlands.

42

Kirilenko, Tkachenko, Rud, Kulik

MMT is noted for three important features: relative universality (within the wide class of geometries), good convergence, and high accuracy. Being a leader in the calculation speed and accuracy, and providing the fast solution of very complicated minimax problems, MMT does not loose its position with wide-spread expansion of the mesh methods. Perhaps, a single negative feature of MMT is the necessity of individual consideration of each new problem arising in practice. Moreover, an appropriate qualification of a microwave designer in analytical treatment of the boundary-value problem is required. Up to this point, even bounded by a definite class, there were no mode-matching based tools providing consideration of arbitrary geometries. Therefore, to solve the actual problem, one must spend more time for the mathematical treatment and the development of corresponding algorithm and program code than for the calculations themselves. The milestones of a new generalized approach to the implementation of mode-matching procedures are presented below. Such solutions may be named as those based on the generalized mode matching technique (GMMT). First of all, the generalization consists in a possibility to obtain the solution of the boundary-value problems with an “unpredetermined” topology of boundaries. In other words the case-in-point is an arbitrary configuration within a wide class of the objects with piecewise coordinate boundaries. Secondly, the generalization consists in an automatic generation of all required structural data for the creation of a corresponding set of the GMMT matrix operators. Thirdly, all structural peculiarities of the specified geometry must be taken into account: longitudinal and transversal symmetry of the device; symmetry of excited fields; symmetry of separate complicated waveguide lines and their regular parts, arising at and dividing into the parts with a perfectly electric (magnetic) wall in the plane of symmetry; the connectivity of the waveguide cross-sections, symmetry of the plane junctions of separate waveguides, etc. Finally, the implementation of a unified criterion of the accuracy control, both for algorithms of full mode bases search and for the procedures of an automatic electromagnetic assembling by S-matrix technique, can be treated as a generalization.

2. PRE-PROCESSING PROCEDURE It is clear that an automatic MMT approach must be based on two milestones, namely, on a pre-processing procedure (A), aiming to recognize the internal structure of the object under consideration and to prepare the data for numerical algorithm, and on a solver as itself (B), destined to calculate a

Technique and Models of Waveguide Objects

43

given-size mode bases of the complicated WGs specified by pre-processor and the S-matrices of plane junctions of these WGs. The flowchart of Procedure "A" is presented in Fig.1. Purports of its steps are clear from the captioning data. The object under consideration must be specified by its edge points and, correspondingly, a cross-section of the generalized piecewise-coordinate WG line may be presented as the set of rectangular subregions assigned, for example, by the edge point ( x ( j ) , y ( j ) ) , height h ( j ) , and width w( j ) . The preprocessor must find a corresponding matrix of ( x ( j ) , y ( j ) , a ( j ) , h( j ) ), j 1, 2,...J which completely defines the crosssection of WG line. This data permits further recognition of the connectivity of WG line boundary to form the structure of a determinant matrix equation according to rectangles’ common boundaries and other geometry peculiarities required for fast mode basis calculation. Specification of the object geometry by means of project-file Longitudinal segmentation of the object into regular fragments Transversal dissection of the fragments and separation of individual waveguides Segmentation of the cross-sections into the sets of “canonical” subregions

No

Is the object uniform along the transversal axes?

Analysis of the connectivity of the individual cross-sections (the number of TEM-modes) Analysis of the possible symmetry of the generalized crosssections, individual lines cross-sections and transversal symmetryof the object as a whole

Yes

Analysis of the transversal symmetry of the object as a whole

Analysis of the longitudinal symmetryof the object Separation of waveguide plane junctions and introduction of virtual waveguides, if necessary Determination of the matrices of the subregion overlappings for each of plane junctions Forming the structural scheme of the microwave circuit or its bond graph

Figure 1. A flow-chart of the pre-processing procedure.

3. MODE BASES CALCULATION The determinant structure depends on the version of the technique used for the field matching (see remarks below) and on the cross-section topology which can be rather complicated. For example, the cross section of the WG lineshownin Fig.2 is the simplest of the cross-sections of WG lines arising as

44

Kirilenko, Tkachenko, Rud, Kulik

the result of IC (Fig.2) decomposition and described by nine subregions. Such a line has the connectivity degree equalling four and is described by nine rectangles. When using the conventional approach1, 3, 4, the subregions’ fields are directly matched on the common boundaries at projecting the E field on the “wide” parallel-plate WG basis and the H -field on the “narrow” parallel-plate WG basis that leads to the determinant equation of the tentative structure shown in Fig. 3.

6

2

7 1

5

3

8

10

9

4

Figure 2. Dissection of the shielded third order IC low—pass filter by a plane and the crosssection of arisen WG line to be calculated.

E

1,2,3,4

H ! 1,2

E

 5,2,3,4

H

5,2

! E

5,6,7,8,9

H

5,6

! E

10,6,7,8,9

H !

10, 6

1

2

!

5

5

!

6

6

! 10

I

M

EM !

2

0

0

!

0

0

!

0

ȟM !

ȟ !

ȟE !

! !

0 !

0 !

! !

0 !

0 !

! !

0 !

0

EM

M

!

I

E

!

0

0

!

0

0

ȟE

ȟ

!

ȟM

ȟEM !

0

0

!

0

!

!

!

!

!

!

!

!

!

!

!

0

0

0

!

E

I

!

M

EM !

0

0

0

0

! ȟEM

ȟM

!

ȟ

ȟE

!

0

!

!

!

!

!

!

!

!

!

!

!

0

0

0

!

0

0

! EM

M

!

I

0 !

0 !

0 !

! !

0 !

0 !

! !

ȟ !

! ȟM ! !

ȟE !

0

Figure 3. The tentative structure of determinant equation corresponding to the WG line sketched in Fig.2.

The labels over columns designate the vector of unknowns which correspond to a column. For example, 2 and 2  describe the vector of unknown amplitudes of parallel-plate WG modes of the 2nd subregion that propagate along the axis OY in the positive and negative directions, correspondingly. The labels on the left rows describe the origin of a row

Technique and Models of Waveguide Objects

45

equation. For example, the row E  5,2,3,4 is the result of E-field matching at the common boundary of the 5th sub-region with the 2nd, 3rd and 4th. Here, we used the following tentative designations: The block matrices M and conjugated M are the matrices of coupling integrals between modes of adjacent parallel-plate WG's. I, ȟ and E are the diagonal matrices of units, propagation constants and propagation phase or attenuation coefficients (along the distance h ( j ) ). The total order of determinant is defined by the number of space harmonics m( j ) taken into account in each sub-domain. Naturally, at the numerical solution, the subdomain expansion sizes must be chosen according to Mittra’s rule, namely, m( j ) must be proportional to a ( j ) . Taking into account the availability of so many zero block matrices, several schemes of determinant calculations can be proposed. Generally speaking, the investigation of various calculation schemes showed the case of arbitrary geometry, the most straightforward way of operating with the whole matrix, turns out to be the best one. Firstly, this way provides the lowest probability of blanks in large-sized mode bases and, secondly, it is characterized by the best behaviour of determinant value facilitating the roots search. Omitting the procedure of dispersion equation solution for the set of cutoffs f c( n )
46

Kirilenko, Tkachenko, Rud, Kulik

expansions, but the special bases taking into account the field singularities near the edges as well. The amplitudes of these expansions play the role of unknowns in the final uniform matrix equations. To understand the structure of determinant equations arising at implementation of the “aperture field approach”, let us consider Fig.4 that represents a common boundary (aperture) " n " within its surroundings of subregions “l(n)” (at the left) and “r(n)” (at the right), and the other neighboring common boundaries “n1”, “n2”, …,”n8”. The following designation will be used below: ( j) CBleft ( n1 , n2 , n3 ) is the list of common boundaries (CB) on the left side of ( j) region “j” and CBright

( n4 , n5 ) is the list of common boundaries on the right

side of region “j”.

Figure 4. A common boundary “n” of a cross-section of complicated WG line within its surroundings.

Let us represent the z-component of Herz-vector for the TE-modes within the “j” subregion as § ª Am( j ) cos(Zm( j ) ( y  y ( j ) ))  º· § mS ( j) · cos x x  ¨  « »¸ ¦ ¨ ¸ j ( ) j j j j ( ) ( ) ( ) ( ) ¨ ©a ¹ ¬« Bm cos(Zm ( y  h  y )) ¼» ¸¹ m 0 ©

M ( j)

3 hz

with unknown coefficients Am( j ) , Bm( j ) and represent the transversal electrical field as Ex( n ) ( x) 

w3 hz wy

p( n )

¦x x" n "

p 1

(n) p

f p( n ) ( x), x  " n "

Technique and Models of Waveguide Objects

47

where the functions f p( n ) ( x) has a singularity O  r 1/ 3 near the edges, the behavior as O  r 0 near the electrical wall, and the behavior as O  r1 near the magnetic wall. After projection of the functional equation describing the Ex-field matching, on the set of cos mS  x  x ( j ) a ( j ) we obtain



JG  j A

N ( j ) 1Ȧ(mj ) 1S j 1

¦

JJJG ( j ) n  CB right



G (n) F ( jn ) x

JG  j JG  j G ( n ) JG  j and the similar expression for B . Here, A , B , x are the vectors of

unknowns, N ( j ) 1 , Ȧ (mj ) 1 , S  j 1 are diagonal matrices of norms, propagation constants, etc. The matrix F ( jn ) consists of the coupling integrals between f p( n ) ( x) and eigen-functions of parallel-plate waveguide modes. At matching the tangential component of magnetic field parallel to the edges, we obtain the functional equations described by functions that must decrease as O  r 2 / 3 near the edges, behavior as O  r 0 or O  r 1 near the electrical or magnetic wall, correspondingly. Projecting these equations on the set of functions g (pn ) ( x) , having the proper behavior, and eliminating the JG  j JG  j unknown vectors A , B , we obtain a row of the matrix dispersion equations, produced by “n” aperture by the field matching: G ( n ,l ( n )) N ( l ( n )) 1Ȧ ( l ( n )) 1C( l ( n )) S ( l ( n )) 1 G

n ,l ( n )

G

n ,r ( n )

N (l ( n )) 1Ȧ (l ( n )) 1S (l ( n )) 1

¦

JJJG ( n ) sCB lleft

N ( r ( n )) 1Ȧ ( r ( n )) 1S ( r ( n )) 1

G  n , r ( n ) 1Ȧ ( r ( n )) 1C( r ( n )) S ( r ( n )) 1

¦

JJJG ( n ) sCB lright

F

F

l ( n ), s

l ( n ), s

x( s ) 

x( s ) 

¦

F r ( n ), s x ( s ) 

¦

F  r ( n ), s x ( s ) 0

JJJG ( n ) sCB rright

JJJG r ( n ) sCB left

(1)

where the matrices G  nj are similar to F ( jn ) with functions g (pn ) ( x) instead of f p( n ) ( x) . The set of equations (1) round the subregion’s common boundaries

form the determinant equation. The block order of this matrix is defined by the number of common boundaries between subregions and can be less than

48

Kirilenko, Tkachenko, Rud, Kulik

the block order of the determinant equation produced by the conventional mode-matching technique, especially for the lines rising at analysis of the multilayer ICs. Both approaches have been realized in C++ code aimed to calculate fullmode basis of a complicated WG line. It was verified on many well-known configurations, and compared using different sets of functions f p( n ) ( x) and

g (pn ) ( x) , starting from weighted Gegenbauer and Chebyschev polynomials C1p 6( or 7 6)  x c

c

2

x



2 1/ 2 1 6( or 7 6)



,

Tp  x c

c

2

x



2 1/ 2



,

Up x /c

c

2

x



2 1/ 2



up to conventional

trigonometric functions. The global conclusion is the usage of the “aperture field” matching provides an excellent numerical convergence and, consequently, an appreciable decreasing of the calculation time (by the order), that is especially remarkable at implementation the functions corresponding to the field singularities. Another important feature of such an approach is an absolute absence of the “relative convergence phenomenon” that leading to the possibility of considering the structures containing the subdomains of very different sizes. The issue is the implementation of conventional approach forces to support the necessary relation between the sizes of the subdomain mode expansions, and consequently, to operate with very large matrices even when the modes are only taken into account within the narrowest subregion. Finally, in the second approach, it is unnecessary to use artificial receipts typical for conventional ones, using in cases when the common boundary of subregions could not be treated as a “small” subregion aperture within a “big” one. The conventional field matching here requires the implementation of zero-length virtual subregions, increasing the number of unknowns.

Technique and Models of Waveguide Objects

49

Figure 5. Overlapping of the “j” subregion of the “p”-waveguide and the “k” subregion of the “0” waveguide.

4. S-MATRIX CALCULATION Using the MMT for calculating the S-matrix of a plane junction of the waveguide “0” with the waveguide “p”, we must calculate the set of coupling integrals M lq where “l” and “q” are the mode numbers. As the eigen-mode fields are given in a piecewise manner, each coupling integral is reduced to the sum of partial integrals over the overlapping of “p”waveguide subregions with “0”-waveguide subregions (see Fig. 5). One of the pre-processor duties is to furnish data about the overlapping of subregions of two waveguide lines being connected. As a consequence, we obtain the following sum for each of coupling integrals K (0) J ( p )

M lq

¦ ¦ ³ e k 0 j 0 Sˆ

(l ) 0

˜ e(pq ) dS , Sˆ

S0( k ) ˆ S p( j )

( x  S p( j ) , yst d y d y fin )

where e(0l ) is the eigen-function of the “l” mode in the waveguide “0” S p( j ) is the cross-section of "j"-subregion of "p"-waveguide. The requirements M lq 0 for different modes of the same WG or for the TE mode of a “big” WG, and for the TM or TEM modes of a “small” WG, can serve for control of the calculation accuracy. The numerical experiments show that at the cutoff accuracy of 104 y 105 these control values are of the same order.

50

Kirilenko, Tkachenko, Rud, Kulik

5. APPLICATIONS First of all, the created code was verified by the frequency response data relative to microwave passive devices obtained earlier by the personal analytical treatment of electromagnetic problems and program realization. They were the set of ridged waveguide evanescent mode filters, combline bandpass filters, lowpass waffle-iron filters, septum polarizers, multilayer circuits, etc., ending with corrugated horns and other aperture antennas. We present here, only three examples of GMMT applications that are united by an exoticism of geometry or of the MMT application. Let us return to the IC low-pass filter shown in Fig. 2, which required calculating the full mode bases of twelve multiconductor WG lines. The frequency response of this filter, having passband near 1 GHz, is presented in Fig. 6. The calculation accuracy was defined by the number of modes having cutoffs below f CUT and by the number of space harmonics taken into account in the narrowest subregion nmin . The curves in Fig. 6 illustrate convergence of results with increasing f CUT and nmin . For a good field approximation, the tens waveguide modes must be taken into account. As the IC housing dimensions are 0.38×3.05 mm and dielectric filling has the permittivity H 7.8 then f CUT value has to be close to 400! 500 GHz. With results obtained by EMSIGHT, the comparison has shown a good coincidence within the passband and at the stopband beginning, and a disagreement in prediction of a parasitic passband. The latter can be caused by decreasing the finite element method accuracy as the frequency increases7.

Technique and Models of Waveguide Objects 40

FCUT=400 GHz (nmin=3) FCUT=500 GHz (nmin=3) FCUT=500 GHz (nmin=4) FCUT=500 GHz (nmin=2)

H 

35 30

Return Loss, dB

51

25 20 15 10 5

Ins. Loss > 20 dB

0 0

1

2

3

4

5

6

7

8

Frequency, GHz Figure 6. The frequency response of IC low-pass filter calculated by GMMT.

0 -5 -10

Loss, dB

-15 -20 -25 -30 -35

Experimental filter [1] Redesigned filter in 24x12 mm 2 housing 2 Double semi-ring filter in 16x8 mm housing

-40 -45 830

835

840

845

850

855

860

865

870

Frequency, MHz Figure 7. Responses of the single and double semi-ring filters.

An interesting result was obtained while attempting to update the specific configuration of a recently proposed8 small-sized filter. The minimax procedure incorporated into the developed GMMT solver was used for the reconstruction of filter geometry, having one semi-ring as a resonant cavity,

52

Kirilenko, Tkachenko, Rud, Kulik

and for the optimization of a new, more complicated configuration with double- and triple-semi-rings (see Fig.7). Increasing the number of semirings allows reducing the filter dimensions8. The last example illustrates an unconventional application of MMT for calculating an iris in a circular WG basing. This involves the step-wise approximation of WG smooth boundaries in order to ascertain a capability of the developed GMMT to calculate objects with smooth boundaries. Such a test calculation was compared with exact results obtained by the conventional MMT (Fig.8). It rather unexpectedly achieved a qualitative coincidence of amplitude-phase characteristics even at N 5 (!), where N is the number of steps on a circle quarter, and the total coincidence at N 17 . It must be noted that the iris response calculation stipulates not only the search of full mode bases for the wide and narrow WGs but the calculation of the plane junction of these WG's, and further application of the S-matrix technique as well. S thin iris required exact calculation of the fringing field interaction by higher modes. 60

Return Loss, dB

50

40

Exact MMT solution and stepwise approximation at N=17 N=5 HFSS

30

20

10

0 6

8

10

12

14

16

18

20

Frequency, GHz Figure 8. Frequency response of the iris in circular WG calculated by MMT, HFSS and by GMMT with stepwise approximation of smooth boundaries.

Technique and Models of Waveguide Objects

53

6. CONCLUSIONS The algorithms that generalize the application of mode-matching technique to the structures having the piece-wise Cartesian coordinate surfaces have been developed. This automatic approach to the field matching concerns not only recognizing the internal structure of a waveguide line and forming dispersion equation, but calculating the S-matrices of the plane-junctions as well. Saving the high speed and accuracy of calculations inherent to the mode-matching based solutions, the developed program code moves them close to the mesh methods in general. The research described in this publication was made possible in part by Award No. UE25004-KH-03 of the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF) and INTAS Award No 01-0373.

7. REFERENCES 1. F. Arndt, R. Beyer, J. Reiter, T. Sieverding, and T. Wolf, Automated Design of Waveguide Components Using Hybrid Mode-Matching/ Numerical EM Building Blocks in Optimization Oriented CAD Frameworks—State-of-the-Art and Recent Advances, IEEE Trans. Microwave Theory Tech. 45(5), 747-760 (1997). 2. M. K. Thumm and W. Kasparek, Passive High-Power Microwave Components, IEEE Trans. Plasma Science 30(3), 755-786 (2002) 3. G.V. Kisunko, Electrodynamics of Hollow Systems, VKAS Publ., Leningrad (1949) (in Russian). 4. A. Wexler, Solution of Waveguide Discontinuities by Modal Analysis, IEEE Trans. Microwave Theory Tech., 15, 508-517 (1967). 5. G. Veselov, N. Platonov, and E. Slesarev, About taking into account the field singularities in the mode-matching technique, Radiotekhnika 35(5), 27-34 (1980) (in Russian). 6. V.P. Lyapin, V.S. Mikhalevsky, and G.P. Sinyavsky, Taking into account the edge condition in the problem of diffraction of waves on step discontinuity in plate waveguide, IEEE Trans. Microwave Theory Tech.. 30(7), 1107-1109 (1982). 7. A. Kirilenko, D. Kulik, L. Rud, V. Tkachenko, and P. Pramanick, Electromagnetic modeling of multilayer microwave circuits by the longitudinal decomposition approach, 2001 IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, 1257-1260 (2001). 8. A. Kirilenko, D. Kulik, V. Tkachenko, The automatic mode-matching solver application by the example of complicated shape cavities design, Proc. NUMELEC-03, Toulouse, rep. PO2.25, (2003).

ELECTRIC FIELD INTEGRAL EQUATION ANALYSIS AND ADVANCED OPTIMIZATION OF QUASI-OPTICAL LAUNCHERS USED IN HIGH POWER GYROTRONS Jeff Neilson Calabazas Creek Research, Saratoga, CA 95070, USA

Abstract

Modern high-power gyrotrons typically use a mode converter and launcher to convert the high order cavity mode to a Gaussian like output mode. Total efficiencies (cavity power to usable Gaussian power) of the conversion are usually 85-95%. The analysis codes used to design these systems are based on approximate techniques that are not sufficiently accurate to allow design of higher efficiency converters. We have developed an analysis code based on the electric field integral equation, which provides very accurate calculations for the radiated fields. An advanced surface synthesis technique was developed to improve the converter efficiency.

Key Words

Quasi-optical launcher, integral equation, gyrotron

1

INTRODUCTION

A typical method for accomplishing beam/RF separation in modern high power gyrotrons uses a combination of an internal mode converter and stepcut launcher [1]. The internal converter uses perturbations of the waveguide surface to convert the output mode from the cavity into a set of modes whose combined fields have a Gaussian-like profile. This Gaussian-like profile can then be efficiently launched, focused and guided by small mirrors inside the vacuum envelope of the gyrotron. Figure 1 depicts such a launcher and guide system. The current analysis method for these converter/launcher systems is performed in two steps. First, the waveguide mode converter is analyzed using coupled mode theory. Then the radiated fields are calculated from the waveguide cut using the Stratton-Chu formulation [2]. This is, in principle, an exact calculation if the true fields on the waveguide wall are known; however, the act of cutting open the waveguide can perturb the fields from those calculated using the closed waveguide solution.For the fields produced by the waveguide converter, this approach has given good results because the [

55 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 55–63. © 2005 Springer. Printed in the Netherlands.

56

J. Neilson

converter waveguide cut is done in regions where the field intensity is low, resulting in small perturbations to the waveguide fields. The combination of the mode converter analysis with the Stratton-Chu formulation has been a useful design tool. Experience has shown, however, that launcher systems designed for high average power gyrotrons using this analysis have typically shown significant diffraction losses not predicted by the codes and less than efficiencies. It is thought that this less-than-optimal performance may come from code analysis inaccuracies. Measurements of the radiated fields from the converter/launcher systems differ from those predicted by theory [3]. As average gyrotron power is increased, the internal loss due to this calculation error will grow and further increase the construction complexity and expense of the gyrotron. An exact analysis of the launcher system, in addition to eliminating design uncertainties due to analysis approximations, would allow for arbitrary wall deformation in the launcher surface. Such flexibility would give tube engineers a way to explore alternative designs for achieving higher efficiencies and for designing improved converters that are more easily manufactured or more compact. For an analysis code to be a useful design tool, the code must do its calculations without exorbitant amounts of CPU time or expensive super-computers.

Window RF Launcher and Mode Converter

Reflector

RF

Electron Beam

Electron Beam

Cavity

Reflector

Figure 1. Typical configuration for whispering gallery mode to Gaussian mode converter system used in modern high power gyrotrons.

Electric Field Analysis

57

When the original work on this problem was done, it was known that, in principle, an exact formulation of the problem could be stated through the use of surface integral formulations of Maxwell’s equations. This approach was not taken because of the CPU and memory requirements made such an approach intractable. However, the integral equation approach has now become viable because of several factors. In the short period of time since the original analysis was done, calculation speed in engineering workstation computers has increased more than an order of magnitude. In addition, new techniques for solving integral equation formulations of large body scattering have been introduced. These new techniques, such as the fast multipole method [4], greatly reduce the computational requirements. In this paper, we show the application of the electric field integral equation (EFIE) for calculation of the radiation from the converter and launcher system. Using the multi-level fast-multipole algorithm, we have performed calculations for a converter/launcher system and compared the calculations to measurements. Results from this code have shown the feasibility and accuracy of the integral equation approach. Using a more generalized surface formulation, numerical synthesis of a converter surface has been performed. This optimization approach has resulted in designs of significantly shorter length and reduced diffraction losses than designs using the current designs methodology.

2

EFIE FORMULATION

For observation points lying on a conducting surface S which, forms the waveguide converter and launcher, the electric field integral equation (EFIE) is given by

S

i G ( r, r' ) ⋅ J ( r' ) dS' = 4π ------E ( r ) kη

(1)

for r on surface S, where J(r) is the unknown surface current, Ei(r) is the incident waveguide source field and

1- ∇∇′ g ( r, r' ) G ( r, r' ) = I – ---2 k

(2)

58

J. Neilson

This equation is applied to the launcher surface and the unknown surface current J(r) is discretized for numerical solution using the method of ik R

e g ( r, r' ) = -------------r – r'

(3)

moments (MOM) [5]. The solution time and memory requirements for the MOM solution are dramatically decreased by use of the multi-level fast multipole algorithm. The GMRES algorithm is used for iterative solution of the surface currents. The excitation field is the mode emanating from the gyrotron cavity. The incident electric field on the surface S induced from this field is calculated using the vector Huygens principle and is given by – ikR

i 1 - ∇' ⋅ J ( r' ) 1----------------+ ikR-R ˆ e –ik R dS' E ( r ) = jωµ --------- J( r' ) e------------ dS' – ------------2 R 4π 4πωε R S

S

1- 1----------------+ ikR-e – ikR R ˆ × M ( r' ) dS' + ----2 4π R s

(4)

where the magnetic and electric surface currents are given as i

M ( r ) = – nˆ × E ( r )

(5)

i J ( r ) = nˆ × H ( r )

(6)

and Ei, Hi are the electric and magnetic field of the incident mode. Use of Eq. for calculation of the incident field is not an exact formulation of the problem. Ideally, the surface current at aperture would consist of the incident field of the excitation mode and an unknown surface current, which represents the field resulting from multiple reflections between the waveguide ends and surface S. Inclusion of an unknown surface current on the aperture was not done as it substantially increases both solution complexity [6] and the number of unknowns. Since the structure to be modeled is much larger than the free space wavelength, the reflected field will be significantly smaller than the excitation field and its neglect will not impact the calculation.

Electric Field Analysis

3

59

EXAMPLE CALCULATION

The radiated field of a 110 GHz, TE22,6 converter and launcher was calculated using the EFIE formulation. The cylinder wall variation for this launcher has the form of

r ( φ, z ) = r o + α z + ε 1 cos ( H 1 ( z ) + 3φ ) + ε 2 cos ( H 2 ( z ) + φ )

(7)

with a total length of 150mm and a spiral cut length of 5mm. The mesh used to model the converter and launcher had a density of approximately 7 triangles wavelength for a total of 160K unknowns. Sixty iterations were used to calculate the unknown surface currents for a normalized residual (a)

(b)

22

22

-5

20

-5

20

-10

18

-10

18

-15

16

-15

16

-20

14

-25

12

-1

0

1

2

Azimuth (radians)

3

4

-20

14

-25

12

-1

0

1

2

Azimuth (radians)

3

4

Figure 2. Radiated field intensity in dB on cylinder (R=5.6 cm) surrounding launcher. Cylinder axis is offset 1.16 cm (towards launcher cut) from launcher axis. (a) Calculated intensity. (b) Measured intensity.

error of the surface current less than 0.01. The error in energy conservation was 1.5%. The total run time and memory requirements were 45 minutes and 500MB on a 1.5GHz Pentium IV The calculated and measured intensity of the radiated phi component of electric field is shown in Figure 2. This calculation was done for the field on a cylinder of radius 5.6 cm surrounding the launcher. The measured and calculated field contours are remarkably similar, especially considering the difficulty in obtaining this measurement accurately, requiring generation of a high purity TE22,6 mode, and measurement in the near field zone of the launcher The design length was constrained to be shorter than the optimal length so therewere significant amounts of surface current along the spiral cut .

[

60

J. Neilson

of the launcher.The radiated field from the edge surface currents gives rise to the large amount of sidelobes seen in both the calculations and measured fields. The calculated result using the EFIE analysis is considerably closer to the measured result than that obtained by the Stratton-Chu (S-C) calculations, which is shown in Figure 3. Significant differences exist between this calculation and the measurement. Since the S-C calculation does not model the large edge currents that are present in this launcher, the lack of good agreement is not surprising.

22 -5

20 -10

18 -15

16 -20

14

-25

12

-1

0

1

2

3

4

Figure 3. Stratton-Chu calculation for the radiated field intensity in dB on cylinder (R=5.6 cm) surrounding launcher.

4

ADVANCED OPTIMIZATION OF Q-O LAUNCHER MODE CONVERTER

Launcher converter designs have been based on the Denisov type design approach using two azimuthal variations (Eq. 7). The amplitudes H and H(z)have been typically modeled as constants to linearvariation.For constant diameter launchers that are not much above cutoff this approach can be used to generate a beam with high Gaussian content and low diffraction losses.However,fortapered launchers there is increased coupling to unwanted

Electric Field Analysis

61

parasitic modes which reduce the beam quality and increase diffraction losses. By generalizing the surface model as

z

N

r ( φ, z ) = r o + αz +

a n ( z ) cos n=1

β n ( z ) dz ± l n φ 0

and using numerically optimized functions for an and En, significantly more compact designs with less diffraction loss can be achieved. The most successful launcher design tested in a gyrotron to date (140 GHz TE28,8 launcher designed at FZK and tested in a 1MW CW Thales tube[7]) was shown to have very low diffraction losses (1.5%) and high Gaussian content. Using the new design approach, a redesign of this launcher was undertaken. A new design using the azimuthal variations L=1,2,3 and 6 was generated that was 20% shorter than the existing design with virtually no diffraction losses and higher Gaussian content. Plots of the calculated azimuthal component of the electric field intensity on a cylinder for the original and improved design are shown in Figure 4.

(b)

(a) 28

32

26

30

-5

-5

24

28

-10

-10

22 ) m c( 20 -15 si x A 18 -20

26

) m c( si x A

24 22

-20

16

20 -25

18 16

-15

0

1

2

3 4 Azimuth (Radians)

5

Azimuth (radians)

6

-25

14 12

0

1

2

3 4 Azimuth (Radians)

5

6

Azimuth (radians)

Figure 4. Radiated field intensity in dB on cylinder (R=10 cm) surrounding launcher. (a) Original design. (b) Optimized design using generalized surface form.

62

5

J. Neilson

CONCLUSIONS

The feasibility and accuracy of the EFIE approach has been demonstrated by the close agreement between measurement and calculation. The results of the EFIE calculation are also better than what can be achieved using the Stratton-Chu calculation in conjunction with the coupled mode analysis. Using the calculations provided by the EFIE analysis, the diffracted power losses can now be determined. The optimization technique developed has been shown to give significant improvements in performance of QO converters while reducing the length. These improvements can result in cost reductions for gyrotron manufacturing; the result of reduced magnet size and lowered processing times.

6.

ACKNOWLEDGEMENT

The authors would like to thank Prof. Ron Vernon and Mike Perkins at University of Wisconsin who performed the test launcher measurements. This research is supported by DOE Small Business Innovative Research grant number DE G.G. Denisov, A.N. Kuftin, V.I. Malygin, N.P. Venediftov, D.V. Vinogradov and -FG03-00ER82965.

REFERENCES [1] [2]

[3]

[4]

[5]

V.E. Zapevalov, “110 GHz gyrotron with built-in high-efficiency converter,". J. Electronics, vol. 72, nos. 5 and 6, pp. 1079-1091, 1992. M. Blank, K. Kreischer, and R.J. Temkin, “Theoretical and Experimental Investigation of a Quasi-Optical Mode Converter for a 110-GHz Gyrotron,” IEEE Trans. Plasma Science, vol. 24, No. 3, pp. 1058-1066, June 1996. D. Denison, T. Chu, M. Shapiro and R.J. Temkin, “Gyrotron Internal Mode Converter Reflector Shaping from Measured Field Intensity,” IEEE Trans. Plasma Science, vol. 27, No. 2, pp. 512-519, April 1999. W. Chew, J. Jin, C. Lu, E. Michielssen and J.Song, “Fast Solution Methods in Electromagnetics,” IEEE Trans. on Ant. and Prop., vol. 45, no. 3, pp. 533-543, Mar 1997. R.F. Harrington, “Matrix Methods for Field Problems,” Proc. IEEE, vol. 55, pp. 136-148, 1967.

Electric Field Analysis [6]

[7]

63

R. Bunger and F. Arndt, “Moment-Method Analysis of Arbitrary 3-D Metallic NPort Waveguide Structures,” IEEE Trans. on Microwave Theory and Tech., vol. 48, no. 4, pp. 531-537, April 2000. G. Dammertz,et.al,”Prototype of a 1 MW, CW Gyrotron at 140 GHz for Wendelstein 7- X,”,28th Intl Conf IRMMW, Sep 2003, pg121.

COMPARISON OF TWO OPTIMIZATION CRITERIA FOR QUASI-OPTICAL POWER TRANSMISSION LINES

N. N. Voitovich2, B. Z. Katsenelenbaum1, O.V. Kusyi2, 2

Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine 1 Institute of Radioengineering and Electronics, Russian Academy of Science, Moscow, Russia;

Abstract:

Key words:

1.

Two optimization criteria for antenna-rectenna power transmission lines are compared. The criteria describe the energy transmission coefficient and the mean-square residual of obtained and desired fields in the rectenna plane. The behavior of each criterion on functions optimal for another is studied. Numerical results for rectangular and circular apertures are shown and analyzed (a part of results is published in [1]; a mistype in [2] is corrected). microwave power transmission, paraxial optics, phase front optimization.

INTRODUCTION.

PROBLEM FORMULATION

Problems connected with long beams of electromagnetic field arise while transmitting the power between two antennas (i.e. from a solar power station onto the Earth) [3 – 6]. Field U ( x, y ) generated on transmitting antenna, creates field V ([ ,K ) in the plane of receiving antenna (rectenna). In the paraxial approximation, the field V is expressed (with accuracy to a constant factor) by U as

V ([ ,K )

ñ U ( x, y ) exp[ic ( x[  yK )]dxdy , 2S ³D

(1)

where D is the antenna domain in the dimensionless coordinates, ' is therectennadomain, n~ kaD d istheFresnelparameter, a , D are characteristic 65 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 65–72. © 2005 Springer. Printed in the Netherlands.

66

Voitovich, Katzenelenbaum, Kusyi

linear sizes of the antenna and rectenna, respectively, d is a distance between the antenna and rectenna (see Figure 1), and ka 2 d  S .

Figure 1. Transmit and receive antennas.

The following two criteria are usually formulated for power transmitting lines: a) the energy transmission coefficient

L(U )

V

2 '

/U

2 D

;

(2)

b) the mean-square difference between a given field in the rectenna plane and a received one

V (U )

V0  V

2 f

f f

³ ³ V ([ ,K )  V ([ ,K ) 0

2

d [ dK .

(3)

f f

Here V0 is a desired field distribution in the rectenna plane which is zero outside the rectenna and constant on modulus on it and U D and V ' are usual mean-square norms on the antenna and rectenna apertures respectively and V f is such a norm in the whole rectenna plane and V0 is assumed to be normalized as V0

'

1.

In this paper, the question of how one of the criteria behaves on the functions optimizing another, is considered. Of course, the field on the antenna, being optimal for one criterion, is not optimal for the other. Field

Two Optimization Criteria for Power Transmission Line

67

U L ( x, y ) , providing the optimal transmission coefficient, creates the field in the rectenna plane, for which the value of functional (3) is much larger than its minimal value V (U V ) . However, it turns out that the function U V which provides the minimum to functional (3), gives almost optimal value of functional (2). The investigation is carried out in cases when variables are separable, namely, for rectangular and circular apertures.

2.

RECTANGULAR APERTURES Let the antenna and rectenna be equi-oriented rectangles of sizes bE . Then

2a u 2b , 2D u 2 E , respectively, and (for simplicity) aD U ( x, y ) u ( x)u (ay / b) , V ([ ,K ) v([ )v(DK / E ) , 1

c 2S ³ u ( x)e icx[ dx .

v([ )

(4)

1

Functional (2) becomes of the form

L(U ) l 2 (u ) ,

(5)

where

l (u ) v

D

³

1 1

_ v([ ) _2 d[ ,

v u

a

2

2

u a,

D

³

1 1

_ u ( x ) _2 dx

(6) are one-dimensional mean-

square norms on the antenna and rectenna apertures. The function ul , which provides the maximum to the functional l , is the first eigenfunction u1 of the integral equation

Onun ( x)

2

S³

sin( x  x ') un ( x ')dx ' 1 x  x' 1

corresponding to the maximal eigenvalue

,

(7)

O1 l (ul ) . The functional (3)

68

Voitovich, Katzenelenbaum, Kusyi

V 1 (u )

relates to its one-dimensional analogue

v ([ )  v0 ([ )

2 f

V (UV ) 2V 1 (uV )  V 12 (uV ) . We assume that

vV

D

as (8)

1 . The function uV is calculated by the

formula

uV ( x)

3.

1

c 2S ³ v0 ([ )eicx[ d[ .

(9)

1

CIRCULAR APERTURES

In the case of circular antenna and rectenna of radii a and D , 1 2 respectively, the azimuth-independent fields are U ( r M ) (2S ) u (r ) , 1 2 V ( U T ) (2S ) v( U ) , 1

v( U ) c ³ u (r ) J 0 (crU ) rdr .

(10)

0

We give the main formulas analogous to those for the rectangular apertures:

L(U ) l (u ) , l (u )

where

vD

1

is 2

³ _ v( U ) _ 0

expressed

Ud U , u

1

a

by

³ _ u (r ) _ 0

(11) the 2

same

formula

(6)

with

rdr . The homogeneous equation

for the function ul maximizing the functional has the form

Onun (r ) c ³

1 0

rJ 0 (cr ') J1 (cr )  r ' J 0 (cr ) J1 (cr ') un (r ')r ' dr ' . (12) r 2  r '2

Two Optimization Criteria for Power Transmission Line

69

The following relation is valid for the second functional

V (U ) V 1 (u )

2

v  v0 f .

(13)

The function uV is calculated by the formula 1

uV (r ) c ³ v0 ( U ) J 0 (kr U ) U dU . 0

4.

(14)

NUMERICAL RESULTS In Figs. 2, 3 the values of the functionals on U V , uV and ul are shown.

At small c the values of each functional on both functions ul , uV are almost the same, because the functions themselves are close.

Figure 2. The behavior of the functionals.

At larger ñ the behavior of l (uV ) seems rather surprising: it is close to

l (ul ) at any ñ . This fact can be explained by the following arguments. It is easily seen

70

Voitovich, Katzenelenbaum, Kusyi

Figure 3. The behavior of the functionals.

2

l (u ) 1 

V (u )  v0  v D u

(15)

2 a

for any c and u . Since, obviously, at u of (15) tends to be zero as c o f , then

uV the numerator in the fraction

lim l (uV ) 1, c of

(16)

is what explains the asymptotical behavior of l (uV ) . According to (4), (9) (and, analogously, (10),(14)), vV Kv0 , where K is an integral operator in the homogeneous equation (7) or (12). It is the first iteration of the initial function v0 in the power method for calculating the maximal eigenvalue

O1 of the equation K *vn

Onvn

(17)

Two Optimization Criteria for Power Transmission Line

71

with the same kernel (see, f. e. [7]). Express v0 in the form f

v0

¦C v

n n

(18)

n 1

then f

vV

On Cn vn ) . 2 O1

O1 (C1v1  ¦ n

At small c we have

(19)

On  O1 , n 2,3... , thus, vV is proportional to

vl and l (uV ) is close to l (ul ) , as noted above. At intermediate c , only several eigenvalues On are notably smaller than 1 and larger than 0 . Only the eigenfunctions vn corresponding to these intermediate eigenvalues in the expansion (18) makes the value l (uV ) smaller than l (ul ) . The range of values c , at which their relative contribution is noticeable, is not too wide.

Figure 4. Erroneous and valid curves in comparison and the ratio of losses.

For the case of rectangular apertures a part of the above results is presented in [2]. In particular, in Figure 6.4 from [2] the relations l (uV ) / l (ul ) and V 1/ 2 (uV ) / V 1/ 2 (ul ) are shown. They are copied in Figure 4 above as the lowest and dashed lines.Note that the higher curve in Figure 6.4

72

Voitovich, Katzenelenbaum, Kusyi

from [2] (dashed line in Figure 4) is erroneous. The valid curve (and its description) obtained from the results of this paper, is presented in Figure 4. In this figure, we also show the ratio of losses 1  L(UV ) / 1  L(U l ) for two solutions considered here.

5.

REFERENCES

1. Katsenelenbaum B. Z., Kusyi O. V., Voitovich N. N., “Comparison of two Optimization Criteria for Power Transmission Lines.” in Proc. of Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2003), 131-135, Lviv, 2003. 2. Katsenelenbaum B. Z., Electromagnetic Fields - Restrictions and Approximation. WILEYVCH, Berlin, 2003. 3. Fadeev V. G., Vanke V. A., “Optimization of the transmitting antenna of solar space power system,”. J. of Communications Technology and Electronics 1999; 44; 775-779 (Russian). 4. Katsenelenbaum B. Z., Microwave power transmission by a long beam. Proc. of Seminar/Workshop DIPED-99, 17-21, Lviv, 1999. 5. Korshunova E., Shaposhnikov S. S., Vaganov R. B., “Focal Spot without the nearest diffraction sidelobes,” Proc. of Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2001), 126-131, Lviv, 2001. 6. Kusyi O. V., Shaposhnikov S. S., Vaganov R. B., Voitovich, N. N., “Bicriterion optimization problems for power transmitting line,” Proc. of Seminar/Workshop DIPED{2002), 127-130, Lviv-Tbilisi, 2002. 7. Fox A. G., Li T., “Resonant modes in a maser interferometer,” Bell Sys. Tech. J. 1961; 40; 453-458.

A GENERAL PURPOSE ELECTROMAGNETIC CODE FOR DESIGNING MICROWAVE COMPONENTS W. Bruns [email protected]

H. Henke Technische Universitaet Berlin [email protected]

Abstract

A general purpose electromagnetic code has been developed based on the finite difference method. The code computes resonant fields and arbitrary time dependent fields. The objects may contain linear dielectric and magnetic materials as well as lossy materials, open boundaries, and may be periodic in three dimensions. Scattering parameters are computed via an FFT of the impulse response. In the time domain, the excitation is by port modes, by relativistic charges or through free moving charges (particle in cell). Different measures have been taken in order to speed up the code. Symmetries are used whenever possible, gridcells are only allocated to field regions and parallel computing is possible. The code is well suited for designing travelling and standing wave structures in the millimeter wave range and in particular millimeter wave tubes.

Keywords:

FDTD, Parallel Computation, PIC

1.

INTRODUCTION

The code, called GdfidL, is based on the finite difference method. The coefficients of the difference equation are derived by the finite integration method. In the first sections, the underlying approximations of Maxwells equations are described, then, some efficiency improvements are scetched. It follows a description of the implemented parallel computations. At the end the treatment of free moving charges is described.

1.1

Principle: Time stepping the fields

The basic approach is time stepping of the fields. It is the famous FDTDalgorithm introduced by Kane S. Yee in 1966 [1]. With a suitable small time step, one can compute the new fields simply by performing curl-operations on 73 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 73–91. © 2005 Springer. Printed in the Netherlands.

74

W. Bruns, H. Henke

the fields, and adding the result, scaled by a material depended factor, to the old fields. The electromagnetic field at a time t is given by the field at an earlier time, and by the excitation, e.g. currents.

= t0 ) + [µ]−1 H(t) = H(t

= t0 ) + [ε]−1 E(t) = E(t


t  τ =t0
t 

τ =t0

    




dτ −∇×E 


− κE
−G
dτ ∇×H

   

(1)

Computing the new H. The magnetic field at the time t + ∆t/2 is computed from the fields at earlier times, by replacing the time integration by a multiplication of the integrand at the center of the integration interval with the width of the timestep.
+ ∆t/2) = H(t
− ∆t/2) − [µ]−1 H(t
− ∆t/2) − ∆t ≈ H(t

t+∆t/2



dτ ∇×E

τ =t−∆t/2 
 [µ]−1 ∇×E t

(2)

The algorithm is time reversible when the electric field is taken in the middle of the integration interval.

Computing the new E.
+ ∆t) = E(t)
E(t + [ε]−1

t+∆t


 τ =t




− κE
−G
dτ ∇×H 



− [ε]−1 κE
 ≈ E(t) + ∆t [ε]−1 ∇×H −[ε]−1

t+∆t
τ =t

t+∆t/2

(3)


dτ G


+ ∆t/2) is computed by linear interpolation beThe dependent current κE(t

tween the values of E(t + ∆t) and E(t). The integration of the current dependent terms can be carried out exactly, when the time dependence of the currents is known.

2.

SPACE DISCRETIZATION

For every practical computation, one must restrict oneself to a finite number of degrees of freedom. For example, when performing a mode matching computation, one only computes with a finite number of mode amplitudes, assuming that the ignored amplitudes are so small that their effect can be ignored. The finite difference algorithm does not attempt to compute the electromagnetic field everywhere, but only at selected points in space.

A General Purpose Electromagnetic Code for Designing

75

The finite integration algorithm, which in free space is equivalent to the finite difference algorithm, attempts to compute integral values of the electromagnetic field over small integration areas. The Finite Integration algorithm substitutes curl equations by difference equations for the line in
Maxwell’s
· d
s and
H
· d
s along discrete edges ∆
s. The unknowns are tegrals E electric and magnetic voltages between the points of a primary and a dual grid, fig. 1.


H


E Figure 1.

Primary grid (dark) for the electric field and dual grid (light) for the magnetic field.

The derivation of the finite difference coefficients starts from Faradays and Amperes law: −

d dt d dt




· dA
= µH

A






· d
s E

(4)


· d
s
H

(5)

δA


· dA

= εE

A




δA


In the Finite Integration Algorithm, the areas we integrate over are the faces of the primary grid A and the faces of the dual grid A
. When the material boundaries are just tangential or normal to these faces, we assume a constant average field strength over these faces: −



µdA A



A


d
H ·
nA ≈ dt

d

·
nA ≈ εdA E dt





· d
s E

(6)


· d
s
H

(7)

δA



δA


The line integrals on the right sides of the above equations are sums of four line integrals along the edges of the primary and dual grid, respectively. In order

76

W. Bruns, H. Henke

to get line integrals also on the left sides, we integrate the equations over the edges of the primary or dual grid. −








· d
s ds
µdA ∆s
∆s
A 
s
d
H · d
δA
· d
s ≈
E ds
dt ∆s ∆s A
εdA

d dt


· d
s
≈ H

E δA


(8) (9)

Assuming that the contour integrals on the right sides stay constant, we arrive at: −







d 1
· d
s
≈
· d
s
H E ds
dt ∆s
∆s
A µdA δA

d 1
· d
s ≈
· d
s

E H ds
dt ∆s ∆s A
εdA δA


(10) (11)

Our unknowns are now the line integrals of the fields

along the edges of the
· d
s and h ≈ H
· d
s, we can drop the primary and dual cells. With e ≈ E approximation signs and write −

The values


∆s



d 1
h = ds
(e1 + e2 − e3 − e4 ) dt ∆s
A µdA 1 d
ds (h1 + h2 − h3 − h4 ) e =
dt ∆s A
εdA


1 A


εdA


ds and




∆s



1 A

µdA

(12) (13)

ds
are the coefficients of the differ-

ence equations. The values hi and ei are the line integrals of the field strengths surrounding the element under consideration.

2.1

Computing the FD-Coefficients

GdfidL
further approximates the FD-coefficients by assuming for the co
efficients
1εdA
ds that the value A
εdA
is constant over the integration A


path ∆s. Therefore GdfidL uses an FD-coefficient of





A


ds εdA


. The area over

which the permittivity has to be integrated is the vicinity of an edge of the primary grid. Four cells belong to this vicinity, each cell may be filled with up to two different materials. Figure 2 illustrates the situation
where the material boundaries in the four cells touch the edge. The integral A
εdA
in the FD-coefficient now is
A


εdA
=

1 8



(ε1,1 + ε2,1 )A1 + (ε1,2 + ε2,2 )A2

+(ε1,3 + ε2,3 )A3 + (ε1,4 + ε2,4 )A4

(14)

A General Purpose Electromagnetic Code for Designing

77

Figure 2. Left: The FD-coefficients to compute an electric component from the surrounding magnetic components depend on up to eight different permittivities. The marker indicates the location of the electric component. The areas A1 , A2 , A3 , A4 are the areas of faces of the primary grid cells touching the edge where the electric component is defined on. The thick lines indicate edges of the primary grid, the thin lines indicate edges of the dual grid. Right: The marker indicates the location of the magnetic component. The FD-coefficients to compute a magnetic component from the surrounding electric components depend on up to four different permeabilities. Two of the permeabilities are the permeabilities in the shown cell, the other two belong to the cell above the paper plane. The thick lines indicate edges of the primary grid, the thin lines indicate edges of the dual grid.




The value ds of course is the length of the edge of the primary grid.
To evaluate the coefficient of a magnetic component
1µdA ds
, we inA

tegrate the permeability in the vicinity of a dual edge. Since a dual edge is the connection of the two centers of two primary cells, the dual edge lies
within two primary cells. GdfidL assumes that in each primary cell the integral A µdA is constant. Then, with up to two different materials in each primary cell, the FD-coefficient for a magnetic component is

1 1
ds
= 2 A µdA



∆1 ∆2 + (µ1,1 + µ2,1 )A1 /2 (µ1,2 + µ2,2 )A1 /2



(15)

Figure 2 illustrates the material distribution in one of the two primary cells involved.

78

W. Bruns, H. Henke

EIGENVALUE COMPUTATION, PERIODIC BOUNDARY CONDITIONS

3.

Equations 12 and 13 may be written as matrix equations for arithmetic vectors
e and
h with the unknown integrated electric and magnetic field strengths over the primary and dual edges: −

Here the elements of (C)e are ± ±





1 A


εdA


d
e = (C)h
h dt

d
h = (C)e
e dt



1 A

µdA

(16)

ds
and the elements of the (C)h are

ds. The matrices are extremely sparse, with only up to 4 nonzero

entries per row. In case of resonant fields we substitute jω for from equations 16 (C)h (C)e
e = ω 2
e

d dt

and obtain (17)

If the boundary conditions at the outer boundaries of the computational volume are simple ones, ie. if the outer boundaries can be assumed perfectly electric conducting or perfect magnetic conducting, then the matrix of the eigenvalue problem (C)h (C)e is real. For periodic boundary conditions at the outer surface of our computational volume, some of the matrix elements become complex, because the periodicity requires that eg. the electric field at a lower boundary has to be the same as the field at the corresponding upper boundary, multiplied with a complex factor e−jϕ . GdfidL uses subspace iteration as implemented in an algorithm of Tueckmantel [4] to search for the lowest nonzero eigenvalues of 17. This algorithm needs some hundred to some thousand iterations of the form: (18)
yi+1 = (C)h (C)e
yi − γi
yi where the γi are the zeroes of some polynomial. Since the algorithm requires only matrix times vector operations, and not the matrix itself, it is not necessary to really construct and store the matrix. GdfidL implements the matrix times vector operation in a four step process, without performing a complex matrix times vector operation. Two steps are very similiar to the operations needed to perform a single time step in a FDTD algorithm. The grid is extended such, that above the last gridplane of the computational volume an auxiliary plane with the same material distribution as the very first plane is placed. Below the lowest plane of the computational volume, an auxiliary plane with the same material distribution as the last plane is placed. This is done for all cartesian directions where periodic boundary conditions are to be enforced. In the first step, a complex auxiliary vector
x is computed.
x := (C
)e
yi

(19)

A General Purpose Electromagnetic Code for Designing

79


e Here
the entries of the real matrix (C ) are the real valued FD-coefficients ±
1 ds in the artificially enlarged volume. If the vector
yi would contain µdA

the integrated electric field strengths of a resonant field with frequency ωn , then this auxiliary vector
x would be the integrated magnetic field strengths of jωn
h. This step is similiar to the computation of the H-field update in an FDTD-algorithm. To compute the auxiliary vector, it is not necessary to store the matrix (C
)e , but only to be able to perform a H-field update. In the second step, the periodic boundary conditions for the H-fields are applied to the complex auxiliary vector
x. This is: The components of
x that lie at the lower boundaries of the computational volume are multiplied by a complex factor ψ = exp(jϕ) and the result is copied to the corresponding components at the upper planes. ϕ is the wanted phase shift. Figure 3 illustrates this procedure for a 2-dimensional grid, when periodic boundary conditions in a single direction are to be enforced.

Figure 3. Left: The periodic boundary conditions for the magnetic field are enforced by taking the values at the lower plane, multiplying them by a complex factor and assigning the result to the magnetic field components at the upper plane. Right: The periodic boundary conditions for the electric field are enforced by taking the values at the upper plane, multiplying them by a complex factor and assigning the result to the electric field components at the lower plane. The thick lines indicate edges of the primary grid, the thin lines indicate edges of the dual grid.

In the third step, the vector update
yi+1 := (C
)h
x − γi
xi

(20)

is performed. The elements of (C
)h are the real valued FD-coefficients in the artificially enlarged volume. This step is similiar to the E-field update in a FDTD-algorithm. Again, the matrix (C
)h is not needed explicitly. In the fourth step, the periodic boundary conditions for the electric field are applied to the vector
yi+1 . This is: The components of
yi+1 that lie at the upper boundaries of the computational volumes are multiplied by a complex factor ψ = exp(−jϕ) and the results are copied to the components at the lower planes.

80

3.1

W. Bruns, H. Henke

Example for Periodic Boundary Conditions

The periodic boundary conditions are applied to compute the dispersion relation in a periodic arrangement of spheres connected by round rods. Figure 4 shows an elementary cell and the computed dispersion diagram.

Figure 4. Above: Elementary cell of a 3D array of conducting spheres, connected by round conducting rods. The lattice constant a is the same in all three directions, the radius of the spheres is 0.375 a, the radius of the rods is a/10. Shown is the real part of the eletric field of π the fundamental mode with
k = (1, 1, 1) 4a . Below: The band structure for the first few modes in the 3D array.

A General Purpose Electromagnetic Code for Designing

81

FASTER FD-IMPLEMENTATION

4.


In addition
to the commonly known FD-optimization that computes with


· d
s and E
· ds instead of H
and E
[3] two algorithmic improvements H have been found and implemented.

4.1

Single sweep through memory

Normally the H- and E-update in FDTD-codes are performed as follows: For all Timesteps: DO Update all H-components, Update all E-components, ENDDO For all Timesteps The above algorithm in every timestep reads all the E components to update all H-components, then reads all the H-components to update all E components. In every timestep, all field-components are touched twice, but with a long CPU-time distance between. Careful inspection of the update process reveals that it is possible to update the H components of a cell, and immediately after that the E-components can be updated, since they are no longer needed to update other H-components. The second use of the field components will be much faster on cache-based computers, since the field components will already be in the cache. The old E-components can be overwritten while stepping through the mesh. E.g. for lossfree problems it might look like: REAL, DIMENSION(1:3,0:nx+1,0:ny+1,0:nz+1) :: & Eds, Hds, dsoEpsA, dsoMueA DO iz= 1, nz, 1 DO iy= 1, ny, 1 DO ix= 1, nx, 1 Hds(1,ix,iy,iz)= Hds(1,ix,iy,iz) - dt*dsoMueA(1,ix,iy,iz) & * ( Eds(2,ix ,iy ,iz )-Eds(2,ix ,iy ,iz+1) & + Eds(3,ix ,iy ,iz )-Eds(3,ix ,iy+1,iz ) ) Hds(2,ix,iy,iz)= Hds(2,ix,iy,iz) - dt*dsoMueA(2,ix,iy,iz) & * (-(Eds(1,ix ,iy ,iz )-Eds(1,ix ,iy ,iz+1)) & + Eds(3,ix ,iy ,iz )-Eds(3,ix+1,iy ,iz ) ) Hds(3,ix,iy,iz)= Hds(3,ix,iy,iz) - dt*dsoMueA(3,ix,iy,iz) & * ( Eds(1,ix ,iy ,iz )-Eds(1,ix ,iy+1,iz ) & -(Eds(2,ix ,iy ,iz )-Eds(2,ix+1,iy ,iz ))) !! !! Now we can update the Eds-components of the cell since !! they are no longer needed for the remaining H-updates. !! All used H-components have already been updated:

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W. Bruns, H. Henke !! Eds(1,ix,iy,iz)= Eds(1,ix,iy,iz) + dt*dsoEpsA(1,ix,iy,iz) & * (-(Hds(2,ix ,iy ,iz ) - Hds(2,ix ,iy ,iz-1)) & + Hds(3,ix ,iy ,iz ) - Hds(3,ix ,iy-1,iz ) ) Eds(2,ix,iy,iz)= Eds(2,ix,iy,iz) + dt*dsoEpsA(2,ix,iy,iz) & * ( Hds(1,ix ,iy ,iz ) - Hds(1,ix ,iy ,iz-1) & -(Hds(3,ix ,iy ,iz ) - Hds(3,ix-1,iy ,iz ))) Eds(3,ix,iy,iz)= Eds(3,ix,iy,iz) + dt*dsoEpsA(3,ix,iy,iz) & * (-(Hds(1,ix ,iy ,iz ) - Hds(1,ix ,iy-1,iz )) & + Hds(2,ix ,iy ,iz ) - Hds(2,ix-1,iy ,iz ) ) ENDDO ENDDO ENDDO

A similiar optimization can be applied in the discretized curl-curl operator that is used for eigenvalue computation. The optimization saves about 30 % CPU-time on typical desktop computers.

4.2

Computing only in field carrying Gridcells

The Finite Difference algorithm can be easily implemented if one represents the fields as 4-D arrays. An example of how simple the FDTD-update procedure might look was shown in the previous section. This approach has the disadvantage that memory (and CPU) is also used for cells that are totally inside perfect electric or magnetic materials. But for many realistic geometries, the volume carrying fields is only a fraction of the total rectangular volume. Then it would be advantageous to deal only with the cells which have a nonzero field. Figure 5 shows such a geometry, where less than 10% of the computational volume really needs to be considered for the field computation. One possible scheme could be the use of linked lists, where every field carrying cell has the information about its neighbours. This needs 6 indices per field cell in addition to the 12 floating point words for the field components and their coefficients. This approach was used in the former ”GdfidL” [5] [6]. The ”GdfidL” of today has a grid organization that needs only a single index per cell. The fields itself are stored in 2D-arrays, where the second index is the number of the cell. An INTEGER array ”NrofCell” is used to extract the topology information. The FDTD-update with the single index per cell might look like: REAL,DIMENSION(1:3,0:*) :: Eds, Hds, dsoEpsA, dsoMueA INTEGER, DIMENSION(0:nx+1,0:ny+1,0:nz+1) :: NrofCell DO iz= 1, nz, 1 DO iy= 1, ny, 1 DO ix= 1, nx, 1

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Figure 5. A model of the BESSY cavity with attached waveguides and tuning plungers. The three large damping waveguides are attached to the cavity at different heights, such that no symmetry plane is left. Because of the large waveguides, most of the enclosing box is filled with electric conducting cells. Only 8 % of the computational volume is filled with interesting gridcells. 92 % of the gridcells can be ignored.

i= NrofCell(ix,iy,iz) IF (i .LT. 1) CYCLE !! skip when no field possible !! !! indices of neighbour cells in positive directions !! ipx= NrofCell(ix+1,iy ,iz ) ipy= NrofCell(ix ,iy+1,iz ) ipz= NrofCell(ix ,iy ,iz+1) Hds(1,i)= Hds(1,i) - dt*dsoMueA(1,i) & * ( Eds(2,i)-Eds(2,ipz) + Eds(3,i)-Eds(3,ipy) ) Hds(2,i)= Hds(2,i) - dt*dsoMueA(2,l) & * (-(Eds(1,i)-Eds(1,ipz)) + Eds(3,i)-Eds(3,ipx) ) Hds(3,i)= Hds(3,i) - dt*dsoMueA(3,i) & * ( Eds(1,i)-Eds(1,ipy) -(Eds(2,i)-Eds(2,ipx))) !! !! indices of neighbour cells in negative directions !! imx= NrofCell(ix-1,iy ,iz ) imy= NrofCell(ix ,iy-1,iz ) imz= NrofCell(ix ,iy ,iz-1) Eds(1,i)= Eds(1,i) + dt*dsoEpsA(1,i) & * (-(Hds(2,i) - Hds(2,imz)) + Hds(3,i) - Hds(3,imy) ) Eds(2,i)= Eds(2,i) + dt*dsoEpsA(2,l) &

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W. Bruns, H. Henke * ( Hds(1,i) - Hds(1,imz) -(Hds(3,i) - Hds(3,imx))) Eds(3,i)= Eds(3,i) + dt*dsoEpsA(3,i) & * (-(Hds(1,i) - Hds(1,imy)) + Hds(2,i) - Hds(2,imx) ) ENDDO ENDDO ENDDO

5.

PARALLEL COMPUTATION: LOCAL FIELD UPDATE

The core of the Finite Difference Method is the discretisation of the curloperators. With these discretised curl operators, one computes time dependent fields (FDTD) via the discretised form of 1


H((n + 1/2)∆t) = H((n − 1/2)∆t) − ∆t ∇×E(n∆t) µ

(21)

1


+ 1/2)∆t) (22) E((n + 1)∆t) = E(n∆t) + ∆t ∇×H((n ε and one finds resonant fields in lossfree structures by searching for eigenvalues of the discretised form of 1 1

= ω2E ∇× ∇×E ε µ

(23)

Most of the CPU-time is spent in applying these discretised curl operators. However, they are quite easily parallelised by using subvolumes. For example, when performing a FDTD calculation, the algorithm for each subvolume is: For all Timesteps: DO Compute local H by applying the local curl operator to the local E For all Directions: DO Send tangential H to the neighbour Receive tangential H from neighbour ENDDO For all Directions Compute local E For all Directions: DO Send tangential E to the neighbour Receive tangential E from neighbour ENDDO For all Directions ENDDO For all Timesteps Figure 6 scetches a local subvolume. The tangential H-components at the lower boundaries of the local volumes must be sent to the neighbour volumes in negative directions. Correspondingly, the tangential E-components at the upper

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boundaries must be sent to the neighbour volumes in positive directions. For correct results, the tangential components from a neighbour in eg. x-direction must be received before data can be sent in eg. y-direction.

Figure 6. The dark lines and circles represent the electric field components in a local volume. The light ones represent the magnetic field components. The tangential E field components at the upper boundaries of the local volume (thick dark) and the tangential H field components at the lower boundaries (thick light) can be computed from the local information. These components are sent to the neighbour volumes. The tangential E field at the lower boundaries (dashed dark) and the tangential H field at the upper boundaries (dashed light) cannot be computed from the local information. These components are received from the neighbour volumes.

5.1

Parallel computation: Excluding unneeded gridcells

The Finite Difference Method in cartesian coordinates is easily parallelised, since the subdivision of the total rectangular computational volume is easily done, if one restricts oneself to rectangular subvolumes. One just has to partition the grid such, that each processor has about the same number of gridcells. This approach works well, when electromagnetic fields can exist in a large fraction of the volume. However, most realistic RF-devices, if computed in a rectangular volume, do not lead to a grid where most gridcells are filled with vacuum or a dielectric. The opposite is the case: Complicated devices, for which the computation inherently is time consuming, have an enclosing rectangular box of which 90% or more is filled with electric conducting material. If one subdivides such a volume into as many subvolumes as there are processors, most processors will work on parts of the volume where the fields are known to be zero a priori. What a horrible waste of resources. Finite Element based codes do not have that problem. Since they anyway have to deal with their complicated mesh-topology, dealing with nonrectangular sub-volumes is their daily bread. But if one wants to stick with

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the inherently easier implementation and cheaper execution of classical Finite Differences, one has to stick to rectangular subvolumes. There is a way out: Each processor works on more than one subvolume. If we subdivide the total volume in many more subvolumes than we have processors, then we can discard the subvolumes where no fields can exist, and spread the remaining ones evenly over the available processors. This approach is halfway between classical Finite Difference and the complicated topology of Finite Element Meshes. As a typical example,figure 7, we take the cavity of figure 5.

Figure 7. A model of the BESSY cavity with attached waveguides and tuning plungers. This is the same cavity as shown in figure 5. In this figure, the different colours indicate the used subvolumes. The total volume is subdivided in 8x24=192 subvolumes, of which 122 can be discarded. The total number of gridcells is about 16 millions. GdfidL needs about 3 GBytes of RAM and six hours wall clock time on an eight processor PC Cluster (total cost 8.000 EUR) to accurately compute the first 120 resonant fields in that structure.

Local field computation. When performing a FDTD calculation, the algorithm for a single subvolume per processor is: For all Timesteps: DO Compute local H by applying the local curl operator to the local E For all Directions: DO Send tangential H to the neighbour volumes Receive tangential H from the neighbour volumes ENDDO For all Directions Compute local E For all Directions: DO

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Send tangential E to the neighbour volumes Receive tangential E from the neighbour volumes ENDDO For all Directions ENDDO For all Timesteps However, if one wants to have only a single thread of execution, the field update for more than one subvolume per processor must be done slightly more complicated, since otherwise deadlocks will occur: For all Timesteps: DO For all Subvolumes: DO Compute local H by applying the local curl operator to the local E ENDDO For all Subvolumes For all Subvolumes: DO For all Directions: DO Send tangential H to the neighbour volumes Receive tangential H from the neighbour volumes ENDDO For all Directions ENDDO For all Subvolumes For all Subvolumes: DO Compute local E ENDDO For all Subvolumes For all Subvolumes: DO For all Directions: DO Send tangential E to the neighbour volumes Receive tangential E from the neighbour volumes ENDDO For all Directions ENDDO For all Subvolumes ENDDO For all Timesteps

5.2

Grid Generation

It is crucial that the grid generation is parallelised as well, otherwise that step would be the most time consuming part. The generation of the grid and the FDcoefficients is made in two steps: In the first step, each processor gets assigned the same number of subvolumes to generate the coefficients for. Subsequently, each subvolume is inspected, how many gridcells can carry a nonzero field. The subvolumes with only zero field are discarded, and the remaining ones are spread over the available processors such, that a: each processor has about the same number of interesting grid-cells to deal with, and b: that the communication between subvolumes on different processors is minimised. This spreading over the available processors is implemented via a call of the METIS [9] pack-

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age. In the second step, each processor generates the mesh and the coefficients for the assigned subvolumes.

6.

SIMULATING FREE MOVING CHARGES

Free moving charges are simulated by the ’Particle in Cell’-algorithm. The algorithm uses a large number of charges of finite size and fixed shape, fig. 8. Free moving charges show up in Maxwells equations as a current density. To compute the electric field at the next timestep, the charge which has traversed a face of the dual grid must be computed. This is done with an algorithm similiar as the one described by Villasenor [7], extended for a grid with uneven spacings. That charge amount, multiplied by
a factor of dsoEpsA
· d
s changes, in =
∆s , is the amount by which the electric unknown E εdA addition to the change due to the curl of H. The charge is accelerated by the electric field, and rotated by the magnetic field at its actual position. Therefore, the electric and magnetic field must be known at the same time. The normal FDTD-algorithm does not compute the magnetic field at the same times as the electric field. Instead, the magnetic field is only known half a timestep away. The natural assumption, that the magnetic field at the time where the electric field is known, would be the average of the magnetic field before and after, leads to the computation of the magnetic field in two half steps. One step, to compute the magnetic field at the time when it is needed to compute the Lorentz-force on the charges, and the other half step to compute the magnetic field at the time t = (n + 1/2)∆t. The computation of the acceleration and rotation is performed by an algorithm invented by Boris [2]. The optimised implementation of Buneman, as can be found in the TRISTAN [8] code, is used.

6.1

Parallel Computation

Moving charges change the electric field in their immediate vicinity, and their velocity is changed by the electric and magnetic field in their immediate velocity. Therefore it is natural to perform all the charge related computations on the processor who is responsible for computing the electromagnetic field within the volume where also the charge is in. While the charges are drifting through the computational volume, they will leave the domain of one processor and enter the domain of another processor. Since the computation of the magnetic field in two halfsteps is only required in the vicinity of charges, the algorithm with the two half steps is only needed for subvolumes where charges are in. The charge free subvolumes can be treated with the standard FDTD algorithm.

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Figure 8. The dark arrows represent the electric field components. The light ones represent the magnetic field components. For integrating the Lorentz-force, the force due to the magnetic field must be known at the same time as the force due to the electric field. The fields at the center of mass of the charge (black circle) is computed by linear interpolation of the fieldcomponents nearest to the position of the center of mass. The circles are at the positions of the fieldcomponents which are involved in computing the x- and y-components.

6.2

Use of symmetries for Particle Pushing

The force on a particle is computed by an interpolation of 2 x 3 x 8 nearby field components, see figure 8. This interpolation must be modified for particles which are near to a plane of symmetry, figure 9. GdfidL uses an auxiliary gridplane. The fieldcomponents in this auxiliary gridplane are computed such, that the fields near the plane of symmetry obey the wanted symmetry. For a magnetic wall: The normal electric field component in the auxiliary plane is the negative one of the normal component inside of the computational volume. The normal magnetic voltage is doubled. Since no current may traverse a magnetic wall, it must be enshured that no net charge traverses the magnetic wall. When, due to the particle pushing, the particle has traversed the symmetry plane, the position of the particle is reflected back into the computational volume. The sign of the normal component of the particles velocity is changed. This is scetched in figure 10.

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Figure 9. The dark arrows represent the electric field components. The light ones represent the magnetic field components. The shaded area is outside of the computational volume. At the border of the computational volume, magnetic boundary conditions shall be applied. For interpolating the Lorentz-force, the magnetic voltages whose paths cross the magnetic boundary condition, have to be multiplied by two (thick light arrows). The tangential magnetic components outside of the computational volume must be set to the negative value of the corresponding magnetic components just inside (dashed light arrows). The normal electric components outside must be set to the negative value of the corresponding electric components inside (dashed dark arrows).

Figure 10. The dark arrows represent the electric field components, or convection currents. The shaded area is outside of the computational volume. The two quadratic patches are a charge cloud before and after the particle pushing. At the border of the computational volume, magnetic boundary conditions shall be applied. When a charge cloud would traverse the magnetic wall due to the particle pushing, its convection current outside of the computational volume must be reflected back into. The normal components outside (dashed dark arrows) must be subtracted from the corresponding normal components inside. The tangential convection currents must be doubled (thick dark arrows).

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REFERENCES

[1] K. S. Yee, “Numerical Solution of initial boundary value problems involving maxwell’s equations in isotropic media”, IEEE Transaction of Antennas and Propagtion 14 (1966) 302 [2] Boris, J. P., “Relativistic plasma simulation-optimization of a hybrid code”, in Proceedings of the Fourth Conference on the Numerical Simulation of Plasmas Naval Res. Lab., Wash. D.C., 1970. [3] Th. Weiland, “Ein Verfahren zur Berechnung von Wirbelstroemen in massiven, dreidimensionalen, beliebig geformten Eisenkoerpern”, etz Archiv, H. 9 (1979), pp. 263-267 [4] J. Tueckmantel, “An improved version of the eigenvector processor SAP applied in URMEL”, CERN/EF/RF 85-4, 4 July 1985 [5] W. Bruns, “GdfidL: A Finite Difference Program for Arbitrarily Small Perturbations in Rectangular Geometries”, IEEE Transactions on Magnetics, vol. 32, no. 3, May 1996, pp. 1453-1456 [6] W. Bruns, “GdfidL: A Finite Difference Program with Reduced Memory and CPU Usage”, Proceedings of the PAC-97, Vancouver, vol. 2, pp. 2651-2653, http://www.triumf.ca/pac97/papers/pdf/9P118.PDF [7] J. Villasenor, O. Bunemann, “Rigorous charge conservation for local electromagnetic field solvers”, Computer Physics Communications 69 (1992) 306 [8] http://webserv.gsfc.nasa.gov/ESS/exchange/contrib/macneice/pic-tristan.html [9] George Karypis, Vipin Kumar, “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs”, University of Minnesota, Department of Computer Science, Minneapolis, MN 55455, Technical Report: 95-035, http://wwwusers.cs.umn.edu/∼karypis/metis/

CHAPTER 2

QUASI-OPTICAL DEVICES AND SYSTEMS

AMPLIFICATION AND GENERATION OF HIGHPOWER MICROWAVE BY RELATIVISTIC ELECTRON BEAMS IN SECTIONED SYSTEMS Edward Abubakirov1, Nikolay Kovalev1, Victor Tulpakov2 1 2

Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia Moscow Radiotechnical Institute, Moscow, Russia

Abstract:

The highest powers of microwave radiation produced with devices driven by high-current relativistic electron beams amount to 109-1010 W in pulses of 1100 ns duration. As the high-frequency electric fields in the devices are limited with microwave breakdowns, further enhancement of microwave pulse energy requires broader interaction space. The main problem with such oversized and, accordingly, multi-mode structures, is keeping coherence of output radiation. Because of this problem, special means for mode selection must be applied. In the paper, methods of mode selection based on sectioning of the operating space are discussed and examples of their experimental realization are presented.

Key words:

high-power microwaves, multi-mode systems, mode selection.

1.

INTRODUCTION

The main problem of powerful microwave electronics is preventing breakdowns in electron devices and their output elements. Note that surface processing gives only a limited effect because even the pure metal is disrupted with high electric fields. So, at pre-breakdown fields the only opportunity to enhance the RF power is to increase the cross-section of microwave devices. However, in the oversized system the intense electron beam can excite several modes with different frequencies and spatial structures, which means loss of coherence. Some methods to suppress parasitic excitation can be borrowed, with a proper adaptation, from the “classic” microwave electronics, but most of mode selection methods in microwave devices driven by intensive relativistic electron beam need a specialized approach [1, 2]. The paper is devoted to principles, peculiarities and realizations of mode selection methods based on sectioning the interaction space of a relativistic electron microwave generators and amplifiers. The method uses longitudinal 95 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 95–103. © 2005 Springer. Printed in the Netherlands.

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separation of the interaction space into several parts, so that coupling of these parts would depend on partial rf field structures and the device performance would be realized only at a definite set of modes in sections. The main attention in the paper is paid to devices, whose operation is based on the Cherenkov mechanism of stimulated radiation. In such a system, a rectilinear electron beam formed with the simplest guns interacts with an electromagnetic wave which phase velocity is close to the velocity of electrons. Cherenkov devices are especially attractive for centimeter and long millimeter wave bands.

2.

SCHEMES OF SECTIONED DEVICES

The principle of sectioning can be applied to a wide variety of microwave sources. The simplest versions are following (Fig.1 and 2): (a) a sectioned amplifier, which consists of a sequence of amplifying sections, pierced with a common electron beam; (b) a resonant traveling wave tube (TWT), that is an amplifier with a selective feedback provided with narrowband reflectors (along with passive reflectors, the active ones can be used as well); (c) a cascaded oscillator representing a selective though low efficient oscillator followed with an efficient amplifier not coupled to the upstream oscillator electromagnetically, but excited with the modulated electron beam.

e-beam

Mode2

Mode3 Microwave output

Microwave input

Mode1

Figure 1. Sectioned amplifier.

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Reflection Mode 2 Mode 1

AMPLIFYING Mode1

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EM-wave

Reflection Mode 1 Mode 2

e-beam

Modulation Mode 1

AMPLIFYING Mode 2 EM-wave

Figure 2. Sectioned oscillators: resonant TWT (top) and cascaded oscillator (bottom).

3.

ELEMENTS OF SECTIONED MICROWAVE SOURCES

Mode selective sectioned devices can be composed of forward and backward wave sections, Bragg reflectors, mode converters, etc.

3.1 Forward-wave amplifiers In traditional TWTs, to avoid self-excitation of the slow wave structure, rf absorbers are widely used. However, in the HPM electronics, SWS are oversized in order to avoid breakdown and the absorbers are not efficient. Electrodynamic decoupling between sections (see Fig.1) seems to be the most promising opportunity to prevent the spurious self-excitation.

3.2

Reflectors

Passive reflectors. Reflectors made on a base of hollow metallic waveguides with smooth corrugated sidewalls [3] are widely used in highpower microwave electronics. Selective properties of such reflectors are provided with resonant coupling of operating electromagnetic waves which

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parameters must satisfy Bragg conditions. For the helically corrugated waveguide r ( z , M ) R  a cos(h z  m M ) , the condition is

h1  h2 h , m1  m2 m (1) where h1, h2 are propagation constants and m1, m2 and azimuth indexes of operating waves. To enhance the selectivity, more than two modes can be coupled in double corrugated structures [4] and multi-channel feed-back systems [5]. Active reflectors. A backward wave amplifier (BWA), operating below its excitation threshold, can be regarded as reflector or converter, which couples electromagnetic wave and space charge waves of the electron beam. In such sections, the electromagnetic wave modulates the electron beam or, modulated electron beam excites electromagnetic wave. The beam as an active medium provides simultaneous transformation and amplification of waves. The advantages of the active reflector are:

 a high gain G ~ (1 − J J st ) at the electron current J approaching the start current Jst of the section (Fig.3) ;  a narrow amplification frequency band ∆f f ~ (1 − J J st ) that can provide an additional mode selection and reduce an interference of the electron beam noise;  an electrodynamic decoupling between sections since the amplified electromagnetic signal accompanying the modulation of the electron beam is extracted from BWA in the direction of the cathode, whereas the modulated electron beam proceeds in the opposite direction. A strong dependence of the BWA gain on amplitudes of coupled waves makes the active reflector analogous to a saturated mirror that favors to fast transient time and high efficiency of the device [6]. −1

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Gain

150

99

0.99

100

0.97 0.95

50

0.90

0 2,6

2,8

3,0

3,2

3,4

3,6

(k||-Z/v)L Figure 3. Amplification in a BWA at various ratios of operating and start current.

3.2

Self-exciting sections

The cascaded oscillator (Fig.2) is featured with operation of two or more sections in the non-linear regime. The main problem is combining stability of self-exciting in the first section with efficient microwave radiation in the second one. An analysis [7] shows that the simplest version of cascaded oscillator can be realized only as a trade-off between efficiency and stability relative to fluctuations of electron beam parameters. The reason is an unsuitable phase correlation between energy and density modulation of particles in the beam on the output of the section. So, adding of remodulating or phase-correction sections can improve the situation.

4.

EXPERIMENTAL SECTIONED DEVICES

4.1 Resonant TWTs Anexperimental version of the resonant TWT was made as a combination of an amplifier with two Bragg reflectors. The operating mode of the amplifying section was the lowest slow non-symmetric hybrid wave (HE11) with rotating transverse structure. This mode can be easily transformed into

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11,4

100

11,3

80

11,2

P,arb. units

frequency, GHz

Gaussian wave beam by a simple horn antenna. The selective feedback was realized by 5-entry helically corrugated Bragg reflectors which coupled the rotating HE11 mode to counter-rotating modes TE41. The cathode reflector consisted of two identical parts; a mechanical rotation of one part resulted in a tunable phase shift and, so, in a frequency tuning of the oscillator. The X-band oscillator was driven with a 1.3MeV, 10 kA, 150 ns electron beam formed with a cold emission gun. The electron beam was guided with a pulsed (quasi-static) magnetic field. The microwave power was radiated through a horn antenna and polyethylene window and registered with semiconductor “hot carriers” sensors [8]. The peak power was about 1.5 GW and the pulse duration was 30-40 ns. Rotation of parts of the cathode reflector allowed tuning the frequency of the oscillator within 10.9-11.4 GHz 3 dB band (Fig.4) [2, 9].

11,1 11,0

60 40 20

10,9

0 10,8

-30 -20 -10

0

10

20

30

40

50

M, degree

10,8

10,9

11,0

11,1

11,2

11,3

11,4

frequency, GHz

Figure 4. Frequency tuning and output power of resonant TWT.

4.2 Cascaded Oscillators In a cascaded oscillator, the simplest self-exciting section is the orotron that is a Cherenkov oscillator with an open high-selective cavity. The cavity cannot withstand high rf fields and, so, is appropriate only for low-efficient part of the sectioned oscillator. Such a cascaded oscillator [2] was realized with an orotron operating at TE312 mode of a circular cross section cavity. The orotron provided axissymmetric rf modulation of the electron beam, which, in its turn, excited a traveling wave section operated at slow TM01 mode of a circular corrugated waveguide. The cascaded oscillator was realized with the same electron beam as for the resonant TWT; it produced pulsed power about 2 GW at 9.1 GHz, and the pulse duration reached 100 ns.

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4.3

101

Sectioned Amplifiers

The simplest version of the sectioned amplifier stable in the absence of input signal represents a combination of a narrowband BWA modulating the electron beam and an output wideband TWT power amplifying section. The first, proof of principle, X-band amplifier of the sort produced 100 MW [10]. Later, a GW power amplifier of extended cross section was designed [11]. The amplifier (Figs. 5 and 6) driven with 0.8-0.9 MeV, 6 kA, 0.2 µs electron beam consisted of:  quasi-optical mode converter (5) transforming the input signal produced with a 100 kW pulsed 9.1 - 9.6 GHz tunable magnetron to the rotating TE41 mode of the circular waveguide;  backward wave amplifier (4) operating in a whispering gallery TE41 mode and serving as a pre-amplifier; horn (3) matched the BWA to the electron gun space;  output traveling wave section (6) operating in the slow hybrid HE11 mode of the corrugated circular waveguide;  horn antenna (8), simultaneously serving as the electron beam collector;  input (9) and output (10) vacuum windows;  electron beam guidance pulsed solenoid (11) combined with the vacuum case (2);  diode with a field emission cathode (1). Maximum output power of the amplifier was about 1100 MW (Fig.7) at 47 dB gain and 20% efficiency. Amplification bandwidth was about 1%. The measured output wave pattern was close to Gaussian.

Figure 5. Block diagram of the gigawatt amplifier.

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Figure 6. Design of the amplifier system.

Figure 7. Waveforms of (a) accelerating voltage, (b) heterodyned signal, (c) output power, and (d) spectrum of radiation S(f), which is shifted down with the local oscillator operating at the frequency 8.98 GHz.

4.4

Pulse-periodic operation of sectioned devices

Subsequent to the above mentioned single pulse devices, sectioned microwave oscillators operating at high pulse repetition rates were developed recently. A “super-radiation” BWO with selective pre-modulating section delivered 2 GW, 1 ns pulses at 700 pps with 2.5 kW average power [12]. Similar results were demonstrated in experiments with sectioned BWO made

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recently by IAP and MRTI: the device produced 600 MW/15 ns pulses at 500 pps during 3s bursts.

5.

CONCLUSION

Driven with high-current relativistic-electron accelerators, generators and amplifiers with sectioned interaction space are capable of delivering gigawatt-nanosecond microwave pulses, ~103 pulses per second being available.

6. 1.

2.

3. 4. 5.

6.

7. 8. 9. 10. 11. 12.

REFERENCES Kovalev N., Petelin M., Mode selection in microwave relativistic electron generators with distributed interaction, in Relativistic microwave electronics, IAP AS USSR, Gorky, (1981). Abubakirov E., Fuchs M., Gintsburg V. et al, Cherenkov relativistic oscillators of coherent electromagnetic radiation with multimode sectioned electrodynamic systems. Proc. of 8th Int. Conf. on High-Power Electron Beams. World Scientific, 2, 1105-1110, (1991). Kovalev N., Orlova I., Petelin M., Wave transformation in a muti-mode waveguide with corrugated walls, Izv.vuzov. Radiofizika, 11: 783-786, (1968). Ginzburg N., Peskov N., Sergeev A., Two-dimensional double-periodic Bragg resonators for free electron lasers, Optics Commun., 96, 254-258, (1993). Abubakirov E., Fuchs M., Kovalev N., High-selectivity resonator for powerful microwave sources, Proc. 11th Int. Conf. on High Power Particle Beams, Prague, 1, 410413, (1996). Abubakirov E., Kovalev N. Relativistic BWO as a part of sectioned generators and amplifiers, Proc. of 2-d Int. Workshop on Strong Microwaves in Plasmas, IAP, Nizhny Novgorod, 2, 788-793, (1993). Abubakirov E., Smorgonsky A., On an achievement of stable operation in a relativistic sectioned oscillator, Radiotekhnika i electronika, 35: 133-139, (1990).. Denis B., Pozhela Yu. Hot electrons. Vilnus: Mintis, 1971. Abubakirov E., Denisenko A., Savelyev A. et al., Frequency tunable relativistic resonant TWT, Pisma ZhTF, 26: issue 4, 14-18, (2000). Volkov A., Zaitsev N., Ilyakov E. et al., Realization of high gain in power microwave pulse amplifier with explosive emission gun, Pisma ZhTF, 18: issue 12, 6-10, ( 1992). Abubakirov E., Denisenko A., Fuchs M. et al. X-Band Gigawatt Amplifier, IEEE Trans. on Plasma Science, 30: no.3, 1041-1051, (2002). Korovin S., Lubutin S., Mesyats G. et al., Generation of sub nanosecond pulses in 10 GHz band with high peak and average power, Pisma ZhTF, 30, issue17, 23-31, (2004).

MICROWAVE DEVICES WITH HELICALLY CORRUGATED WAVEGUIDES

V. L. Bratman1, A.W. Cross2, G. G. Denisov1, A. D. R. Phelps2, S.V. Samsonov1 1

Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia Department of Physics, University of Strathclyde, Glasgow, UK

2

Abstract:

Helical corrugation of the inner surface of an oversized circular waveguide provides very flexible dispersion characteristic of an eigenwave. Under certain corrugation parameters, the eigenwave can possess a sufficiently high and almost constant group velocity over a wide frequency band in the region of close-to-zero axial wavenumber. This makes it attractive for broadband gyroTWTs and gyro-BWOs with reduced sensitivity to electron velocity spread. Another set of parameters ensures an operating wave with a strong frequency dependant group velocity over a frequency band, which is sufficiently separated from any cutoffs. Such wave dispersion is favourable for frequencychirped pulse compression at very high power levels. An overview of experiments on the helical-waveguide gyro-devices and the pulse compressor is presented.

Key words:

gyrotron-type devices; gyro-TWT; gyro-BWO; waveguide with helical corrugation; microwave pulse compression.

1.

INTRODUCTION

Metal hollow waveguides with various types of periodic corrugation are used widely in high-power microwave electronics. One such structure consists of a helical corrugation in the wall of a circular cylindrical waveguide, which involves both an axial and azimuthal periodicity. The surface of a helically corrugated waveguide can be represented in a cylindrical coordinate system (r, M, z) as follows: r(M, z) = r0 + l cos(mB M + kB z) .

(1)

Here r0 is mean radius of the waveguide, l is amplitude of the corrugation, mB and kB=2S/d define the azimuthal number and axial component of the 105 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 105–114. © 2005 Springer. Printed in the Netherlands.

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Bragg periodicity vector, respectively, and d is the corrugation period (Fig.1). Such a corrugation provides asymmetry of the wave dispersion for circularly polarized modes resulting in additional mode selection and control of their dispersion characteristics. These properties make waveguides with a helical corrugation attractive for a large number of applications 1, 2. In particular, they have recently been successfully used as interaction regions in gyro-TWTs 3, 4, gyro-BWOs 4, 5 and as a dispersive medium for passive microwave pulse compression 6.

Figure 1. Schematic view of a waveguide with a three-fold right-handed (mB=-3) helical corrugation.

It is important to note that the latter applications rely on significantly different mode dispersion for their operation. For a gyro-TWT the most favourable operating wave is that which has a constant and sufficiently high group velocity over a wide frequency band in the region of close-to-zero axial wavenumber. In contrast, the operating wave for a pulse compressor should have a strongly frequency dependant group velocity over a frequency band which is separated from the cutoff frequency of the waveguide. These very different requirements can be satisfied by waveguides with quite similar geometry. In both cases, the parameters of the helical corrugation are chosen such that two partial modes, one close to cutoff and one propagating, are resonantly coupled (Fig.2). In experiments with the use of the helical waveguides in gyro-devices and for pulse compression, a three-fold (|mB|=3) helical corrugation (Fig.1) was used that coupled the TE2,1 (mode 2) and the TE1,1 (mode 1) circularly polarized modes of opposite rotation. The frequency band of main interest is mostly situated below the cutoff frequency of the TE2,1 mode, and therefore by having a sufficiently smooth down-tapering of the corrugation amplitude, the operating eigenmode totally transforms into the TE1,1 mode which was used to inject and extract the microwave energy from the helical structure.

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Figure 2. Schematic dispersion diagram for a helically corrugated waveguide: k=Z/c is the wave vector, kz is its axial component, k0 corresponds to the frequency of exact Bragg resonance, c and d are unperturbed (partial) modes of the smooth waveguide; W1 and W2 are Floquet harmonics of the operating eigenmode; Wu1 and Wu2 are Floquet harmonics of the upper eigenmode.

2.

HELICAL-WAVEGUIDE GYRO-DEVICES

Depending on the direction of the guiding magnetic field, and with respect to the sign of the azimuthal number of the profile mB., the most selective configuration for gyro-devices with helically-rippled waveguides is when an axis-encircling electron beam resonantly interacts at the second cyclotron harmonic with a co-rotating TE2,1 component of the operating eigenmode, which is scattered on the corrugation into forward (for TWT) or backward (for BWO) propagating TE1,1 mode The operating waveguide for a Ka-band gyro-TWT 4, 7 has been designed to provide wave dispersion (Fig.3), which is matched within the maximum frequency band to an 80-keV electron beam having a pitch ratio of 1.2. In this experiment, an axis-encircling electron beam was formed in a thermionic gun with a reversed magnetic field near the cathode (cusp) 7, 8. A magnetic field of up to 0.7T at the interaction region was produced by a pulsed (3 ms) solenoid. A high-voltage power supply was capable to generate pulses of voltage up to 80kV and current up to 20A with a flat-top duration of up to 10Ps. The highvoltage and magnetic systems operated at a pulse repetition rate of up to 1Hz. A driving microwave pulse of duration up to 3Ps was produced by one of two

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magnetrons with mechanical tuning of the radiation frequency covering the range between 33.4GHz and 36.8GHz at power of about 10kW.

Figure 3. Properties of the gyro-TWT operating eigenmode: a) dispersion diagram (dashed line corresponds to unperturbed electron-cyclotron wave); b) group velocity as a function of frequency.

In the regime of zero-drive stable amplification, the gyro-TWT electron efficiency was measured to be 27-28% for beam voltages from 50 to 80kV and beam current in the range of 4–8 A. The saturated gain of 23-25dB was measured at an input power of about 0.5kW. The linear gain of 30-35dB was obtained when the input power was less than 0.1-0.3kW. The maximum output power amounted to 180kW when the voltage was 80kV and beam current was 8.5-9A. The most broadband operation of the gyro-TWT (Fig.4) was demonstrated at a beam voltage of 80kV, which agreed well with the theoretical predictions. As was clear from the measurements, the maximum –3dB bandwidth of the gyro-TWT exceeds 3.2GHz, or 9% (upper frequency boundary of the amplification lies beyond the frequency bandwidth provided by the RF driving sources that were available). Along with the gyro-TWT the use of a helically corrugated waveguide is advantageous for realization of a smooth-frequency-tunable gyro-BWO where the operating eigenmode has a negative group velocity. Analysis of the helical-waveguide gyro-BWO capabilities showed that this device may be attractive for a number of technological applications, for which CW kilowatt-power gyrotrons are actively used [9]. This was the motivation of a project aimed at realizing a CW tunable gyro-BWO with a power of several kilowatts at a frequency of about 24GHz 5.

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Figure 4. Instantaneous bandwidth of the gyro-TWT at various parameters.

Specific features of the CW helical-waveguide gyro-BWO as compared to our previous experiments were the use of a magnetron-injection gun (MIG) typical for conventional gyrotrons and a low-voltage (20kV) electron beam. It should be noted that an electron beam produced by a MIG is not an axis-encircling beam, which may affect the selectivity of the configuration discussed above, namely, a possibility of the spurious TE1,1 mode excitation at the second cyclotron harmonic also appears in the regime of the gyroBWO (Fig.5). Correspondingly, the MIG was designed to produce an electron beam with a radius of about 1.5mm at which the starting current of the parasitic gyro-BWO oscillations slightly exceeded that of the operating mode. The experiments demonstrated the selective second harmonic operation of the gyro-BWO at the desired mode for the designed values of the magnetic field, beam voltage and current in the CW (several hours) regime. The measured maximum output power, frequency range and tuning band (Fig.6a) were in reasonable agreement with the design. Rather large variations in the output power (oscillating behavior of power vs. B-field) can be explained by the improperly matched output window. The tuning characteristic of the gyro-BWO can be smoothed by the use of a broadband multiple-disc lowreflection window whose operation has been successfully tested in gyro-TWT experiments 4. At a beam current of 2A, gyro-BWO operation was tested in the regime with a single-stage energy recovery (depressed collector). When the collector potentialincreased from zero to almost 10 kV the tube efficiency grew from 15% to 23% (Fig.6b). Along with a substantial increase in the device efficiency, the use of the depressed collector allows reduction of the

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voltage of the main power supply down to almost 10kV, which makes the gyro-BWO significantly more attractive for technological applications.

Figure 5. Dispersion diagram for the CW gyro-BWO (the dashed lines correspond to the partial modes.

a)

b)

Figure 6. Experimental results for the gyro-BWO at accelerating voltage of 20 kV and beam current of 2 A: a) the tuning characteristic (the dashed line corresponds to doubled cyclotron frequency); b) the energy recovery results.

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111

HELICAL-WAVEGUIDE PULSE COMPRESSOR

A phenomenon of compression of smoothly frequency modulated (chirped) electromagnetic pulses in a dispersive medium is well known and actively used in microwave electronics (radars) and laser physics 10. Hollow metal waveguides representing dispersive media (group velocity of an eigenmode is a function of frequency) are attractive for the microwave pulse compression 11 because of their capabilities of handling very high power, relative compactness and simplicity. Analysis of possibilities to increase the power of frequency-swept radiation using copper (the losses are important) waveguides at lower-order modes shows that X-band pulses of 50-200 ns in duration with a frequency modulation of 2-15% can be compressed in the waveguides with reasonable (less than 10 m) lengths into 0.5-3 ns pulses with 10-100 times higher peak power containing 30-60% of the input pulse energy. This set of parameters makes the proposed type of pulse compression attractive to increase the power from non-resonant relativistic Cherenkov devices, such as TWT and BWO, resulting in microwave sources of multi-gigawatt peak power. However, for this application, the use of a conventional (smooth-bore) waveguide, has serious limitations due to its being operated very close to cut-off. In optimum cases, the frequency at the beginning of an input pulse should be only 0.5-1% above the cutoff frequency. If a TWT is used to drive the compressor then it is inevitable that the low-frequency part of the amplification band is below the cutoff which will then be reflected from the compressor back to the amplifier resulting in its possible parasitic selfoscillation (RF isolation using unidirectional elements is problematic at very high power). If a relativistic BWO is used as a source of frequencymodulated pulses for a smooth-waveguide compressor, then the necessary frequency sweep can be produced only by using a difficult-to-realize accelerating voltage modulation. The two problems of wave reflection from a compressor and optimum frequency modulation can be simultaneously solved using a waveguide with a special helical corrugation of its inner surface 6. As was mentioned in the introduction, the geometry of the waveguide can be similar to that used for the gyro-devices but the parameters of the corrugation should be chosen in a way such that the eigenwave group velocity is a rapidly varying function of frequency (Fig.7). The helical symmetry allows the frequency regions with zero or negative group velocity of the eigenwave to be avoided, which ensures good rf matching of the compressor with the input source over a sufficiently wide frequency band. In addition, the flexibility of the wave dispersion allows its optimisation for a given frequency modulation of an input pulse by varying the corrugation parameters.

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b)

Figure 7. Eigenmode properties of a helically corrugated waveguide for pulse compression: a) dispersion diagram; b) group velocity and losses for a 2.08 m long waveguide.

The operation of a helical-waveguide compressor was studied theoretically and confirmed in an experiment where a 70-ns 1-kW pulse from a conventional TWT was compressed in a 2.08 meter long helical waveguide. The output pulse had a peak power of 10.9 times higher than the input pulse and duration of about 3 ns (Fig.8). The experimental results were in very good agreement with the simulations which also predicted that with two times faster frequency sweep at the end of the pulse (which was beyond the capabilities of the input source used) the power compression ratio and efficiency can be increased to 18.7 and 65%, respectively.

a)

b)

Figure 8. Pulse compression in the helically corrugated waveguide: a) experimental results; b) simulation results.

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For a helical compressor the optimum negative frequency sweep can quite naturally be realized at the falling edge of a relativistic BWO pulse. For example, if a BWO generates hundreds of MW during 50 ns over a voltage drop from 700 kV to 400 kV, this frequency modulated radiation can be compressed up to 10-20 times in power with efficiency higher than 50%. In addition, because of its reflection-less properties a helical compressor can be used effectively at the output of a powerful amplifier. A favourable wave dispersion can be also synthesized for higher-order modes resulting in an increase of the helical waveguide diameter by 1.5-2 times (without significant overlapping of the coupling bands) and correspondingly in an enhancement of its rf breakdown strength. A combination of a moderately relativistic BWO or TWT with a helical waveguide compressor may result in a multi-gigawatt short-pulse microwave source which is attractive for a number of applications including radars and plasma chemistry. A design based on detailed numerical simulations of a relativistic BWO capable of generating a frequency-modulated pulse to be compressed is currently under development.

4.

CONCLUSION

The helical corrugation of the inner surface of an oversized circular waveguide that resonantly couples two circularly polarized partial modes having significantly different group velocities provides an eigenwave with a very flexible dispersion characteristic. This eigenwave is advantageous for use both in broadband gyrotron-type devices and in frequency-modulated pulse compressors.

5.

ACKNOWLEDGEMENTS

This work was supported by the Presidium of Russian Academy of Sciences and the Russian Foundation for Basic Research under grants 01-0216780 and 04-02-16698 and EPSRC, UK.

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REFERENCES

1. Kovalev N. F., Orlova I. M., Petelin M. I. Wave transformation in multimode waveguide with corrugated walls, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11 (5), 783-786 (1968). 2. Thumm M. Modes and Mode Conversion in Microwave Devices, in Generation and Application of High Power Microwaves, Proc. of 48th Scottish Universities Summer School in Physics, St Andrews, R. A. Cairns and A.D.R. Phelps Eds.: Institute of Physics Publishing, 1996. 3. Bratman V.L., Cross A.W., Denisov G.G., He W., Phelps A.D.R., Ronald K., Samsonov S.V., Whyte C.G. and Young A.R., High-Gain Wide-Band Gyrotron Traveling Wave Amplifier with a Helically Corrugated Waveguide, Phys. Rev. Letts., 84 (12) 2746-2749 (2000). 4. Bratman V.L., Cross A.W., Denisov G.G., Glyavin M.Yu., He W., Luchinin A.G., Lygin V.K., Manuilov V.N., Phelps A.D.R., Samsonov S.V., Thumm M., Volkov A.B. Broadband Gyro-TWTs and Gyro-BWOs with Helically Rippled Waveguides. Proc. 5th Int. Workshop Strong Microwaves in Plasmas, A.G. Litvak Ed., Nizhny Novgorod, Russia, 2002, pp. 46-57. 5. Samsonov S.V., Denisov G.G., Bratman V.L., Bogdashov A.A., Glyavin M.Yu., Luchinin G.A., Lygin V.K., Thumm M., Frequency-Tunable CW Gyro-BWO with a Helically Rippled Operating Waveguide, IEEE Trans. on Plasma Sci. (Special Issue on High Power Microwave Generation), June 2004 (to be published). 6. Samsonov S.V., Phelps A.D.R., Bratman V.L., Burt G., Denisov G.G., Cross A.W., Ronald K., He W. and Yin H. Compression of frequency modulated pulses using helically corrugated waveguides and its potential for generating multi-gigawatt RF radiation, Phys. Rev. Letts., 92, 118301 (2004). 7. Samsonov S.V., Bratman V.L., Denisov G.G., Kolganov N.G., Manuilov V.N., Ofitserov M.M., Volkov A.B., Cross A.W., He W., Phelps A.D.R., Ronald K., Whyte C.G., Young A.R. Frequency-broadband gyro-devices operating with eigenwaves of helically grooved waveguides, Proc. 12th Symp. on High Current electronics, Tomsk, Russia, 24-29 Sept. 2000, G. Mesyats, B. Kovalchuk, and G.Remnev Eds., pp. 403-407. 8. Rhee M.J., Destler W.W. Relativistic electron dynamics in a cusped magnetic field. Phys. of Fluids, 17 (8) 1574-1581 (1974). 9. Bykov Yu., Eremeev A., Glyavin M., Kholoptsev V., Luchinin A., Plotnikov I., Denisov G., Bogdashev A., Kalynova G., Semenov V., and Zharova 24 - 84 GHz Gyrotron Systems for Technological Microwave Applications, IEEE Trans. on Plasma Science, 32 (1) 67-72 (2004). 10. E. Hecht, Optics. New York: Benjamin Cummings, 2002, 4th Ed. 11. R.A. Bromley, B.E. Callan, Use of waveguide dispersive line in an f.m. pulse-compression system, Proc. IEE 114 (9) 1213-1218, (1967).

QUASI-OPTICAL TRANSMISSION LINES AT CIEMAT AND AT GPI

Á. Fernández1, K. Likin2, G. Batanov3, L Kolik3, A. Petrov3, K. Sarksyan3, N. Kharchev3, W. Kasparek4, R. Martín1 1

EURATOM-Ciemat Association for Fusion, Avda. Complutense, 22, 28040 Madrid (Spain) Present address. University of Wisconsin, Madison, Wisconsin (USA) Institute of General Physics, Russian Academy of Sciences, Moscow (Russia) 4 Institute of Plasma Research, University of Stuttgart, Stuttgart (Germany) 2 3

1. INTRODUCTION The Electron Cyclotron Resonance Heating (ECRH) method has proven to be a highly efficient tool for plasma breakdown, localized heating, current drive, MHD activity control, stabilization of Neoclassical Tearing Modes (NTM), etc, in plasmas confined by a strong magnetic field. Moreover, the relative simplicity of the launching systems and the big progress in the development of powerful microwave sources and high power transmission systems made this heating method very attractive for many fusion experiments [1, 2]. To get the maximum efficiency in the absorption of the electron cyclotron (EC) waves, the microwave beam must conform to the following. (1) be launched into a plasma in the right direction with respect to the magnetic field; (2) have an appropriate wave polarization; (3) have a wave pattern with a maximum along its axis and low side lobes; and (4) be focused on a plasma axis. The output wave beam parameters and the total efficiency strongly depend on the launching antenna and on the transmission line. At a high power level (hundred’s of kW), oversized waveguides, and/or large mirrors must be used in order to avoid arcing inside a line and on an antenna. This entails some general requirements in the transmission systems: - the main mode must have low ohmic losses along the line and, in the case of a mirror line, low diffraction losses; - high mode purity: small conversions of the main mode into other modes, i.e. the conservation of wave polarization and intensity distribution;

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the microwave power should not cause any arcing inside the transmission line; - the beam must have a fixed polarization at the output of the transmission line; and - elements for measuring and monitoring the forward and reverse power should be compatible with operation at high power. All of these requirements are easily fulfilled using quasi-optical transmission lines. Quasi-optical lines operating with the main mode (TEM00) have the following advantages: - the wave pattern has one central lobe along the beam axis; - the wave beam can be easily focused in the plasma center, and focusing is important in the cases of small and medium cross-section sizes of the plasma column; - the incident angle of the beam can easily be varied; and - the wave polarization can be changed, and any polarization of the wave can be achieved, by means of two corrugated mirrors with different corrugation depths. As compared to corrugated oversized waveguides, quasi-optical lines have some disadvantages; one of them is the relative large cross-section that implies more occupied room. Hybrid lines, i.e. a combination of waveguides and mirrors, can be a solution when there is not enough room available around the launching port. This paper describes the main parameters of the components of the quasi-optical and hybrid transmission lines, which are used for ECRH and Electron Cyclotron Current Drive (ECCD) experiments in the TJ-II stellarator at CIEMAT in Madrid (Spain) and in the L-2M stellarator at the General Physics Institute (GPI) in Moscow (Russia).

2. QUASI-OPTICAL TRANSMISSION LINES AT CIEMAT The TJ-II stellarator is a mid-size four-period heliac axis device, with a major radius of R = 1.5 m and a magnetic field B |1T. It has been in operation since 1997 [3]. The magnetic field is obtained using a set of helically positioned toroidal coils, two central conductors, and two vertical field coils. By changing the currents that flow through the central conductors, a wide range of magnetic configurations can be achieved. In each configuration the plasma position, size and shape change and the ECRH system must heat in every configuration on- and off-axis without inducing any current by ECCD. In addition, it should induce currents on- and off-axis when it is required.

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In order to fulfill all the requirements two quasi-optical transmission lines have been designed to launch the millimeter wave power into the plasmas. The lines are located at two toroidal stellarator symmetric positions [4,5]. Each transmission line is fed by a gyrotron of 300 kW, 1 s pulse length at 53.2 GHz (as it corresponds to the second harmonic of the electron cyclotron frequency in the TJ-II plasmas). The tubes were designed and manufactured by GYCOM Ltd. (Nizhny Novgorod, Russia). Both lines use a set of 9 mirrors plus one movable elliptical launcher located inside the vacuum vessel. The first quasi-optical transmission line (QTL1) has 8 curved mirrors and 2 grooved plane reflectors to transmit the power from the gyrotron to the plasmas. The beam is focused by the internal mirror at plasma center with a beam waist of 9.5 mm. The beam diameter is 100 mm at the barrier window. The mirrors are aluminum, except for the internal one, which is made of stainless steel. The mirrors are fixed on mounts, which allow the alignment of the mirror orientation in two planes with micrometers. A schematic of the side view of this line can be seen in Figure 1.

TJ-II

A

B 2020mm

2495 mm 2495 mm 30º 30º

Figure 1. Side view of the first transmission line.

The gyrotron output radiation is Gaussian-like with a purity of 96%, but it is astigmatic, i.e. the wave beam cross-section is elliptical. With the first two matching mirrors, this astigmatism is corrected. This is important, on one

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hand because the beam is axisymmetric through the rest of the line and, on the other hand, if the gyrotron must be changed, the same beam parameters can be achieved by changing only these two mirrors. The main parameters of the mirrors are summarized in the following table (Table 1). Table 1. Parameters of the first two mirrors. Dimensions in mm Mirror Focal distance in incidence plane Focal distance in perpendicular plane Mirror size in the incidence plane Mirror size in perpendicular plane

1 Hyperbolic -1904.4 1075.2 411.0 186.0

2 Ellipsoidal 714.7 1626.1 478.0 338.0

The distance between mirrors, the beam waists position, and the beam size on the mirrors are shown in Table 2. The gyrotron window is the reference plane and the distance between the window and the first mirror is 700 mm. The beam waists in vertical and horizontal planes are not located at the window: as Table 1 shows, in vertical plane the waist is wo=18.14 mm placed 12.3 mm inside the gyrotron, and in horizontal plane wo=23.15 mm placed 179.6 mm outside the gyrotron. After the second mirror, the beam cross-section is circular. Table 2. Distances between mirrors, beam waists position and beam size on the mirrors. All the dimensions are in mm. The distances are positive in the propagation direction

Nr.

1

Distance between mirrors 700.0

2

400.0

3 4 5 6 7 8 9 10 P

3188.4 800.0 3188.4 800.0 3988.4 1249.0 2020.0 1535.0 272.0

w0in

18.14 23.15 48.0 18.0 59.8 59.8 59.8 59.8 59.8 83.9 27.6 30.1 9.5

Distance w0inmirror

712.3 520.4 1861.7 831.1 1196.1 1993.5 1194.9 1992.4 1996.0 729.4 777.4 711.8

wmirror

w0out

72.7 46.5 84.5

48.0 18.0 59.8

Distance w0outmirror -1461.7 -431.1 1992.3

69.7 84.6 69.7 84.5 84.6 85.3 57.6 52.0

59.8 59.8 59.8 59.8 83.9 27.6 30.1 9.5

-1193.5 1993.5 -1192.4 1992.4 519.6 1242.6 823.2 272.0

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In general, to heat the plasmas by EC waves at the second harmonic, an elliptical polarization is required. Since the output radiation of the gyrotron has a linear polarization, it is necessary to incorporate polarizers for choosing the optimal polarization. Two corrugated mirrors, an elliptical polarizer, and a twister are set in positions 3 and 5. The first receives the required elliptical polarization and the second one rotates the polarization plane. To avoid arcing at high-power level, the corrugations have a sinusoidal shape. This groove shape is very important in determining the polarizer’s performance. The groove profile of each mirror is given in Table 3. Table 3. Groove shape. Dimensions in mm

Polarizer Elliptical polarizer (3) Twister (5)

Amplitude 0.738 1.065

Period 3.381 3.381

It is very important to be aware of the power being delivered into the plasma in each discharge. To measure a fraction of the forward and reverse power, two mirrors with an integrated directional coupler have been designed. One of these mirrors is installed at the beginning of the line to measure the output power from the gyrotron. The other mirror, the 9th, i.e. the nearest mirror to the vacuum vessel, measures the power at the end of the line. Thus, the transmission losses can be estimated. In Figure 2, a schematic drawing of the structure can be seen.

T=1.5 mm

Mirror surface

Array of holes

Rectangular waveguide

a=3.98 mm

a=4.78 mm WR-19 Figure 2. Schematic drawing of the mirror with coupling holes.

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A small amount of the microwave power impinging on the mirror is coupled into a rectangular waveguide. The width of the rectangular waveguide is chosen so that the propagation constant is equal to the wave vector for the incidence angle [6]. Using a taper, the dimension is increased until it reaches the standard WR-19. To improve the radiation pattern, i.e. to get low side lobes and a narrow antenna pattern, the diameter of the holes is varied to produce a truncated Gaussian taper of the coupling efficiency. Owing to the symmetric design the device works as bi-directional coupler, i.e. it is also possible to detect and measure the radiation reflected from the plasma. Once calibrated, the power during each shot can be measured. Calorimetric measurements with a cylindrical water load are also carried out in both lines. With a movable mirror placed after the second mirror and with an additional fixed mirror, the beam is diverted to the load. In Figure 3, the position of the load and the mirrors are shown. The load is 2 m long and its internal diameter is 80 mm. The beam waist diameter at the aperture is 26.3 mm. In a single pulse operation, the maximum gyrotron pulse length is 100 ms. T o co n trol u nit

W ater lo ad

G yro tro n

Figure 3. Cylindrical water load and movable mirror.

The losses along the first transmission line are quite reasonable-approximately 8%, and the beam distortion is negligible. Table 4 shows the second transmission line has 10 mirrors and includes a movable mirror inside the vacuum vessel. The power is launched through the lateral port A6. The beam is focused at plasma center and in the absence of any plasma, the waist is about 9.5 mm, as in QTL1. The polarization is linear along the line and the polarization plane can be changed by means of the first corrugated mirror.

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Table 4. Parameters of the second line. All values are given in mm

Distance between Nr mirrors 1 2 3 4 5 6 7 8 9 10

700 400 4200 400 4200 400 4200 2865 3000 1535

Mirror Mirror size Curvature Curvature size in in radius in radius in vertical horizontal vertical horizontal plane plane plane plane 329 172 f f 294 376 1682 1430 527 304 4383 f 462 360 1730 f 397 348 1781 f 460 296 4060 f 281 432 1515 2469 456 323 2821 1301 261 185 1965 982 188 168 504 393

wo_vert wo_hor 18.08 43.0 45.41

25.03 38.0 35.8 41.6

45.6 28.5 39.9 30.2 9.5

26.2 40.3 29.3 9.5

The layout of Mirror 10 inside the vacuum vessel in the QTL1 sector is shown in Figure 4. In QTL2, the mirror is located in the upper port due to the helical axis of the TJ-II plasmas. The parameters of both internal mirrors are identical and at a fixed launching angle, both beams have the same waist (9.5 mm) on the magnetic axis. The launching angle can be changed in both toroidal and poloidal directions with a flexibility of M=r20º in the toroidal direction, and 0º
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Figure 4. Layout of the last mirror inside the vacuum vessel in the QTL1 sector.

It is necessary to verify the design of the mirrors, before the installation of the line, so low power tests to measure the beam propagation characteristics were performed. A corrugated horn antenna was designed to simulate the output radiation from the gyrotron. It radiates a Gaussian beam (99% coupling efficiency with Gaussian beam mode) with a beam waist of 18 mm [7]. To measure the wave beam parameters along QTL1 [8], a low power mm-wave network analyser was used at a fixed frequency of 53.2 GHz. The analyser delivers a voltage signal proportional to the power (in dB), which is read by a PC. At the same time, the PC drives the motors of a xy-scanner, which allows the receiving antenna to move along two axes transversal to the propagation direction. The measurements were carried out in the Laboratory of the Insitute für Plasmafosrchung (IPF) of Stuttgart University (Germany). The mirrors were placed at approximately the same distances as in the actual transmission line. The beam pattern was measured at different distances from the mirrors to reconstruct the beam propagation. The measured beam patterns were in agreement with the parameters calculated in the paraxial optics approximation. In all cases, the beam waist is

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varied in accordance with the focus length of the mirrors. In Figures 5 and 6, some of the results are presented as an example.

200

90,0

150

150

80,0

100 Y (mm) 50

70,0

100

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0

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-200 -200 -150 -100 -50 0 50 100 150 200 X (mm)

-150 -150

-100

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0 50 X (mm)

100

150

Figure 5. Power distribution and cross-polarization in a cross-section (3730 mm) after 2nd mirror.

0

0

dB

dB

-5

-5

-10

-10

-15

-15

-20

-20

Teor. Exp. d=1920 mm Horizontal

-25 -30 -200

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0 mm

50

Teor. Exp. d=1920mm Vertical

-25

100

150

200

-30 -150

-100

-50

0 mm

50

100

150

Figure 6. Cross-section in horizontal and vertical planes. Comparison between theoretical calculations and measurements Gaussian efficiency: 97%.

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The wave beam parameters along QTL2 were measured at a lowpower level in E- and H-planes point by point with a microwave probe (open-ended standard waveguide) at CIEMAT. In Figure 7, the power distribution after the couple of first and second mirrors at different distances from the second mirror is shown as an example. The beam shape is Gaussian and the calculated and measured beam widths along the line are in agreement with each other.

E-plane dB

L = 1.0 m Exp. Calc.

-5

L = 2.7 m

L = 1.8 m

dB

0

dB

0

Exp. Calc.

-5

-10

-10

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-5

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-10

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0 50 Y , mm

100 150

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0 50 Y, mm

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dB

0

L = 1.8 m

-5

-5

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-5

Exp. Calc.

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-10

Exp. Calc.

-15

-100

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0 50 X, mm

100

150

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Exp. Calc.

-15

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-20 -150

L = 2.7 m dB

0

-100

-50

0 50 X, mm

100

150

-150 -100

-50

0 50 X, mm

100

150

Figure 7. Power distribution across the wave beam after the couple of first and second mirrors at different distances from the second mirror.

The final tests were made at high power level, with mirrors in their fixed position, in the TJ-II experimental hall. A special device (MED-2) was designed and fabricated at General Physics Institute and was tested at CIEMAT. The MED-2 can measure the microwave power distribution at the high-power level (>100 kW) in the K frequency band. The main element of

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the device is a tiny absorbing head with the thermal resistor, namely, bolometer. To measure the distribution, a set of 29 of these bolometers are mounted on a target. Two types of targets can be used: a linear target and a cross one. The cross target allows to measure the distribution along two axes simultaneously while the linear target is able to measure broader beams. Both targets can be rotated around the beam axis. The dimensions of the cross target are 9x9 cm2 and its spatial resolution is 6 mm. In a single pulse, the 27 cm linear target can measure the power distribution with the resolution of 9 mm in one plane. The dummy load is put behind the targets in order to reduce a microwave stray radiation around the bolometers. Due to the possibility of arcing, the microwave power density on the bolometers should not exceed 30 kW/cm2. The noise in the measuring circuit mostly determines the sensitivity of the MED-2 device. In terms of the noise level, the minimum microwave power density that the bolometers can distinguish is about 100 W/cm2. The targets were placed at different cross-sections along the QTL1 and the QTL2 [9]. The data were collected in 3 pulses in each position. The gyrotron power was 300kW and the pulse length 5ms. As an example, Figure 8 shows the power distribution in front of TJ-II window (125 mm) in the vertical plane and in the horizontal plane.

dB 0

Exp. Theor.

-5

-10

-15

-15

0 50 mm

100 150

Theor.

-5

-10

-20 -150 -100 -50

Exp.

dB 0

-20 -150 -100

-50

0

mm

50

100

150

Figure 8. Power distribution in vertical and horizontal planes in front of the TJ-II window for QTL1.

3. QUASI-OPTICAL TRANSMISSION LINES AT GPI The mirror transmission lines of the L-2M stellarator (R = 1 m, ap = 11 cm, Bo = 1.35 T) have been successfully used for carrying out ECRH experiments since 1982 [10.11]. It is necessary to remark that, with time, the old lines were upgraded according to the needs of new experiments [12] and

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only the actual versions of the quasi-optical transmission lines are presented in this paper. One mirror and one hybrid line are in operation now on the L2M stellarator to transmit the microwave high power from the gyrotrons to the plasma. The ECRH experiments in L-2M are carried out with the extraordinary waves at the second harmonic of the electron gyrofrequency Ȧ0=2Ȧhe. Two GYCOM gyrotrons (BRIDDER-1) at f=75GHz, with Gaussian output radiation deliver 300 kW each. Due to some limitations in the operation of the high voltage power supply, only one of the gyrotrons with a pulse duration up to 20 ms, or both gyrotrons with the pulse duration about 10-12 ms and total launched power of approximately 400 kW can be used in the present experiments. One of the transmission lines consists of four cylindrical mirrors [13]. The layout and the spatial parameters of this quasi-optical transmission line is shown in Figure 9.

Figure 9. Scheme and distances of the mirrors of the quasi-optical transmission line.

The microwave power is launched into plasma from the low magnetic field side through the side port (its diameter is 86 mm) with linear polarization at the L-2M window. The electric vector of the output gyrotron beam lies in the horizontal plane and with the first couple of mirrors, the plane of polarization is rotated 90 degrees so that the wave electric vector is perpendicular to the magnetic field on the L-2M plasma axis. The launched beam is focused on the magnetic axis in a spot of 40 mm. There is a possibility to change the launching angle within ±3 degrees in the poloidal plane, for instance, to get maximum absorption in a vicinity of the saddle

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point. The dimensions of mirrors are 250x350 mm2 and their curvature radii are in the range of (0.9 – 2) m. A thin dielectric film as a beam splitter and two horn antennas are used for monitoring the launching and reflected power (see Figure 9). The estimated reflection from the film is approximately 10-6. The other transmission line is a hybrid line. It consists of 5 mirrors and one piece of oversized stainless steel waveguide with copper coating on its internal surface (the waveguide internal diameter is 70 mm). The layout of the transmission line is shown in Figure 10.

Waveguide Ø70mm, l=2140mm

Mirror 1,2

1000

Mirror 4,5 660

750

Gyrotron Stand

Mirror 3

Distance between mirrors 1&2 and 4&5 1000mm

Figure 10. Layout of the mirrors and the oversized waveguide and main parameters of the transmission line

The parameters of the oversized waveguide part are presented in the Table 5. Table 5. Parameters of waveguide

Waveguide length Waveguide diameter Distance between centre of 5th mirror and waveguide

2140 mm 70 mm

50 mm

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Á. Fernández, et. al.

To rotate the plane of polarization 90 degrees, and to get the right polarization inside the L-2M vessel, the spatial layout of the first two mirrors is the same as used in the first line. The 5th mirror focuses the Gaussian beam on the aperture of the waveguide in a space of 46 mm with a plane phase front. Mainly, two modes (TE11 + 1/4 TM11) are calculated to propagate along the waveguide. The length of the waveguide piece is chosen to be equal to the wavelength of the TE11 and TM11 beat wave so that the output wave distribution is to be the same as the input one. The diameter of the launched beam at the plasma edge is greater than that from the first transmission line, and it is about 60-65 mm. It should be noted that once aligned, the transmission lines operate at a high power level without any arcing. The main features of both transmission lines are summarized as follows: - The mirrors are moveable and can be aligned with special gears. - All elements of the quasi-optical lines are placed inside shielding boxes. - The microwave power is measured by a calorimeter. - To monitor the launching power and the power reflected from the plasma, a thin dielectric film and two receiving antennas are installed at the output of the transmission lines. - The transmission coefficient of the mirror line is about 0.9. The losses are mostly due to the side lobes in the output wave pattern of the gyrotrons. - Two cylindrical mirrors are used to change the plane of the linear electric field polarization. - The length of each transmission line is near 4-6 meters. Both types of the presented QTLs have been used for a long time in the ECRH experiments at L-2M. During their exploitation, no problems connected with breakdowns, mechanical deformation or alignment procedures occurred.

4.

CONCLUSIONS

The quasi-optical techniques in the TJ-II and in the L-2M stellarators demonstrated that they are suitable for designing transmission lines for ECRH and ECCD experiments. The mirror and hybrid lines show good performance and high reliability in these experiments. In the TJ-II stellarator, the internal mirrors focus the beam and its movements, allow on- and off-axis heating, as well as ECCD experiments with both lines. The appropriate wave polarization can be obtained with

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corrugated polarizers. The power delivered to the vacuum vessel and the reflected power are measured. In the L-2M, the transmission lines have been used to ECRH experiments since 1982 with good results. The transmission coefficients of the lines of both stellarators are each greater than 0.9.

5.

REFERENCES

[1] V.Erckmann et al. “20 years of ECRH at W7-A and W7-AS”. Nuclear Fusion 43 (2003) 1313-1323 [2] E.Westerhof et al. “Electron cyclotron resonance heating on TEXTOR”. Nuclear Fusion 43 (2003) 1371-1383. [3] C.Alejaldre et al. “First plasmas in TJ-II stellarator”. Plasma Physics and Controlled Fusion. Vol.41, A539-A548. 1999. [4] A.Fernández et al.“Quasi-optical transmission lines for ECRH at TJ-II stellarator”. International Journal of Infrared and Millimeter Waves. Vol.21. No.12. December 2000.1945-1958. [5] A.Fernández et al. “Design of the upgraded quasi-optical transmission line”. International Journal of Infrared and Millimeter Waves. Vol.22. No.5. May 2001.649-660. [6] L.Empacher et al. ‘New Developments and Tests of High Power Transmission Components for ECRH on ASDEX-Upgrade and W7-AS’. Proceedings of the 20th International Conference on Infrared and Millimeter Waves. December 1995. Florida (USA). pp. 473-474 [7] J.Teniente et al. “Corrugated horn antenna for low-power testing of the quasi-optical transmission lines at TJ-II stellarator”. International Journal of Infrared and Millimeter Waves. Vol.20. No.10. October 1999.1757-1769. [8] A.Fernández et al. “Cold tests of the upgraded TJ-II transmission line”. Proceedings of the 26th International Conference of Infrared and Millimeter Waves. Toulouse. France. 2001. [9] K.Likin et al. “Wave beam parameters into the TJ-II transmission lines”. Proceedings of the 24th International Conference of Infrared and Millimeter Waves. Monterey. USA. 1999. [10] Andryukhina E. et al. Sov.J.Pis’ma v ZhETF, v40, n9, p377 (1984). [11] Batanov G. et al. Sov.J.Fizika Plasmy, v12, n6, p762 (1986). [12] G.M.Batanov, et.al. Power transmission lines used for plasma heating in L-2 stellarator. Preprint IOFAN ʋ 35 (1991), Moscow [13] K.M.Likin Absorption efficiency of electromagnetic waves into “Liven-2” stellarator at the electron cyclotron resonance. Ph.D. Thesis, IOFAN, Moscow (1994)

SUPERRADIANCE OF INTENSE ELECTRON BUNCHES N. Ginzburg1, M. Yalandin2, S. Korovin3, V. Rostov3, A. Phelps4 1-Institute of Applied Physics, Nizhny Novgorod, Russia; 2-Institute of Electrophysics, Ekaterinburg, Russia; 3-Institute of High-Current Electronics, Tomsk, Russia; 4-Physics Department, Strathclyde University, Glasgow, UK

Abstract:

One of the attractive methods of generating an ultrashort electromagnetic pulse is based on stimulated emission from intense extended electron bunches. Radiation from such bunches may be considered as a classical analogue well known in quantum electronics as Dike's superradiance effect (SR). Superradiance of classical electrons may be associated with different mechanisms of stimulated emission (cyclotron, Cherenkov, bremsstrahlung etc). Different types of SR were recently observed experimentally at millimeter and centimeter wavelength bands. Progress in this research has enabled a new type of millimeter band generator to be created, which is capable of generating unique short (200-300 ps) electromagnetic pulses at super high peak powers exceeding 1 GW.

Key words:

superradiance, intense electron bunch, subnanosecond microwave pulses.

1.

INTRODUCTION

Recently, considerable attention has been devoted to developing new methods of generating intense, ultrashort electromagnetic pulses based on classical analogy of the superradiance (SR) effect that is well known in quantum electronics1. In this process, incoherent emission induces a small macroscopic polarisation in an inverted medium of limited dimensions, which gives rise to the growth of an electric field, and consequently an increasing polarisation in space and time. As shown in2-5 in the classical region SR can be realised for extended electron bunches with space length which essentially exceeds the operating wavelength (otherwise effective traditional spontaneous emission) while at the same time is less or comparable with the interaction length (in contrast with traditional mechanism of stimulated emission of quasi-continuous electron beams which are used extensively in microwave

131 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 131–146. © 2005 Springer. Printed in the Netherlands.

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electronics). Coherent emission from the entire electron ensemble can only occur when a self-bunching mechanism typical for stimulated emission develops. Another natural condition of coherent emission is the mutual influence of different fractions of the electron bunch. In the absence of external feedback such influence can be provided by slippage of the wave with respect to electrons due to a difference between the electron velocity and the electromagnetic wave group velocity. Superradiance of classical electrons can be related to several different mechanisms of stimulated emission: cyclotron, Cherenkov, bremsstrahlung etc. In this paper, we present the basic theoretical description of the above mechanisms. These investigations stimulated the experiments on the observation of SR from intense electron bunches produced by short-pulse high-current accelerators6-14. By now, the progress in these researches has enabled a new type of millimetre wave generator to be created capable of producing unique short (200-300ps) electromagnetic pulses at super high peak powers exceeding 1GW.

2.

CYCLOTRON SUPERRADIANCE IN GROUP SYNCHRONISM CONDITIONS

Cyclotron superradiance is realised in the ensemble of electrons rotating in a magnetic field. The features of cyclotron type of superradiance have most in common with SR in atomic systems because in both cases emission occurs from a system that has discrete quantum levels. Cyclotron SR involves the process of azimuthal self-bunching and subsequent coherent emission in an ensemble of initially unphased excited cyclotron oscillators. The self-bunching mechanism is caused by the dependence of the gyrofrequency on the electron energy like that occurring in conventional cyclotron resonance masers (CRM) with quasi-continuous electron beams. A distinguishing feature of superradiance is that the ensemble of cyclotron oscillators forms an isolated electron bunch (moving or resting), in which in the ideal case each particle has an infinite lifetime. Due to this fact, on the one hand, the SR instability has no threshold and on the other hand, it provides the fundamental pulse character of the process. Cyclotron superradiance can occur in both free space or within waveguides. The most favourable condition for waveguide cyclotron SR is the condition of group synchronism4, when the longitudinal velocity of the electrons V|| is close to the group velocity of the wave:

Superadiance of Intense Electron Bunches

133

V|| | V gr .

(1)

When wave group velocity tends to electron longitudinal velocity (see condition (1)) the mutual influence of different parts of the electron bunch is caused by dispersion expansion of the electromagnetic pulse. In the reference frame K c , moving with the longitudinal electron velocity, the radiation frequency under condition (1) is close to the cut-off frequency of the waveguide mode. In this sense, the group synchronism regime has a number of advantages in common with the interaction regimes in gyrotrons in which the operating mode is also excited at a quasi cut-off frequency. Due to the rather low rate of electromagnetic energy, extraction from the electron bunch in this regime the maximum gain of the SR instability is realized. One more factor is the decrease of sensitivity to the spread in the electron parameters, including the longitudinal bunch dynamics, due to Coulomb repulsion and the differences between the initial electron velocities. It is convenient to analyse cyclotron SR in the commoving reference frame K c where the electron bunch as whole is at rest and radiates isotropically in the r z c directions. The radiation field can be presented in the form G G G E c Re E A ( rA ) Ac( z c,t c ) exp( iZ c t c ) , (2) Here, E A rA is the transverse field profile in the waveguide, Zc is the cut-off frequency, and Ac( z c,t c ) is the slow varying field amplitude. In accordance with the dispersion, the process of electron bunch radiation is described by the system of equations consisting of the parabolic equation for the field amplitude and the motion equations for electrons written for subrelativistic transverse electron velocity E Ac 0 VAc 0 c  1 , namely 2S  w 2 a wa i 2if ( ] c )GJ , J 1 S ³ E  dT 0  2 wW c w] c 0    2 wE   iE  ( E   '  1 ) ia (3) wW c

>

@



exp>i( T 0  r cos T 0 )@, r  1, T 0  >0 ,2S @, a W c 0 0 Wc 0 ˆ Here E  exp( iZc t )( E xc  iE yc ) / E Ac 0 is the normalised electron velocity, a 2eAc mcZc E Ac 30 J m 1 R0 Z c c , ] c z cE Ac 0 Z c c , W c t cE Ac 20 Z c 2 ,

E





' 2( Z Hc  Z c ) Z c E Ac 20 is the detuning of the cyclotron frequency in the commoving frame from the cut-off frequency and G is the parameter proportional to electron current, R0 is injection radius of the hollow electron beam. The function f ( ] c ) describes the axial distribution of the electron

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Ginzburg, Yalandin, Korovin, Rostov, Phelps

density. The initial conditions are written under the assumption that in the initial state the electrons are distributed uniformly in cyclotron rotation phases, aside from small fluctuations assigned by parameter r. 0.010

P

' 

' 

0.005

' 

0.000 0

10

20

30

W

Figure 1. Pulses of cyclotron SR for different parameter ' that characterizes detuning from group synchronism regime.





Temporal evolution of the radiation power P Re a wa* w] for different values of the detuning parameter ' is presented in Fig. 1 for the parameters corresponding to the experimental values6: operating mode TE21, waveguide radius R=0.5cm, beam injection radius R0=0.2cm, pitch factor g E A E|| ~ 1 , total current I=200A, particle energy 200 keV, pulse length b b c J || 7 cm. The radi5ated field has the form of a short pulse with typical duration about several reciprocal gains. The maximum growth rate and maximum pulse amplitude are achieved at the grazing condition ' 0 . The estimated duration of SR pulse amounts to 300 ps for the peak power level of about 8 MW. Detuning from the group synchronism regime leads to the gain and the SR pulse peak power decreasing. The experiments on the observation of cyclotron SR6 were carried out based on the sub-nanosecond high current accelerator RADAN 30315 , which generated a single 200 keV, 200A electron bunch with duration 300-500 ps. The transverse velocity was imparted to the electrons by the kicker (system with strongly inhomogeneous magnetic field). SR pulses were observed in the two regions corresponding to the grazing regime with TE21 and TE11 modes. An oscilloscope trace of the cyclotron SR pulses in group synchronism with TE21 mode is presented in Fig. 2a. In the experiments, the maximal peak power of the 40 GHz SR pulses was 400 kW for a pulse duration of about 400ps (i.e. of the order of 10 cyclotron oscillations). We should emphasise the dramatic reduction of the peak power and gain for the detuning from group synchronism regime by the varying of the guide magnetic field (Fig. 2b). It is connected with the longitudinal dynamics of the

Superadiance of Intense Electron Bunches

135

real electron bunch caused by the Coulomb repulsion and dispersion of the initial electrons’ velocities. In the exact group synchronism regime, when in the moving frame the radiation frequency tends to the cut-off frequency, with waveguide wavelength O c tending to infinity, this results in the longitudinal displacement of the electrons being less significant. As we increase the magnetic field and go away from the cut-off frequency O c falls and the same displacement can strongly reduce the radiation. Practically the entire microwave signal disappeared when the magnetic field detuned from the group synchronism condition. 1.0

a)

P/Pmax

b)

0.8 0.6 0.4

1 ns 0.2

400 kW 0.0 11

12

13

H, kOe

Figure 2. (a) An Oscilloscope trace of cyclotron SR pulse. (b) Experimental dependence of peak power on guide magnetic field.

3.

CHERENKOV SUPERRADIANCE

The Cherenkov SR pulses can be produced by a bunch of electrons moving along rectilinear trajectories in slow wave structures (SWS). Two varieties of Cherenkov SR have been studied. The first one is associated with the interaction with the forward propagating wave under synchronism (4) Z hV||0 . where Z and h are the frequency and longitudinal wave number respectively. Such an interaction can be realized in the dielectric loaded waveguide. The second type of Cherenkov SR studied occurs in the case of interaction with the slow spatial harmonic of the backward wave in periodically corrugated waveguide under synchronism condition (4), where h h0  h , h0 is the longitudinal wave number of the fundamental harmonic, h 2S d , d is the corrugation period. For the both cases the longitudinal component of the electric field of the synchronous wave can be presented in the form E z Re>E A rA A z ,t expiZt  ihz @ ,

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Ginzburg, Yalandin, Korovin, Rostov, Phelps

where E A rA is the transverse profile of synchronous field component,

A z ,t is the slow varied complex amplitude. Under the assumption of a small variation of particles’ velocity the radiation of the electron bunch can be described by the equations 3/ 2 ­° ª wT º ½° iT ® «1  Q ¾ F ] Re a e w] »¼ ° °¯ ¬ ¿ , 1 2S iT wa wa r B F ] f W ³ e dT 0 S 0 wW w]

w 2T w] 2

>

@

(5)

where the upper and lower signs correspond to the interaction with the forward and backward wave, respectively. Here we use the following dimensionless variables ZC( t  z / V||0 ) eAEA rb ZCz , a W , , ] V C 2 J 03V0 mZ0 1 r V||0 / Vgr 0

T Zt  hz is the phase of an individual particle with respect to the field of the synchronous harmonic, V gr is the group velocity of electromagnetic wave,

J0

1  E

1 / 2

||0

,Q

2J 02 C . C

 § eI b Z ¨ ¨ 2 mc 2J 3 0 ©

· ¸ ¸ ¹

1/ 3

,

 2 is the Pierce parameter, Z { 2 E A rb k 2 N is the coupling impedance, N

is the waveguide norm, I b is the electron bunch current, rb is the electron injection radius. The function F ] defines the longitudinal profile of the wave coupling impedance (tapered, for example, by varying the corrugation L

depth). This function is normalised as 1 L ³ F ] d]

1 , where L

ZCl V0

0

is the dimensionless length of the interaction space. The function f ( W ) describes the current pulse profile. Below we assume that electron density is constant ( f W 1, W  >0 ,T @ ) within dimensionless bunch duration Tbunch

Z0 C 1 r V0 / V gr

't b

apart from small initial density perturbations at the system entrance:

Superadiance of Intense Electron Bunches

T]

~

0

137

~

T 0  J cos T 0 , J  1, T 0  >0 , 2S , wT / w]

] 0

0.

(6)

These perturbations initiate the development of SR emission. For uniform SWS: F ] 1 formation of a short superradiance pulse is shown in Fig.3a and Fig.3b for forward and backward wave propagation respectively. This process is caused by electron bunching and slippage of the wave with respect to the electrons due to the difference between the wave group velocity and the electron longitudinal velocity.

Figure 3. Formation of a short superradiance pulse for forward (a) and backward (b) wave propagation.

The distinctive feature of superradiance is the linear dependence of peak power on the square of the number of radiating particles1, 2. For backward wave interaction the dependence of the SR pulse amplitude on the electron pulse duration is shown in Fig.4 for the constant beam current, Q 0.2 . The peak amplitude is proportional to the electron pulse duration until this duration is rather short T<6. It corresponds to a square law dependence of the radiation power on the total number of electrons in the bunch. Saturation of the growth of the peak amplitude occurs when the electron pulse duration exceeds a certain value T>6, and electron pulse becomes too long to provide coherent radiation from all particles over the pulse length. A similar dependence takes place for SR in the forward wave. For a rather long electron bunch, the “multi-spikes” generation regime is realised because the various parts of a bunch radiate almost independently. In the case of the backward wave interaction, such a regime is similar to the self-modulation regime in the BWO driven by the quasi-stationary electron beam16. In the case of interaction with the forward wave such a regime is refereed to as self-amplified spontaneous emission (SASE)2 .

138

Ginzburg, Yalandin, Korovin, Rostov, Phelps 4

|a|

2

T bunch

0

0

2

4

6

8

Figure 4. Dependence of SR pulse amplitude on the electron pulse duration for the constant beam current.

It is important to note that in certain conditions the SR pulse peak power can substantially exceed the power of the electron beam because a short SR pulse that forms in the initial stage of the interaction can accumulate energy from different fractions of the extended electron bunch. This fact does not contradict the energy conservation law because the SR pulse total energy is still smaller than the total beam kinetic energy. Let us introduce the power conversion factor as the ratio of the SR pulse peak power to the electron beam power:

Ȁ

J 0  1

2

Q a max

. 8 In the case of “forward” Cherenkov SR in the uniform SWS, the conversion coefficient can essentially exceed a factor of one if the interaction distance is rather long L !! 1 and normalised electron bunch duration: Tbunch | L . The evolution of SR pulse in this case is shown in Fig.5. After formation of a SR pulse at the initial stage of interaction, its trailing edge is fed by the subsequent fresh electron fractions with small (noise level) modulation. In the given case, conversion factor achieves 3 and can increase further with increasing interaction distance. In the case of “backward” Cherenkov SR in a uniform SWS the conversion factor K<1 for ultra-relativistic energy of electrons ( J 0 !! 1 ). In the range of moderate electron energies ~300-500 keV a conversion factor can slightly exceed unity K~1.2 and K reaches a maximum value ~1.4 for non-relativistic energies7.

J0

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139

Figure 5. Formation of SR pulse with peak power exceeding the electron bunch power (K=3) in the case of forward emission in the uniform SWS.

Figure 6. (a) Formation of SR pulse with peak power exceeding the electron bunch power (K=4) in the case of backward emission in the non-uniform SWS. (b) Amplitude of synchronous space harmonic.

In order for the backward wave interaction to get a substantial excess of power conversion factor over unity, it is necessary to use the uniform SWS with variable coupling impedance. It is beneficial to realise a situation where despite the linearly growing energy and power of the microwave pulse as it propagates through the system, the electric field strength in the synchronous harmonic acting upon the electrons is a constant. The impedance profile satisfying the above condition may be presented in the form7

F ]

a0 ­ ° 1/ 2 ] º °ª ® « p0   p0  1 » ]0 ¼ °¬ ° a0 ¯

if

0 d] d]0

, if

]0 d] d L

(7)

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Ginzburg, Yalandin, Korovin, Rostov, Phelps

where the parameter p0 characterises relative impedance variation. The 2

evolution of the radiation power aW ,] in the case of a tapered coupling impedance for p0

90 and ] 0

0.93 L is presented in Fig.6a. In this

situation, the amplitude of the synchronous space harmonic F ] aW ,] is practically constant (see Fig.6b). In the considered situation, a conversion factor K of 4 may be achieved. Thus, the use of a non-uniform profile allows the SR pulse peak power to be increased essentially.

4.

EXPERIMENTAL OBSERVATION OF THE CHERENKOV SUPERRADIANCE

Experiments with both forward and backward mechanisms of Cherenkov SR have now been carried out. In the experiments with forward emission, dielectric loaded waveguides were used. In these experiments, SR pulses with power about 1MW and duration ~300ps were generated8. SR pulses with much higher peak power were achieved for the “backward” mechanism of SR in corrugated waveguides. In this section, we briefly discuss these experiments.

4.1. SR Experiments with Uniform Slow Wave System In the first experiments the uniform SWS in the form of periodically corrugated circular waveguide was used with corrugation period 0.35 cm, depth 0.075 cm and mean diameter D/O = 0.89,10. After reflection from cutoff, narrowing on the cathode side of the SWS a SR pulse propagates in the forward direction and radiated into the outside space via a horn antenna. To decrease the parasitic reflection of the SR pulse at the output and abrupt perturbation of the beam at the SWS input, the edges of SWS were equipped with several corrugation periods of adiabatically decreasing depth. High current electron bunches were transported through the interaction space in a longitudinal guiding magnetic field created either by a pulsed solenoid ( BZ ~ 2.5  5 T ) or by a superconducting magnet ( BZ max ~ 8.5 T ). The dependence of the SR pulse peak power on the value of the guide magnetic field is presented in Fig. 7. Similar to the traditional BWO the fall in the power near the magnetic field value ~3 T is caused by cyclotron absorption when the cyclotron resonance condition for the fundamental waveharmonic is

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matched. The maximal peak power of the SR pulse was obtained for a value of the magnetic field exceeding the cyclotron resonance value. A typical oscilloscope trace of the Ka-band microwave signal is presented in Fig. 8. The observed microwave pulses had a duration of about 300 ps and a rise time of 200 ps. Frequency measurements using a set of cut-off waveguide filters showed that the main peak had a central frequency of ~38 GHz with relative radiation spectrum bandwidth of about 5%. The radiation pattern corresponded to the excitation of the TM01 mode. The absolute peak power was calculated by integrating the signal from the detector over its radial position. For the electron bunch with energy of ~ 290 keV and peak current of about 2kA, the peak power was about 150 MW in the single pulse regime10. For the same SWS, operation in the repetition rate mode at 25 Hz was realized with a peak power of the SR pulses ~60 MW.

P/Pmax

H, T 0.0

2.0

4.0

150 MW

1 ns

6.0

Figure 7. Dependence of SR pulse peak power on value of guide magnetic field. Figure 8. Typical oscilloscope trace of the Ka-band microwave signal in uniform SWS.

Alongside the investigation of the generation of subnanosecond SR pulses at Ka-band, similar experiments were performed at W-band (75 GHz) and G-band (150 GHz)10. The W-band SR pulses possessed a sharp leading edge <120 ps and peak power about 10-15 MW. In the G-band, the measured pulse rise time did not exceed 75 ps, which was the limit of the transient characteristic of the 5 GHz oscilloscope. The estimated W-band SR pulse peak power was not less then 5-10 MW. To increase SR pulse peak power in the following experiments in Ka-band advanced SWS have been used11. Obviously, an important factor limiting the peak power is dispersion spread of the SR pulse during its propagation across the SWS in backward and forward directions. To diminish the influence of this factor a slightly oversized SWS with D/O = 1.3 and a resonant reflector for electromagnetic pulse extraction have been implemented. In the experiments performed at the RADAN-303BP with an electron current of 2.1

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kA and an electron energy of 290 keV in a high magnetic field (5.5 T), using the new advanced SWS allowed 200–250 ps microwave pulses to be obtained with a maximum peak power of 420 MW. In a low magnetic field (~ 2 T), the peak power decreased to 240–280 MW.

4.2. SR Experiments with Non-Uniform Slow Wave System. Production of SR Pulse with Peak Power Exceeding the Electron Beam Power The next step was the use of non-uniform SWS with coupling impedance that increased towards the collector end7,12-14. The geometry of SWS was optimised using a one-dimensional time-dependent model and the KARAT code. The first experiments using non-uniform SWS were performed in the Xband7,12. As a source of electrons, the accelerator based on the SINUS-150 compact generator was used. It provided a 4 ns electron bunch with current of 2.6 kA and particle energy of 330 keV. The SWS had a length of L=36 cm (~12O) with a corrugation period of 1.3 cm. Thus, the maximal power of the electron bunch achieved 0.85 GW. The strength of the magnetic field, when generated by a pulsed solenoid, reached 3 T. The pulse energy achieved was ~0.6 J. The power conversion coefficient was estimated to be 1.4 with a maximum microwave power of 1.2 GW. The next experiment with maximum power conversion achievement (1.8) was performed by using the SINUS-200 compact generator (pulse width 9 ns, voltage up to 330 kV, beam current 5 kA)7. The SWS had the length of L=65 cm (~20O). The amplitude of the corrugation increased from 0.1 to 0.25 cm along the system (which corresponded to a variation of the coupling impedance from ~0.3 ȍ up to ~2 ȍ). The waveforms of the vacuum diode voltage and microwave detector signal are given in Fig.9. After reconstruction of the signal shape taking into account the nonlinearity of the detector, the following parameters of the microwave pulse were obtained: central frequency 9.3 GHz and peak power ~3 GW with a 0.65 ns width.

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143

330 kW

U P

1.2 GW

2 ns / div

Figure 9. The waveforms of the vacuum diode voltage and microwave detector signal for Xband SR in non-uniform SWS.

Similar experiments were carried out in Ka-band13. The non-uniform SWS with increasing corrugation depth had a length of about 12 cm (~ 14O) and a mean diameter ~1.3O. The SWS was optimized numerically using the axially symmetric version of the KARAT code. The simulation included the formation of the electron bunch in the coaxial vacuum diode. The geometry of the experimental set up used in the simulation is presented in Fig.10a. In the simulation, it has been demonstrated that in a strong magnetic field of up to 6.5 T, it is possible to achieve a conversion factor of about 1.7. Thus, a 2.5 kA, 290 keV electron bunch with a power ~700 MW can emit a SR pulse with a peak power of over 1 GW and duration less than 300 ps. (Fig.10b). The above results were obtained experimentally (Fig.11) based on the RADAN 303BP accelerator13.

Figure 10. KARAT simulation of Ka-band SR in non-uniform SWS. (a) Geometry of interaction space, (b) SR pulse.

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Figure 11. Oscilloscope trace of 1 GW 300 ps (FWHM) Ka band SR pulse.

The PIC-simulations demonstrated that in the low guiding magnetic field ~2T (less than cyclotron resonance value), the peak power of SR pulse generated in non-uniform SWS should be about 400MW. This regime has been used in the experiment for production of SR pulses at high repetition rate14. These experiments were performed in the Ka-band exploiting a hybrid high-voltage modulator17 consisting of a SM-3NS nanosecond driver and a sub-nanosecond hydrogen peaking switch. The driver had several stages of energy compression based on solid-state opening switches. The experimental set up is presented in Fig.12 together with a typical microwave signal recorded by the 6 GHz stroboscopic oscilloscope. This waveform was obtained for a 1 kHz pulse repetition frequency. Processing the detector signal gave the pulse width equal to 250 ps with a 190 ps rise-time. The microwave energy measured by a calorimeteric method was 65 mJ per pulse, which corresponds to a peak power of 260 MW. The average microwave power over the train of pulses was 200 W at a pulse repetition frequency of 3.5 kHz. In a few series with the electron beam parameters increased to the limit allowed by the modulator, microwave pulses with 80 mJ of energy and 300 MW of peak power were produced.

Figure 12. Experimental set up for production of Ka-band SR pulses with repetition frequency 3.5 kHz based on hybrid modulator and typical microwave signal recorded by the 6 GHz stroboscopic oscilloscope.

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5.

145

SUMMARY

Several different mechanisms of superradiance from intense short electron bunches have been studied both theoretically and experimentally. The progress in these researches has enabled a new type of microwave generator to be created capable of producing unique short (200-300 ps electromagnetic pulses at Ka-band and 600-800 ps at X-band) at super high absolute peak powers exceeding 1 GW. The effect of spatial accumulation of microwave energy in lengthy slow-wave structures with non-uniform coupling has been used to generate SR pulses with peak power substantially surpassing the peak power of the driving beams. Another important achievement is the realization of a source of SR pulses operating with high repetition frequency. At Ka-band, the average microwave power over the train of pulses was 200 W, at a pulse repetition frequency of 3.5 kHz. These new sources of short HPM pulses may find application in novel radar systems with high-spatial resolution, in electromagnetic compatibility testing, as well as in biomedical experiments.

6.

ACKNOWLEDGMENTS

The authors thank all of their many colleagues for helpful discussions and for their contributions as co-authors in the original publications that are listed below in the References. This work was supported by the Russian Fund for Fundamental Research and by the UK EPSRC and MoD.

7.

REFERENCES

1. J.C.MacGillivray, M.S.Feld Theory of superradiance in an extended, optically thick medium. Phys. Rev. A, 14, 1169-80 (1976). 2. R.Bonifacio, N.Piovella, B.W.J.McNeil Superradiant evolution of radiation pulses in a freeelectron laser. Phys. Rev. A, 44, 3441-52 (1991) 3. N.S. Ginzburg Superradiance effect from bunches of relativistic electron-oscillators. Sov. Tech. Phys. Lett., 14, 197-201 (1988) 4. N.S.Ginzburg, I.V.Zotova, A.S.Sergeev Cyclotron superradiance of moving electron bunch in the group synchronism condition. Pis’ma v ZhETF, 60(7), 501-506 (1994) 5. Ginzburg N.S., Novozhilova Yu.V., Sergeev A.S. Generation of short electromagnetic pulses by electron bunch in BWO-like slow wave structure. Sov.Tech.Phys.Lett., 22,35964 (1996). 6. N.S.Ginzburg, A.S.Sergeev, I.V.Zotova, A.D.R.Phelps, A.W.Cross, V.G.Shpak, M.I.Yalandin, S.A.Shunailov, M.R.Ulmaskulov Experimental observation of cyclotron superradiance under group synchronism conditions. Phys.Rev.Lett., 78, 2365-69 (1997)

146 7.

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A.A.Elthaninov, S.D.Korovin, V.V.Rostov, I.V.Pegel, G.A.Mesyats, S.N.Rukin, V.G.Shpak, M.I.Yalandin, N.S.Ginzburg Production of short microwave pulses with a peak power exceeding the driving electron beam power. Laser and Particle Beams, 21, 187-196 (2003) 8. N.S.Ginzburg, A.S.Sergeev, I.V.Zotova, Yu.V.Novozhilova, R.M.Rozental, A.D.R.Phelps, A.W.Cross, V.G.Shpak, M.I.Yalandin, S.A.Shunailov, M.R.Ulmaskulov Experimental observation of Cherenkov superradiance from an intense electron bunch. Opt. Comm., 175 (1-3), 139-146 (2000) 9. N.S.Ginzburg, I.V.Zotova, Yu.V.Novozhilova, A.S.Sergeev, N.Yu.Peskov, A.D.R.Phelps, A.W.Cross, K.Ronald, G.Shpak, M.I.Yalandin, S.A.Shunailov, M.R.Ulmaskulov, V.P.Tarakanov Generation of powerful subnanosecond microwave pulses by intense electron bunches moving in a periodic backward wave structure in the superradiant regime. Phys.Rev. E, 60(3), 3297-3304 (1999) 10.N.S.Ginzburg, I.V.Zotova, A.S.Sergeev, A.D.R.Phelps, A.W.Cross, V.G.Shpak, S.A. Shunailov, M.R.Ulmaskulov, M.I.Yalandin, V.P.Tarakanov Generation of ultrasoft microwave pulses based on cyclotron superradiance. IEEE Plasma Sci., 27, 462-70 (1999), 11.S.D.Korovin, G.A.Mesyats, V.V.Rostov, M.R.Ulmaskulov, K.A.Sharypov, V.G.Shpak, S.A.Shunailov, M.I.Yalandin High effective generation of subnanosecond microwave pulses in the ralativistic BWO. Pis’ma v ZhTF, 28 (2), 81-87 (2002) 12.A.A.Elthaninov, S.D.Korovin, V.V.Rostov, I.V.Pegel, G.A.Mesyats, M.I.Yalandin, N.S.Ginzburg Cherenkov superradiance with peak power exceeding the power of electron beam. Pis’ma v ZhETF, 77(6), 314-318 (2003) 13. S.D.Korovin, G.A.Mesyats, V.V.Rostov, M.R.Ulmaskulov, K.A.Sharypov, V.G.Shpak, S.A.Shunailov, M.I.Yalandin Subnanosecond source of microwave pulses of 38 GHz with peak power of 1 GW. Pis’ma v ZhTF, 30 (3), 68-74 (2004) 14. D.M.Grishin, V.P.Gubanov, S.D.Korovin, S.K.Lubutin, G.A.Mesyats, A.V.Nikofirov, V.V.Rostov, S.N.Rukin, B.G.Slovikovsky, K.A.Sharypov, V.G.Shpak, S.A.Shunailov, M.I.Yalandin Generation of powerful subnanosecond microwave pulses of 38 GHz with repetition frequency 3500 Hz. Pis’ma v ZhTF, 28 (19), 24-31 (2002) 15. G.A.Mesyats, V.G.Shpak, S.A.Shunailov, M.I.Yalandin Desk-top subnanosecond pulser research, development and applications Proceedings of the SPIE International Symposium of Intense Microwave pulses vol.2154, Los Angeles, CA, 1994, pp. 264-268 16. N.S.Ginzburg, S.P.Kuznetsov, T.N.Fedoseeva Theory of transit processes in relativistic BWO. Izv. VUZov, Radiofizika, 21(7), 1037-52 (1978. 17. M.I.Yalandin, S.K.Lubutin, S.N.Rukin, B.G.Slovikovsky, M.R.Ulmaskulov, V.G.Shpak, S.A.Shunailov Generation of high voltage subnanosecond pulses with peak power up to 300 MW with repetition frequency 2 kHz. Pis’ma v ZhTF, 27 (1), 81-88 (2001).

TRANSMISSION LINE COMPONENTS FOR A FUTURE MILLIMETER-WAVE HIGHGRADIENT LINEAR ACCELERATOR* J. L. Hirshfield,1,3 A. A. Bogdashov,2 A. V. Chirkov,2 G. G. Denisov,1,2 A. S. Fix,2 S. V. Kuzikov,1,2 M. A. LaPointe,3 A. G. Litvak,2 D. A. Lukovnikov,2 V. I. Malygin,2 O. A. Nezhevenko,1 M. I. Petelin,1,2 Yu. V. Rodin,2 G. V. Serdobintsev,4 M. Y. Shmelyov,2 V. P. Yakovlev1 1

Omega-P, Inc., New Haven, CT 06511 Institute of Applied Physics, RAS, Nizhny Novgorod, 603600 Russia 3 Department of Physics, Yale University, New Haven, CT 06511 4 Budker Institute of Nuclear Physics, Novosibirsk, 630090 Russia 2

Abstract

1.

The motivation for developing millimeter (mm)-wave high-power components stems from the need to extend understanding of high RF field limits in accelerator structures, and thereby to open the possibility for development of RF technology for a future multi-TeV linear collider. A summary is given of preliminary results from the Yale/Omega-P 34-GHz magnicon, the first mm-wave accelerator-class amplifier whose existence makes possible extensions to high frequency of basic experimental studies of RF breakdown and surface fatigue. Such studies can support development of high-gradient structures for the CERN two-beam accelerator CLIC or alternate advanced structures. An overview is given of high-power mm-wave transmission line components now being developed for this application.

INTRODUCTION

It has been long recognized that rf breakdown [1] and rf-induced surface fatigue [2] will limit the magnitude of accelerating gradient and lifetime that can be achieved in room-temperature metal structures, and that rf surface magnetic field establishes the gradient limit in super-conducting structures [3]. For room-temperature (“warm”) structures operating at 11.424 GHz, operation with an accelerating gradient up to about 65 MV/m has been achieved (with < 10 breakdown events per hour), while for superconducting ________________ *Supported by US Department of Energy, Office of High Energy Physics.

147 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 147–163. © 2005 Springer. Printed in the Netherlands.

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(“cold”) structures operating at 1.3 GHz, the corresponding gradient is about 35 MV/m. But risks inherent in the warm option and its apparent complexity were evidently of sufficient concern to lead an international panel convened by ICFA to recommend in August 2004 that hereafter development efforts for a project to develop the International Linear Collider (ILC) be focused on the cold option [4]. The goal of this effort is to be the evolution of a design for a ∼40-km long 0.5 – 1.0 TeV collider, using 1.3 GHz RF technology. This design is to be implemented in two stages, 0.5 TeV at first, and upgrade towards 1.0 TeV later on. No provision for up-grade beyond 1.0 TeV is contemplated for ILC. The only widely-recognized approach to allow an energy reach beyond 1 TeV is the two-beam concept CLIC [5]. One reason the two-beam approach was originally conceived was that no accelerator-class high-power mm-wave amplifier existed that would allow a design based on external injection of rf power to drive the accelerator. But now that the means for production of sufficient drive power has been demonstrated using the CLIC drive beam (albeit in short pulses), it is recognized that stand-alone rf power sources are still needed for development of CLIC structures and components, and for their rf conditioning. Now, with emergence of a mm-wave 34-GHz magnicon amplifier [6] designed for 45 MW pulsed output in repetitive 1.0 µsec pulses, the candidate to fulfill that role is at hand. In fact, a design is evolving at Omega-P for a similar 50 MW, 30 GHz version; this tube, together with a quasi-optical Ka-band passive rf pulse compressor also under development by Omega-P, IAP/Gycom, and Yale, could be a stand-alone source to constitute a 100 MW/140 nsec/50 Hz rf power station for CLIC. At this writing, the 34-GHz magnicon has not yet undergone full RF conditioning and has not reached its full design power. However, preliminary results are sufficiently established to allow use of the magnicon’s present output power for surface fatigue and rf breakdown tests. These tests cannot be conducted without a wide complement of high-power mm-wave components for rf transmission, manipulation, and diagnostics. Many of these components must be over-moded or quasi-optical to accommodate the peak power levels that are required. This paper reports progress in development of these components. But first, a brief description of the 34-GHz magnicon itself is given.

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2. 34-GHz, 45-MW, PULSED MAGNICON AMPLIFIER A full description of this amplifier is given in a recent publication [6], and thus need not be repeated here. Design parameters are listed in Table I, a diagram of the device is shown in Figure 1, and a photograph is shown in Figure 2. RF conditioning of this tube commenced in March 2003, but was suspended in June 2003 by administrative fiat; work recommenced in July 2004. Results cited here were obtained after about only 50 hours of actual RF conditioning, corresponding to about 2×105 pulses. For these tests, the 1.5 µsec wide modulator pulse and the RF drive pulse were shortened to ∼0.5 µsec to facilitate conditioning to high power with a reduced incidence of breakdown events; this necessitated sacrifice of the flat-top for the modulator voltage pulse. Figure 3 shows typical waveforms for the gun voltage and current pulses. Table I. Design parameters for 34-GHz magnicon amplifier

operating frequency output power pulse duration pulse repetition rate Efficiency rf drive frequency rf drive power Gain beam voltage beam current magnetic field in deflecting cavities magnetic field in output cavity beam area compression beam diameter maximum current density

34.272 GHz 44-48 MW 1.5 µs 10 Hz 41-45 % 11.424 GHz 150 W 54 dB 500 kV 215 A 13 kG 22.5 kG 2500-3000:1 1.0 – 0.8 mm ∼25 kA/cm2

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Figure 1. Outline diagram of 34-GHz magnicon. 1 - electron gun, 2 – cavity chain, 3 output wave-guide (WR28), 4 – input wave-guide (WR90), 5 – superconducting coils, 6 - iron yoke, 7 – cryostat, 8 - beam collector.

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Figure 2. Photograph of 34-GHz magnicon, without lead shielding around cryomagnet and beam collector.

0

-100

-50

-200

-100

-300

-150

-400

-200

Collector current (A)

Gun voltage (kV)

0

-250

-500 -1

0

1

2

3

4

Time (µsec)

Figure 3. Gun voltage and current waveforms with the shortened modulator pulse. Voltage is the higher amplitude trace in the figure.

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This frequency-tripling magnicon requires drive power at 11.43 GHz, and through the gain action of five deflection cavities multiplies the transverse momentum of the electron beam prior to the beam’s entry into the output cavity. Diagnostic signals from three of the gain cavities are shown in Figure 4. Spectral measurements confirmed the monochromatic nature of these signals to better than 30 dB. 0.5

Cavity 3

X-band gain cavities (a.u.)

0

Cavity 5 -0.5

Cavity 6 -1

-1.5 0.5

1

1.5

2

2.5

Time (µsec)

.

Figure 4. Diagnostic signals at 11.43 GHz from deflection cavities 3, 5, 6.

Traces of 34.3 GHz output signals from the four WR-28 output waveguides, terminated in high-power calorimetric vacuum loads, are shown in Figure 5. These signals are obtained from the forward sampling ports of dual directional couplers installed in each output waveguide. Calibration of the crystals and coupling factors allow inference that a peak value of 10.5 MW for the total power output from the magnicon was achieved under these conditions, with a gain of about 54 dB. While this output is only about 25% of the design power (due to operation at low gun voltage and gun current, and corresponding low rf drive power, and at a modest 1-2 Hz repetitive pulse rate), it still represents a record for a mm-wave amplifier suitable for accelerator applications. This power level is already sufficient for planned experiments on pulsed heating and surface fatigue in rf cavities [7], and of breakdown studies in high-gradient accelerator structures [8].

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0.5

φ=0

Output Cavity (a.u.)

0

φ=π/2

-0.5

φ=π

-1

φ = 3π / 2 -1.5

-2 0.5

1

1.5

2

2.5

Time (µsec)

Figure 5. Traces of 34.293 GHz pulses from the four WR-28 magnicon output wavegides. Shorted slotted line measurements confirmed the absence of spurious frequencies in the output to better than 30 dB.

The recently-resumed 2004 experimental campaign on this tube has as its objective confirmation of the 45 MW design output, using the WR-28 vacuum loads that are already installed on the tube and configured with suitable thermistors for calorimetric power measurements. Once this confirmation is completed, components will be installed on one output arm of the tube to allow surface fatigue tests to proceed, using a test cavity [7] that is already fabricated. This is possible, since only about 5 MW of peak power is required for the surface fatigue tests.

3.

HIGH-POWER Ka-BAND COMPONENTS

For the 100’s of MW peak power levels of interest for accelerator applications at Ka-band, it is essential that over-moded transmission line components be used. This fact can be made quantitative by reference to Figure 6, which shows the power level that would be transmitted at 34.3 GHz (in the absence of reflections) by a cylindrical waveguide operating in the TE11 mode at three values of peak rf electric field at the waveguide wall, as a function of waveguide radius. Also shown, along the top of the plot, are the cutoff radii for higher order waveguide modes.

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M ode R (m m ) c

TE11 2 .5 7

TM 01 3 .3 5

TE01 TM 11 5 .3 4

TE21 4 .2 6

TE12 7 .4 3

TE31 5 .8 5

TM 21 7 .1 5

TM 02 7 .6 9

1000

E

m ax

(r= R )

= 7 5 M V /m

600

Power P

TE11

(MW )

800

5 0 M V /m

400 2 5 M V /m

200

0 2

3

4

5

6

7

8

W a v e g u i d e r a d iu s R ( m m )

Figure 6. Power transmitted in the TE11 mode in cylindrical waveguide at 34.3 GHz as a function of waveguide radius, for three values of peak rf electric field at the waveguide wall. Cutoff radii for higher-order modes are indicated along the top of the plot, showing the presence of higher-order modes for a waveguide radius greater than 3.35 mm.

Figure 6 shows, for example, that if transmission of 200 MW is desired and if a peak surface rf electric field of (75, 50, 25) MV/m can be safely sustained, then (1, 2, 7) higher-order modes can also propagate, in addition to the TE11 mode. If 400 MW transmission is desired, the number of higherorder modes become (2, 4, >7). The peak surface electric field that can be sustained depends upon surface treatment, level of vacuum, and rf pulse width. Furthermore, allowance should be made for higher fields that would result from reflections from an unmatched load. Clearly, for 100’s of MW of transmitted power, higher-order-mode components must be used.

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Figure 7. Mode converter, WR-28 to TE01 mode in 13-mm diameter cylindrical waveguide.

Figure 8. Miter bend, TE01 cylindrical waveguide tapers, and mode mixers. Low-power measurement on miter bend shows 99% pure mode transmission at 34.3 GHz.

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Overmoded Ka-band components that have been designed and built for use at high power include mode converters, tapers, miter bends, windows, vacuum pump-outs, power combiners/splitters, and phase shifters. Drawings and photographs of these components are shown in Figures 7-18.

Figure 9. Vacuum pump-out section in TE01 mode 63-mm diameter cylindrical waveguide.

Transmission Line Components

Figure 10. Vacuum window in TE01 mode 63-mm diameter cylindrical waveguide.

Figure 11. Four-wave power combiner/splitter with TE11 13-mm diameter cylindrical waveguide feeds.

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Figure 12. Photograph of an assembly of high-power, high-vacuum Ka-band components, including a miter bend and window, prior to installation on the 34-GHz magnicon.

Transmission Line Components

Figure 13. Design of WR-28 high-power phase shifter.

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Figure 14. Photograph of WR-28 phase shifter.

Figure 15. Photograph of WR-28 waveguide phase shifter under test.

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Figure 16. Photograph of low-power test prototype of Ka-band resonant ring [9].

40

Gain

30

20

10

0 34.260

34.265

34.270

34.275

34.280

34.285

f, GHz

Figure 17. Measured power gain in prototype Ka-band resonant ring, showing 35:1 effective power gain [9].

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Figure 18. Possible layout of Ka-band components for combining power from all four outputs of the 34-GHz magnicon.

DISCUSSION Emergence of an operating accelerator-relevant, 10’s of MW, 34GHz pulsed magnicon ushers in possibilities for experiments to explore high E- and H-field limits in accelerator structures and components in parameter ranges that were not heretofore accessible. High-power components that have been developed and built for distributing the 34-GHz power to test cells and experimental structures include mode converters (Figure 7), miter bends (Figure 8), vacuum pump-outs (Figure 9), vacuum barrier windows (Figure 10), four-way power combiner (Figure 11), phase shifters (Figure 13), and a highgain resonant ring (Figures 16-17). A layout for combining the four outputs of the magnicon into one transmission line has been designed, using four phase shifters and four windows (Figure 18). However, if a window can be developed to safely handle the full 45 MW peak power of the magnicon, a simpler layout could be designed. The 34-GHz technology described here can be redesigned and built at 30 GHz, for tests and conditioning of structures and components for the proposed future multi-TeV collider CLIC.

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REFERENCES 1. J. W. Wang, G.A. Loew, "Field emission and RF breakdown in highgradient room-temperature structures", SLAC-PUB-7684, Oct. 1997. 2. O.A. Nezhevenko, "On the limitation of accelerating gradient in linear colliders due to the pulse heating", PAC97, Vancouver, 1997, p.3013. 3. B. Aune et al., “Superconducting TESLA cavities,” Phys. Rev. ST.Accel. Beams 3, 092001 (2000). 4. Final International Technology Recommendation Panel Report, September 2004, http://www.ligo.caltech.edu/~skammer/ITRP/ITRP_Report_Final2.pdf. 5. R.W. Assmann, F. Becker, R. Bossart, et al, “A 3 TeV e+e– linear collider based on CLIC technology,” CERN 2000-008, 28 July 2000. 6. O.A. Nezhevenko, M.A. LaPointe, V.P. Yakovlev, J.L. Hirshfield, “Commissioning of the 34-GHz 45-MW pulsed magnicon,” IEEE Trans. Plasma Sci., vol.32 pp. 994-1001, June, 2004. 7. O.A. Nezhevenko, V.P. Yakovlev, J.L. Hirshfield, and G.V. Serdobintsev, “Pulsed heating experiments at 34 GHz,” PAC2003, Portland, May 11-16, 2003, pp. 2881-2883. 8. O.A. Nezhevenko, V.P. Yakovlev, J.L. Hirshfield, G.V. Serdobintsev, S.V. Schelkunoff, B.Z. Persov, “34.3 GHz accelerating structure for high gradient tests,” PAC2001, Chicago, June 17-22, 2001, pp. 38493851. 9. A. Bogdashov, G. Denisov, D. Lukovnikov, Yu. Rodin, and J. L. Hirshfield, “Ka-band resonant ring for testing components for a highgradient linear accelerator.” (submitted for publication)

FERRITE PHASE SHIFTERS FOR Ka BAND ARRAY ANTENNAS

Yu. B. Korchemkin1, V. V. Denisenko1, N. P. Milevsky2, V. V. Fedorov2 1

JSC «Radiophyzika», Moscow, Russia, 2JSC «Ferrite-Domen», St.-Petersburg, Russia,

Abstract:

Electronically controlled phase shifters for millimeter wave phased arrays can be based on using semiconductor and ferrite elements. However, for high power radar the latter are more advantageous. At the Ka band, ferrite subarrays capable of broad-angle intense wave beam scanning are available.

Key words:

microwave beams; gyrotron; beam phase front; quasi-optical transmission line; phase shifter, Ka-band, ferrite sub-array, phased array antenna, radar.

1.

INTRODUCTION

In phased array antenna (PAA) radars, the wave beam scanning can be sufficiently wide, if electrically controlled elements at the aperture are spaced at 0.6-0.7 of the wavelength. Consequently, shortening the wavelength results in a number of evident engineering problems. In high power millimeter wave radars, these problems can be solved only by using phased arrays of a passive type1, where key components of the elementary channel are the phase shifter and its driver.

2.

COMPARISON OF FERRITE AND SEMICONDUCTOR PHASE SHIFTERS AT KA BAND

Table 1 presents a typical performance of semiconductor and ferrite phase shifters at Ka-band PAA’s2, 3. Though the switching time and control power for high switching rate of semiconductor phase shifters are less than ferrite ones, but the insertion loss, maximum microwave power level and cost of

165 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 165–175. © 2005 Springer. Printed in the Netherlands.

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ferrite phase shifters are better than the same parameters of semiconductor phase shifters. That is why ferrite phase shifters are used more frequently.

Table 1. The comparison of semiconductor and ferrite Ka-band phase shifters Parameter Phase shifter type ferrite semiconductor 1. Insertion loss, dB 1.0- 2.0 1.5 – 3.0 2. Bit number 3-6 2-3 3. Maximum microwave power, W peak 100 -5000 1 – 10 average 1 -10 0.1 - 1 4. Switching time, µs 10 – 100 0.1 - 1 5. Control power, W, for switching rate: 500 Hz 0.01– 0.05 0.05 – 0.1 5000 Hz 0.1- 0.5 6. Typical cost, USD 10 -100 50 - 200

3.

STRUCTURES AND PERFORMANCE OF AVAILABLE PHASE SHIFTERS

Ferrite phase shifters may be either of feed-through or of reflection type. In the feed-through phase shifters, the magnetization may be either longitudinal or transverse. As symmetric longitudinally magnetized phase shifters are nonreciprocal, in reflect phase shifters the transverse magnetization is more frequently used2. The performance of longitudinal magnetization phase shifters is shown in Table 2. These phase shifters are produced by the «Ferrite-Domen» together with «Radiophyzika» and are used in the PAAs described below. The feedthrough phase shifter “A” operates with linear polarized wave and handles the highest microwave power in comparison with others: maximum peak power is 4000W and maximum average power is 40W. Other three phase shifters operating at circular polarized waves provide lower microwave powers. Such a phase shifter represents a circular metallized rod (Fig.1a) of Lithium or Zinc ferrite with 4500 G saturation magnetization and two yokes of special ferrite 107P with remanence ratio more than 0.85. The ferrite rod is magnetized longitudinally with using winding located on the ferrite rod or two windings located on the yokes. Fig. 1b shows the magnetization hysteresis loop. All phase shifters have 3 bits control, approximately 20 degrees phase error, and less than 1.8 dB insertion losses. Reflect phase shifter “D” has the smallest cross-section.

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Table 2. The ferrite phase shifters performances Phase shifter designation Number of Figure Type Frequency band, % Polarization Number of bits Phase error, degree (max) Insertion loss, dB: average maximum Switching time, Ps, (max) Aver. switching energy, PJ Max. microwave power, W average peak Dimensions, mm

“A” 2b) Feedthrough 6 Linear 3 r22.5

“B” 3b) Feedthrough 4 Circular 3 r 20

“C” 4d) Reflect 3 Circular 3 r22.5

“D” 5b) Reflect 3 Circular 3 r22.5

1.4 1.7 130 160

1.3 1.8 70 120

1.2 1.7 30 80

1.3 1.8 36 40

40 4000

2 100

2 100

2 100

22×35×180

‡8u42

‡8u48

5.6u5.5×48

+Br Yoke

Windings

Metalized ferrite rod

E A

D

Hc

H

L

C

B

- Br

b)

a)

Figure 1. Structure and hysteresis loop of phase shifter section.

The phase shift control is carried out by the voltage pulses applied to the magnetization winding on the cycle “Reset” (A o B o C )- “Set”( C o D o E). The differential phase shift 'M is in direct proportion to the pulse voltage U, pulse width 't, ferrite rod length L, and in inverse proportion to the number of turns N in the winding:

' M r | r const

U 't L. N

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Thus, the phase shifters are analogues in character. The discrete phase control is implemented with the use of discrete voltage pulse widths.

4.

APPLICATIONS OF PHASE SHIFTERS

The feedthrough phase shifter “A”, was used in PAA of “Ruza” radar (Fig. 2) developed in “Radiophyzika” to phasing 120 large aperture radiators. Each radiator presents 60 cm two reflector antenna, so the beam scan angle is 50’. At the input and output of the phase shifter (Fig. 2b), there are polarizers and transitions from circular to rectangular waveguide. The control circuit provides 3-bit performance. The switching time including circle “ResetPause-Setup” is no more than 160 µs. This phase shifter is capable to operate at 4000 W peak/40 W average microwave power. The control winding is placed on the yokes, and the ferrite rod cooling is provided with metal radiators (Fig. 2c). The phase shifter “B” was used in a feedthrough PAA (Fig. 3), developed by the Research Center Altair, Moscow4. The array contains 5648 elements arranged nonequidistantly along spiral lines with approximately uniform element density. An average spacing between elements is about 2O. Phase shifters and its 3-bit drivers are mounted on flexible boards curved along the mentioned spirals. A beam steering controller is located around of the PAA aperture. An application of nonequidistant structure allows to avoid grating lobes and provide the gain of about 48 dBi over r15 scan area which is close to limit for the used element spacing. For increasing the beam scan angle it is necessary to decrease spacing between elements of an array. To meet these requirement at r(20q – 45q) scan angles, the reflect phase shifters “C” and “D” were used, the phase shifter drivers and radiators being placed behind the multi-element PAAs aperture.

Ferrite Phase Shifters for Ka-Band Array Antennas

169

b) phase shifter “A” and its driver circuit,

a) phased array antenna,

c) phase shifting section structure

Figure 2. Phased array antenna and phase shifter of “Ruza” radar.

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b) phase shifter “B” a) phased array antenna,

Figure 3. Feedthrough phased array antenna developed in Research Center Altair and its phase shifter.

The phase shifter “ɋ” is used in the reflect PAA developed by «Radiophyzika» Co. (see Fig. 4b). The phase shifter consists of a longitudinally magnetized circular ferrite rod of lithium ferrite 1ɋɑ12. The rod is metallized around except one rod-end, which is connected to the 7.2 mm diameter circular waveguide via the multi-step dielectric transformer. Two ferrite yokes provide the phase shifter with the latched stages. Three windings by 45 turns are used for controlling the phase shifter magnetization.

Ferrite Phase Shifters for Ka-Band Array Antennas

171

a) module for large aperture phased array antenna,

b) phased array antenna with monopulse feed,

c) 118-element subarray,

d) phase shifter “C”

Figure 4. Reflect type phased array antenna with r25q scan area.

The phase shifter is controlled by volt–second method (flax method) by means of a special chip 1109KT5. The phase is shifted with 45 degree steps provided with three pulses of 1.2, 2.4, and 4.8Ps duration. The phase shifter switching time is about 30 Ps. To decrease the phase errors caused by the technological scatter of parameters, we chose phase shifters with close linear phase dependence on the set pulse width. The phase shifters and the driver circuits are assembled into two type subarrays, which include elements 88 and 118. The integration of phase shifters and its drivers in the subarray reduces the production cost, provides the assembling of the phased array simple, and increases its maintainability and

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reliability. The 118-element subarray is shown in Fig. 3b. The elements are arranged in 6 rows and 20 columns in a hexagonal grid with spacing of 9.9 mm. The subarray consists of six printed boards. Each printed board contains the following main components: twenty phase shifters with 3-bit drive chips 1109KT5, a few storage capacitors, address decoders, and voltage stabilizers. By tuning the Set pulse voltage, the phase error was reduced to r 15 degrees. Two phased array antennas shown in Fig. 4a and Fig. 4b have the same hexagonal aperture and consist of 12 subarrays with 118 elements and 24 subarrays with 88 elements. Each PAA includes 3528 phase shifters. The elements are arranged over hexagonal grid with spacing of 9.9 mm that equals to 1.1Ȝ. Both arrangement and element flat-topped radiation pattern provide the antenna with wide electron scan area of about r25q. The PAA shown in Fig. 4ɚ has one channel feed with reverse radiation and can be used as a module of the large aperture antenna analogues to the “Ruza” radar antenna. The PAA shown in Fig. 4b has a monopulse feed and can be used as an autonomous antenna of a multifunction radar. The reflect phase shifter “D” and the 80 element subarray (Fig. 5) were developed for PAA with r45qscan angle. The element arrangement is hexagonal and spacing is about 6 mm. In comparison with the phase shifter “C”, the phase shifter “D” is assembled with the radiator that connected to metallized rod via circular waveguide section filled with Teflon. The number of windings is reduced from three to two and cross-section dimension is reduced from 8 mm to 5.6 mm. Phase shifter has four flexible leads for soldering to a printed board.

a) subarray,

b) phase shifter “D”

Figure 5. Subarray and phase shifter for phased array antenna with r45q scan area.

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173

In addition to the scan angle expansion, we reduced PAA cost per channel, as well as heating and dc power supply. Decreasing of dc power is achieved by reduction of the phase shifter switching energy from 80 PJ to 40 PJ and replacing TTL IC to CMOS IC (complementary metal-oxide semiconductor) in driver circuits. MOSFET transistors are used for forming phase shifter magnetizing current. For example, for 500 Hz switching rate, the supply power per one phase shifter in the previous version subarray was equal to 155 mW, then in the new version subarray it is about 38 mW. There is a beam steering controller in each subarray. The controller is designed using SpartanTM –II FPGA (Field–Programmable Gate Array). This IC is produced by «Xilinx» Co. on XC2S400 crystal base. The controller calculates phase shifter code taking into account phase shifter coordinates in aperture, phase radiation pattern of the feed, initial phases and temperatures of phase shifters. The significant decrease of the cost of new subarray is achieved by excluding requirements to identity of phase shifters (phase dependencies versus time). It permits to simplify a phase shifter technology, to decrease its rejection rate and cost. When phase shifter is mounted to the subarray, its phase dependence on the control pulse width is measured and fixed in subarray FLASH.

5.

METHODS FOR FURTHER REDUCTION OF CONTROL POWER

Let us consider the 10000 element PAA with the subarrays described above and phase shifters «D» with average switching energy 40 PJ. The total power supply is equal to 380 W for switching rate of 500 Hz, and achieves 750 W for switching rate of 2500 Hz.

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The switching energy Wsw of a latching phase shifter is determined by the hysteresis loop energy Whyst and energy Wmet dissipated in the rod metallization due to eddy current induced by magnetic field variation. Wsw |Whyst  Wmet ,

where

Whyst

2 'B H c V

,

Wmet

2 4 'B 2 S A t sw rmet

,

2S a U - shorted turn resistance of the rod metallization, t - switching sw Gl time, 'B - magnetic induction difference, Hc - coercive force, V, SA - volume and cross-section area of magnet circuit, G - metallization thickness, U characteristic resistance of metallization. For phase shifter «D» the eddy current dissipated energy Wmet is about a half of switch energy Wsw. Above equations show that Wmet decreasing is possible by increasing the resistance rmet, for example, by the metallization thickness G decreasing, or by the specific resistance of metallization U increasing. But, this method is limited because of the insertion loss increases when metallization thickness approaches to a skin-effect thickness. Therefore, the most efficient way of switch energy reduction would be using a ferrite rod without metallization. In the open ferrite rod the surface mode can transfer due to high value of ferrite permittivity (H/Ho | 16) like in a dielectric waveguide. To develop a phase shifter without metallization of the ferrite rod, it is necessary to solve two problems: the excitation of the dielectric waveguide, and the reduction of the yoke and windings influence on the wave propagation. The reduction of the hysteresis loop energy Whyst is possible by decreasing the coercive force Hc of phase shifter magnetic circuit (for phase shifter «D» it is equal 2 Oe). This can be provided with the use of a ferrite with narrow hysteresis loop (Hc <<1 Oe). But in this case, a square of hysteresis loop (remanence ratio) decreases, and a complicated driver with continuous magnetization current is needed. «Ferrite-Domen» Co. with co-operation of «Radiophyzika» Co. have begun development of a Ka band phase shifter with low power supply. Lithium –Zinc ferrite with saturation magnetization of 4500 G and coercive force of less than 0.5 Oe was synthesized. We have developed and tested the breadboards of phase shifter with ferrite rod without metallization. These rmet

Ferrite Phase Shifters for Ka-Band Array Antennas

175

breadboards are characterized by the switching energy of less than 5 PJ and magnetization current of no more than r 30 mȺ.

6.

CONCLUSION

The ferrite phase shifters and drivers fit for the Ka band PAAs are developed in Russia. The multi-element PAA pilot samples are also developed and tested. So there is a good foundation for the development of different purpose Ka band radars in the near future. The works described in this paper have involved many personnel of “Radiophyzika” and “Ferrite-Domen” over twenty year’s period, and the authors wish to acknowledge their contribution. Additionally we would like to thank Dr. A. Tolkachev (general designer of “Radiophyzika” Co.) for the organization of the presented works.

7.

REFERENCES

1. V. Denisenko, Yu. Korchemkin, A. Shishlov, A. Tolkachev Phased Array Antennas of Millimeter Waves in Russia: Status and Trends. Millennium Conference on Antennas&Propagation, Davos, Switzerland, 600(2000). 2. A.A. Tolkachev, Yu.B. Korchemkin, A.V. Majorov, and N.P. Milevsky, Phase Shifters for Millimeter-Wave Band Multi-Element Phased Array Antennas, Proc. of Int. Symp. on Antennas and Electromagnetics (ISAE'97), Xian, China, 583-586(1997). 3. Shiban K. Koul, Bharathi Bhat, Microwave and Millimeters Wave Phase Shifters (Artech House, 1991). 4. F.I. Emelchenkov, Main integral parameters of non-equidistant array antennas with uniform dens arrangement of radiators over an aperture, Shipbuilding industry, General-theoretic series, No.22 , Exhibit 1(1989), (in Russian).

PROPAGATION OF WAVE TRAINS OF FINITE EXTENT ON WIDE, THIN-WALLED ELECTRON BEAMS

Edl Schamiloglu2 and Nikolay Kovalev1 1 Institute of Applied Physics, Russian Academy of Sciences, 603600 Nizhny Novgorod, Russia; 2Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131 USA

Abstract:

The method of increasing the power radiated from microwave oscillators by enlarging the transverse dimensions of their interaction spaces and, therefore, the cross sections of electron beams is limited by conditions of single mode generation or generation of spatially coherent radiation. For systems that are open in the transverse direction in which the largest dimensions can be achieved, the limitations are associated with the distortion of wave trains of finite length and their diffraction on the ends of limiting screens, as occurs in quasi-optics. The properties of electromagnetic wave trains are usually accounted for in studies of the selective properties of oscillators. However, the properties of electron wave trains, which have not been adequately explored, as a rule, are not accounted for. In this paper, we study a simple example, the diffraction properties of magnetized thin-walled electron beams of infinite transverse dimension. For small wave amplitudes, we consider wave trains propagating along the guide magnetic field as well as across it (without taking into consideration non-linear effects). The basic components of the diffusion tensor are found. The diffraction of the wave trains on the edge of the screen, which is transparent to electrons, has been considered qualitatively. The maximum transverse dimensions of a relativistic BWO with an electrodynamic system open in the transverse direction are estimated.

Key words:

high power microwaves; quasi-optics; mode selection; BWO

1.

INTRODUCTION

In high current electron beams used in relativistic high power microwave (HPM) electronics, various effects associated with the microwaves and the 177 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 177–184. © 2005 Springer. Printed in the Netherlands.

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E. Schamiloglu, N. Kovalew

static space charge of beam electrons often occur. These effects, typically, are not taken into account because of the difficulties associated with studying them, thereby leading to incorrect solutions.

1.1

Model Assumptions

Here we will consider one of numerous manifestations of the effects connected with the diffraction properties of waves in strongly magnetized electron beams with infinite transverse extent (Fig. 1). In this simplest model, we consider electron waves. Unlike electromagnetic waves, a point (or a line) of the condensation of the spectrum of electron waves is absent, and half of the beam electron beams are slowed, which can transfer negative pseudo-energy (Fig. 2).

Figure 1. A wide sheet electron beam propagating between two metal planes.

We assume that the current density of the electron beam is much less than the current density limited by own space charge of electrons, i.e.

j0 << j scl ≈

mc 3 γ 03β 03 e L2⊥

(1)

and Bursian’s instability is avoided. Here e and m are the charge and rest mass of an electron, c is the speed of light in vacuum, J0

1  E

2 1 2 0

(2)

is the relativistic factor,

E0

v0 c , v 0

(3) is the steady state velocity of electrons, and L1 is the height of the electron beam transport channel.

Propagation of Wave-Trains on Electron Beams

179

Figure 2. Brillouin diagram for electron waves when the beam current is much less than the space-charge-limited current.

2.

ANALYSIS OF THE PROBLEM

We consider processes that vary as exp(-iZ t) and employ Gaussian units. Assuming waves with small amplitude, the self-consistent system of equations comprises Maxwell's equations, the continuity equation, and the equations of motion for electrons: G G ’ u E ikH G G 4S G ’ u H ikE  jz 0 c wj Z Z 2 i j  h pU wz c 4S wU Z  i U Ez wz v0

(4)

where

h p2 {

Z 2p v02

4SUe mJ 03v02

(5)

is the plasma wave number, Zp is the plasma frequency, k=Z/c, U is the beam density, and

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E. Schamiloglu, N. Kovalew

U

m 3 J 0 v0v e

(6)

is the kinetic potential attributed to Chu.1 The kinetic potential U = 0 when 2 Q0=0. Although Q0 and G hp in the system of equations given in 2(4) can be functions of position (r ) , we consider here the case Q0 = 0 and hp =0. For processes described by the system of equations in (4), the complex Poynting’s theorem can be written as G G 1 G ½ ­ c ’ ˜ ® Re E u H *  jU * z0 ¾ 0, 8 2 S ¯ ¿

>

where the term

G S kin

@

(7)

G 1 jU * z0 2

(8)

represents energy flow of which is transferred by electrons. Since this flow is proportional to v0 , in the coordinate system moving with electrons kin . Using the two-frequency Lorentz’s lemma, we obtain an expression for the accumulated energy density:

G w

0

W

1 ­ dZH 2 dZP 2 8S 2½ H  Re jU *  h 2p U ¾ . E  ® 16S ¯ dZ dZ v0 ¿

(9)

For a plane wave the density of kinetic energy can be written as

Wkin

1 ­ 8S 2½ * 2 ® Re jU  h p U ¾ 16S ¯ v0 ¿

1 16S

­ 2 2 hz  Z v0 ½ ¾ (10) ® h p U hz  Z v0 ¿ ¯

from which it follows for slow waves that slow Wkin 0

(11)

slow Wkin !0.

(12)

and for fast waves

This result implies that the energy flow of fast waves is parallel to the group velocity whereas for slow waves they are anti-parallel.

Propagation of Wave-Trains on Electron Beams

181

For plane waves that vary as exp [i(hzz + h՚r՚ )] and with Hz = 0, we obtain the dispersion relation k 2 − hz2 − h⊥2 ( hz − k β 0 ) 2= h p2 k 2 − hz2 (13)

(

)

(

)

and the relations for the amplitudes

U = −i

Ez ; hz − k β 0

j = ic

kh p2 E z

( hz − k β 0 )

2

Hx =

,

(14)

hhE E y = − 2y z 2z . k − hz

hhE E x = − 2x z z2 , k − hz

kh E H y = − 2 x z2 ; k − hz

khy E z , k 2 − hz2

Equation (13) couples terms related to electromagnetic waves (k2 - hz2 h՚2) and electron waves (hz – k/E0)2 through a coupling coefficient that is proportional to the charge density (hp2) of the electron beam. Therefore, according to Eq. (7), normal waves can transfer energy in the direction of electron motion, as well as across their motion. In addition, wave trains will spread out in any direction of their propagation. When the trains propagate only in the z-direction, fields of the wide wave beam C2<
³ 

(15)

or G E zr (r )

f

ª

G §G G ³ E h exp««¬i¨¨© h r r z

A

A A

r

hA2 J 02 E 02 2k

f

2

·º G h p z ¸» dhA ¸» ¹¼

(16)

where C

2k 2

J 02 E 02 h p LhA2

|

a2 SJ 02 E 02 h p OL k

(17)

plays the role of the Fresnel parameter with the upper signs pertaining to slow waves and the lower signs pertaining to fast waves, and a is the width of the wave train.

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E. Schamiloglu, N. Kovalew

The integral equation in (16) for complex amplitudes of slow and fast waves is equivalent to the parabolic partial differential equation J 02 E 02 h p wE zr Bi ' A E zr (18) 2 wr

2k

with an imaginary diffusion coefficient. Equations for the slow and fast waves are different, and therefore the spreading of the wave trains affects electron bunching, and accordingly, the value of the self-consistent microwave current.

3.

RESULTS One of the solutions of Eq. (18) with w wx E zr

J 0E0 k

0 is a Gaussian wave beam 2 § · hp ¨r i k y ¸ exp (19) ~z ¨ 2J 2 E 2 h ~z ¸ 0 0 p ¹ © 2

with ~ z

z i

k 2a2

J 02 E 02 h p

.

(20)

During propagation, the wave beam width a (z) increases (as illustrated in Fig. 3) according to a2

a 02  J 04 E 04

h p2 z 2 k 4 a 02

,

which is the same for both slow and fast waves.

(21)

Propagation of Wave-Trains on Electron Beams

183

Figure 3. Illustration of the spreading of a Gaussian wave train.

4.

DISCUSSION

As in quasi-optical devices, the spreading of wave trains as described by Eq. (21) can be used as an additional means of mode selection. Obviously, the faster the spreading, the more effective is the discrimination. When space charge is not taken into account (hp=0), this effect of additional selection is lost. Indeed, the greater the space charge, the more effective is this mechanism of selection. According to Eq. (21), a conventional criterion of applicability of this mechanism of mode selection is J 02 E 02

hp L k 2 a 02

|1

(22)

which also follows from Eq. (17). When the space charge density hp is much lower than the value determined by Eq. (22), the spreading of wave trains is small and almost the same for any wave; that is, this additional mechanism of mode selection is absent. In the opposite case, when the space charge density hp is very large, the spreading of the operating wave is also large, leading to large losses.

184

5.

E. Schamiloglu, N. Kovalew

CONCLUSIONS

The effects considered in this paper show that in HPM devices driven by high current electron beams, space charge not only limits the process of forming dense electron bunches, but can improve the device's selective properties and even achieve phasing of separate parts of the interaction space. In contrast, the large space charge density can lead to hopping from one mode to another and, accordingly, to hysteresis effects. This incomplete enumeration of effects demonstrates how rich and varied is the influence of space charge on the operation of oscillators and amplifiers. In our paper, we have not touched upon important problems connected with the scattering of wave trains on irregularities, which can lead to various instabilities. Obviously, the peculiarities of these problems are associated not only with the existence of waves with negative energy, but also with the absence of contrary propagating waves when space charge density is not very large, and with a condensation of the wave spectrum mentioned in the Introduction.

6.

REFERENCE

1. L.J. Chu, “A Kinetic Power Theorem,” presented at Annual IRE Conference on Electron Tube Research, Durham, N.H., 1951.

QUASI-OPTICAL MULTIPLEXERS FOR SPACE COMMUNICATION AND RADAR WITH SYNTHESIZED FREQUENCY BAND

M. Petelin2, G. Caryotakis1, Yu. Postoenko2, G. Scheitrum1, I. Turchin2 1-Stanford Linear Accelerator Center, USA; 2-Institute of Applied Physics, Nizhny Novgorod, Russia

Abstract:

In radar and communication systems, a broad frequency band can be synthesized of several narrow ones. At millimeter and sub-millimeter waves, the multiplexer for combining narrow-banded channels can be composed of quasi-optical mirror cavities. However, mutual adjustment of the cavities for radar and communication should be quite different. In the radar with synthesized frequency band, an adaptive spectrum regularization algorithm provides automatic shrinkage of the range resolution scale with the target approaching.

Key words:

communication, radar, signal processing, optimized algorithms, range resolution.

1.

INTRODUCTION

The channel capacity of communication systems1 and the range resolution of radar2 are known to increase with expansion of the frequency band. A broad frequency band can be composed of narrow sub-bands, each channel being served with own transmit-receive duplexer, transmit and receive amplifiers and ADC2 (Fig. 1). The whole system is mastered with a general control and a signal-processing unit. The channels are connected with a common antenna by means of a multiplexer. In the transmit mode, the multiplexer combines narrow-banded sub-signals and in the receive mode (according to the reciprocity principle) the received signal is distributed between frequency sub-bands.

185 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 185–198. © 2005 Springer. Printed in the Netherlands.

186

M. Petelin, G. Caryotakis, Yu. Postoenko,G. Sheitrum, I. Turchin Z1 TR module

Common TR control and signal processing unit

Z2 TR module

Multiplexer

ZN TR module

Zj transmit-receive module Zj

Amplifier

TR switch Digitized signal

ADC

Analogous receiver

Figure 1. Scheme of synthesizing frequency band.

Multiplexers (Fig. 2) may have various configurations4-7; in particular, they can represent chains of degenerate-mode cavities4. At decimeter and centimeter wave bands, these cavities coupled with standard (single-mode) waveguides are used which have dimensions commensurable with the wavelength. However, at higher frequencies, capacity of such devices is limited by the ohmic absorption and at high power levels, by the RF breakdown. To avoid these difficulties at the millimeter wave band, the multiplexer cavities should be quasi-optical (Fig. 3).

Q-O Multiplexers for Space Communication Z2

187 ZN

minor loss

S2

SN

Z1, Z2 , Z3 Z1, Z2 , … ZN-1

Z1

Z1, Z2 , … ZN

S3 Z3 Figure 2. Multiplexer combining partial narrow-band signals, Z1, ZN are central frequencies of partial transmit bands, S1, SN – resonant elements. Opposite directions of wave flows correspond to splitting the received signal into narrow-band parts.

Z1, … Zj-1

Zj minor loss

Zj Z1, … Zj-1

Z1, … Zj (a)

minor loss

Z1, … Zj (b)

Figure 3. Quasi-optical circular cavities with perforated (a) and corrugated (b) mirrors as elements of multiplexers.

Such a technique seems attractive, in particular, for radars based on using klystrinos8, 9. The klystrino (Fig. 4) is a compact W-band amplifier planned that would deliver 100 kW pulse and 1 kW average power; the frequency band will be 0.1%.

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Figure 4. The klystrino (project): compact high power 94 GHz amplifier.

2.

CIRCULAR MIRROR CAVITY AS AN ELEMENT OF MULTIPLEXER

If the cavity shown in Fig. 3a is over-coupled with identical input and output perforated mirrors, the wave transmission and reflection coefficients T j (Z ) and R j Z are described by equations10 R j (Z )

T j (Z )

Z  Z cj

Z  Z cj  iZ ccj

iZ ccj

Z  Z cj  iZ ccj

,

,

(1)

(2)

where Z j Z cj  iZ ccj is the cavity eigen-frequency, and Z ccj is the decrement of free oscillations caused by radiation through the perforation. For the partial signal whose spectrum is centered around frequency Z = Z cj , the j -th cavity is absolutely transparent at the central frequency and gives only a minor reflection at close non-resonant frequencies; so this partial signal, except the minor loss, proceeds to further, (j+1)-th… N -th, cavities. The same j -th cavity being illuminated, from another direction, with partial

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signals composed around frequencies Z1c ... Z cj 1 reflects them, almost entirely (except minor resonant loss through the j -th cavity), in the downstream direction to (j+1)-th… N -th, cavities. The circular cavity with perforated reflectors (Fig. 3a) is convenient as a comprehensive elementary model, but would be subject to breakdown. From the latter viewpoint, eliminating the perforation and substituting a corrugation (Fig. 3b) (that keeps formulas 1 and 2 valid) could transform the system to practical use. Four-mirror cavities seem especially appealing in this regard.

3.

SIGNAL COMBINING AND DIVIDING BY THE CHAIN OF CIRCULAR CAVITIES

The multiplexer (Fig. 2) with circular cavity elements (Fig. 3) can operate 1) in the transmit mode, combining partial narrowband signals of different frequencies; and 2) in the receive mode, dividing the received wideband signal into narrowband channels. In the transmit mode of the multiplexer (Figs. 2, 3), the transmission coefficient of the signal passing through the j-th multiplexer channel (the ratio of the complex amplitude of the wave at the multiplexer output to the complex amplitude of the wave entering the input of the j-th cavity) has the form [11]





TM j Z T j Z exp iM j Z

N

– Rk Z expiM k Z ,

(3)

k j 1

H rad Z

N

¦ TM j Z H 0 j Z .

(4)

j 1

In the receive mode of the multiplexer, the wave flows proceed in directions opposite to those shown in Figs. 2, 3, so the received wideband signal is split into narrowband components. The ratio of the complex

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amplitude of the wave appearing at the output of the j-th cavity to the complex amplitude of the wave entering the N-th cavity is RM j Z TM j Z

where TM j Z is determined by the formula (3).

4.

MULTIPLEXER OPERATION IN RADAR AND COMMUNICATION SYSTEMS

Tuning of a multiplexer should be adjusted to the specified application, namely a communication system or a radar. In the communication system, to increase the isolation between adjacent frequency bands, they should be separated with gaps of maximum depth12. In the radar, quite the contrary, the dip between partial frequency bands should be minimal: to lower the side lobes of the autocorrelation function of the radiated signal.2 S t

³ H rad Z

2

expiZt dZ .

(5)

These dips cannot be eliminated by a multiplexer adjustment; so, to obtain a radar range resolution 'r=c/2'Z corresponding to the total synthesized bandwidth 'Z, an adaptive algorithm with a spectrum regularizer should be used (see Section 5). The proper optimization of a multiplexer is provided by adjustment of distances, and thus phase shifts, between cavities: - in a multi-channel communication system, neglecting the frequency dependence of phase shift between cavities in the vicinity of frequency Y j , the gap is most deep (Fig. 5) under the counter-phase condition





arg T j H 0 j Z Y j









 arg R j T j 1 exp i< j 1 H 0 j 1 Z Y j ,

where \ j Z M j Z 

N

¦M k Z  argRk Z ;

k j 1

(6)

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- in a radar, the dip depth is minimized (Fig. 6) under the opposite condition





arg T j H 0 j Z Y j









arg R j T j 1 exp i< j 1 H 0 j 1 Z Y j

(7)

In Figs. 5, 6 thin solid lines show Lorentz-shaped partial signals, dashed line shows transmission coefficient TM2 for signal entering the second channel, bold solid line shows integral signal at the multiplexer output. 0

dB

-5 -10 -15 -20 -25

Z1

Z2

Z3

Z4

Z5

Figure 5. Transmit mode of the multi-channel communication system.

0

dB

-5 -10 -15 -20 -25

Figure 6. Transmit mode of the with synthesized frequency band.

In the radar receive mode, the signal reflected from the target is filtered by the multiplexer so that the relative signal spectral intensity between eigen-frequencies of cavities becomes still less than in the transmitted signal, that is illustrated with Fig. 7 calculated for an isolated motionless target.

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M. Petelin, G. Caryotakis, Yu. Postoenko,G. Sheitrum, I. Turchin 0

dB

-5 -10 -15 -20 -25

Figure 7. Radar receive mode: thin line – received spectrum; dashed line – multiplexer transmission coefficient for the third channel, thin solid line - input signal spectrum Hin, and bold solid line - signal spectrum at the output of the third cavity.

5.

ADAPTIVE SIGNAL PROCESSING ALGORITHM FOR RADAR WITH SYNTHESIZED FREQUENCY BAND

In a radar with synthesized frequency band, 1) the transmitted signal spectrum has dips between central frequencies of neighboring sub-bands, and 2) atmospheric fluctuations may cause random dispersion of electromagnetic propagation lengths at different sub-bands. Both effects can be compensated by adequate signal processing (Fig. 8) : a) If a target is distant, and thus the signal-to-noise ratio (SNR) is low, only narrow regions near the spectrum maxima are of use. In this asymptotic case, the signal processing should be reduced to matched filtration2 aimed only to provide the highest target detection sensitivity. As the effective signal spectrum is composed of narrow isolated sub-bands, the point target image at the receiver output is surrounded with high side lobes and, thus, the range resolution is relatively poor. b) If the target approaches and the SNR grows high even within the transmitted spectrum dips, the received signal-processing algorithm should be automatically modified, be a regularization, to enlarge the weight of transmitted dips components, which is equivalent to smoothening of the transmitted spectrum. c) The propagation length fluctuations can be eliminated by the brightpoint method based on the target range calculation basing on the results of matched filtration in every channel. Using this data, the random phase differences between the neighboring receive channel signals canbe compensated, and the radar signal can be reconstructed

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d) in the total integrated frequency band providing the maximum range resolution. ADC 1

Matched filter 1

ADC 2

Matched filter 2

ADC N

Matched filter N

Bright-point method

Phase compensation by the target distance estimation

Phase amendments Mj Coherent sum of the signals considering phase correction

Determination of the regularizer

Matched filter in the integrated frequency band

D

Inverse filter with regularizer

SNR

Computation of the regularizer D as a function of SNR Target image

Figure 8. Block-diagram of signal processing in radar with synthesized frequency band.

Applied to a single motionless target, this signal-processing algorithm is illustrated with a computer simulation shown in Figures 9 – 14. The primary signal is assumed linear-frequency-modulated (LFM) and covering subbands of all partial channels (Fig. 9). This signal filtered by high power narrow-banded amplifiers enters the multiplexer shown in Fig. 2. The spectrum and envelope of the signal radiated from the antenna are shown in Figures 9, 10.

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M. Petelin, G. Caryotakis, Yu. Postoenko,G. Sheitrum, I. Turchin 0

dB

-10

-20

-30

0.5

1

1.5 2 2.5 Frequency, GHz

3

3.5

Figure 9. Forming a high power broadband signal in the transmitter of the chirp radar, using multiplexer: thin dashed line – reference LFM spectrum (broadband, low power), thin solid lines - FRFs of amplifiers, bold line – spectrum of the irradiated broadband high power signal.

0

dB

-10

-20

-30

1

1.5

2 Time, Ps

2.5

3

Figure 10. Envelope of the irradiated LFM signal.

Fig. 11 shows results of matched filtration in a single channel and in the integrated frequency band. The peak width at the output of the matched filter in a single channel corresponds to the channel bandwidth GZ ('r = c/2GZ). The envelope of signal at the output of the matched filter applied for integrated frequency band has the central peak and the side lobes. The width of each lobe corresponds to the whole frequency band 'Z ('r = c/2'Z). The wider the bandwidth of each channel, the lower is the side lobes level.

195

Q-O Multiplexers for Space Communication 30

dB

20 10 0 -10

-30

-20

-10

0 Time, ns

10

20

30

Figure 11. Forming high power broadband signal in the transmitter of the chirp radar, using multiplexer: thin dashed line – reference LFM spectrum (broadband, low power), thin solid lines - FRFs of amplifiers, bold line – spectrum of the irradiated broadband high power signal.

The side-lobes effect is caused by the dips in the transmitted spectrum and, thus, in the received one (Fig. 12). To suppress this effect one can use non-matched filtration, in particular, an inverse filter with a regularizer. The mask for the inverse filter with regularizer parameter D is given with the following equation. Mask6Z

MaskI Z , D

4

¦ H rec n Z n

¦ H ar n Z

2

D

n

where Mask6 - is the mask for matched filter, that provides maximum SNR at the output, Hrecj – spectra of the received signals at multiplexer outputs, Harj - FRF of the analogous receiver. The denominator in this formula provides smoothing of the received spectrum: amplification of the spectrum dips is more than of its maximums.

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M. Petelin, G. Caryotakis, Yu. Postoenko,G. Sheitrum, I. Turchin 0

dB

-10

-20

-30

0.5

1

1.5 2 2.5 Frequency, GHz

3

3.5

Figure 12. Solid line - spectrum of the received integrated signal (coherent sum of the received signals considering phase correction). Dashed line – mask of the inverse filter with regularizer.

dB

20 10

a)

0 -10

-20

-10

0 Time, ns

10

20

dB

20 10

b)

0 -10 -20

-10

0 Time, ns

10

20

Figure 13. Signal at the inverse filter output at different regularization parameter D: a). D = 20dB, SNR = 27dB – matched filter, 't = 4 ns ('r = 1.2 m), b) D = -34dB, SNR = 20dB, 't = 0.9 ns ('r = 0.26 m). 0 dB corresponds to the noise level.

Fig. 13 shows signals at the output of the inverse filter with regularizer at different magnitudes of D. The major parameters of the signal at the output of the inverse filter with regularizer – side lobes level and SNR at the output of the filter at different SNR at the analog part output and at different relative bandwidth of a single channel GZ / 'Z are shown on Fig. 14, 15.

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197

Figure 14.. SNR and the side lobes level at the output of the inverse filter with regularizer vs. the SNR at the analog receiver output.

6.

SUMMARY

The use of multiplexers composed of circular mirror cavities seems a promising method for enhancing both the power and the frequency band of communication and radar systems at millimeter wavelengths. A radar with a synthesized frequency band provides enhancement of the target detection range and the range resolution, if the atmospheric fluctuations are compensated using a proper numerical method.

7.

REFERENCES

1. C. E. Shannon, A mathematical theory of communication, Bell System Tech. J, 27(4), 623656, (1948). 2. M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill Book Company, N.Y. 1980). 3. M. I. Petelin, G. Caryotakis et al, Quasi-optical components for MMW fed radars and particle accelerators, in AIP Conf. Proc. 474, 304 – 315 (1998). 4. G. Matthaei, L. Young, E. Jones, Microwave Filters, Impedance-Matching networks, and coupling structures (McGrow-Hill, NY, 1964). 5. X. P. Liang, K. A. Zaki, A. E. Atia, A rigorous 3 plane mode-matching technique for characterizing wave-guide T-junctions, and its application in multiplexer design, IEEE Trans. MTT, 39 (12), 2138-214 7 (1991) 6. V. I. Belousov, G. G. Denisov, N. Y. Peskov, Quasi-optical multiplexer based on reflecting diffraction grating, Int. J of IR&MMW, 12 (9), 1035-1043 (1991).

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7. Y. Rong, H. W. Yao, K. A. Zaki, T. G. Dolan, Millimeter-wave Ka-band H-plane diplexers and multiplexers, IEEE Trans. on MTT, 47(12), 2325 (1999). 8. G. Scheitrum, B. Arfin, B.G. James, P. Borchard, L. Song, Y.Cheng, G. Caryotakis, A. Haase, B. Stockwell, N. Luhmann, B.Y. Shew, The klystrino: a high power W-band amplifier, Int. Vacuum Electronics Conference, 2000, Abstracts, p. 22. 9. G. Scheitrum,; B. Arfin,; A. Burke, G. Caryotakis, A. Haase,; Y. Shin, Design, fabrication and test of the klystrino, 29th IEEE International Conference on Plasma Science (ICOPS) 2002, IEEE Conference Record, Abstracts, p. 200. 10. M. I. Petelin, I. V. Turchin, “Frequency characteristics of resonators coupled with waveguides”, Journ.of CT&E, 46(12), 1331-1334 (2001). 11. I. V. Turchin, A Multiplexer Composed of Circular Reflector Cavities, Journ. of Communications Technology and Electronics, 48(6), 624-628, 2003. 12. M. Mouly, M. B. Pautet, The GSM System for Mobile Communications (Palaiseau: Cell and Sys, 1992).

ACTIVE COMPRESSION OF RF PULSES

A. L. Vikharev1,2, O. A. Ivanov1,2, A. M. Gorbachev1,2, S.V. Kuzikov1, V. A. Isaev1, V. A. Koldanov1, M. A. Lobaev1, J. L. Hirshfield2,3, M. A. LaPointe2, O. A. Nezhevenko2, S. H. Gold4 and A. K. Kinkead5 1

Institute of Applied Physics, Nizhny Novgorod, 603600 Russia Omega-P, Inc. 202008 Yale Station, New Haven, CT 06520-2008, USA 3 Department of Physics, Yale University, POB 8120, New Haven, CT06520-8120 4 Plasma Physics Division, Naval Research Laboratory, Washington DC, USA 5 LET Corporation, Washington DC, USA 2

Abstract:

1.

The active RF pulse compression is considered as a candidate for using in feed systems of future electron-positron colliders. The key component of the compressor is an electrically controlled switch changing one state for another in a time much shorter than the desired RF pulse width. For an X-band twochannel RF compressor based on TE01-mode energy storage cavities, a gas discharge switch is proposed. Designs, low- and high-power tests of some versions of the compressor are described in this paper. At high-power tests carried using the Omega-P/NRL 11.424 GHz magnicon, 50 MW compressed RF pulses have been produced. The application of developed plasma switches for an electrically controlled switching of an existing passive pulse compressor SLED-II for increasing its efficiency as proposed by SLAC is discussed. The low-power test of the plasma switch for X-band active SLEDII compressor is described.

INTRODUCTION

It is widely accepted that microwave pulse compression is required for a future high-gradient electron-positron colliders in order to achieve the high peak RF power level (~500 MW in 100–400 ns pulses at frequency 11.424 GHz). For this purpose, the active pulse compressors are rather promising due to achieving high power gain higher than ten [1,2]. The key component of this compressor is an electrically controlled switch changing one state for another in a time much shorter than the desired RF pulse width. In this paper, two-channel X-band active rf pulse compressor that employs gas discharge switch tubes as active elements is considered. Designs, low- and high-power tests of some versions of the compressor are described. The each compressor utilizes an oversized cylindrical resonator operating in the axis-symmetric break down-proof TE01n mode (with n >>1), input 199 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 199–218. © 2005 Springer. Printed in the Netherlands.

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reflector and output reflector containing gas-filled switch tubes that can be externally discharged by application of a high-voltage pulse. Each channel of the two-channel compressor is connected to the driving generator and the load (the accelerating structure) via a novel 3-dB quasi-optical coupler. Two-channel compressor makes it possible to isolate the generator from the reflected microwave power at the initial stage of energy storage and to make the compressor design simpler. As proposed by SLAC [3], the efficiency of a pulse compressor of the SLED-II type could be increased by changing both the phase of the microwave source and the coupling coefficient of the delay line. In the existing SLED-II system the resonant delay line is coupled with the source via an iris with a constant reflection coefficient. Replacement of the iris with an active component makes it possible to create an active SLED-II system. In this paper use of a plasma switch as the active element is discussed. Design and low-power test of the plasma switch are described.

2.

TWO-CHANNEL ACTIVE RF PULSE COMPRESSOR WITH COMBINED INPUT/OUTPUT UNIT

The scheme of the two-channel active pulse compressor with combined input-output unit [4] is shown in Fig.1. The compressor consists of two identical channels. Each of the compressor channels has mode converters (TE01 o TE11, TE11 o TE01) connected with smooth tapered transitions and a resonator formed by a input-output reflector, a section of a cylindrical oversized waveguide and a cone-shaped reflector. The central part of the cavity for storing microwave energy is a section of an oversized 1m long waveguide 80 mm in diameter, which is equipped with a tapered 400 mm long transition to a narrower waveguide. The diameter of the latter waveguide was 55 mm, and the TE01 mode is the only propagating mode of all the axially symmetric ones. 4

1

6

7

8

9

6

7

8

9

3

2 5

Figure 1. Schematic diagram of the two-channel active compressor with combined input/output unit operating in the TE01 mode: 1 - driving generator, 2 - load, 3 - 3dB directional coupler, 4 - first channel, 5 - second channel, 6 - TE01-mode converter, 7 - inputoutput electrically controlled reflector, 8 - storage cavity, 9 - reflector.

Active Compression for Rf Pulses

201

The input-output reflector consists of active and passive sections. The scheme of the combined output reflector is shown in Fig.2. The active section is based on step-wise widening of a circular waveguide. This stepped widening section comprises a cylindrical TE031 mode resonator containing one or two quartz ring-shaped gas-discharge tubes. The passive section is a waveguide section with an over-critical narrowing. This combined input-output reflector makes it possible to reduce intensity of the electric field in the region of gas discharge tubes in the active section. By changing dimensions of the over-critical waveguide narrowing in the passive section, one can change the transmission coefficient and thus control the amplitude and duration of the compressed pulse. The frequency characteristics of such a combined output reflector are shown in Fig.3.

Figure 2. Output reflector with active and passive sections: 1 - circular waveguide, 2 stepped widening, 3 - gas-discharge tube, 4 - diaphragm.

R

R

3

1

1

3 2

2 1 f0 (a)

1 f

f

f0 (b)

Figure3. Frequency characteristics of the output reflector for (a) the condition of energy storage, and (b) for the condition of energy extraction. Frequency characteristics are shown of (1) the active section, (2) the diaphragm, and (3) total characteristics.

Schematic diagram of the experimental set-up for high-power tests of the two-channel active X-band rf pulse compressor with combined input-output reflector is shown in Fig.4.

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13 13

7

13

IV 13 4

1

8

II

16

5 33

5

8

I

8

III

2

9

6

Pref 12 18

7

9

11

Pinc 12

11 17

19

20

14

22 15

1

9 9

13

CH2

8

13

CH1

13

13

9

Pcom 12

Pch 2 12

Pch 1 12

9 11

9 11

9 11

21

10

Figure 4. Schematic diagram of the experimental set-up for high-power test of twochannel compressor: 1 – single-channel compressor, 2 - magnicon, 3 – quasi-optical 3-dB directional coupler, 4 – waveguide line, 5 – output window, 6- phase shifter, 7 – matched load, 8 – 55.5-dB directional coupler, 9 – coaxial waveguide, 10 – screen room, 11 – attenuator, 12 – detector, 13 – ion pump, 14 – high-voltage pulse generator, 15 – shielding box, 16 – divider, 17 – trigger generator, 18 – modulator, 19 – delay generator, 20 – trigger amplifier, 21 – pulse transformer, 22 – high-voltage power supply.

In the two-channel compressor, a 3dB directional coupler is one of the main elements of the compressor. The coupler makes it possible not only to decouple the generator from the reflected microwave power at the initial stage of energy storage, but also allows operating of each channel to one load. Fig.5 shows the frequency characteristics of the developed quasioptical 3dB hybrid coupler with arms III and IV terminated in reflecting shorts, and arm II terminated in a matched load, Fig.4. In evidence are 50:50 balanced splitting of the incident signal at 11.424 GHz from arm I into arms III and IV, >90% summing into arm II, and small reflections back into arm I. This quasi-optical 3-dB directional coupler operates on the principle of image multiplication in oversized rectangular waveguide [5]. The device is expected to operate at the multi-100 MW peak power level without encountering rf breakdown.

R

Active Compression for Rf Pulses

203 II

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

IV

III

I 11300

11400

11500

f (MHz)

Figure 5. Measured frequency characteristic of the 3dB quasi-optical directional coupler.

The high-power tests were carried out using the Omega-P/NRL X-band magnicon [6]. Fig.6 shows incident, reflected and output power pulses for this two-channel configuration when the plasma switch tubes are not fired. The difference between incident and output pulses is the energy stored in the compressor. In this example, 70% of the incident rf energy is stored with the balance being reflected into the output arm of the 3-dB hybrid, mainly during the first half of the pulse. P, MW 10

8

Pinc

6

4

Pcom 2

Pref 0

0

0.5

1

1.5

time, Ps

2

2.5

Figure 6. Traces of the incident Pinc, reflected Pref and output pulses without discharge of plasma switch.

Typical oscillogram of compressed pulse obtained when the plasma switch tubes in both channels are fired simultaneously, using an 80 kV trigger pulse of duration 100 nsec is shown in Fig.7. The maximum power of the compressed pulse reached 40-53 MW for pulse durations of 40-60 nsec, depending on the gas pressure in the discharge tubes. The accuracy of power measurements in these experiments was about r10%.

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A. L. Vikharev, et. al P, MW 60

Pcom

40

20

Pinc 0

0

0.4

0.8

1.2

1.6

2

time, Ps

Figure 7. Oscillogram traces of the incident Pinc and compressed Pcom pulses with external firing of the plasma switches. The gas pressure 0.4 Torr, pulse duration 43 ns, power of the compressed pulse 53 MW, power of the incident pulse 5.1 MW, total compression efficiency 56%.

3.

TWO-CHANNEL ACTIVE RF PULSE COMPRESSOR OF TRANSMISSION TYPE

The second version of the X-band active compressor that was developed and tested was a two-channel active pulse compressor of transmission type. A schematic diagram and the experimental set-up for high-power tests are shown in Fig.8. Each of the compressor channels had the same design as the first version of the compressor except of the input and output reflectors. The storing resonator of each of the channels was formed with a Bragg reflector and an output reflector with modified plasma switch. Unlike the previous experiment, the energy was directed into the storing resonator via the Bragg reflector, and was directed out via the output reflector. The compressor (channels CH1 and CH2) was connected to the magnicon (2) via the singlemode 3-dB directional coupler (3) by means of the waveguide line (4), in which the window (5) was installed to separate the vacuum chambers of the magnicon and the compressor.

Active Compression for Rf Pulses

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7

7

13

13

13 8

CH2

IV

I

4 5

6

16

3

9

18

11

12

13 VII

7

22

13

9

9

Pmag

VIII 8

3a

14

V 13

9

2

8 15

CH1

III

8

6a

VI

II

13

13

9

Pinc 12

11 17

19

20

Pref 12

P2 12

Pcom 12

11

11

11

21

10

Figure 8. Schematic diagram of the experimental set-up for high-power test of twochannel compressor of transmission type. 1 – single-channel compressor, 2 - magnicon, 3 – single-mode 3-dB directional coupler, 3a – quasi-optical 3-dB directional coupler, 4 – waveguide line, 5 – output window, 6- phase shifter, 6a- phase shifter, 7 – matched load, 8 – 55.5-dB directional coupler, 9 – coaxial waveguide, 10 – screen room, 11 – attenuator, 12 – detector, 13 – ion pump, 14 – high-voltage pulse generator, 15 – shielding box, 16 – divider, 17 – trigger generator, 18 – modulator, 19 – delay generator, 20 – trigger amplifier, 21 – pulse transformer, 22 – high-voltage power supply.

In order to decouple the microwave generator from the reflected signal, the single-mode 3-dB directional coupler (3) was used. The microwave power fed into branch I was divided in two in branches III and IV. In the energy storage regime the power reflected from the input Bragg reflectors into branches III and IV was added in the output branch, II. In this case no microwave power entered branch I (the electromagnetic waves reflected from each compressor channel were added with opposite phases in this branch). The phase difference 'M 0 required for division of the input power of the magnicon in two between branches III and IV of the single-mode 3-dB directional coupler was set by using the phase shifter (6). Single-channel compressors (CH1 and CH2) were connected to branches III and VI by means of single-mode waveguides. The output reflectors of each of the singlechannel compressors were connected to the input of the quasi-optical 3-dB coupler (3a). Thus, the compressed pulses from each of the compressor channels were fed to the input (branches V and VI) of the quasi-optical 3-dB directional coupler. At the same time, the compressed pulses at the output of the 3-dB coupler were added in phase, into branch VII and in antiphase, into

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branch VIII. The phase difference, 'M 0 , at the inputs of branches V and VI of the 3-dB directional coupler, which was required for coherent addition of the compressed pulses, was set by means of an additional phase rotator (6a). To eliminate spurious reflections, matched loads were built into branches II, VII, and VIII (7). The signals proportional to the power incident on the compressor, Pinc, the power reflected from the compressor, Pmag and Pref (branch I and branch II), and the total power of the compressed pulse, Pcom (branch VII) were registered. The compressor was switched from the regime of microwave energy storage into the regime of its output by means of electrically controlled output reflectors with modified plasma switch, Fig.9. The calculated frequency characteristics of the output reflector in the energy storage and energy removal regimes are shown in Fig.10.

6

1

5

4

2

3 Figure 9. Modified output reflector at the TE01 active mode: 1 – circular waveguide, 2input diaphragm, 3 – output diaphragm, 4 – output waveguide, 5 - adjustment device, 6 – gas discharge tubes. T, 10-6 8

0.5

6

0.4

T

0.3

4

0.2 2

0.1

0

0 11.0

11.2 11.4 f, GHz

ɚ)

11.6

11.0

11.2 11.4 f, GHz

11.6

b)

Figure 10. Dependence of the modified reflector transmission coefficient on the frequency for the regime of energy storage (a) and the regime of energy output (b).

The high-power tests of this compressor were carried out using the Omega-P/NRL X-band magnicon, also The characteristic oscillograms of the

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207

incident signal, Pinc, the signal reflected to the magnicon line, Pmag, and the signal reflected from the compressor, Pref are shown in Fig.11 when the plasma switch tubes are not fired. The difference between incident and reflected from the compressor pulses is the energy stored in the compressor. In this example, 69% of the incident rf energy was stored. 6

Pinc P, MW

4

Pref

2

Pmag 0 0

400

800

1200

1600

2000

t, nc Figure11. Oscillogram traces of the incident Pinc, reflected to the magnicon line, Pmag, and the reflected from the compressor, Pref pulses without discharge of plasma switch.

Typical oscillogram of compressed pulse obtained when the plasma switch tubes in both channels are fired simultaneously is shown in Fig.12.

Pcom

Pinc

Figure 12. Oscillogram traces of the incident Pinc and compressed Pcom pulses with external firing of the plasma switches. The gas pressure 0.3 Torr, pulse duration 55 ns, power of the compressed pulse 25.4 MW, power of the incident pulse 3.2 MW, power gain 8.

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4.

TWO-CHANNEL ACTIVE RF PULSE COMPRESSOR WITH PLASMA SWITCH BASED ON MODE CONVERSION

The scheme of the third version of the active two-channel compressor in which a plasma switch is based on conversion of the TE02 mode into the TE01 mode is used, is similar to the first version shown in Fig.1. In comparison with the first version, this compressor has not an input-output reflector, and a plasma switch is placed at the end of the storage resonator instead of a reflector (9). The schematic diagram of one channel of this compressor is shown in Fig. 13. gas discharge tubes

TE02

TE01 input and output waveguede

a) TE01 TE01 ~1% TE02

TE01 storage cavity

plasma switch

TE02 TE01

b)

c)

Figure 13. (a) Schematic diagram of the one channel of the active compressor with switch based on conversion of the TE02 mode into the TE01. (b) - mode conversion during energy storage; and (c) during energy extraction.

In the regime of power storage, the resonator is fed by the TE01 mode of a circular waveguide. The switch provides weak coupling of the feeding mode into the TE02 mode, which is cutoff at the entrance due to over-critical narrowing. Thus, the microwave power is stored in the TE02 mode. The discharge tubes of the switch are placed in the field weakened by the diaphragm, and their scattering action is counterbalanced within the required limits, by the internal diaphragm.

Active Compression for Rf Pulses

209

Non-vacuum plasma switch based on mode conversion was calculated, manufactured, and tested at a low power level at operating frequency 11.424GHz. This version of the plasma switch is based on a resonance reflector made as a widening of the cylindrical waveguide hooded with a small-diameter diaphragm. A schematic drawing of the switch is shown in Fig.14. 1

2

3 4 5 6

Figure 14. Plasma switch based on mode conversion: 1 - mechanical adjustment, 2 sliding short, 3 - gas discharge tubes, 4 - stepped widening, 5 - diaphragm, 6 - circular waveguide.

The switch is a resonator formed by step-wise widening of the circular waveguide and limited with diaphragm at one end. The length of the reflector can be changed by moving the short circuit by means of a special adjustment device. The axially symmetric TE23 mode is excited in the reflector. Two gas-discharge quartz tubes 8mm in diameter each and shaped as rings with external diameters equal to the waveguide diameter were placed into the reflector. Each of the tubes had electrodes that fed in highvoltage pulses that formed plasma in the tubes. The principle of operation of the switch is as follows. In the energy storage regime the power is stored at the TE02 mode, which is reflected from the switch completely without scattering into the TE01 mode. The latter is achieved by mutual compensation of radiation flows, which are formed by scattering at the diaphragm and radiation from the waveguide widening that acts as a resonator. The plot of the coefficient of reflection and conversion in the storage regime is shown in Fig. 15a. It is seen that at the resonant frequency 11.424 GHz the TE01ÆTE02 conversion is negligibly small. The switch is performed due to a discharge initiated in two quartz tubes at the bottom of the resonance switch. The tubes are separated by a ring diaphragm to reduce fields at the apertures in the switch walls, which are required to ignite the discharge. The coefficients of conversion into the TE01

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mode and of reflection of the TE02 mode into itself are shown in Fig.15b. At the working frequency, the mode-to-mode conversion coefficient is of the order of 30%, which is required to obtain a 100MW compressed pulse with duration ~50 ns.

a)

b)

Figure 15. Coefficients of reflection of TE 02 mode into itself and of conversion into TE01 mode during the storage regime (a) and coefficients of conversion into the TE01 mode and of reflection of the TE02 mode into itself during the extraction of energy (b).

The oscillogram of the compressed pulse is shown in Fig. 16. P, a.u. 0.5

0.4

0.3

0.2

0.1

0 0

100

200

300

400

t, ns Figure 16. Envelope of compressed pulse of the active compressor with plasma switch based on mode conversion.

The power gain obtained in the low-power experiments was 7-8 with duration of the compressed pulse 100 ns. To achieve a higher compression coefficient, one has to increase the Q-factor of the storing resonator and the coefficient of TE02-to-TE01 conversion in the output reflector. Estimates show that optimization of the input horn may make the Q-factor 1.5-2 times as high and the compression ratio, correspondingly, will be ~10-11.

Active Compression for Rf Pulses

5.

211

ANTICIPATED PARAMETERS OF ACTIVE RF COMPRESSORS WITH PLASMA SWITCHES

Low- and high-power tests showed that developed two-channel active pulse compressors would provide: 1. coherent superposition of compressed pulses from both channels; 2. compressed pulse with high power gain (in the range 10-12); 3. high stability of the phase of the compressed pulse (the output radiation phase within the 0.5 degree variation range); 4. high efficiency of pulse compression in the range 60-65%; 5. 3-fold reduction of electric field in the plasma switch in the second and third versions of compressor as compared to the first version, corresponding to a 5-10-fold increase of output power. Thus, design parameters for the X-band active two-channel rf pulse compressor with plasma switches could be as listed in Table 1. Table 1. Parameters of the X-band active compressor with plasma switches

Parameters Frequency Ohmic cavity Q Loaded cavity Q Input pulse width Output pulse width Power gain Input power Output power Efficiency

6.

Values 11.424 GHz 110,000 25,000 1.2-1.5 Ps 0.1 Ps 10-12 50 MW 400-500 MW 60-65%

ACTIVE SLED-II RF PULSE COMPRESSOR WITH DEVELOPED PLASMA SWITCHES

In the existing SLED-II system, the resonant delay line is coupled with the source via an iris with a constant reflection coefficient, Fig.17. As proposed by SLAC [3], the efficiency of a pulse compressor of the SLED-II type could be increased by changing both the phase of the microwave source and the coupling coefficient of the delay line. Replacement of the iris with an active component makes it possible to create an active SLED II system.

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A. L. Vikharev, et. al Phase shifter Klystron

Resonant delay line

Iris

3-db coupler

Accelerating structures

Fig.17. Schematic of SLEDII rf pulse compression system [7].

As it was noted in [3], an increase in the coupling of the line will reduce the amount of energy left over after the output pulse is finished. This allows more energy get out of the storage line during the compressed pulse. A onestep change in line coupling just before the start of the output pulse is considered, as this could be more easily realized in practice. Let us assume that in the time interval Gt (such that Gt << W) just before the last time bin, the phase of the incoming signal is reversed and the coupling iris reflection coefficient is changed from R0 to Rd. The iris reflection coefficient need not be reduced completely to zero. It then follows that the amplitude of the wave entering the accelerating structure will be given by [3] ª C 1 · 2 º § 2 2 ¨ 1  ( R0 p ) (1) « ¸ ». E s Ein ˜ Rd ˜ 1  (1  R0 ) p ˜ « ¨ 1  R0 p ¸ » ¹ »¼ © «¬ The compressed pulse takes place in the interval (C–1)W d t < CW. From Eq. 1 one can determine the efficiency of the system, K. It is found by dividing the energy of the compressed pulse by the total incident energy, namely:

K

1 § Es ¨ C ¨© Ein

2

· ¸¸ . ¹

(2)

Active Compression for Rf Pulses

213

Table 2 lists the values of efficiency of active SLED II system for various values of compression ratio C at optimal R0 and Rd. In these calculations, the system is assumed to be loss-free, i.e. p =1. Table 2: Active SLED-II power gain and compression efficiency, for no loss [3]. Compression Ratio, C 4 6 8 10 12 16 24

Discharging just before the last time bin R0 Rd M 0.646 0.536 3.48 0.775 0.443 5.09 0.835 0.386 6.72 0.869 0.346 8.34 0.892 0.317 9.97 0.920 0.275 13.2 0.947 0.225 19.7

K(%) 87.0 84.9 84.0 83.4 83.1 82.7 82.2

In the interval between the compression ratios of 6 and 24, the active system has a significant advantage over the passive SLED II system. At the same time (as shown in [3]) the delay line losses do not reduce operation efficiency in a significant way in the range of the compression ratio C = 816. Thus, as seen from Table 2, when C • 6, the active component of pulse compression system should change the iris reflection coefficient from R0 0.8  0.96 to Rd 0.4  0.2 . The plasma switches developed and presented in previous sections are acceptable for realization of the active SLED II system. In these switches, the resonance properties of cavity with gas discharge tubes are exploited. Design and low-power test of one version of the plasma switch are presented below. A schematic drawing of the plasma switch is shown in Fig.18. The plasma switch consists of the reflector and the diaphragm. The diaphragm (iris) was placed into the circular waveguide, where only the TE01 mode propagated. The reflector of the switch is formed by a step-wise widening of the circular waveguide. One of the walls could be moved in the reflector by means of a special adjustment device. Thus, the length of the reflector could be changed. The axially symmetric TE014 mode is excited in the reflector. Two gas-discharge tubes made of quartz were placed in the reflector. They were 8 mm in diameter each and shaped as rings with their external diameters equal to the diameter of the reflector. Each of the tubes had electrodes that fed in high-voltage pulses, which formed plasma in the tubes. The diaphragm could be also moved in the waveguide by means of a special adjustment device. The length of the waveguide between the diaphragm and the reflector was regulated in such a way as to provide the resonance in the “diaphragm-reflector” resonator, when the plasma is produced in the reflector.

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1

1

3

6

5 2 Figure 18. Plasma switch for active SLED II system: 1 - mechanical adjustment, 2 – movable wall, 3 - gas discharge tubes, 4 – stepped widening, 5 – movable diaphragm, 6 – circular waveguide.

The principle of operation of the switch of this type can be easily understood basing on the frequency characteristic shown in Fig.19. 1

|R|2 2

0.8

1

0.6 0.4 0.2 0 1

3

0.8 0.6

4

0.4 0.2 0 10.5

11

11.5

12

12.5

f, GHz Figure 19. Calculated frequency characteristics of the switch with two gas-discharge tubes (1 and 3 – without plasma, 2 and 4 – in the case of gas breakdown): 1 and 2 – characteristics of the step-wise waveguide widening, 3 and 4 – characteristics of the whole switch.

In the regime with a high reflection coefficient from the switch (curve 3), the main part of the power is reflected from the diaphragm at the operating frequency f 0 = 11.424 GHz. The reflection coefficient from the ref lector

Active Compression for Rf Pulses

215

(step-wise waveguide widening) is low (curve 1). When the plasma is produced in the tubes, the frequency characteristic of the reflector is displaced, and the reflection coefficient from it grows (curve 2). In the case of a certain phase incursion between it and the diaphragm, the effect of switch brightening occurs and the reflection coefficient drops sharply (curve 4). The position of the resonance minimum for the switch with the plasma depends on plasma density, geometric dimensions of the reflector and the distance between the reflector and the diaphragm. Thus, by regulating the length of the reflector by means of mechanical adjustment, one can change the position of the minimum at present electron density and, hence, the reflection coefficient in the switched stage. Operation of the plasma switch as a component of the resonant delay line compression system was tested experimentally at a low power level according to the scheme shown in Fig. 20. 16

14

15

3

18

17

17

19

10 12

13

9 20 8 Mt

1

2

21

6

11

8 6

9

5

4

8

7 9

Figure 20. Schematic diagram of the experimental set-up for measurements of characteristics of resonant delay line compression system: 1 - microwave generator, 2 circulator, 3 – Marie mode converter, 4 - oscilloscope, 5,6 -attenuators, 7 - measure of frequency, 8 - directional coupler, 9 - detector, 10 - high-voltage pulse generator, 11 – trigger generator, 12 – rectangular waveguide, 13 - screen room, 14 - electrically controlled reflector, 15 - circular waveguide, 16 – gas-discharge tubes, 17 – smooth tapered transition, 18 – 6m long circular waveguide, 19 – short circuit, 20 – phase shifter, 21 – pulse generator.

The compression system was formed by the plasma switch, smooth tapered transitions a circular copper waveguide 6m long and 70 mm in diameter, and

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A. L. Vikharev, et. al

a short circuit. The resonant delay line was tuned to the operating frequency f0 = 11.424 GHz by means of moving the short circuit and was excited at the TE01 mode of the circular waveguide. The Marie mode converter excites the TE01 mode just before the diaphragm of the plasma switch. We checked operation of the compression system in the regime close to the regime of operation of the active SLEDII compressor, when inversion of the phase of the incident microwave radiation happens simultaneously with the decrease in the plasma switch reflection coefficient. The experiment registered the compressed pulses obtained only for the case of passive compression (when the phase of the incident microwave radiation was inverted), and then when the both types of the compression were used. The oscillograms of the compressed pulses obtained by using different types of compression are shown in Fig.21. In the regime of passive compression the reflection coefficient from the switch did not change with time and remained sufficiently high. Hence, the microwave energy was removed from the delay line during several runs. In that case, the compressed pulse had longer duration and characteristic steps determined by the time of the doubled wave run along the delay line. The use of a combination of the active and passive compression resulted in higher amplitudes and shorter durations of the compressed pulse, Fig.21. Actually, when the reflection coefficient from the switch becomes lower, the energy was removed from the delay line during a smaller number of wave runs in the line. As the result, the power gain reached M = 10–11 at pulse duration W = 70–90 ns. In that case, the shape of the compressed pulse became more rectangular as compared with the pulses obtained during operation in the active compression regime only. P/P0 12 10

2

8 6

1

4 2 0

-50

0

50

100

150

200

250

time, ns

Figure 21. Envelope of the compressed pulse of the compression system with the plasma switch: 1 – passive compression, 2 – combination of active and passive compression.

Active Compression for Rf Pulses

7. 1. 2.

3.

8. 1.

2.

3.

4.

9.

217

ANTICIPATED RESULTS FOR ACTIVE SLEDII RF PULSE COMPRESSOR Developed plasma switches would provide variation of the reflection coefficient in the range from R0 = 0.8 – 0.96 to Rd = 0.4 – 0.2. Calculations of the threshold electric field for microwave breakdown in the tubes and of the values of electric fields near the tubes in the plasma switch showed that the maximum output power in one delay line could reach 200 MW. Thus, active SLED II can have the output power of 400 MW and efficiency of the order of 80%. Low-power tests of developed plasma switches with a 6 m resonant delay line with the round trip power losses equal to D =1.5% showed that it is possible to achieve the following parameters of the active SLEDII compression system: compression ratio C = 10 – 16, power gain M = 7 – 12, and compression efficiency K = 65 – 75%.

CONCLUSION Two-channel TE01 mode energy storage resonators with plasma switches have been shown, in low- and high-power tests, to be promising candidates for high-power RF pulse compressors of next linear colliders. For one version of the two-channel pulse compressor in triggered regime, 50 MW, 60ns output pulses, with energy storage efficiency 70%, energy extraction efficiency 80% and total efficiency 55% were obtained. The different plasma switches for two-channel active pulse compressor have been developed. Compressor with these plasma switches will be able to provide 400-500 MW, 100ns output pulses at 11.4 GHz band and to obtain output pulses with only a slight variation of phase with time (~ 0.5 degree). Plasma switch has been developed for testing with X-band SLED-II for production of flat-top compressed pulses and for increasing the efficiency of SLED-II system.

ACKNOWLEDGMENTS

This work was supported by the US Department of Energy, Division of High Energy Physics.

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2.

3. 4.

5.

6.

7.

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REFERENCES Tantawi S.G., Rath A.E., Vlieks A.E., and Zolotarev M., “Active high power rf pulse compression using optically switched resonant delay line,” Advanced Accelerator Concepts, 7th Workshop, Lake Tahoe, CA, 1996, AIP Conf. Proc., 398, 813 (1997). Vikharev, A.L., Gorbachev, A.M., Ivanov, O.A., Isaev, V.A., Kuzikov, S.V., Kolysko A.L., Litvak A.G., Petelin M.I., and Hirshfield J.L., “Active microwave pulse compressors employing oversized resonators and distributed plasma switches” Advanced Accelerator Concepts, 8th Workshop, Baltimore, Maryland, 1998, AIP Conf. Proc., 472, 975, (1999). Tantawi S.G., Rath A.E., Vlieks A.E., “Active high power rf pulse compression”, Nucl. Instrum. Meth. Phys. Res., A370, 297 (1996). Vikharev A.L., Gorbachev A.M., Ivanov O.A., Isaev V.A., Koldanov V.A., Kuzikov S.V., Litvak, A.G., Petelin, M.I., Hirshfield, J.L. and Nezhevenko, O.A., “ Twochannel active high-power X-band pulse compressor”, Advanced Accelerator Concepts, 9th Workshop, Santa Fe, NM, 2000, AIP Conf. Proc., 569, 741 (2001). Denisov, G.G., Kuzikov, S.V., “Microwave systems based on controllable interference of paraxial wavebeams in oversized waveguides” in Proceeding of Strong Microwaves in Plasmas Workshop, edited by A.G.Litvak, Nizhny Novgorod: IAP, 618 (2000). Vikharev A.L., Ivanov O.A., Gorbachev A.M, Isaev V.A., ., Kuzikov S.V, Gold S.H., Kinkead A.K, Nezhevenko, O.A., and. Hirshfield, J.L. “High-power tests of a twochannel X-band active rf pulse compressor using plasma switches”, High Energy Density and High-Power RF: 6th Workshop, Berkeley Springs, West Virginia, 2003, AIP Conf. Proc., 691, 197 (2003). 2001 Report on the Next Linear Collider, SLAC-R-571, Snowmass 2001; ZerothOrder Design Report, SLAC Report 474, May 1996.

CONTROL OF INTENSE MILLIMETER WAVE PROPAGATION BY TAILORING THE DISPERSIVE PROPERTIES OF THE MEDIUM Asher Yahalom and Yosef Pinhasi Dept. Of Electrical and Electronic Engineering, The College of Judea and Samaria, P.O. Box 3, Ariel 44837, Israel

Abstract

We have developed a space-frequency model for the propagation of a highfrequency signal in an arbitrary dispersive medium. The model can be solved analytically under certain conditions for a Gaussian pulse, revealing the conditions under which pulse compression or expansion occurs. It can also be shown that under appropriate conditions, the delay-time of the pulse can be stretched almost indefinitely and can be shortened so that apparent superluminal propagation is achieved. We further discuss how materials might be tailored for certain pulse characteristics in order to achieve a priori defined amount of compression and delay. This is done using a model of a resonant material susceptibility.

Keywords

Millimeter Waves, Dielectric Model, Delay Time Manipulation, Pulse compression

1.

INTRODUCTION

The purpose of this work is to study the effect that a general dispersive medium in which the complex dielectric permittivity depends on how the frequency is affecting a pulse traveling through this medium. The aim of this study is twofold. One is to understand how a naturally occurring medium affects electro-magnetic pulses traveling inside this medium. This is a typical problem in applications such as communications, radar systems, and energy transfer. In those cases, the medium under consideration is atmospheric air that is a mixture of different gases in which the dielectric properties depends on different conditions such as temperature, humidity and the existence of rain. Another purpose of this study is to describe a method for which one can

219 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 219–239. © 2005 Springer. Printed in the Netherlands.

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affect the properties of the electromagnetic pulse such as its power, width and time of propagation (delay time) by introducing a dielectric medium in its path. In particular, we have studied how a material with an absorption line can be used to obtain the desired modifications. This of course will be shown to depend on the intrinsic properties of the absorption line that include its strength, resonance frequency, and width. As a model for such an absorption line a Lorentzian curve was utilized. It will be shown that in order to realize useful features such as pulse compression a non-trivial choice of medium parameters should be considered. Several theoretical papers addressed the problem of distortion occurring when a short pulse is propagating in absorptive and dispersive media, including gases and plasmas [13-19]. They also studied the delay and pulse shape evolution along the path of propagation. Gibbins [18] extended earlier investigations [14,16] and examined distortions of short Gaussian pulses, modulating millimeter waves and propagating in the atmosphere. An approximation of the wave propagation factor was used to derive analytical expressions for the pulse shape. Conditions for pulse broadening and compression were identified. In this work, we study how the parameters of a resonant dielectric curve effects the pulse propagating through the medium; specific analytic formulas are derived for pulse compression and expansion, as well as time-delay and power reduction. Choosing the “right” resonance characteristics allows us to tailor the medium, in order to achieve a desirable optical effect.

2.

MILLIMETER WAVE PROPAGATION IN A DIELECTRIC SUBSTANCE

The time dependent field E t represents an electromagnetic wave propagating in a medium. The Fourier transform of the field is:

E f

f

³ E t ˜ e

f

 j 2Sft

dt

(1)

Control of Intense Millimeter Wave Propagation

221

Propagation of electromagnetic waves in a medium can be viewed as transformation through a system (see Figure 1).

Figure 1: Linear system representing propagation of electromagnetic waves in a medium.

In the far field, transmission of a wave, radiated from a localized (point) isotropic source and propagating in a (homogeneous) medium is characterized in the frequency domain by the transfer function, derived in Appendix A of [27]:

Hf {

E out  f Ǽin  f

d0 ˜ e  jk  f ˜ d d0  d

(2)

Here, k  f 2Sf PH is a frequency dependent propagation factor, where İ and µ are the permittivity and the permeability of the medium, respectively. The transfer function H  f describes the frequency response of the medium. Its inverse Fourier transformation corresponds to the temporal impulse response ht . In a dielectric medium, the permeability is

equal to that of the vacuum P

P 0 and the permittivity is given by

H f H r  f ˜ H 0 . If the medium introduces losses and dispersion, the relative dielectric constant H r  f is a complex, frequency dependent function, for which it’s real and imaginary parts satisfy the Kramers - Kronig

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relations [24-25]. The resulting index of refraction n f presented by:

H r  f can be

n f 1  N  f

(3)

Where N  f N r  f  j ˜ N i  f is the complex refractivity of the substance. The propagation factor can be written in terms of the index of refraction:

k f

2Sf ˜ n f c

(4)

Substituting expressions (3) and (4) in equation (2), assuming horizontal propagation in a homogeneous medium, results in the transfer function:

H f

d0 ˜ e >D  f  jE f @˜d d0  d

(5)

2Sf ˜ Ni  f c

(6)

where

D f  Im^k ( f )`

and

E f

Re^k ( f )`

2Sf ˜ >1  N r  f @ c

are the attenuation coefficient and wave number of the propagating wave

Control of Intense Millimeter Wave Propagation

223

respectively. The power transfer function along the propagation path is given by: 2

Hf

2

§ d 0 ·  2 D  f ˜d ¨¨ ¸¸ ˜ e  d d 0 © ¹

(7)

Transmission of Broadband Modulated Signal

2.1

Assume that a carrier wave at f 0 is modulated by a wide-band signal

Ain t :

Ein (t )

^

Re Ain t ˜ e j 2 Sf 0t

`

(8)

The Fourier transform of the transmitted field is:

E in ( f )

1 1 * A in  f  f 0  A in >  f  f 0 @ 2 2

(9)

Where A in  f is the Fourier transform of the complex envelope Ain t . After propagating along a path with a distance d, the field is:

E out ( f )

1 1 A in  f  f 0 ˜ H  f  A in * >  f  f 0 @˜ H *  f 2 2 (10)

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Since the transfer function H  f is the Fourier transform of a real function,

H f

H *  f . The inverse Fourier transformation of Eq. (10), results

in a received field given in the time domain by:

^

Re Aout t ˜ e j 2 Sf 0t

Eout (t )

`

(11)

Where the complex envelope of the signal obtained at the receiver cites is given by:

Aout t

f

³ A  f ˜ H  f  f ˜ e in

 j 2 Sft

0

df

(12)

f

2.2

Ultra Wide Band Pulse Modulation

Assume that the transmitted waveform is a carrier modulated by a Gaussian envelope:

Ain t e



t2 2 V in 2

(13)

characterized by a standard deviation V in . Fourier transformation of the pulse results in a Gaussian line-shape in the frequency domain:

A in  f

2S ˜ Vin ˜ e



1  2 SVin f 2

2 (14)

Control of Intense Millimeter Wave Propagation shown in Figure 6. bandwidth is

Vf

225

The corresponding standard deviation frequency

1 2SV in

. The full-width half-maximum (FWHM) is the –

3-dB bandwidth and is equal to B

2 ln2 ˜ V f # 0.265 ˜ V in 1 .

Figure 2: The normalized Gaussian line shape.

In order to calculate the pulse shape Aout t after propagation along a horizontal path in the atmospheric medium, we substitute the Fourier transform (14) into expression (12). Analytical result can be found if the complex propagation factor (5) is approximated in the vicinity of the carrier frequency f 0 , by a second order Taylor expansion [14-16]:

1 2 k  f # k 0  k '˜ f  f 0  k ' '˜ f  f 0 2

(15)

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where k 0 { k  f 0 , k ' { dk df

, k''{ f0

d 2k df 2

.

The second order approximation

f0

given in Eq. (15) can be used if the standard deviation V in of the Gaussian pulse satisfies 2

1

¦ n! ˜ k

(n)

˜ V in

n 0

n

f

1 (n) n ˜ k ˜ V in , 3 n!

!! ¦ n

resulting in a complex envelope:

Aout t

V d0 ˜ in ˜ e d0  d V

§ k 'd · ¸ ¨t © 2S ¹  2V 2

2

˜ e  jk 0 ˜ d ,

(16)

where:

V2

2

Vin  j

k'' ˜d 2S 2 .

Expression (16) is valid if

^ `

Re V 2

2

V in 

D' ' d

2S 2

! 0.

(17)

This condition is always satisfied if D ' ' ! 0 . However, at frequencies for which the attenuation curve is convex D ' '  0 (in the vicinity of absorption 2

lines) the analytical results are only valid for V in ! 

D' ' d

2S 2

! 0 . Another

interpretation of this result is that for a given initial pulse width V in , the

 2 distance should not exceed d   2SV in in order for (16) to be valid. D' '

Control of Intense Millimeter Wave Propagation

227

The magnitude (absolute value) of the complex envelope given by (16) has a Gaussian shape: t t 2

Aout t

ª º  2V outd 2  1 D ' d 2 d 0 V in ˜ ˜ exp« D 0 ˜ d  » ˜e 2 2SV in 2  D ' ' d ¼ d0  d V ¬

(18) with a temporal delay:

º D' E' ' d 1 ª «E' »˜d 2 2S «¬ 2SV in  D' ' d »¼

td

(19)

and a standard deviation V out given by: 2

Vout

2

Vin

2

ª E' ' d º « 2»  2S ¼ D' ' d ¬   2S 2 V 2  D' ' d in 2S 2

(20)

These results, which can be obtained from the solutions derived in [14,16], show that in the framework of the approximation (15), a Gaussian magnitude Aout t is preserved while propagating in the medium (although its width changes) and thus can be retrieved by the receiver. For a short distance (or a wide pulse), the time delay can be approximated by t d |

E' ˜d . 2S

This becomes the exact solution at

attenuation peaks, where D ' 0 . When D ' '  0 , the denominator of Eq. (19) may become arbitrary small, (however should be kept positive in order to satisfy the validity condition (17)). In that case the time delay is approximately t d | 

1 D' E' ' d 2 , resulting in and arbitrary long 2S 2SV in 2  D' ' d

delay in the pulse arrival at a distanced.

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Examination of Eq. (20) reveals that when D ' ' t 0 the pulse always widens along the path of propagation. However, for D ' '  0 (e.g. in the vicinity of absorption frequencies), the pulse may become narrower while propagating in the atmospheric medium. Pulse compression occurs when

V in 2 d

!

1

2S 2 D ' '

obtained for V in For

long

D ' '

d

2

2S

2

2



 E ' ' 2 . In both cases minimum pulse width is

 E' '  D' ' resulting in V

propagation

distances,

the

2 out min

time

2

E '' d . 2S 2

delay

approaches

1 td o D' ' E'D' E' ' ˜ d and the standard deviation approaches 2SD' ' 1 2 V out o D' ' 2 E' ' 2 ˜ d . 2 2S D' '



3.



TAILORING THE PROPERTIES OF THE MEDIUM

So far are discussion has concentrated on a medium with fixed dielectric properties, the only thing remaining is calculating its effect on a propagating signal. In this section we intend to look at the problem of signal propagation from a different angle. The problem we address is what type of medium should one construct in order to achieve a certain modification in a given signal such the change of width (pulse compression), time of propagation or pulse power.

3.1

The Medium

We assume a gaseous medium, which contain molecules, since the most interesting effects occur near resonances we choose to study the behavior of the pulse near resonance frequencies. The resonant susceptibility can be derived from a simple model in which a dissipative oscillator is excited by a time dependent electric field [28]. In this case the susceptibility Ȥe is given by

Control of Intense Millimeter Wave Propagation

229

F

Fe ( f )

f f 1( ) 2  j ( )Q 1 fr fr

(22 )

in which fr is the resonant frequency and Ȥ is a measure of the “strength” of the resonance, the quality factor Q is a measure for how many periods can the oscillator oscillate before its energy is dissipated. It also measures the Lorentzian width since for large enough Q, | F e ( f ) | drops to about 44%

Figure 3: Graph of

f fr

| Fe |

for Q=10 and Ȥ=1.

1 (see Figure 3). F e ( f ) is related to the Q complex propagation factor k ( f ) used in the transfer function given in Eqn. percent of its value for

1r

(3) by the formula:

k f

2Sf ˜ Hr c

2Sf ˜ 1 Fe ( f ) c (23)

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In what follows we make the approximation: F ˜ Q H 1  1 this will enable us to write the propagation factor as a sum of two terms:

k f

2Sf 2Sf 1 ˜ 1 Fe ( f ) # ˜ (1  F e ( f )) c c 2

ks ( f )  kr ( f ) (24)

One term is the free space propagation factor given by:

2Sf c

ks ( f )

E s ( f ) (D s

0) ,

(25)

while the other is the “resonant” propagation factor given by

kr ( f )

Sf c

˜ Fe ( f )

E r ( f )  jD r ( f ) .

(26)

This allows the factorization of the transfer function as follows:

H

d0 e  jkd d  d0

HS Hr

(27)

This will result in a simpler numerical scheme in which we only need to integrate H r in order to calculate A , from which it is trivial to calculate

Aout , namely

A t

f

³ A  f ˜ H  f  f ˜ e

 j 2Sft

d0 d j A (t  )e d  d0 c

2Sf 0 d c

in

r

0

f

Ÿ Aout t

3.2

df (28)

Analytical Calculations

The analytical calculations of the various quantities such as delay time, pulse width and pulse power include the calculations of derivatives up to second order of D
and
E . But first we will differentiate between trivial “free propagation” effects and non-trivial “resonant” effects. Following equation (19) we can write the contributions to td as

Control of Intense Millimeter Wave Propagation

td

ES ' d  tr 2S

tS  tr

231

d  tr , c

(29)

in which tr is the “resonant” delay time give only in term of resonant quantities:

tr

1 2S

ª º D r ' E r ''d « E r ' »˜d . 2 2SV in  D r ' ' d »¼ «¬

(30)

The other quantities of interest that can be dissected in this way are the pulse width (see equation 20):

V out 2 V s2

V r2 V s2 Ÿ V in 2

(31) 2

V r2

ª Er ''d º « 2 » D r ''d ¬ 2S ¼  2S 2 V 2  D r ' ' d in 2S 2

From the above formula it is obvious that a change in the pulse width is only due to the resonant contribution, in the free propagating scenario the pulse retains its width as expected. To calculate change in pulse power we use equation (18) with t t d , to obtain PF

Aout td

PFs

d0 d0  d

PFs ˜ PFr Ÿ

(32)

º ª D r ' d 2 1 ˜ exp «  D 0 r ˜ d  » 2 2 d  2 SV D ' '  Dr '' d 2 Er ''d 2 in r ¼ ¬  ) ( ) 2 2 ( 2S ) ( 2S )

V in

PFr 4

(V 2 in

The free space power factor PFs just scales linearly with the distance as expected, for the resonant part PFr we obtain a more complex expression, which contain dominant exponential factors.

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The Derivatives of Propagation Factor

All the above interesting quantities depend on the derivative of the propagation factor. Those are depicted in Figure 4 for
and in figure 5 for
; in the plots and tables below, the derivative is taken with respect to the normalized frequency

f instead of the frequency f . fr

Figure 4: Graph of

Dˆ F

D Sf r c

for Q=4.

Control of Intense Millimeter Wave Propagation

Figure 5: Graph of

Eˆ F

E Sf r

233

for Q=4.

c

Furthermore we tabulate the value of
and
and their derivatives for future use in the table below: Table 1: Complex propagation factors at the 60-GHz band

at resonance 1st derivative 2nd derivative 3rd derivative

Dˆ

Eˆ

Q 0 -8Q3 24Q3

0 -2Q2 2Q2 6(8Q4 – Q2)

Third order derivatives are taken in order to estimate the range of validity of the analytical approximation; this is done by taking up to the third term in the right hand side of 2

1

¦ n! ˜ k n 0

(n)

˜ V in

n

f

1 (n) n ˜ k ˜ V in . 3 n!

!! ¦ n

(33)

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Pulse with a Carrier Frequency at Resonance

By inspecting figures 4 and 5, we see that the medium effect on the signal can be divided into two regimes. One is the “on” resonance effect in which the carrier frequency is equal to the resonance frequency f 0 f r ; in this case, the simple expressions from Table 1 can be used. Otherwise, more involved expressions that are functions of

f must be utilized; those fr

expressions are more easily comprehended graphically than algebraically. In the expressions one should bear in mind that the following approximations are made: from equation (33) in which derivatives are taken to the third order, one derives the condition:

1 !! H 2

2Q

(35)

V in f r

in the case that Q is large. This means that the width of the Gaussian in the frequency domain should be much smaller than the width of the Lorentzian curve. Furthermore, from equation (17), we obtain an additional condition of validity that takes the following form for resonant frequencies:

V in 2 ! 8Q 3 ˜

F tS 4Sf r

.

(36)

Bearing in mind the above conditions we can now calculate the various quantities of interest. For the resonant delay time we obtain the result:

tr

1 E r '˜d 2S

t S FQ 2 .

(37)

The negative sign of tr indicates that signal arrives faster than should be expected by speed of light propagation, hence it appears super-luminar. However, this is only an illusion, which is caused by the infinite extent of the Gaussian pulse. In fact, the super luminal Gaussian results from the tail of the original Gaussian as is explained in many papers and textbooks [28,29,30]. (The propagation of the pulse still has causal characteristics that can be described by the Sommerfeld forerunner [31]). Figure 6 shows the result of a numerical calculation that results in a 7.5 seconds advance of the pulse propagating inside the material over free-pulse propagation. The parameters used for this calculation are given in Table 2, in MKS units.

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Fig. 6: Numerical calculation of super Luminal propagation

Table 2: Parameters used for super Luminal calculations in MKS units

To calculate the effect of the resonance on the pulse width, we rewrite equation (20) using the normalized
and
of figures 4 and 5; a normalized V in 2 is introduced, as follows.

V out 2 Vˆ in

2

F tS 4Sf r

ª 2 Eˆr ' '2 º » «Vˆ in  Dˆ r ' ' 2 Vˆ in  Dˆ r ' ' ¼ ¬

4Sf r V 2 F t s in

(38)

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Using the entries from Table 2, this can rewritten as

V out 2

F tS 4Sf r

ª 2 4Q 4 º 3 ˆ   V Q 8 ». « in Vˆ in 2  8Q 3 ¼ ¬

(39)

The previous formula clearly shows that the largest pulse expansion in the time domain (and hence the best coherence in the frequency domain) is 2 achieved when V in is very close to 8Q 3 . Introducing the small parameter

'2

Vˆ in 2  8Q 3 we obtain the pulse expansion coefficient: V out 2 Q # 2. 2 2' V in

ER 2

(40)

For minimal expansion and compression we utilize an equation from Section 2.2, which gives the width of the input signal needed to achieve maximum compression. It has the resonant value:

V in 2

d  E ' '  D r ' ' 2S 2 r

Ft S Q 2 2Sf r

(1  4Q) ,

(41)

for which the minimal width of the output signal and compression ratio can be written as:

V out CR

2 min

2

Er '' d

2

V out

2S 2 2 min

V in 2

Ft S Q 2 Sf r

(42)

2 1  4Q

We see that whatever the effect, time delay, pulse expansion or compression, the size of the effect depends on the quality factor of the Lorentzian. As a final point for this section, we investigate the resonant power factor taking into account the validity limits of the analytical approximation such as those given by equations (35,36). In this case, we obtain the expression

PFr

'2  8Q 3

4

ª 16S 2Q 3 º . ˜ exp «  2 3 2» '4  4Q 4 ¬ ( '  8Q )H 2 ¼

(43)

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237

In case that Q !! ' this reduces to the more simple expression

PFr

ª 2S 2 º 2 Q ˜ exp « 2 » . ¬ H2 ¼

(44)

This expression shows that in order for the analytic approximation to be satisfied: H 2  1 , the reduction in power should be very large, an effect that can be counter balanced by extremely high Q values. This means that the effects can be realized for intense input radiation, and intense millimeter wave radiation in the case of a signal in the EHF band.

4.

CONCLUSIONS

The space–frequency approach for the propagation of electromagnetic waves in dielectric media, is presented in this paper. It enables consideration of how the absorptive and dispersive characteristics of the materials that compose the media, affect the transmission of wide-band signals. Using a complex representation of a frequency-dependent refraction index, a transfer function that describes the frequency response of the medium is formulated. Atmospheric transmission of millimeter waves, modulated by ultra-short Gaussian pulses, is studied analytically and numerically in the frequency domain revealing spectral effects on pulse propagation delay, width and distortions. Using second order expansion of the propagation factors lead to the derivation of approximated analytical expressions for the delay and width as a function of distance and carrier frequency. Conditions under which pulse compression or expansion occurs were identified. The analytical solution is found to be limited in describing narrow-band links where not too short pulses are involved. For wide band applications the numerical model use is required We further suggested a way to “tailor” the features of the medium, in order to obtain some desired effects on the signal. Such effects as pulse compression, expansion, or introducing a ”negative” time delay can be realized for a Lorentzian absorption line in which the pulse carrier frequency is equal to the resonance frequency of the absorption line. Unfortunately for such effects to be realized, and in order to compensate for the large absorption, the signal must be transmitted using highly-intense millimeterwave radiation.

238

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REFERENCES

1. H. T. Friss: “A note on a simple transmission formula”, Proc. IRE 34, (1946), 254-256 2. J. D. Kraus: “Antennas”, McGraw-Hill, (1988) 3. R. K. Crane: “Propagation phenomena affecting satellite communication systems operating in the centimeter and millimeter wavelength bands”, Proc. Of the IEEE 59, (2), (1971), 173-188 4. R. K. Crane: “Fundamental limitations caused by RF propagation”, Proc. IEEE 69, (2), (1981), 196-209 5. L. J. Ippolito: “Radio propagation for space communication systems”, Proc. IEEE 69, (6), (1981), 697-727 6. H. J. Liebe: “Atmospheric EHF window transparencies near 35, 90,140 and 220 GHz”, IEEE Trans. On Antennas and Propagation 31, (1), (1983), 127-135 7. R.A. Bohlander, R. W. McMillan: “Atmospheric effects on near millimeter wave propagation”, Proc. Of the IEEE 73, (1), (1985), 49-60 8. N. C. Currie, C. E. Brown: “Principles and applications of millimeter-wave radar”, Artech House (1987) 13. O. E. Delange: “Propagation studies at microwave frequencies by means of very short pulses”, Bell Syst. Tech. J., 31, (1952), 91-103 14. M. P. Forrer: “Analysis of millimicrosecond RF pulse transmission”, Proc. IRE 46, (1958), 1830-1835 15. L. E. Vogler: “Pulse distortion in resonant and nonresonant gases”, Radio Sci., 5, (1970), 1169-1180 16. G. I. Terina: “On distortion of pulses in ionospheric plasma”, Radio Eng. Electron. Phys. 12, (1967), 109-113 17. D. B. Trizna, T. A. Weber: “Brillouin revisited: Signal velocity definition for pulse propagation in a medium with resonant anomalous dispersion”, Radio Sci., 17, (1982), 1169-1180 18. C. J. Gibbins: “Propagation of very short pulses through the absorptive and dispersive atmosphere”, IEE Proc. 137, (5), (1990), 304-310 19. A. Maitra, M. Dan, A. K. Sen, S. Bhattacharyya, C. K. Sarkar: “Propagation of very short pulses at millimeter wavelengths through rain filled medium”, Int. J. of Infrared and Millimeter waves 14, (3), (1993), 703-713 20. J. H. van Vleck: “The absorption of microwaves by oxygen”, Phys. Rev. 71, (1947), 413424 21. P. W. Rosenkranz: “Shape of the 5 mm oxygen band in the atmosphere”, IEEE Trans. On Antennas and Propagation 23 (1975), 498-506 22. H. J. Liebe, P. W. Rosenkranz, G. A. Hufford: “Atmospheric 60GHz oxygen spectrum: new laboratory measurements and line parameters”, J. of Quantitative Spectroscopy and Radiative Transfer 48, (1992), 629-643 23. F. Giannetti, M. Luise, R. Reggiani: “Mobile and personal communications in the 60GHz band: a survey”, Wireless Personal Communications 10, (1999), 207-243 24. H. A. Kramers: “Some remarks on the theory of absorption and refraction of X-rays”, Nature 117, (1926), 775 25. R. de L. Kronig: “On the theory of dispersion of X-rays”, J. Opt. Soc. Am. 12, (1926), 547-557 26. A. Yariv: “Quantum Electronics”, Wiley (1988)

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27. Y. Pinhasi, A. Yahalom, O. Harpaz & G. Vilner “Study of an Ultra Wideband Transmission in the Extremely High Frequency (EHF) Band” accepted by IEEE Transactions on Antennas and Propagation (2004). 28 J. D. Jackson “Classical Electrodynamics”, Wiley Text Books; 3rd edition (1998). 29 S. Chu & S. Wong PRL 48, 738 (1982). 30 Katz, R.R. Alfano, S. Chu and S. Wong PRL 49, 1292 (1982). 31 M. Mojahedi, E. Schamiloglu, F. Hegeler and K. J. Malloy PRE 62,4, (2000).

HIGH-POWER MILLIMETRE WAVE TRANSMISSION SYSTEMS AND COMPONENTS FOR ELECTRON CYCLOTRON HEATING OF FUSION PLASMAS

W. Kasparek1, G. Dammertz2, V. Erckmann3, G. Gantenbein1, M. Grünert 1, E. Holzhauer1, H. Kumric1, H.P. Laqua3, F. Leuterer4, G. Michel3, B. Plaum1, K. Schwörer 1, D. Wagner4, R. Wacker1, M. Weissgerber4, W7-X ECRH Teams at IPP Greifswald3 and Garching4, at IPF Stuttgart1 and FZK Karlsruhe2, ECRH team on ASDEX Upgrade at IPP Garching4 1

Institute for Plasma Research, University of Stuttgart, D-70569 Stuttgart, Germany, e-mail: [email protected] Karlsruhe Research Center, Association EURATOM-FZK, Institute for Pulsed Power and Microwave Technology, D-76021 Karlsruhe, Germany 3 Max-Planck-Institute for Plasma Physics, Ass. EURATOM-IPP, D-17491 Greifswald, Germany 4 Max-Planck-Institute f. Plasma Physics, Ass. EURATOM-IPP, D-85748 Garching, Germany 2

1.

INTRODUCTION

At the Institute for Plasma Research at the University of Stuttgart, high-power millimetre wave transmission systems for electron cyclotron heating (ECRH) and current drive (ECCD) of fusion plasmas are developed. Present work concentrates on the 140 GHz, 10 MW CW ECRH system for the stellarator W7-X [1] which is currently built at the Max-Planck-Institute for Plasma Physics (IPP) in Greifswald. There, the millimetre wave power of 10 gyrotrons will be transmitted fully optically via two multi-beam waveguides (MBWG)

241 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 241–252. © 2005 Springer. Printed in the Netherlands.

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with a length of about 50 m [2]. Other activities contribute to a broadband system which is under construction for the tokamak ASDEX-Upgrade at IPP Garching. This system [3] will employ multi-frequency gyrotrons in the range of 105 – 140 GHz and oversized corrugated waveguides to transmit the millimetre waves to the plasma. In the frame of this work, several principles and components have been developed, which are of general interest for high-power transmission of millimetre waves. This includes multi-beam transmission, beam diagnostic components, broadband polarizers, and frequency diplexers. In the following, these components are briefly described, and theoretical as well as experimental results will be discussed.

2.

MULTI-BEAM WAVEGUIDE SYSTEM FOR ECRH ON THE STELLARATOR W7-X

2.1 System overview For the stellarator W7-X, currently under construction at IPP Greifswald, a 140 GHz, 10 MW CW ECRH system is built up [1,2]. The RF power will be delivered by 10 gyrotrons developed at the Research Center Karlsruhe (FZK) [4], and transmitted from the source to the plasma via quasi-optical transmission lines [5]. The mirrors and other components are placed in an underground duct connecting the gyrotron building with the experimental hall. The design of the transmission system is illustrated by the CAD drawing in Fig. 1. The set-up consists of single-beam and multi-beam elements. For each gyrotron, a matching optics unit (MOU) of five single-beam mirrors is used, as shown in Figs. 1 and 2a. Two of these mirrors match the gyrotron output to a Gaussian beam with the correct beam parameters, two others are used to set the appropriate polarization needed for optimum absorption of the radiation in the plasma. A fifth mirror directs the beam to an array of plane mirrors (beam combining optics, BCO), which is situated at the input plane of a multi-beam wave guide (MBWG) [5]. This MBWG is designed to transmit up to seven beams (five 140 GHz beams, one optional 70 GHz beam plus a spare channel) from the gyrotron area (input plane) to the stellarator hall (output plane). It consists of 4 focusing mirrors in a confocal arrangement. Additional plane mirrors are installed to fit the transmission lines into the building. At the output plane of the MBWG, another mirror array (beam distribution optics, BDO) separates the beams again and directs them via vacuum barrier windows to individually movable antennas (plug-in launchers, PILA) in the torus. To transmit the power of all gyrotrons, two symmetrically arranged MBWGs are installed in the beam duct as shown in Figs. 1b and 2b.

243

High-power Millimetre Wave Transmission

a)

PILA

BCO BDO MOU

MBWG

b)

Figure 1: Schematic design of the 140 GHz/10 MW transmission system for ECRH on W7-X. a) cross-section, b) top view.

The beam duct is used simultaneously as a stable support for the optics, for shielding of the microwaves and installation of dummy loads, calorimeters, absorbers for stray radiation as well as for cooling systems. All mirrors are water-cooled. They have been carefully designed [6] with respect to low mechanical distortion due to the heat load imposed by the ohmic loss [7] of the copper surfaces. The mirrors have been tested at FZK at the test stand for the development of the 140 GHz, 1 MW CW gyrotron [4]. In this test stand, the output beam of the prototype gyrotron is guided via two focussing mirrors and two polarising mirrors to the dummy load. During high-power tests with a power of up to 890 kW (540 kW) and a pulse length of 3 (15) minutes all mirrors performed well and no serious problems were observed. No arcing was seen on the corrugated surfaces of the polarizers, provided that they were clean. At IPP Greifswald, the first gyrotron became operational at the end of 2003. Since then, the transmission system is regularly used for high-power tests of this gyrotron.

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Figure 2: View into the transmission duct of the ECRH system on W7-X. a) The left picture shows matching optics and polarizers for one gyrotron, b) the upper picture is a view into the beam duct with two large multi-beam mirrors and the MD mirrors which can focus one beam at a time into the dummy loads seen at the bottom.

2.2 General aspects of multi-beam waveguide transmission The MBWG is a confocal system [8, 9] consisting of four focusing mirrors (and additional three plane mirrors to straighten the beam path), which must simultaneously provide low-loss propagation of all (on-axis and off-axis) beams and correct imaging from the input to the output plane. The principle is illustrated in Fig. 3, where one unit consisting of 2 mirrors in Z-configuration is sketched. Mirrors for a single-beam waveguide can be designed straightforward (see [10] and references therein), but for a compact MBWG design the individual beams overlap on the mirrors, so that no optimisation of corresponding sections of the mirror surfaces is possible. To fulfil all requirements, diffraction calculations with Gaussian beam mode analysis were performed [9]. The codes were bench-marked by experiments which confirm the numerical results. The investigations showed that simple elliptical paraboloids lead to minimum mode conversion losses. Furthermore, the studies showed, that the remaining mode conversion on the curved surfaces cancels after four mirrors, if these mirrors are installed in the proper orientation [9]. This is demonstrated by mode analysis of the field patterns at various positions of the MBWG: At the input plane of the MBWG, where the 140 GHz beams are closely packed and parallel, a pure gaussian

High-power Millimetre Wave Transmission

245

beam is assumed. In the focal plane behind the first mirror, the beams cross the optical axis. In the focal plane behind the second mirror (c.f. Fig. 3), the initial beam pattern is nearly recovered, the mode analysis, however, yields a TEM00-purity of only 96.1 %. After four mirrors, the spurious modes have cancelled and the beams cross the output plane exactly perpendicularly in the nominal position, which is proven by a mode purity of 99.8%. Figure 3: Principle sketch of a confocal 2-mirror A detailed discussion of the MBWG system (Z-configuration). properties of confocal multi-beam waveguides is given in [9]. A general conclusion is, that a large number of beams can be transmitted through such systems with low loss and simultaneously high mode purity. This feature could be used in high-quality imaging systems in plasma diagnostics as well as in astronomy and telecommunication.

2.3 Low-power test of a prototype MBWG system The ECRH system for W7-X will finally comprise more than 160 water-cooled mirrors for beam matching and polarisation adjustment, transmission, switching of beams, and for the launchers. Due to the complexity of the system and in order to test its over-all performance and stability, a full-scale prototype has been built. Amplitude and phase measurements of the beams have been performed at the characteristic planes using various field scanning devices together with a vector network analyser. As an example, Fig. 4 gives the beam power and phase distributions for all transmission channels at the output plane of the MBWG. For each channel, the patterns show an almost rotationally symmetric amplitude distribution and only small variations of the phase and thus demonstrate the good imaging characteristics of confocal systems even for off-axis beams. The mode analysis of the measured beam patterns at the exit of the multibeam section yields a TEM00-mode purity of ≥ 98 %. The total transmission efficiency of the prototype system (17 mirrors) including diffraction due to imperfect surfaces, ohmic loss, typical misalignment, and atmospheric absorption was checked by calorimetric methods and yielded 90±2 %, which is in good agreement with the theoretical value of 92 %.

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Figure 4: Measurements of power density and phase distributions for seven 140 GHz beams at the output plane of the MBWG. Scale: 3 dB/colour step, 20°/colour step.

3.

COMPONENTS FOR BEAM DIAGNOSTICS AND POLARISATION CONTROL

3.1 Power monitors and in-situ alignment control For power monitoring in quasi-optical transmission lines, various methods are used: In the first mirror of the W7-X system, a waveguide coupler [11] is integrated into the mirror surface. To get high performance also for CW operation, the coupling waveguide is embedded into the copper surface by electro-forming techniques without any discontinuities. Additionally, thermocouples in the copper surface as well as in the cooling channels allow insitu calorimetry of the power lost on the mirror surface with a time resolution of about 1 s. In the last mirror in front of the torus window, a coupler employing a holographic grating is used to couple a sample beam into a matched antenna (focusing mirror with scalar horn). The subsequent receiver simultaneously will provide a power signal and measure the spatial and angular deviation of the sample beam from its nominal direction in the co-ordinate system of the torus [12]. Thus, an alignment error correction signal is generated which can be used for alignment control. Alternatively to the grating coupler, a compact direction-finding antenna employing four waveguide couplers integrated into a mirror surface can be used [13]. These systems can reach high angular resolutions (close to the diffraction limit) as shown in Fig. 5, where the output signal is plotted as a function of the angle of incidence of a high-power beam.

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A system for overall control of the mirror alignment is in -12 preparation. It consists of a -18 swept-frequency reflectometer operating at a test frequency (188 -24 GHz), which is higher than the angle perp. to plane -30 heating frequency [14]. Each of inc. γ = 0 degrees -36 mirror of the transmission line is 42 43 44 45 46 47 48 equipped with a shallow grating (horizontal) angle of incidence α (degrees) designed for −1st -order LittrowFigure 5: mount at 188 GHz. Therefore, a Error signal for angular alignment of a mirror small amount of the test beam at measured in a high-power 84 GHz test set up. this frequency is reflected at each mirror surface; the reflected signals are maximum for correct alignment and can be used to optimize the alignment of each mirror. A successful demonstration of the principle on a prototype transmission line was performed.

pow er (dB )

-6

3.2 Broadband Polarizers Polarizers are needed to optimize the coupling of the microwave beam to the magnetized plasma at any angle of injection with respect to the confining magnetic field. Usually, a pair of grooved mirrors is used in high-power systems [15]. The corrugations are designed such that the phase difference ∆φ between the TE polarization (electric field E parallel to the grooves) and the TM polarization (E perpendicular to the grooves) is ∆φ = 180° for a polarisation rotator and ∆φ = 90° for an elliptical polarizer [c.f. 16]. For high power operation under atmospheric conditions, sinusoidally shaped grooves must be used to avoid arcing. Typical profiles for such polarizers are characterized by a period of p = 0.5λ, and depths of d = 0.37 λ for the rotator and d = 0.26 λ for the elliptical polarizer. In principle, this kind of grooves provides a solution for a single frequency only. Although the combination of two polarizers shows some broadband characteristics [17], attempts were made to develop broadband polarising surfaces. The design is based on grooves with period p > λ/2, width w ≥ λ/2, and a high aspect ratio of 0.5 < w/p < 1. For higher frequencies of the operation range, this groove profile allows the penetration of the TE wave into the grooves and thus an adjustment of the effective corrugation depth. The application of such a polarizer is limited to small angles of incidence α to avoid grating lobes ( p < λ/(1 + sinα) ) and is complicated by the possible excitation of surface waves (Wood´s anomaly) close to or within the operating range. An example for a polarization rotator designed by using a finite difference time domain (FDTD) code is given in Fig. 6. One can see

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that the phase shift between TE and TM polarization is 180° ±10° (which corresponds to a cross-polarization of < 2%) within a relative bandwidth of 30%. However, Wood´s anomaly here at 142 GHz causes a phase jump and strong absorption in a band of a few GHz within the operation range, which could be confirmed by experiments with high frequency resolution. More details, also concerning elliptical polarizers, are given in [18]. 2 40

Phase difference [deg]

Figure 6: Phase difference between TE and TM polarization for a broadband polarization rotator. Grating design: period p = 1.5 mm, groove depth d = 0.95 mm, groove width w = 1.25 mm, trapezoidal fins with rounded tops. Solid line: calculation showing Wood´s anomaly at 142 GHz. Squares: measurements at discrete frequencies.

( α = 5 .5 de g)

ca lcu latio n:

2 20 2 00

( α = 0 de g )

m ea su re m e nt: squ are s, α = 5 .5 °

1 80 1 60 1 40 1 20 1 00

1 10

1 20

1 30

1 40

1 50

1 60

F requency [G H z]

4.

QUASI-OPTICAL COMPONENTS BASED ON RECTANGULAR (CORRUGATED) WAVEGUIDES

4.1 Remote steering antenna for ECRH and ECCD Low-order modes in strongly oversized rectangular or square waveguides are characterized by beat-wavelengths, which are integer fractions of the length LB = 8a2/λ, where a is the width of the corresponding side wall [19]. This fact leads to periodic revivals of field structures in the waveguide, i.e. to imaging properties of these waveguides. Therefore, rectangular waveguides have a great potential for the design of quasi-optical components, for example hybrid beam splitters [20]. An important development for ECRH is the “remote-steering antenna”[21]. Here, the steering mirror - which in conventional antennas is close to the (thermonuclear) plasma - is at a remote position. The beam steering of this mirror is translated by an imaging square waveguide of length LRS = 4a2/λ [22] to the output of the waveguide near to the plasma (sketch in Fig. 7a). The scheme works with high performance up to steering angles of ϕ = 12°. The examples in Fig. 7b and 7c show measured radiation patterns for ϕ = 0° and ϕ = 10°, respectively. At larger angles, the imaging characteristics are smeared out as the paraxial approximation for the propagation constants of the waveguide modes excited by the input beam breaks down [23]. The remote

249

High-power Millimetre Wave Transmission

steering antenna was tested also with high-power [24, 25] and is now designed for ECCD applications in the international fusion experiment ITER [26].

a) -ϕ

ϕ input beam

Y Axis (mm)

b)

300 250 200 150 100 50 0

Y Axis (mm)

rectangular waveguide L = 4a2/λ

ϕ = 0 deg

0

c)

vacuum window

200

400

600

800

1000

1200

800

1000

1200

X Axis (mm)

300 250 200 150 100 50 0

ϕ = 10 deg.

0

200

400

600

plasma

Figure 7: a) Principle of a remote steering antenna based on a corrugated square waveguide. b) Radiation pattern of a remote steering antenna, L = 7.5 m, a =60 mm, f = 158 GHz, measured at a distance of 1.7 m from the output of the waveguide for ϕ = 0°. c) same as b), for ϕ = 10°. Scale: 3dB / colour step.

X Axis (mm)

Possibly, the scheme of the remote steering antenna could be of interest for RADAR and communication technology; for example, it could serve as a remotely steered or conically scanned feed horn.

4.2 Frequency diplexers Oversized rectangular waveguides can also be used for the design of frequency diplexers [27]. For this case, the diplexer consists of a combining waveguide (length l, width wc) with two input waveguides (width w1, w2, fed with the TE10-mode) at one end, and the output waveguide at the other end (see Fig. 8).

f2 input

f1 input

f1 + f2 output

Figure 8: Principle design of a diplexer based on rectangular waveguides

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A fourth waveguide with an integrated absorber prevents reflections of spurious field components. By optimizing the dimensions of the diplexer, one can find solutions, where the power losses of the fundamental TE10-mode are below 3 % for both frequencies. As a proof of principle, a 45 GHz / 70 GHz diplexer was designed yielding l = 510 mm and wc = 2w1 = 2w2 = 2wout = 14.6 mm. The result of measurements is displayed in Fig. 9. The curves agree well with the calculations; as one can see, the frequency separation of the two channels is very high. The loss of typically 0.8 dB is due to ohmic absorption, as the waveguides were oversized only in one dimension to limit the mechanical effort for this prototype under test. Present developments include an investigation of a different design, which is based on the angular Talbot effect, as well as the possibility to build other components (multiplexers, band filters).

Figure 9: Frequency characteristics for a 45 GHz / 70 GHz diplexer in oversized rectangular waveguide.

5.

CONCLUSION

Systems and components for the transmission of high-power millimetre waves like multi-beam transmission, beam diagnostic components, broadband polarizers, remote steering antennas, and frequency diplexers have been discussed. The devices have been developed for ECRH systems, where typical powers of 1 MW per beam are applied. These components can be adapted to a variety of applications and therefore might be of general interest for highpower as well as low-power transmission of millimetre waves.

Acknowledgement Part of this work has been performed in the frame of the Project Microwave Heating (PMW), ECRH for W7-X hosted at FZK Karlsruhe (collaboration between FZK Karlsruhe, IPP Garching and Greifswald, and IPF Stuttgart).

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References 1. Erckmann, V. et al.: The W7-X project: Scientific basis and technical realization. Proc. 17th IEEE/NPSS Symposium on Fusion Engineering, San Diego, USA (1997). Ed. IEEE, Piscataway, NJ 1998, 40 –48. 2. Kasparek, W. et al.: ECRH and ECCD for the stellarator W7-X. In Strong Microwaves in Plasmas 1999, ed. A.G. Litvak, Inst. of Appl. Physics, Nizhny Novgorod (1999), 185 - 204. 3. Leuterer, F. et al.,: Plans for a new ECRH system for ASDEX-Upgrade. Fusion Eng. and Design 66 – 68 (2003), 537-542. 4. Dammertz G. et al. : Development of a 140-GHz, 1-MW Continuous wave gyrotron for the W7-X Stellarator, IEEE Trans. Plasma Science, PS-30 (2002), 808-818. 5. Empacher, L., et al.: Design of the 140 GHz/10 MW CW ECRH system for the stellarator W7X. In Fusion Technology 1996, Elsevier Science B.V. Amsterdam (1997), 541-544. 6. H. Hailer, G. Dammertz, V. Erckmann, G. Gantenbein, F. Hollmann, W. Kasparek, W. Leonhardt, M. Schmid, P.G. Schüller, M. Thumm, M. Weissgerber: Mirror development for the 140 GHz ECRH system of the Stellarator W7-X. Fusion Eng. and Design 66-68 (2003), 639 –644. 7. Kasparek, W., A. Fernandez, F. Hollmann, and R. Wacker: Measurement of ohmic loss of metallic reflectors at 140 GHz by a 3-mirror resonator technique. Int. J. Infrared and Millimetre Waves 22 (2001) 1695-1707. 8. Goldsmith, P.F.: Quasi-optical Systems. IEEE Press, Chapman and Hall, Publishers, New York (1998) ISBN 0-7803-3439-6. 9. Empacher, L., Kasparek, W.: Analysis of a multiple-beam waveguide for free-space transmission of microwaves. IEEE Trans. Antennas Propagat. AP-49 (2001) 483–493. 10. M. Thumm and W. Kasparek: Passive high-power microwave components. IEEE Trans. Plasma Science, PS-30 (2002) 755-786. 11. Empacher, L. et al.: New developments and tests of high power transmission components for ECRH on ASDEX-Upgrade and W7-AS. Proc. 20th Int. Conf. on Infrared and Millimeter Waves, Lake Buena Vista (Orlando), 1995, 473-474. 12. J. Shi and W. Kasparek: A grating coupler for in-situ alignment of a gaussian beam principle, design and low-power test. IEEE Trans. Antennas Propagat. (2004) in press. 13. W. Kasparek, H. Idei, S. Kubo, and T. Notake: Beam Waveguide Reflector with Integrated Direction-Finding Antenna for In-Situ Alignment. Int. J. Infrared and Millimeter Waves 24 (2003) 451-472. 14. Gantenbein, G., L. Empacher, V. Erckmann, F. Hollmann, W. Kasparek, M. Weißgerber and H. Zohm: Simulations and Experiments on a multi-beam waveguide ECRH transmission system. Proceedings of the 20th Symp. on Fusion Technology, Eds. B. Beaumont, P. Libeyre, B. de Gentile, G. Tonon. Ass. EURATOM-CEA Cadarache, France, Vol. I, (1998) 423 –426. 15. V.I. Belousov, E.V. Koposova, I.M. Orlova et al., in Gyrotrons, ed. V.I. Flyagin, Institute of Applied. Physics, Gorky, USSR, 1989. 16. Y.L. Kok and N.C. Gallagher: Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating. J. Opt. Soc. Am. A5 (1988), 65 –73. 17. D. Wagner, G. Grünwald, F. Leuterer, F. Monaco, M. Münich, H. Schütz, F. Ryter, R. Wilhelm, H. Zohm, T. Franke, G. Dammertz, H. Heidinger, K. Koppenburg , M. Thumm, X. Yang, W. Kasparek, G Gantenbein, H. Hailer, G.G. Denisov, A .Litvak, V. Zapevalov: Status

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of the New ECRH System for ASDEX Upgrade. Proc. of the 13th Joint Workshop on ECE and ECRH (EC-13), May 2004, Nizhny Novgorod, Russia, http://www.ec13.iapras.ru/ 18. G. Gantenbein, M. Grünert, E. Holzhauer, W. Kasparek and R. Wacker: Characteristics of broadband polarizers. To be published (2004). 19. L.A. Semenov, and A.T. Rivlin: Transmission of images through optical waveguides. Laser Focus Feb. 1981, 82-84. 20. S. V. Kuzikov: Wavebeam multiplication phenomena in RF power distribution systems of high-energy linear accellerators. Int. J. Infrared Millimeter Waves, 19 (1998) 1523–1539. 21. R. Prater, H.J. Grunloh, C.P. Moeller, J.L. Doane, R.A. Olstad, M.A. Makowski, and R.W. Harvey, "A design study for the ECH launcher for ITER", Proc. 10th Joint Workshop on ECE and ECRH, Ameland, The Netherlands, 1997, ed. by T. Donne and A.G.A. Verhoeven, World Scientific, Singapoore, 1997, ISBN 981-02-3219-5, 531-540. 22. A.V. Chirkov, G.G. Denisov, W. Kasparek, and D. Wagner: Simulation and experimental study of a remote wave beam steering system. Proc. of the 23rd Int. Conf. on Infrared and Millimeter Waves, Colchester 1998, eds. T.J. Parker and S.R.P. Smith, ISBN 0-9533839, 250-251. 23. W. Kasparek, G. Gantenbein, B. Plaum, R. Wacker, A.V. Chirkov, G.G. Denisov, S.V. Kuzikov, K. Ohkubo, F. Hollmann, D. Wagner: Performance of a remote steering antenna for ECRH/ECCD applications in ITER using four-wall corrugated square waveguide. Nucl. Fusion 43 (2003), 1505 - 1512. 24. K. Takahashi, C. Moeller, K. Sakamoto, K. Hayashi, T. Imai: High power transmission experiment of remote steering launcher, Fusion Eng. and Design 65 (2004), 589 - 598. 25. G. Gantenbein, V. Erckmann, W. Kasparek, B. Plaum, K. Schwörer, M. Grünert, F. Hollmann , L. Jonitz , H. Laqua , G. Michel , F. Noke , F. Purps , A. Bruschi , F. Gandini, S. Cirant, A. G. A. Verhoeven et al: High-power tests of a remote steering launcher mock-up at 140 GHz. Proc. of the Joint Workshop on ECE and ECRH, May 2004, Nizhny Novgorod, Russia, http://www.ec13.iapras.ru/. 26. A.G.A. Verhoeven, M.P.A. van Asselen, W.A. Bongers, B.S.Q. Elzendoorn, M.F. Graswinckel, R. Heidinger, P. Hellingmann, and D.M.S. Ronden: The ITER Remote Steering ECW Upper-Port Launcher. Proc. of the 28th Int. Conf. on Infrared and Millimeter Waves, Otsu, Japan, Oct 2003, ed. N. Hiromoto (2003), 379 - 380. 27. B. Plaum, E. Holzhauer, and W. Kasparek: Optimization of a frequency diplexer based on the Talbot effect in oversized rectangular waveguides. Int. J. Infrared and Millimeter Waves 24 (2003), 311-326.

SPACE-FREQUENCY MODEL OF ULTRA WIDEBAND INTERACTIONS IN MILLIMETER WAVE MASERS

Y.Pinhasi, Yu.Lurie, and A.Yahalom The College of Judea and Samaria, Dept. of Electrical and Electronic Engineering, P.O. Box 3, Ariel 44837, Israel

Abstract:

Intense radiation devices such as microwave tubes, free-electron lasers (FELs) and masers, utilize distributed interaction between an electron beam and electromagnetic radiation. We developed a three-dimensional, space-frequency theory for the analysis and simulation of radiation excitation and propagation in electron devices and free-electron lasers operating in millimeter wavelengths. The total electromagnetic field (radiation and space-charge waves) is presented in the frequency domain as an expansion in terms of transverse eigen-modes of the (cold) cavity, in which the field is excited and propagates. The mutual interaction between the electron beam and the electromagnetic field is fully described by coupled equations, expressing the evolution of mode amplitudes and electron beam dynamics. The approach is applied in a numerical particle code WB3D, simulating the interaction of a free-electron laser operating in the linear and non-linear regimes.

Key words:

free-electron maser, spontaneous and super-radiant emissions, space-frequency 3D model.

1.

INTRODUCTION

Electron devices such as microwave tubes and free-electron lasers (FELs) utilize distributed interaction between an electron beam and electromagnetic radiation. Many models have been developed to describe the mutual interaction between the gain medium (electron beam) and the excited radiation. These models are based on a solution of Maxwell equations and the Lorenz force equation in the time domain.Contrary to space-time models formulation of the electromagnetic excitation equations in the frequency domain inherently takes into account dispersive effects arising from the cavity and the gain medium. Moreover, it facilitates consideration of the statistical features of the electron beam and the excited radiation, necessary for the study of spontaneous 253 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 253–270. © 2005 Springer. Printed in the Netherlands.

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emission, synchrotron amplified spontaneous emission (SASE), superradiance and noise. In this paper we develop a space-frequency model, which describes broadband phenomena occurring in electron devices, masers and FELs and characterized by a continuum of frequencies. The total electromagnetic field is presented in the frequency domain as a summation of transverse eigenmodes of the cavity, in which it is excited and propagates. A set of coupled excitation equations, describing the evolution of each transverse mode, is solved self-consistently with beam dynamics equations. This coupled-mode model is employed in a three-dimensional numerical simulation WB3D [1]. The code was used to study the statistical and spectral characteristics of the radiation generated in a free-electron laser, operating in the millimeter wavelengths in various configurations. The theory is demonstrated also in the case of “grazing”, when the group velocity of the radiation is equal to the axial velocity of the electrons, resulting in a wide-band interaction between the electron beam and the generated radiation. The numerical results presented throughout this paper, are of a waveguide-based, pulsed beam free-electron maser (FEM), illustrated schematically in Fig.1. The code WB3D was used to investigate radiation excitation in a millimeter wave FEM, with operational parameters given in Table 1. When a FEL utilizes a waveguide, the axial wavenumber follows 2S the dispersion relation k z  f f 2  f co 2 , where f co is the cut-off c frequency and c is the light velocity. In synchronism, the dispersion relation 2S f for electron beam is given by k z  f  k w , where v z 0 is the velocity vz0 2S of the accelerated electrons and k (O is the wiggler w

Ow

w

period). The corresponding

Figure 1. Schematic llustration of a pulsed beam free-electron laser.

255

Space-frequency model of ultra wide-band interactions Table 1. Operational parameters of millimeter wave free-electron maser. Waveguide

Accelerator Electron beam energy: Electron beam current:

Ek

I0

1y 3 MeV

1A

Rectangular waveguide:

1.01 cm u 0.9005 cm

Mode:

TE01

Resonator

Wiggler

Magnetic induction:

Bw

2000 G

Period:

Ow

4.444 cm

Total reflectivity:

R

2.62 m

Number of periods:

Nw

20

Finesse:

F

59.6

Power out-coupling:

T

1%

Round trip length:

Lc

2.62 m

dispersion curves of the FEM are shown in Fig.2. When the beam energy is set to E k 1.375 MeV , there are two separated intersection points between the beam and waveguide dispersion curves, corresponding to the “slow” ( v g1  v z 0 ) and “fast” ( v g 2  v z 0 ) synchronism frequencies 29GHz and 100GHz, respectively ( v g is the group velocity of the radiation at the respective frequency). Lowering the beam energy to E k | 1.066 MeV , results in a single intersection at 44GHz (“grazing limit”), where the beam dispersion line is tangential to the waveguide dispersion curve ( v g v z 0 ).

Figure 2. FEM dispersion curves.

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2. PRESENTATION OF THE ELECTROMAGNETIC FIELD IN THE FREQUENCY DOMAIN The electromagnetic field in the time domain is described by the space-time electric Er, t and magnetic Hr, t signal vectors. r stands for the x, y, z coordinates, where  x, y are the transverse coordinates and z is the axis of propagation. The Fourier transform of the electric field is defined by: Er, f

f

 j 2S f t d t ³ Er, t e

(1)

f

where f denotes the frequency. Similar expression is defined for the Fourier transform H r, f of the magnetic field. Since the electromagnetic signal is real (i.e. E r, t Er, t ), its Fourier transform satisfies E r, f Er, f . Analytic representation of the signal is given by the complex expression [2]: ~ ˆ r, t Er, t { Er, t  j E (2) where Eˆ r , t

1 f Er , t ' d t' ³ S f t  t'

(3)

is the Hilbert transform of Er, t . Fourier transformation of the analytic ~ representation (2) results in a “phasor-like” function Er, f defined in the positive frequency domain and related to the Fourier transform by: ­2 Er, f f ! 0 ~ Er, f 2 Er, f ˜ u  f ® (4) 0 f 0 ¯

The Fourier transform can be decomposed in terms of the “phasor like” functions according to: 1~ 1~ Er, f Er, f  E r, f (5) 2 2 and the inverse Fourier transform is then: f ­°f ~ ½° Er, t ³ Er, f e  j 2S f t d f Re ® ³ Er, f e  j 2S f t df ¾ (6) °¯ 0 °¿ f

257

Space-frequency model of ultra wide-band interactions

3.

THE WIENER-KHINCHINE AND PARSEVAL THEOREMS FOR ELECTROMAGNETIC FIELDS

The cross-correlation function of the time dependent electric Er, t and magnetic H r, t fields is given by: f

³ ^ ³³ >Er, t  W u H r, t @˜ zˆ dx dy` d t

R EH z ,W

(7)

f

Note that for finite energy signals, the total energy carried by the electromagnetic field is given by W z R EH z ,0 . According to the Wiener-Khinchine theorem, the spectral density function of the electromagnetic signal energy S EH z , f is related to the Fourier transform of the cross-correlation function R EH z ,W through the Fourier transformation: S EH z , f

f

 j 2S f W d W ³ R EH z ,W e

f

>

@

³³ Er , f u H r , f ˜ zˆ dx dy (8) ~ ­ 1 ~ ˆ   u ˜ ! E r , f H r , f z dx dy f 0 °° 4 ³³ ®1 ~

~ ° ³³ Er , f u H  r , f ˜ zˆ dx dy f  0 ¯° 4 Following Parseval theorem, the total energy carried by the electromagnetic field can also be calculated by integrating the spectral density S EH  z, f over the entire frequency domain:

>

>

W z

f

³ S EH z, f d f

f

f ª 1

^~

@ @

~

`

@

`

º

³ « ³³ Re Er, f u H r, f ˜ zˆ dx dy » df ¼ 0 ¬2

(9)

We identify:

^>

d W z 1 ~ ~ Re ³³ Er, f u H r, f ˜ zˆ dx dy (10) 2 df as the spectral energy distribution of the electromagnetic field (over positive frequencies).

258

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Y.Pinhasi, Yu.Lurie,A.Yahalom

MODAL PRESENTATION OF ELECTROMAGNETIC FIELD IN THE FREQUENCY DOMAIN

The “phasor like” quantities defined in (4) can be expanded in terms of transverse eigenmodes of the medium in which the field is excited and propagates [3]-[5]. The perpendicular component of the electric and magnetic fields are given in any cross-section as a linear superposition of a complete set of transverse eigenmodes:  j k zq z  j k zq z º ~ ~ ª E A r , f ¦ «C  q  z , f e  C  q z , f e »¼ Eq A x, y q¬ (11)  j k zq z  j k zq z º ~ ~ ª  H A r , f ¦ «C  q  z , f e H x , y  C q z, f e q A »¼ q¬ C  q z , f and C  q z , f are scalar amplitudes of the qth forward and ~ backward modes respectively with electric field Eq A  x, y and magnetic ~ field H q A  x, y profiles and axial wavenumber: ­ 2 2 k ! k A q (propagating modes) ° k  kA q k zq ® (12) ° j kA q 2  k 2 k  k A q (cut - off modes) ¯ Expressions for the longitudinal component of the electric and magnetic fields are obtained after substituting the modal representation (11) of the fields into Maxwell's equations, where source of electric current density ~ J r, f is introduced:  j k zq z  j k zq z º ~ ~ ª E z r , f ¦ «C  q  z , f e  C  q z , f e »¼ Eq z x, y ¬ q



1 ~ J z r, f j 2S f H 0

(13)

 j k zq z  j k zq z º ~ ~ ª H z r, f ¦ «C  q  z, f e  C q z, f e »¼ H q z  x, y ¬ q

The evolution of the amplitudes of the excited modes is described by a set of coupled differential equations:

259

Space-frequency model of ultra wide-band interactions d C r q z , f dz

(14) º ·~ 1 B j k zq z ª«§¨ Z q ¸ J r, f r zˆ J~ r, f » ˜ E~ x, y dx dy e ³³ ¨ z q A Nq » « Z q ¸¹ ¼ ¬© The normalization of the field amplitudes of each mode is made via each mode's complex Poynting vector power: ~ ~ N q ³³ Eq A  x, y u H q A  x, y ˜ zˆ dx dy (15) B

>

@

and the mode impedance is given by: ­ P0 k 2S f P 0 ° k zq ° H k Zq ® 0 zq k zq ° P0 k z q ° H0 k 2S f H 0 ¯

for TE modes

(16) for TM modes

Substituting the expansion (11) in (10) results in an expression for the spectral energy distribution of the electromagnetic field (over positive frequencies) as a sum of energy spectrum of the excited modes: 2 2º d W z 1ª C  q  z, f  C  q z , f » ˜ Re N q ¦ « df 2¬ ¼ q

^ `

Propagating



¦ q Cut - off

5.

^

` ^ `

Im C  q z, f C  q z , f ˜ Im N q

(17)

THE ELECTRON BEAM DYNAMICS

The state of the particle i is described by a six-component vector, which consists of the particle's position coordinates ri xi , yi , z i and velocity vector v i . The velocity of each particle, in the presence of electric Er, t and magnetic Br , t P 0 H r , t fields, is found from the Lorentz force equation: ½ d vi 1 ­° e 1 >Eri , t  v i u Bri , t @  v i d J i °¾ (18) ® J i °¯ m v z i dz ° dz ¿ where e and m are the electron charge and mass respectively. The fields represent the total (DC and AC) forces operating on the particle, and include

Y.Pinhasi, Yu.Lurie,A.Yahalom

260

also the self-field due to space-charge. The Lorentz relativistic factor J i of each particle is found from the equation for kinetic energy: dJi 1 e  v i ˜ Eri , t (19) 2 dz m c v zi where c is the velocity of light. The time it takes a particle to arrive at a position z, is a function of the time t0i when the particle entered at z=0, and its instantaneous longitudinal velocity v z i z along the path of motion: z

ti z t 0i  ³

1

0 v z i  z '

d z'

(20)

The current distribution is determined by the position and the velocity of the particles in the beam: Q N§ v · J r, t  ¦ ¨ i ¸ G x  xi G  y  yi G >t  ti z @ (21) N i 1¨ v zi ¸ ¹ © Here Q I 0 T is the total charge of the e-beam pulse with DC current I 0 and temporal duration T. The “phasor like” current density is given by: f ~ J r, f 2 u  f ³ J r, t e  j 2S f t d t f

Q N § v 2 u  f ¦ ¨ i N i 1¨ v z i ©

6.

· ¸ G  x  x G  y  y e  j 2S f t i  z i i ¸ ¹

(22)

SPONTANEOUS EMISSION

Random electron distribution in the e-beam cause fluctuations in current density, identified as shot noise in the beam current [6]-[11]. Electrons passing through a magnetic undulator emit a partially coherent radiation, which is called undulator synchrotron radiation. The electromagnetic fields excited by each electron add incoherently, resulting in a spontaneous emission with generated power spectral density [12]: d Psp Lw §1 · W sp Psp Lw sinc 2 ¨ T Lw ¸ (23) df ©2 ¹

261

Space-frequency model of ultra wide-band interactions

where Psp Lw is the expected value of the spontaneous emission power, Lw Lw is the slippage time and:  vz0 vg

W sp

T

Z vz0

 k z  k w

(24)

is the detuning parameter. The spontaneous emission null-to-null bandwidth is approximately 2 W sp | 2 f 0 N w . In a FEL, utilizing a magneto-static planar wiggler, the total power of the spontaneous emission is given by [12]: Psp Lw

where a w

1 e I0 8 W sp

2

§ aw · Z ¨¨ ¸¸ Lw 2 © J E z 0 ¹ Aem

(25)

e Bw is the wiggler parameter and kw m c 2

Aem

~ ³³ Eq  x, y dx dy

(26)

2 ~ Eq 0,0

is the effective area of the excited mode. The spontaneous emission power is proportional to e I 0 , where I 0 is the DC beam current. In the low gain limit, the spontaneous emission power grows as the square of interaction length Lw . Analytical and numerical calculations of the spontaneous emission power spectral density of the FEM are shown in Fig.3. (b) dPsp(Lw) / d f [PW/GHz]

dPsp(Lw) / d f [PW/GHz]

(a) 15

8

6

10

4

2

0

20

40

60

80

f [GHz]

100

120

5

0 20

30

40

50

60

70

80

f [GHz]

Figure 3. Spectrum of spontaneous emission for beam energy of: (a) Ek=1.375 MeV and (b) Ek|1.066 MeV (grazing). Analytical calculations (solid line) and numerical simulation (dashed line).

Y.Pinhasi, Yu.Lurie,A.Yahalom

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Figure 4. Evolution of spontaneous emission: (a) spectrum and (b) power along the wiggler. The beam energy is Ek=1.375 MeV.

In high-gain FELs, utilizing sufficiently long undulators, the spontaneous emission radiation excited in the first part of the undulator is amplified along the reminder of the interaction region resulting in synchrotron-amplified spontaneous emission (SASE). The evolution of SASE power along the wiggler when the beam energy is set to Ek=1.375 MeV is shown in Fig.4. Lowering the energy to Ek=1.066 MeV (grazing case) results in the SASE power shown in Fig.5.

7.

SUPER-RADIANCE

When the electron beam is modulated or pre-bunched, the fields excited by the electrons become correlated, and coherent summation of radiation fields from

Figure 5. Evolution of spontaneous emission: (a) spectrum and (b) power along the wiggler at grazing Ek|1.066 MeV).

Space-frequency model of ultra wide-band interactions

263

individual particles occurs. If all electrons radiate in phase with each other, the generated radiation becomes coherent and is termed super-radiant emission [13]-[24]. The power spectrum of the super-radiant emission is related to the spontaneous emission spectrum by [12]: 2 ~ d Psr Lw I  f d Psp Lw (27) ~ df df e I 0 ~ where I  f is the Fourier transform of the electron-beam current. The energy spectral density of the super-radiant power radiated by a single bunch with a temporal Gaussian shape is: 2 d Wsr Lw · §1 k W sp T Psp Lw e 2S T f sinc 2 ¨ T Lw ¸ (28) df ¹ ©2 where k Q is the expected number of electrons in the bunch of total e charge Q I 0 T . In the case of an ultra short bunch, with duration much shorter than the period of the radiation field ( T f  1 ), the total energy of the super-radiant emission is: 1 Q2 8 W sp

2

§ aw · Z 2 ¸ ¨ (29) ¨ J E ¸ A Lw z0 ¹ em © The super-radiance energy is proportional to the square of the total charge Q of the bunch and to the square of the interaction length Lw. The calculated spectral density of energy flux in the case of two wellseparated solutions is shown in Fig.6a. The spectrum peaks at the two synchronism frequencies with main lobe bandwidths of ' f1,2 | 1 , Wsr Lw

W sp1,2

where W sp1, 2 are the slippage times. The corresponding temporal wavepacket (shown in Fig.6b) consists of two “slow” and “fast” pulses with durations equal to the slippage times that modulate carriers at their respective synchronism frequencies. The spectral bandwidth in the case of grazing shown in Fig.7a, is determined by dispersive effects of the waveguide taking into account by the simulation. The corresponding temporal wavepacket is shown in Fig.7b. In the case of a continuous sinusoidal modulated current (pre-bunched beam): i t I 0 >1  m cos2S f 0 t @ (30) at frequency f 0 and modulation depth m, the power of the super-radiant emission:

Y.Pinhasi, Yu.Lurie,A.Yahalom

264 (a)

(b)

10

f = 100 GHz f = 29 GHz

5

Ex [kV/m]

dW(Lw) / df [pJ/GHz]

60

40

0

20 -5

0 20

40

60

80

100

-10

120

2.9

3.1

3.3

f [GHz]

3.5

3.7

3.9

t [nS]

Figure 6. Super-radiant emission from a short T=1 pS electron bunch (T f0=0.1 at Ek=1.375 MeV): (a) Energy spectrum (analytic calculation and numerical simulation results are shown by solid and dashed lines, respectively) and (b) temporal wave packet.

m2 I0 §1 · (31) W sp Psp Lw sinc 2 ¨ T  f 0 Lw ¸ 4 e 2 © ¹ Fig.8 shows the super-radiant power as a function of prebunching frequency f0 for various modulation levels. A comparison is made with simulation results. Super-radiant power emitted by an infinite series of ultra short bunches (impulses) is also shown. In this case the current can be expanded in a Fourier series: f f ª § 2S ·º i t ¦ I 0 T G t  n T I 0 «1  2 ¦ cos¨ n t ¸» (32) © T ¹¼» n f n f ¬« Psr Lw

The resulting spectrum of super-radiant emission contains all harmonics of the prebunching frequency f 0 1 each having a sinusoidal current T modulation with modulation index m=2. Fig.8 shows a curve of the superradiant power (a)

(b)

20

60

10

Ex [kV/m]

dW(Lw) / df [pJ/GHz]

80

40

20

0

-10

0

20

30

40

50

f [GHz]

60

70

80

-20

2.9

3.0

3.1

3.2

t [nS]

Figure 7. That of Fig.6, but at grazing (Ek|1.066 MeV).

3.3

3.4

3.5

Space-frequency model of ultra wide-band interactions

265

Figure 8. Power spectral density of super-radiant emission from a sinusoidally modulated current and from an infinite series of ultra short bunches (impulses). Analytical calculations (solid lines) and numerical simulation results (dashed lines).

emitted by a series of impulses as a function of the fundamental modulation frequency f 0 . The discrepancy between analytical calculations and numerical simulations at high modulation levels is due to stimulated emission effects that arise in the simulations, but not taken into account in the analytical calculations (where the effect of the radiation on electrons in not considered).

8.

SPACE-FREQUENCY MODEL FOR FEL OSCILLATORS

In laser oscillators, part of the radiation excited in the gain medium is coupled-out, while the remainder is circulated by a feedback mechanism, as shown schematically in Fig.9. Assuming a uniform cross-section resonator (usually a waveguide), the total electromagnetic field at every plane z, can be expressed in the frequency domain as a sum of a set of transverse ~ (orthogonal) eigenfunctions with profiles Eq x, y and related axial wavenumber k z q  f . At the beginning of a round-trip n, each of the modes is assumed to have an initial amplitude C q n 0, f and the total field at z=0 is given by: ~ ~ E n x, y , z 0; f ¦ C q n 0, f Eq  x, y (33) q

The field obtained at the end of the interaction (wiggler) region z = Lw can be

Y.Pinhasi, Yu.Lurie,A.Yahalom

266

Figure 9. Schematic illustration of FEL oscillator.

written as: ~ E n  x, y, z

 j k zq  f L w ~ Lw ; f ¦ C q n Lw , f Eq  x, y e q

(34)

Here the amplitude of the qth mode excited by a driving current density of ~ the electron beam J n x, y, z; f is found by integration of the excitation equation (14): C q n Lw , f C q n 0, f 

 j k zq  f z 1 Lw ~ n ~ dx dy dz ³ ³³ J x, y, z; f ˜ Eq x, y e 2N q 0

(35)

The spectral density of the energy flow after the interaction with the electron beam at the nth round-trip is: d W n Lw df

¦ Cq q

n L , f 2 1 Re^N ` q w 2

(36)

After a round-trip in the resonator of length Lc, the field fed back into the entrance (z=0) of the interaction region is:

Space-frequency model of ultra wide-band interactions ~ E n1 x, y, z

267

~ 0; f ¦ C q'n 0, f Eq' x, y q'

(37) º~ ª  j k zq '  f Lc n ¦ « ¦ U q' q" C q" Lw , f » Eq'  x, y e »¼ q ' «¬ q" U q ' q" is a complex coefficient, expressing the intermode field reflectivity of transverse mode q" to mode q', due to scattering of the resonator mirrors or any other passive elements in the entire feedback loop. Scalar multiplication ~ of both sides of Eq. (37) by Eq x, y , results in the initial mode amplitude: Cq n1 0, f ¦ U q q" Cq"n Lw , f e

 j k zq"  f Lc

q"

(38)

which is required in equation (35) to solve the field excited in the consecutive round-trip. In the frequency domain, the total out-coupled radiation obtained at the oscillator output after N round-trips is composed of a summation of the circulated fields (34) inside the resonator: N  j k zq  f Lw ~ ~ E out  f ¦ ƶ q ¦ C q n Lw , f Eq x, y e q

(39)

n 0

where ƶ q is qth mode field transmission of the out-coupler. The energy spectrum of the electromagnetic radiation obtained at the output after N round-trips is given by: d Wout N df

where T q

Yq

2

N

n ¦ T q ¦ Cq Lw , f q

2

n 0

^ `

1 Re N q 2

(40)

is the power transmission coefficient of mode q.

To simplify the analysis, we assume excitation of a single transverse mode. The power spectral density of the spontaneous emission out-coupled power is described by [26]: out d Psp

df

T

1- R 2  4

§1 · R sin 2 ¨ k z Lc ¸ 2 © ¹

˜

d Psp Lw df 2

(41)

where Lc is the resonator (round-trip) length, R U is the total round-trip power reflectivity and T is the power transmission of the out-coupler. The maximum transmission of the Fabry-Perot resonator [25] occurs when

Y.Pinhasi, Yu.Lurie,A.Yahalom

268

k z Lc 2mS (where m is an integer), which defines the resonant frequencies of the longitudinal modes. The free-spectral range (FSR) is the inter-mode frequency separation given by: vg 1 dZ 1 ˜ >k z  f m1  k z  f m @ FSR (42) Lc t r 2S d k z

where v g

dZ d kz

is the group velocity of the radiation and tr is its round-

trip time. The transmission peak is

T

1- R 2

with full-width half-

maximum (FWHM) bandwidth of: FWHM

where F

FSR F

(43)

S4R

is the Finesse of the resonator. 1 R The noise equivalent bandwidth is the bandwidth of an ideal band-pass filter producing the same noise power at its output. The spectral line-shape of the power density of the equivalent band-limited noise at the system's output is uniform within the noise equivalent bandwidth. The noise equivalent bandwidth of a single resonant longitudinal mode is B

S

S

FWHM

FSR . Consequently, the spontaneous emission power 2 2F of longitudinal mode m is: d Psp Lw T out m Psp ˜B (44) 2 df 1- R fm







Since the typical bandwidth of sinc 2 W sp f

is

1

W sp , the number of

longitudinal modes within the spontaneous emission bandwidth is

1

1

W sp FSR

.

Thus the total spontaneous emission measured at the output of the resonator will be: 1 1 1 d Psp Lw T out out  S Psp m # ˜ Psp 2F 1- R 2 W sp W sp FSR df fm (45) 1 T 1 T S ˜ Psp Lw ˜ Psp Lw 2F 1- R 2 2 4 R 1- R 2













269

Space-frequency model of ultra wide-band interactions

9.

RADIATION BUILDUP IN A FEL OSCILLATOR

In the presence of electron beam, the radiation circulating in the resonator is re-amplified in the interaction region at each round-trip. At the first stage of the oscillator self-excitation, the synchrotron undulator radiation emitted by the individual electrons entering the interaction region at random, interferes and combines coherently with the circulating field in the resonator. If the single-pass gain is higher than the total resonator losses (transmission and internal losses), the radiation intensity inside the resonator increases and becomes more coherent. After several round-trips the radiation power is built-up in the linear regime until the oscillator arrives to its nonlinear stage of operation and to saturation. The space-frequency numerical simulation WB3D was employed to demonstrate the development of the radiation, generated in a millimeter wave FEM oscillator. The spectrum of the output power after several radiation round-trips is shown in Fig.10a and the total energy buildup is described in Fig.10b for beam energy of Ek=1.375 MeV. The grazing case is described in Fig.11. 0.8

0.6

0.6

Pout [W]

dPout / df (Lw) [kW/GHz]

(a) 0.8

0.4

0.2

(b)

0.4

0.2

0.0

92

94

96

98

100

102

104

0.0

106

0

50

f [GHz]

100

150

200

Round-trip number

Figure 10. (a) Oscillator output power spectra and (b) total energy buildup in the FEM oscillator when Ek=1.375 MeV. (b)

(a) 8

6

1.5

Pout [W]

dPout / df (Lw) [kW/GHz]

2.0

1.0

4

2

0.5

0.0

0 42

44

46

f [GHz]

48

50

52

0

20

40

Round-trip number

Figure 11. That of Fig.10, but at grazing (Ek | 1.066 MeV).

60

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Acknowledgments The research was supposed by the Israel Science Foundation and the Israel Ministry of Science.

References [1] Y. Pinhasi, Yu. Lurie and A. Yahalom, Nucl. Instr. and Meth. in Phys. Res. A 475 (2001), p.147. [2] Y. Pinhasi, Yu. Lurie, A. Yahalom, and A. Abramovich, Nucl. Instr. Meth. Phys. Res. A 483 (2002), p.510. [3] N. Markuvitz and J. Schwinger, J. Appl. Phys. 22 (1951), 806. [4] L. B. Felsen, Radiation and scattering of waves (Prentice Hall, New Jerzy, 1973). [5] L. A. Vaynshteyn, Electromagnetic waves (Sovietskoye Radio, Moscow, 1957). [6] W. Schottky, Ann. Physik 57 (1918), 541. [7] S. O. Rice, Bell System Tech. J. 23 (1944), 282. [8] S. O. Rice, Bell System. Tech. J. 24 (1945), 46. [9] L. D. Smulin and H. A. Haus, Noise in Electron Devices (The Technology Press of Massachusetts Institute of Technology, 1959). [10] H. Motz, J. Applied Phys. 22 (1951), 527. [11] H. A. Haus and M. N. Islam, J. Applied Phys. 54 (1983), 4784. [12] Y. Pinhasi, and Yu. Lurie, Phys. Rev. E 65 (2002), p.026501. [13] R.H. Dicke, Phys. Rev. 93 (1954), 99. [14] R. Bonifacio, C. Pellegrini, L.M. Narducei, Optics Comm. 50 (1984), 373. [15] K.J. Kim, Phys. Rev. Lett. 57 (1986), 1871. [16] S. Krinsky, L.H. Yu, Phys. Rev. A 35 (1987), 3406. [17] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Optics Comm. 148 (1998), 383. [18] R. Bonifacio, B. W. J. McNeil, and P. Pierini, Phys. Rev. A 40 (1989), 4467. [19] N. S. Ginzburg and A. S. Sergeev, Optics Comm. 91 (1992), 140. [20] A. Gover et al., Phys. Rev. Lett. 72 (1994), 1192. [21] Y. Pinhasi and A. Gover, Nucl. Inst. and Meth. in Phys. Res. A 393 (1997), 393. [22] I. Schnitzer and A. Gover, Nucl. Inst. and Meth. in Phys. Res. A 237 (1985), 124. [23] A. Doria, R. Bartolini, J. Feinstein, G. P. Gallerano, and R. H. Pantell, IEEE J. Quantum Electron. QE-29 (1993), 1428. [24] M. Arbel, A. Abramovich, A. L. Eichenbaum, A. Gover, H. Kleinman, Y. Pinhasi, Y.Yakover, Phys. Rev. Lett. 86 (2001), 2561. [25] A. Yariv, Optical Electronics (Holt Rinehart and Winston, 1991). [26] Y. Pinhasi, Y. Lurie, A. Yahalom, Nucl. Instr. Meth. Phys. Res. A 528, (2004), p.62.

CHAPTER 3

APPLICATIONS OF QUASI-OPTICAL SYSTEMS

BI-STATIC FORWARD-SCATTER RADAR WITH SPACE-BASED TRANSMITTER

A.B. Blyakhman Nizhny Novgorod Research Radio Technical Institute

Abstract:

Keywords:

1.

A multi-positional forward-scatter radar complex is proposed, with the transmitter based on a satellite and the receiving network distributed on the ground. Such a global system would be capable to detect, track and recognize air and space objects, in particular, stealthy ones. detection of stealthy targets, global security.

INTRODUCTION

Recent works on the forward-scatter radar [1 -3] have convincingly demonstrated its main advantages: x When a target enters a zone between the transmit and receive positions, the target radar cross section (RCS) increases by factor of 103 – 104; x the target RCS in the forward-scatter zone does not depend upon the target coating (for instance, absorbing one). These advantages, compared to the conventional monostatic radar, provide much improved opportunities to detect track and identify low flying light aircrafts and helicopters, “Stealth” aircrafts, cruise missiles, hanggliders etc. However, the operation zone of the forward-scatter radar is relatively narrow. Capabilities of the radar can be expanded by using a multipositional system: a chain of bistatic links, each link forming a detection zone stretched between receiving and transmitting posts. A further upgrade of the forward-scatter radar would be using a transmitter placed in space.

273 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 273–281. © 2005 Springer. Printed in the Netherlands.

274

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A. Blyakhman

BISTATIC SPACE-BORNE FORWARD-SCATTER RADAR

The idea of satellite-borne bistatic radar has been discussed beginning in the 80’s [4, 5]. However, recent experimental results give a firmer ground for such projects.

2.1

System Geometry

The transmitting system can be located on satellites with different orbit height. Low orbit location, evidently, will require less radiating power, but a greater number of satellites [4]. However, the organization of continuous observation over the selected territory and its prompt change gets more complicated. So, the continuous global coverage is provided for the orbits of medium height (10 000 km) with 12 satellites, and for the low heights (1 100 km) with 50 satellites. The placement on geostationary orbit provides tactical advantages and enables one to permanently observe the chosen territory. Three satellites provide global coverage, however, it requires greater radiated power. The satellites located on the geostationary orbit enjoy better survivability and can receive navigation information by an easier way than low orbit satellites. In case of geostationary deployment, the interference exerts smaller influence in comparison with lower orbits. There are other factors, which determine advantages and disadvantages of different transmitter siting heights. Simple estimations make it clear that, when a beam width of the transmitting antenna in the main orthogonal section is about 4q, the earth surface with a characteristic dimension of about 3 000 km is radiated. It helps to provide operation in the mode of forward scattering radiolocation simultaneously, with a significantly large group of ground-based receiving stations. Such beam width allows relaxing the requirements for the accurate pointing of the satellite and receiver antenna; and a narrower beam requires greater antenna dimensions and weight. From a military point of view, the most important thing is that the receiving stations are not radiating ones. In other words, they are “invisible”.

2.2

Detection Zone

The main design principles have been developed and approved for bistatic forward scattering radars [1-3]. These principles make it possible to detect, track and identify air targets. These radars use continuous quasiharmonic

Bistatic Forward-Scatter Radar….

275

radiation of the transmitter and measurement of the Doppler frequency bias and determination of the arrival direction of the wave scattered by the target at the receiving position. These principles can be used fully to develop the space-borne forward scattering system. The choice of the frequency range is determined by two factors: dependence of the target’s RCS upon diffraction angle [1] and the loss value on propagation path. Comparative analysis reveals that it is advisable to choose operating wavelength in the range of O = 0,3 – 0,4 m. We know from scientific literature (see for example [6, 7]) that at a frequency of 850 MHz (O = 35 cm) total absorption in the troposphere and in hydrometeors is from 2.5 dB to 0.2 dB, when the satellite elevation angle changes from 0q to 10q respectively. As noted above, the structure of the receiving position can be understood from the previous investigation. In particular, the receiving position may have a multibeam antenna system with the beam length of 5q – 7q and circular polarization due to the Faraday effect. To create a detection zone of the bistatic space-borne radar, we use radar equation for the two-positional system:

Q

PT GT G R O2KFT2 ( E , H )FR2 ( E , H )

4S 3 P0 rT2 rR2

u V (D v , D h ),

where: Q – signal/noise ratio PT – average power of the transmitter P0 – self-noise power of the receiver in the band of optimal processing GT ,GR – gain factors of the transmitting and receiving antennas K – generalized losses (transmission, reception, processing) V(Dv , Dh ) – bistatic RCS of the target, as a function of diffraction angle in the vertical (Dv) and horizontal (Dh) planes FT2 ( E , H ), FT2 ( E , H )  power directional pattern of the transmitting and receiving antenna rT, rf – distance from the transmitting and from the receiving systems to the target The most important features of the system in question are conditioned by bistatic RCS – V(Dv, Dh) function. Figures 1, 2 show bistatic RCS (calculated according to [1]) for a ballistic missile and its warhead as well as a “Stealth” fighter. The validity of the RCS calculation has also been demonstrated

276

A. Blyakhman

experimentally. Independence of the RCS upon the material of the object is explained in [8, 9]. The calculation proves that bistatic RCS of missiles

and “Stealth” aircraft exceeds 104m2 as a maximum and as for the warheads, this value exceeds 103m2 Estimation of the detection zones was conducted for the detection probability D t 0.9 and PT = 500 kW. Figures 3, 4 demonstrate detection zones of “Stealth” fighter (F-117A) and ballistic targets flying along a normal line to a vertical plane that pass over transmitter-receiver line. Thus, calculations demonstrate that forward scattering radar barrier has a very high power potential and provides detection of not only missiles but their warheads at the altitudes maximum possible for these targets (below radio horizon). Air objects including those produced according to “Stealth” technology may be detected simultaneously with the ballistic objects. As explained above, applying this technology to space objects will not change their detection characteristics by forward scattering barrier.

2.3

Detection and Identification Principles

Measurement of the trajectory parameters by the bistatic system with a space-borne transmitter can be carried out in a similar manner as by groundbased systems, [2, 10] since all the main principles of creating these systems are identical. Air objects tracking by ground-based forward scattering system were used in full-scale experiments [1,2]. Features connected with essentially long base-line distance and very far speed of objects can be taken into consideration. Figure 5 demonstrates results of experimental tracking of air objects. Rather high rate of data renewal (1 second and less) makes it possible to form the trajectory of the target in 3-4 seconds after it enters the area covered by the radar barrier. It is certainly, the most important advantage of the system. The bistatic forward scattering radars with quasiharmonic probing signal identify targets by the Doppler spectrum analysis of the returned signal when targets pass the barrier [3]. A two-level classification system was developed and approved in the ground-based systems, in course of the full-scale experiments. It provided identification of the 4 classes of targets with a probability of 0.7-0.8. Thus, the experiments clearly proved the possibility in principle to identify classes of targets by bistatic forward scattering radars.

Bistatic Forward-Scatter Radar….

277

Figure 1. RCS of an aircraft target (F-117A).

Figure 2. 1 - RCS Intercontinental Ballistic Missile (ICBM) Tepkhodon-2 as an assembly. 2- RCS of a warhead of the ICBM Tepkhodon-2.

278

A. Blyakhman

Figure 3. Detection zone of an air target (F-117A). a) Vertical section. b) Horizontal section (flight altitude - 1000m)

Bistatic Forward-Scatter Radar….

279

Figure 4. Detection zone of a space target (vertical section). 1 - RCS ICBM Tepkhon-2 as an assembly. 2 - RCS of a warhead of the ICBM Tepkhon-2.

3.

APPLICATIONS

As an early detection and warning boundary, the radar barrier must function uninterruptedly. The quasi-harmonic probing signal determines rather high efficiency (60-70%) of the transmitter generator. Thus, the power consumed by the transmitting system does not exceed 1 MW. Today, sources of such power may be created on the basis of a nuclear power plant with a life cycle of 7 years. Weight and dimensions of such a plant allow the whole transmitting system to be put into geostationary orbit by domestic space vehicles. It is not a problem to make a mobile ground system, which would be similar to one already tested [1]. As is shown above, a chain of sea and ground-based posts, together with one transmitting system, make it possible to form a surface radar barrier of required configuration with the range of 3 000 km. Each receiving system is able to detect, track, and identify ballistic missiles at a range of more than 6000 km, and it covers all the possible heights of missiles flying. The

280

A. Blyakhman

reduced equipment volume of the receiving post limits its power consumption to several kilowatts. The “Stealth”-technology does not limit the effectiveness of such barriers. It is fairly obvious that beam control of the transmitting system makes it possible to quickly change the area of forward scattering barriers.

Figure 5. Flight tests results of the air targets tracking. Mi-8 helicopter, flight altitude H=200m, target velocity v=44m/s. L-29 jet airplane, flight altitude H=200m, target velocity v=148m/s.

Bistatic Forward-Scatter Radar….

4.

281

CONCLUSION

The forward-scatter radar system with transmitter located on an artificial earth satellite on the geostationary orbit would provide a unique opportunity to detect, track, and identify both large space objects (ballistic missiles and their warheads) and small-RCS (e.g. “stealthy”) ones. Such a collective global security system might be an ideal project for international cooperation.

5.

REFERENCES

1. A.B. Blyakhman, I.A. Runova, Forward Scatter Radar: Bistatic RCS and Target Detection, Proc. IEEE Radar Conf., Waltham, USA, April 20-22, 1999, pp. 203-208. 2. A.B. Blyakhman, A.G. Ryndyk, S.B. Sidorov, Forward Scatter Radar: Moving Object Coordinate Measurement, Proc. of IEEE Int. Radar Conf., Alexandria, USA, May 7-12, 2000, pp. 678-682 3. A.B. Blyakhman, S.N. Matyuguin, Target recognition at forward scatter radar, Radio technique and Electronics, 46(11), 1356-1360, (2001), in Russian. 4. Y. S. Hsu, D. C. Lorti, Space-borne bistatic radar on overview, IEEE Proc., 1986, F133, ʋ 7, pp. 642-648 5. P.K. Lee, T.F. Coffey, Space-Based Bistatic Radar: Opportunity for Future Tactical Air Surveillance, Proc. IEEE Inter. Radar Conf., May 1985, pp. 322-329. 6. Handbook on satellite communications & broadcasting, edited by L. Kantor (Radio & Comm., Moscow, 1984), p. 272, in Russian. 7. Handbook on radar, ed. by M Scolnik 8. P.Ya. Ufimtsev, Black bodies and shady radiation, Radio technique and Electronics, 35(12), 2519-2527, (1989), in Russian. 9. J.I. Glaser, Some results in determination of bistatic RCS of complicated targets; IEEE Trans., 77(5), pp. 8-18, (1989). 10. A.B. Blyakhman, F. N. Kovalev, A.G. Ryndyk, Method to determine coordinates of moving targets by bistatic radar, Radio technique, #1, pp.4-9, (2001), (in Russian).

ANALYSIS OF NANOSECOND GIGAWATT RADAR

A. Blyakhman 1 , D. Clunie 2 , G. Mesiats 3 , R.W. Harris 4 , M. Petelin 5 , G.Postoenko 5 , and B. Wardrop 6 P

P

P

P

P

P

P

P

P

P

P

P

P

P

1 NIIRT, Nizhny Novgorod, Russia; 2 High Power RF Faraday Partnership Lab, Oxon., UK; 3 IEP, Ekaterinburg, Russia; 4 BAE Systems, Chelmsford, UK; 5 IAP, Nizhny Novgorod, Russia; 6 Wylie Consulting, UK P

P

P

P

P

P

P

P

P

P

P

P

Abstract:

If a radar transmitter provides a sufficiently high energy in a short microwave pulse, efficient indication of moving targets among heavy clutter can be obtained by the simplest signal-processing algorithm. Such performance was demonstrated with an X-band 0.5 GW/6 ns/150 pps radar operating with a 3q beamwidth antenna.

Key words:

range resolution, moving target indication, clutter rejection.

1.

INTRODUCTION

During the mid-1990's the Russian Academy of Science and various entities from the UK established a cooperative agreement to investigate a novel radar concept. Eventually, this concept was called, in the UK, Nanosecond Gigawatt Radar, and it acquired the acronym NAGIRA. This system had a number of unique features; the concept has been described in a number of publications [1] & [2]. This paper is the first to describe some of the results obtained with this system. The components of this system have a number of unusual features and a number of key features that affect the overall system performance. These components are described and their associated measurements are shown. Finally, the radar performance characteristics are presented. A number of tests were performed against a variety of targets. Some interesting features of these tests are described and the high range resolution inherent within this system is demonstrated using the returns from a helicopter that show some unique characteristics. 283 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 283–296. © 2005 Springer. Printed in the Netherlands.

284

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A. Blyakhman, et. al.

Organisations Involved

The design, manufacture, and testing of this system involved a number of organisations, including the following: x Russian Academy of Science x x x x x x

Institute of Electrophysics (Ekaterinburg) Scientific Instrument Special Design Bureau (Ekaterinburg) Institute of Applied Physics (Nizhny Novgorod) High Current Electronics Institute (Tomsk) Scientific Design Bureau “ALMAZ” (Moscow) GEC-Marconi Research Centre - Now BAE SYSTEMS Advanced Technology Centre (Great Baddow, Chelmsford, UK) x DERA (Defence Evaluation Research Agency) - Now split into two separate companies DSTL and QinetiQ (Malvern, UK) x UK Ministry of Defence

1.2

Specified & Measured Parameters

The original specification for the system are shown in Table 1. Table 1: NAGIRA System Specification & Measured Parameters

Frequency Frequency stability Pulse Duration Pulse Power Pulse Power stability PRF Pulse Forming Line Cathode Voltage (Vc) Cathode Current (Ic) RF generation Magnetic field Cathode life Transmitted Pulses Mode Converter Beamwidth Beam scan angle

SPECIFICATION 10GHz <0.1% 5ns 0.5GW <1% 150Hz 800KV 5KA

MEASURED 10GHz <0.1% 7.2ns ('t =6%) 0.34GW ~1.5 to 2% 1 Æ 150Hz 655kV 540kV (VVc =0.7%) 4.3kA Relativistic BWO 3 Tesla

~10 7 pulses P

P

>4*10 7 P

TM01 o TM11 TM11 o HE11 3q ±15q

3q ±15q

P

Analysis of Nanosecond Gigawatt Radar SPECIFICATION Receiver Noise Figure Range Resolution MTI cancellation

>30dB

285 MEASURED 6dB 0.7m 13dB or better

After manufacture, testing and adjustment the results obtained were slightly different and resulted from a compromise, to achieve a reasonably stable operating regime.

SYSTEM DESIGN The design of the system contains a number of unusual characteristics. A block diagram showing the major components is shown in Figure 1 . The heart of the transmitter section is the pulse forming line. This is powered from a normal 50 Hz mains power supply. Bulk power storage is supplied by banks of capacitors. The Tesla transformer is fed by a parallel set of fast switching Thyristors. The output of the Tesla transformer ramps up to ~700 kV in a few tens of microseconds. Requisite timing trigger pulses are computer controlled and deterministic. In order to obtain a stable repeatable output the trigatron (embedded within the gas gap switch) is switched when the forming line voltage reaches a set level. This trigatron ionises the gas in the switch and closes the switch, passing the voltage pulse through the transformer to the cathode of the Backward Wave Oscillator (BWO). This pulse generation process results in some timing jitter with a Gaussian distribution of typically a microsecond. This entire system is highly integrated and is contained within a relatively small space. The resultant pulse is then fed via an impedance converter to the cathode of the Relativistic Backward Wave Oscillator. This converter has an input impedance of ~60 Ohms and an output of ~80 Ohms to match the impedance of the BWO. It consists of an oil filled tube approximately 4 m long. The cathode consists of a machined graphite block. As the cathode voltage pulse is applied the electron beam is generated, and this erodes the cathode. Typically, 1 mm of cathode material is eroded per million pulses. During assembly, the cathode is centered within the BWO by using a target, and ensuring that the resultant annular electron beam is symmetrical and central. Despite this, the cathode erosion tends to be asymmetrical. T

T

286

A. Blyakhman, et. al. Receiving Section Analogue to Digital Converter

Detector

IF amplifier

RF Protection Amplifier Device

Mixer

gain control Data Storage & archive

Digital Signal Processing

Display & control

TV Display

TV Camera

Transmitting Section 230 Volt 3-phase power supply

Cryomagnet Pulse Former (Tesla)

Gas gap switch

Impedance Converter

Mode Converter

BWO

mirr or

Reference Pulse

Cryomagnet Control Computer

Vacuum pump 10-6 Torr

Trigatron

T

Figure 1: NAGIRA system block diagram.

The cathode and slow wave structure is contained within a 3 Tesla magnetic field which is generated using a cryomagnet. Lead shielding is necessary to reduce X-rays. Replacement of the cathode requires disassembly of this shielding and removal of the BWO and the cryomagnet, hence the interest in extending cathode life (see Section 4.2). The electron beam is explosively emitted from the graphite cathode and passes through the BWO, interacting with the slow wave structure and generating the RF. Varieties of slow wave structures were tested. Early versions had an efficiency slightly more than 20%; however, these showed instabilities. A stable pulse regime was obtained with devices having an efficiency of 15%. Later versions of the BWO slow wave structure were machined from a single piece of stainless steel, before being welded to the waveguide mirror and output section. Within this tube, the rf is generated in the opposite direction to the electron beam, hence the BWO contains a waveguide mirror that reflects the rf in the opposite direction. The BWO generates rf in the TM 01 mode and this is fed to the mode converter. The mode converter, coverts the rf to H 11 mode, using a swan neck design, it also contains an axi-symmetric horn produces a Gaussian beam. The Gaussian beam is the passed via a large over-moded waveguide through an output window (required to isolate the vacuum from the atmosphere) to the B

B

B

B

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transmitting dish antenna. The system uses two antennas for transmit and receive. There is an isolating septum between the two antennas further isolating the coupling into the receiver. The receiver is a conventional design. The receiving antenna is connected to the receiver using waveguide. The Protection Amplifier Device (PAD) is a tube based electrostatic rf amplifier which provides 20 dB gain (noise figure ~5 dB, bandwidth ~500 MHz), which limits automatically, when the input rf power exceeds 50 dBm, and can reject very high levels of rf power. The rf signal is mixed down to IF using a fixed local oscillator. The gain in the IF amplifiers is controlled by digitally controlled attenuators, either automatically by the computer or manually by the operator and display computer. The detected video signal is passed down a long coaxial cable to the control cabin, where it is digitised, recorded to hard disc, and displayed to the operator. Two cabins were necessary because of the high level of X-rays generated by this transmitter. The BWO was surrounded by lead shielding. However, because frequent maintenance and adjustment is necessary, the amount of shielding was limited. Safety was assured by separating the transmitter from the personnel and the control cabin by about 20 m. The second cabin contained the computers that controlled the transmitter and receiving equipment. There are also computers containing a high speed analogue to digital converter and associated storage on hard disc and tape, for real time control and off-line analysis. The video output of the receiver in the transmit cabin is connected using low loss coaxial cable to control cabin. This is A/C coupled and fed directly to a Signatec 500 MHz 8 bit ADC on a PC ISA card with 256k memory (which gave an instrumented range of 80 km). There was a significant and varying voltage level between the two cabins. This voltage depended upon the transmitter PRF. To overcome this problem it was decided that the ADC should be A/C coupled and a high pass digital filter was incorporated within the signal processing software in an attempt to set the correct DC level. While this was probably the optimum solution in this case, it did reduce the effective dynamic range available to the signal processor by one bit. As the amount of data produced could not be recorded to hard disc for off-line analysis the software used a recording window of 16 kbytes (2.5 km) which could be stored at a rate of 150 Hz continuously. The contents of each window was recorded onto discs and sent to the display PC. The display window width could zoom from 2.5 km to 125 m, and the operator could control the window position and velocity. The other controls allow the antennas to be steered in azimuth, and to alter the IF attenuation. It was originally intended that the IF attenuation would be

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set automatically with range (STC). However, it was quickly discovered because of the diversity of target RCS and ranges that were observed with this system, a fixed attenuation scheme was not practical. Hence, we relied upon the operator to set the correct gain. The main objective for the operator was to keep the target visible within the window. Unfortunately, this means that there was normally too little attenuation, as operators tend to like stable targets that do not fluctuate (as normal targets do).

2.

TEST RESULTS AND ANALYSIS

2.1

Transmitter & Receiver Parameters

The pulse forming line and cathode current and voltages were monitored by built-in sensors, and measured using a digital storage oscilloscope in the control cabin. Both the cathode voltage and current measurements showed a similar profile. Several sensors were used to measure the rf pulse and spectrum. The cathode voltage and current rises to a peak during which the electron beam is formed and the rf is generated (Figure 2). Not all of the energy at the cathode is transferred to the electron beam; approximately half is reflected back towards the transformer and gas gap switch. This is again rereflected back to the cathode, resulting in a long pulse of much lower amplitude after the main pulse. This reflection can cause a secondary rf pulse to be emitted typically 50 nanoseconds after the first pulse, however because the voltage is much lower the frequency is also much lower. This second pulse is unstable and intermittent. The rf spectrum (Figure 2) shows the main pulse spectrum centred on 10GHz. It has regular sidelobes falling away in amplitude and frequency (reminiscent of a magnetron spectrum). At lower frequencies (in this case between 8.5 and 9.2 GHz), the spectrum is much more ragged, and this is due to the secondary pulse. Because the rf of this secondary pulse is much lower than the main pulse bandwidth is, it has no effect on the received radar signal. The cathode current and voltage varies slightly from pulse to pulse (as shown in Figure 2). This, in turn, gives rise to amplitude and frequency jitter in the transmitted pulse. Considerable adjustment and testing occurred with the aim of minimising the pulse jitter. The emphasis was to minimise the frequency, pulse width and amplitude variation so that efficient signal processing could be performed. The result was that the pulse to pulse variation was minimised using a reduced power operating mode.

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Significantly, the long-term stability (measured over a 30-minute duration) was identical to the stability measurements obtained with a few pulses.

Figure 2: Inverted Cathode Current, (peak current 5.4 kA).

The rf pulse was measured using a detector behind the transmit dish and also in the far field. The detector behind the dish was mounted within a waveguide and fed via a small hole in the centre of the dish, in which the waveguide was mounted. It was this detector which triggered the data capture and was used as the "reference pulse" for some of the MTI signal processing algorithms. Suprisingly, the pulse shape measured behind the dish was significantly different from that measured in the far-field (Figures 3, 4).

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Figure 3: Far field Pulse shape.

Figure 4. Far field RF Spectrum, using slow scanning spectrum analyser.

The pulse measured behind the dish appeared to have a slightly slower rise time and the peak power rises by 3 dB during the 7 ns peak. The far field pulse shape is much more uniform. Presumably the rf emitted by the tube and

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mode converter is focused on different parts of the dish and changes during the pulse.

2.2

Aircraft Trial

A test with a Piper 28 light aircraft demonstrated that detection of this target was possible at ranges of 70 km. This matches the theoretical detection performance assuming the aircraft RCS is approximately 2 square metres.

2.3

Ship Trial

The system was mounted near to the seashore, with an elevation above the sea surface of between 5 and 15 m. With this configuration, it is possible to obtain over the horizon propagation [6]. This system frequently detected ships between 30 and 70 km. It was possible to track passenger ferries as they passed in front of the radar (range ~3 km) out to 70 km. One example was an Olau Lines Ferry (Figure 5), which was tracked from 5 km well past the optical horizon (approximately 20 km). The radar image shown in Figure 6 and Figure 7 are examples of snapshots at ranges of 14 km and 41 km and they show some similarities Figure 5: Olau Lines Passenger Ferry. (length positions of major reflection points, velocity, etc). However, there does appear to be some differences between these two snapshots (which are typical of the results obtained). The main reflection now appears towards the front of the ship, rather than the stern, and other major reflections have appeared towards the centre. It is presumed that these differences occur due to the different propagation paths, and the physical configuration of the ship. The results obtained appear similar to those described using conventional radar systems [8]. In a dynamic moving image, the varying bow wave can be observed, and when a rotating radar antenna is present, this can be seen flashing as it rotates.

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Figure 6. Passenger ferry, range 14 km, radial velocity 10 m/s (IF attenuation 44 dB).

Figure 7. Passenger ferry, range 41 km, radial velocity 12 m/s (IF attenuation 8dB).

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293

Helicopter Trials

There are several papers that describe the analysis of helicopter returns in the Doppler and time domain [3], [4], [5], and others that describe high resolution imagery of aircraft [7]. The most commonly described feature of helicopter identification is a helicopter blade flash, when the blades are perpendicular to the radar, but this flash is of very short duration. In the Doppler domain the helicopter is characterised by a large peak (the helicopter body) and a surrounding plateau normally ascribed to the rotating hub. In this trial, a Bell JetRanger III flew over the sea from the radar to a distance of 20 km and then returned, travelling at about 100 knots, at an altitude of approximately 100 m. The data shown here was taken on the inbound leg between 8 and 9 km from the radar. The data had been stored on tape and for some off-line analysis. We took this section and transformed the data from the fixed reference frame to a moving reference frame. The resultant data is shown in Figure 9.

Figure 8: Bell JetRanger Flight-path, from Portsmouth to Selsey Bill and back.

A. Blyakhman, et. al.

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Helicopter blade tip

Helicopter cabin

Time (0.01s/pixel)

2.5m 5m

10m

Figure 9: Image of JetRanger, showing Blade tips in front of helicopter cabin.

The return shows considerable structure from various components in the helicopter. Several features are clearly apparent. The main body of the helicopter is limiting within the radar receiver and this results in the uniformly large return approximately 5 m in length. The tail of the helicopter is difficult to resolve, this is because the amplitude of the return from the body of the helicopter is changing significantly and this is affecting the lower amplitude returns from the tail section. These large reflections combined with anomalous responses within the receiver causes this distortion. The feature in front of the helicopter body is the helicopter blade tip; rotation occured every 50 milliseconds (20 Hz), or five pixels in our picture. The rotation rate does not exactly match the radar PRF so we see regular fading, using this data it appears trivial to estimate the width of the reflecting part of the helicopter blade. The distance between the front of the helicopter body and the blade tip appears to be 7-8 range gates (or 2.5m) which matches the dimensions shown in Table 2.

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Table 2: External Dimensions of the JetRanger III Helicopter

Overall length (including main blades) Length (excluding main blades) Width Height (including main blades) Blade rotation rate Diameter of blades Rotor to cabin front Cabin front to blade tip (maximum)

11.92 m 9.51 m 1.95 m 2.90 m ~10 Hz 33.3 ft 8.8 ft 7.85 ft (2.53 m)

The Radar Cross Section (RCS) of the tip of the helicopter blade is quite small and the RCS of the body of the helicopter is much larger. The helicopter blade tip is easily visible in front of the helicopter because NAGIRA is not affected by range sidelobes in the same way as conventional radar systems. Conventional radar systems use pulse compression to obtain sub-metre resolution and these systems will have range sidelobes [9]. The peak to sidelobe ratio of conventional pulse compression hardware ranges from 25 dB to 55 dB under ideal conditions. In practice, this figure of merit is degraded when the receiver suffers non-linear effects and when there are multiple scatterers, within the uncompressed pulse width. In contrast, NAGIRA is not affected by non-linear effects or (negative-range) sidelobes. It does have an extended tail due to the slow transmitted pulse decay (which can be viewed as positive-range sidelobes) and from unwanted impulse, responses within the receiver, and these effects distort the return after the helicopter body (i.e. positive range).

3.

FUTURE UPGRADES

During and after the trials with this system had finished, we continued to study possible upgrades to the design. Among these were: 1. Replace the cryomagnet, because a liquid helium cryomagnet is not very practical in operational systems. Designs showing operation at lower magnetic fields using an electromagnet (non-uniform fields of 0.7 Tesla & 1 Tesla) were investigated. 2. Extend the Cathode life (from 10 7 to 10 8 pulses), because practical systems must have lower maintenance. A design of an adjustable P

P

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P

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cathode (rotates & moves) was produced. This would maintain the existing graphite cathode as it still appeared to be the best material. 3. Electronic lens to focus and scan the high power RF beam. This concept was demonstrated with particularly promising results. Such a proposal would also require quasi optical rotating joints and a multiplexer and duplexer.

Acknowledgements This work is supported by BAE SYSTEMS Advanced Technology Centre and the UK Ministry of Defence. We would also like to acknowledge the support and hard work of all the many people from both Russia and the UK who participated in this project.

4.

REFERENCES [1] Osipov M. L.; Superwide-Band Radar; Telecommunications and Radio Engineering 49(9), 1995, pp 42-47 [2] Clutterbuck, C.F. Wardrop, B.; Evaluation of an experimental high power, short-pulse radar; IEE Colloquium on Pulsed Power '97 (Digest No: 1997/075), Date: 19 March 1997; Location: London UK; page(s): 3/1 - 3/8 [3] Misiurewicz, J.; Kulpa, K.; Czekala, Z.; Analysis of recorded helicopter echo; Radar 97 (Conf. Publ. No. 449) , 14-16 Oct. 1997 ; Pages:449 - 453 [4] Misiurewicz, J.; Kulpa, K.; Czekala, Z.; Analysis of radar echo from a helicopter rotor hub; Microwaves and Radar, 1998. MIKON '98., 12th International Conference on , Volume: 3 , 20-22 May 1998 ; Pages:866 870 vol.3 [5] Sang-Ho Yoon Byungwook Kim Young-Soo Kim ; Helicopter classification using time-frequency analysis; Electronics Letters Publication Date: 26 Oct. 2000 On page(s): 1871 - 1872 Volume: 36 , Issue: 22 [6] Craig K.H.; Propagation of Radiowaves, 2nd edition (L.W. Barclay (Ed)); Chapter 7.3 - Anomalous propagation: multipath and ducting; IEE. [7] Zyweck, A.; Bogner, R.E.; High-resolution radar imagery of the Mirage III aircraft; Antennas and Propagation, IEEE Transactions on , Volume: 42 , Issue: 9 , Sept. 1994 Pages:1356 - 1360 [8] Perez, M.; Asensio, A.; Gismero, J.; Alonso, J.I.; Monje, J.M.; Casanova, F.; Cortijo, R.; Perez-Ojeda, J.F.; ARIES: a high-resolution shipboard radar; Radar Conference, 2002. Proceedings of the IEEE , 22-25 April 2002 Pages:148 - 153 [9] Cohen, M.N.; An overview of high range resolution radar techniques; Georgia Inst. of Technology., Atlanta, GA, USA; Telesystems Conference, 1991. Proceedings. Vol.1., NTC '91.

HIGH POWER MICROWAVE SPECTROSCOPY

German Yu. Golubiatnikov Institute of Applied Physics of Russian Academy of Sciences; Uljanova 46, Nizhny Novgorod 603950; e-mail: [email protected], http://www.appl.sci-nnov.ru/mwl/

Abstract:

Sources of coherent radiation, tunable over millimeter and sub-millimeter wavebands are successfully used in the absorption spectroscopy of molecules; the high sensitivity being provided by the Radio Acoustic Detector (RAD) with backward wave oscillator (BWO) as a radiation source1. However, as the RAD sensitivity is proportional to the applied microwave power, new opportunities can be provided by using a gyrotron. Demonstration experiment to detect the 615–616 transition of HCOOH molecule had been already performed with a ~1 kW gyrotron2. In the future, fine-frequency-controlled gyrotrons are promising to observe highly exited vibration states of molecules, forbidden transitions of non-polar molecules and very weak lines of rare species in natural abundance3.

Key words:

molecular spectroscopy, nonlinear spectroscopy, radio acoustic detector, BWO, gyrotron, fine frequency control.

1.

MICROWAVE RADIO ACOUSTIC SPECTROSCOPY

The RAD spectrometer (www.appl.sci-nnov.ru/mwl/) has been developed as a general-purpose laboratory spectrometer for study of high-resolution spectra in the mm and sub-mm wave regions. It has an excellent resolution; an extremely high accuracy of frequency measurements, a very good sensitivity and can operate in THz frequency region1,4,5. Fig. 1 presents a traditional block-scheme of the experimental setup (see also Fig. 3). A BWO tunable within a 30% frequency-range is phase locked against a harmonic of fundamental frequency of 78–118 GHz reference synthesizer (KVARZ, Nizhny Novgorod). BWOs cover 30–1200 GHz range), deliver tens of mW at 200–600 GHz and about 1 mW at 1.1 THz; they are produced by the ISTOK Microwave Inc. (www.istok.com). The line-width of a phase-locked BWO is about 1 kHz at 100 GHz and depends upon the 297 J. L Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 297–304. © 2005 Springer. Printed in the Netherlands.

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BWO frequency, spectral purity of the reference synthesizer signal and the phase noise of a phase-lock loop (PLL) electronic circuits. The synthesizer frequency itself, is stabilized against a rubidium standard (5 MHz, 'f/f = 10-11) and controlled via computer. Microwave radiation incident on a cell with a gas sample is absorbed by molecules and the subsequent variation in pressure, due to heat energy released by the molecule upon return to the ground state, is detected by an acoustic cell (RAD spectrometer). The sensitivity of the technique arises from the inherently high efficiency of thermal conversion that occurs in microwave absorption processes. This is combined with a similar efficiency in a highly sensitive microphone that converts the acoustic wave into a voltage signal.

Figure 1. Block–diagram of experimental setup with RAD spectrometer.

The main advantages of the acoustic detection technique are as follows: x the zero base line detection – the radiation power is practically unabsorbed apart from a spectral line; x the sensitivity comparable with sensitivities of cryogenic detectors (but much less cost if to compare with the liquid-He InSb bolometer); x the signal-to-noise ratio (SNR) proportional to the radiation source power; x the extremely broadband detection from microwave to optic range (that depends on cell windows transparency only); x sample under study and detector itself are combined in one unit.

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The small size of the acoustic cell (our cells are about 10 cm length, and 2 cm diameter) also permits better temperature stabilization of the sample and provides easier studying; for example, a molecule such as oxygen6 being sensitive to Earth magnetic field. Acoustic cell could be also used for measurements of radiation power7 with max speed of response 1-10 kHz. As an example, the line profile measurements of weak (N, J) = (7, 6) – (5, 6) rotational transition of oxygen (16O2 ) molecule at 1.12071484(5) THz are presented in Fig.2 (at the left) together with the fit to Voigt line profile6. Another example of line-widths of 118.75-GHz oxygen line, retrieved from the line shape measurements, broadened by pressure of different foreign gases6b are presented as part of Fig. 2. Very small deviations of the line widths from the linear pressure dependence (see residue in Fig. 2, below at the right) have demonstrated the high accuracy of the line shape measurements with RAD spectrometer. Such data are very important for earth observation systems.

Figure 2. Record of the (N, J) = (7, 6) – (5, 6) of 16O2 rotational line. (central frequency is 1.12071484(5) THz). Experimental points are denoted by cross (+), the line (––) represents the fit to Voigt line profile; bottom trace is residuum of the fit. (Left). The 118.75-GHz selfbroadened line widths (boxes), broadened by Ne (circles), and by water (diamonds); linear regression fits to the data are shown by solid lines, the residua of the fits are shown below. (Right).

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OPPORTUNITIES TO USE GYROTRONS IN SPECTROSCOPY

Gyrotrons capable of delivering 103  10 6 W power in the millimeter and sub-millimeter wavebands are very attractive for molecular spectroscopy. A free running, non-stabilized, ~1 kW gyrotron in combination with the RAD has already been used to detect the 615–616 transition of HCOOH molecule2. The SNR was about ~6000. The relatively broad line of formic acid HCOOH was chosen to eliminate noticeable power broadening effect of the line and as a result, the possible changing of the line intensity. However, advantages of the gyrotron can be demonstrated in a full scale system, e.g., for measurements of the spectral line profile and line center shift versus power that is very important for studying non-rigid molecules similar to the water. However this is only possible when fine frequency control is available, that can be done by using a phase-locking loop (PLL) scheme (Fig.3) similar to that used to control BWO frequency. A fraction of the gyrotron radiation split off by a directional coupler is combined in a harmonic mixer with the output of a frequency synthesizer. The frequency difference between the gyrotron and a harmonic of the frequency synthesizer is constrained to 350 MHz by a PLL synchronizer. The error signal produced by synchronizer is then amplified and applied to the gyrotron as additional high voltage power supply. Electrical frequency tuning could be done during a few microseconds. The only difference from the BWO case is the use of a high voltage video amplifier of sufficient power.

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Figure 3. Block-diagram of the gyrotron frequency stabilization system.

This scheme provides the electrical tuning within the gyrotron cavity bandwidth 'Z ~ Z / Q , where the quality factor Q is usually around 1000 and can be specially reduced to some hundreds. This natural cavity bandwidth can be expanded by using two, coupled cavities8. In an X–band gyrotron, the frequency was tuned within 1%. A slow broadband tuning of the gyrotron can be provided by changing the magnetic field in the solenoid and by changing parameters of the cavity, by changing the separation between mirrors in a two-mirror cavity, or by the position of conical rod in a coaxial cavity.

3.

POTENTIALS OF HIGH POWER MICROWAVE SPECTROSCOPY

A thorough review of high power spectroscopy can be found in a book by Letokhov and Chebotayev9. Compared to the optical case, the spectroscopy at microwave frequencies is featured with a very low probability of spontaneous emission between quantum levels. At the submillimeter waveband, such a nonlinear effect as power saturation, or power line broadening, in addition to collision broadening of Lorentzian lines, of rotational transition of dipole molecules, reveals itself at power only of a few milliwatts. It could be observed in the form of so-called Lamb dip10 in

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Doppler broadened line, which favors increasing the frequency resolution. The absolute value of the Lamb dip is usually quite small to observe it directly1 in a spectral line. To enhance the observation of this effect, the frequency modulation technique is used for waves traveling in opposite directions (standing wave). High power could allow observing it directly as effect of nonlinear transparency. The saturation mechanism of nonlinearity was used for experimental demonstration of phase conjugation of gyrotron radiation by degenerate four-wave mixing in gaseous carbonyl sulfide12 (OCS). A phase-conjugate signal restores the initial wave front automatically when it propagates backward through an optically inhomogeneous medium (real atmospheric conditions could be an example). Another application of high power in molecular spectroscopy was considered3 in the form of inducing the electric dipole moment in non-polar molecules by strong microwaves to detect forbidden transitions. As distinct from the dynamic Stark effect, the molecule acquires asymmetry or induced dipole moment via non-resonant enhancing of one of the vibrational states of this molecule. Here is also an advantage of the RAD technique to bring out such a little effect against a powerful background signal. High microwave power allows Doppler-free two photon transitions, as it has been shown by Surin et al.13 in 150 GHz region. There, it used a millimeter wave generator called OROTRON, together with intracavity-jet technique. The generator power was estimated to be approximately 1 W/cm2. Such a power level was enough to detect two photon absorption signals of OCS and CHF3 rotational transitions. So, kilowatt power level of gyrotrons could increase observable frequency range of molecular transitions by the multi-photon absorption technique. It is well known that the upper frequency limits of sub-millimeter microwave spectroscopy is gained by using both frequency multiplication from powerful microwave radiation sources and primary sub-millimeter wave radiation sources are around 1 THz7,14. But, the extension of radiation frequency into THz range by employing moderate power (~1 kW) gyrotrons for frequency multiplication looks very promising for further development of this technique. Such systems look expensive, but nevertheless they are competing in price with laser sideband systems used for generation in the THz range. The high sensitivity which can be obtained with high power gyrotrons would give opportunities to detect very weak lines of rare species in natural abundance. For example, the lines of oxygen isotopes and especially less 1

The direct observation of the power saturation effect in sub-Doppler rotational line of water vapor (at 183 GHz) was first demonstrated by Fabry-Perot resonator technique11 in form of a peak at resonance curve.

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populated higher energy vibrational/electronic states in atmosphere such as oxygen a1'g state, having importance for supersonic jet traces detection, and for understanding stratosphere ozone photochemistry. Gyrotrons with frequency-control could be used for monitoring the water contamination in chemical processes15, for detection of some toxic pollutants such as SO2, NO2, N2O, CO, ClO, H2O2, HNO3, HCN, CH3CN species; etc2.

4.

ACKNOWLEDGEMENTS

The author is grateful to A. F Krupnov and M I. Petelin for encouraging comments and reading the manuscript. The present work was supported by the Grants of Russian Fund for Basic Researches (RFBR) No. 03-02-16125, No. 04-02-04003, the Contract of the Ministry of Industry, Science and Technology of Russian Federation and Program of the Fundamental Studies of the Division of Physical Sciences of the Russian Academy of Sciences. To all these sources of support author expresses his deep gratitude.

5.

REFERENCES 1. 2.

3. 4.

5.

6.

2

Krupnov A.F., Present state of submillimeterwave spectroscopy at the Nizhnii Novgorod Laboratory, Spectrochim.Acta A52, 967-993, (1996). Antakov I. I., S. P. Belov, L. I. Gershtein, V. A. Gintzburg, A. F. Krupnov, G. S. Parshin, Use of large powers of resonant radiation for enhancing the sensitivity of microwave spectrometers (in russian), Pis’ma Zh. Exp.Teor. Fiz. (JETP Letters) 19, 634-637 (1974). Burenin A.V., A.F. Krupnov, To the possibility of observation of rotational spectra of non-polar molecules (in russian), Zh. Exp. Teor. Fiz (JETP); 67, 510-512 (1974). Belov S.P., M.Yu. Tretyakov in: Spectroscopy from Space, edited by J. Demaison et al. (Kluwer Academic Publishers, Netherlands, 2001), Laboratory SubmillimetreWave Spectroscopy, pp.73-90. Krupnov A.F., Phase Lock - In of MM / SUBMM Backward Wave Oscillators: Development, Evolution and Applications, Int. J. of IR and MM Waves 22, 1-18 (2001). Golubiatnikov G.Yu., A.F. Krupnov, Microwave Study of the Rotational Spectrum of Oxygen Molecule in the Range Up to 1.12 THz, J. Mol. Spectrosc.; 217, 282-287 (2003). 6b. Golubiatnikov G.Yu., M.A. Koshelev, A.F. Krupnov, Reinvestigation of pressure broadening parameters at 60-GHz band and single 118.75 GHz oxygen lines at room temperature, J. Mol. Spectrosc. 222, 191-197 (2003).

We hope that gyrotrons with frequency stabilization give new possibilities and widen their application making impacts not only in spectroscopy, but in such areas as radar and plasma research.

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8.

9. 10.

11. 12.

13.

14.

Krupnov A.F., M.Yu. Tretyakov, G.Yu. Golubyatnikov, A.M. Schitov, S.A. Volokhov, V.N. Markov, Technique of Broadband Measurements of Frequency Conversion Efficiency for Each Harmonique in Frequency Multipliers up to Terahertz Range, Int. J. of IR and MM Waves 21, 343-354 (2000). Zasypkin E. V., M. A. Moiseev, L. L. Nemirovskaya, Expansion of a frequency tuning band in gyrotron with coupled cavities, Proceedings of 21st International Conference on Infrared and Millimeter Waves (Berlin 1996), pp. 534-535. Letokhov V.S., V.P. Chebotayev, Nonlinear Laser Spectroscopy (Springer Verlag, Springer Optical Sciences Ser., Vol. 4, 1977). Winnewisser G., S.P. Belov, T. Klaus, R. Schieder, Sub-Doppler Measurements of the Rotational Transitions of Carbon Monoxide, J. Mol. Spectrosc. 184, 468472 (1997). Dryagin Yu.A., A method of measuring the frequency by a high-quality FabryPerot resonator, Radiophysika (in russian). XIII(1), 141-145 (1970). Bogatov N. A., M. S. Gitlin, A. G. Litvak, A.G. Luchinin, G. S. Nusinovich, Resonantly Enhanced Degenerate Four-Wave Mixing of Millimeter-Wave Radiation in Gas, Phys. Rev. Lett. 69, 3635–3638 (1992). Surin L.A., B.S. Dumesh, F. S. Rusin, G. Winnewisser, I. Pak, Doppler-Free TwoPhoton Millimeter Wave Transitions in OCS and CHF3, Phys.Rev.Lett. 86(10), 2002-2005 (2001). Krupnov A.F., M.Yu. Tretyakov, Yu.A. Dryagin, S.A. Volokhov, Extension of the Range of Microwave Spectroscopy Up To 1.3 THz. Journal of Molecular Spectroscopy 170, 79-84 (1995). Tretyakov M.Yu., A.F. Krupnov, S.A.Volokhov, Extension of the Range of Microwave Spectroscopy Up To 1.5 THz, JETP Letters 61, 79-82 (1995).

15. Benck E. C., G.Yu. Golubiatnikov, G.T. Fraser, Bing Ji, S.A. Motika, E. J.

Karwacki, Submillimeter-wavelength plasma chemical diagnostics for semiconductor manufacturing. J.Vac.Sci. and Technol. B21(5), 2067-2075 (2003).

A MULTIPACTOR THRESHOLD IN WAVEGUIDES: THEORY AND EXPERIMENT

J. Puech1, L. Lapierre1, J. Sombrin1, V. Semenov2, A. Sazontov2, M. Buyanova2, N. Vdovicheva3, U. Jordan4, R. Udiljak4, D. Anderson4, M. Lisak4 1

Centre National d’Etudes Spatiales, Toulouse, France; 2Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia; 3Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, Russia; 4Department of Electromagnetics, Chalmers University of Technology, Gothenburg, Sweden

Abstract: New generation telecommunication satellites are designed to cater to a constantly increasing number of users, requiring higher and higher bit rates in the same frequency multiplex. The conjunction of both tendencies implies increasing power levels of rf equipment downstream from the power amplifiers. In this situation, different discharge phenomena may occur inside the microwave devices. The consequences may be damage on the equipment and link budget degradation. In a vacuum environment, microwave (multipactor) discharges inside rf equipment such as waveguides, are caused by an avalanchelike increase of electrons due to the secondary emission when electrons, accelerated by the electric field, hit the walls of the device. A joint project involving the Institute of Applied Physics (Nizhny Novgorod, Russia), Chalmers University of Technology, Geteborg, Sweden and Centre National d'Etudes Spatiales (Toulouse, France) has been set up in order to study this phenomenon. Key words:

1.

multipactor, electron secondary emission, velocity spread, multipactor zones, microwave breakdown, microwave discharges

THE INTRODUCTION

number of applications using space links for telecommunications purposes is increasing: fixed telephony, professional network, TV/radiobroadcasting, mobile services, multimedia… In parallel, there is also a democratisation of the space means. Consequently, new generation telecommunications satellites are designed to cater for constantly increasing

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number of users at the same frequency multiplex. Thus, the number of modulated channels in the same frequency multiplex is increasing. The onboard amplifiers such as Travelling Wave Tubes must be designed to deliver higher and higher output power. Concerning the state of the art of Travelling Wave Tubes, the maximum output power has reached a level of 220 W in Ku band, of 130 W in K band and it is expected to reach 300 W in Ku band and 200 W in K band for the next generation. A classical satellite payload is built up by different elements. After a first stage of amplification, all channels of the frequency multiplex are separated at the level of the Input Multiplexer. Then, after a down-conversion, each channel is amplified by the HPA (High Power Amplifier). The Output Multiplexer re-combines the different channels and a low pass filter is used to suppress intermodulation products. This means that rf equipment downstream from the power amplifiers (Travelling Wave Tubes) are required to withstand increasingly higher power levels. For example, equipment such as Low Pass Filters, which are situated after the Output Multiplexer, must withstand the power of the whole frequency multiplex. Such high power level may initiate discharge phenomena, which can damage or even destroy the component. A discharge in a rarefied atmosphere at pressures below 10-5 mbar is designated as the Multipactor effect. It was first discovered by Farnsworth 1 in 1934. This effect manifests itself as an avalanche-like growth of the electron density and occurs when the electron mean free path is larger than the distance between the metallic walls of the equipment. The physical background of the multipactor effect is that electrons driven by the RF field are accelerated and when hitting the walls of the device, they may create new secondary electrons, provided the impact energy is high enough. Microwave breakdown is an important failure mechanism and disturbs many modern systems such as high power microwave generators, rf accelerators and satellites. As far as space communications are concerned, new generation satellites can use OMUX up to 18 channels. With a 100 W carrier per channel, the manifold and the Low Pass Filter have to withstand a 18 carrier power level equal to N.Psingle carrier = 1 800 W and a peak power of N².Psingle carrier = 32 400 W. Furthermore, the ECSS 15 (European Cooperation for Space Standardisation document) recommends that in the context of multi-carrier operation, when the threshold is above the equivalent CW peak power, the analysis margin must be 6 dB. When this margin is not reached, qualification tests should be performed at Peak Power + 3 dB = 64 kW. It implies very high CW test power levels and very high cost facilities. That is why research effort in Europe is focused on developing accurate means of prediction of this phenomenon. A first theory was given in 1958 by Hatch and Williams 2.

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This demonstrated the possibility of different resonant multipactor modes in a parallel-plate model geometry. Many different theories 3-6 have subsequently been developed, investigating different aspects of the multipactor phenomenon. The first part of this presentation deals with the phenomenon in general. Then, some results for Multipactor between two metallic plates will be presented. Finally, after a brief description of the problems of the Multipactor effect in the context of multi-carrier operation, the discharge will be analyzed for the case of a waveguide configuration.

2.

THE MULTIPACTOR EFFECT

The multipactor effect is caused by a phenomenon of secondary electron emission that accompanies a collision of energetic electrons with any solid surface. The collision results in a release of new electrons from the surface, and the process are statistical in nature, i.e. the number of secondary electrons and their initial velocities are random. A typical distribution of secondary electrons over the energy of the emitted electrons is shown in Fig. 1. Here, the low energy peak is associated with true secondary electrons (typical energy is of the order of the material work function, i.e. several eV, typical value of total fraction is about 80 %), the high energy peak is associated with reflected primary electrons (total fraction is about a few percents), the region between the two peaks is associated with inelastic scattering of primary electrons.

Energy E1 of the emitted electrons

Figure 1. Energy distribution of emitted electrons.

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The average number of new electrons produced by one primary electron is called the secondary emission coefficient. It depends upon the incident energy, Wi, of the primary electron and exceeds unity within a definite energy interval Wmin<Wi<Wmax (see Fig. 2), which is determined by material properties.

Figure 2. Secondary emission coefficient versus incident electron energy.

An exponential increase of free electrons inside rf components is possible when two main requirements are fulfilled. First, the secondary emission coefficient must be greater than unity. Second, the rf field must pull the newly born electrons out from the emitting surface. The latter means that electrons should hit the surface with the proper phase of the rf field. Therefore, it is clear that the electrons should return to the surface in an integer number of rf cycles (or cross the gap between two solid surfaces during an odd number of half rf cycles) in order to repeat the process many times. This idea is the basis of the concept of a resonant multipactor process 8, 18, 19, 4 , which results in the existence of a set of narrow separated zones in a parameter space where the multipactor builds up. Specifically in the case of two-sided multipactor (multipactor in a gap between two parallel plates), resonance is possible if and only if the parameter O ZL VZ lies within one of the bands shown in Fig. 3 10 (here Z stands for angular frequency of RF field, L is gap width, and VZ eE0 /(mZ ) is the amplitude of the electron velocity oscillations in the RF field). It should be noted that within the theory of resonant multipactor, the first of the above requirements can be formulated in a very simple manner 10, viz. V1 d 2VZ  V2 where V1 and V2 are the electron velocities corresponding to the energies Wmin and Wmax respectively.

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One important effect, one which has been missed in the majority of published papers is related to more complicated resonant modes of Multipactor 12, 13. These modes are associated with electron oscillations between two parallel plates such that each gap crossing takes a different time but the total time of some sequence of gap crossings coincides with an integer number of half rf periods. A detailed analysis of such multipactor modes has been performed recently in 10 where they were termed hybrid resonant modes. Specifically, it was found that hybrid modes occupy regions near each classical resonant band in the parameter space as shown in Fig. 3. This results in considerable broadening of the multipactor zones and makes it possible to explain the width of the first multipactor zone, as observed in experiment 20. Nevertheless within the simple theory, which does not take into account a spread of electron initial velocity and the possibility to compensate electron debunching by a high secondary emission coefficient, the multipactor zones remains well separated. In contrast to these predictions, the experimental results typically demonstrate an overlapping of the multipactor zones with the exception of the first one 9. This means that accurate predictions of the multipactor charts require detailed numerical simulations for each particular material because the effect of the electron velocity spread is very difficult to investigate analytically.

Figure 3. Resonant bands of two-sided multipactor versus normalized initial electron velocity.

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NUMERICAL SIMULATIONS

Numerical simulations of the Multipactor effect have been performed using three different codes: a Monte-Carlo, a statistical, and a Particle-inCell code. To construct the Multipactor chart numerically, the following assumption was made. The model considered was the parallel plate model with uniform monochromatic electric field directed perpendicular to the plates.

3.1

The Monte-Carlo Method

The Monte-Carlo algorithm is focused on a random trial of the initial phase and of the initial velocity of the electrons. By using the Monte-Carlo method, a fixed number of trajectories for the primary electrons are taken into account. An observation is made on whether the electron can reach the opposite wall. If it can, the phase and the velocity of the secondaries are randomly chosen. If it cannot, another trajectory is computed.

3.2

The Statistical Method

This method is based on the evaluation of a probability distribution over arrival time for electrons emitted, with arbitrary distribution function over initial velocity and emission time. This distribution can be evaluated by quadrature directly from the equation of electron motion by using a welldeveloped theory for the temporal statistics of the first intersection of a random trajectory with a given plane surface. The number of secondary electrons is then calculated using the dependence of the secondary emission coefficient on impact energy. Furthermore, only those secondary electrons are taken into accounts which are emitted in favourable phases of the RF field. Following this evaluation, one can calculate the distribution function of the secondary electrons over initial velocity and emission time after any number of gap crossings provided this function for primary electrons as well as the secondary emission properties of the plates are known. An integration of the nth distribution function over velocity and emission time results in the number of secondary electrons after the nth gap crossing. The time history of this number determines the evolution of the Multipactor effect.

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The Particle-in-Cell Method

This code simultaneously computes the motion of a great number of electrons (up to 106) inside a gap. A random initial velocity is generated for each secondary particle. Perturbations of the electric field by electron space charge are taken into account.

3.4

Comparisons between Different Methods 14

As far as the dynamics of the electron number is concerned, it is computed in real time within the Particle-In-Cell code. Within the MonteCarlo and the statistical methods, each electron trajectory is computed separately. The number of electrons is known after any fixed number of impacts of all trajectories with the plates. If the electrons come back to their plate of birth, the secondary electrons emitted from this collision are taken into account in the Particle-In-Cell code only. If their velocity is high enough, they participate in the Multipactor process. This explains why the threshold value of the secondary emission coefficient must be higher in the Monte-Carlo or statistical method, than in the case of the Particle-In-Cell code (see Figs. 4-5). The following table (Table 1) gives a comparison of the advantages and disadvantages of the different methods. Table 1. The advantages and disadvantages of the Monte-Carlo method, the Statistical method and the Particle-in-Cell method Monte-Carlo method / Statistical method

Particle-In-Cell method

Computer time

Fast

Slow

Single/multi –carrier case

Single carrier analysis

Single/Multi-carrier analysis

Secondaries

Secondaries emitted with wrong phase primaries are not taken into account

All kinds of secondaries are taken into account

Post-processing capabilities

Easy access to results with different values of Vm after a single computation

Two computations are necessary for each combination of parameters

Real-time dynamics capabilities Possibility to simulate multipactor at the saturation stage

No

Yes

No

Yes

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In the tests, it was assumed that the secondary electrons have a Maxwellian distribution over initial velocities, as described by variable velocity spread VT : f V v exp§¨  V 2 /(2VT2 ) ·¸ . At the first stage, using a step © ¹ approximation of the secondary emission coefficient ( V =const for Wi>Wth), a study of the multipactor threshold Vth has been completed in terms of the dimensionless parameters O and VT VZ (see Figs. 4-5). Note that the results of the simple theory, as shown in Fig.3, gives Vth=1 within an infinite sequence of resonant bands of parameter O whereas V th o f beyond these

Figure 4. Comparisons between Monte-Carlo and statistical methods. Threshold value of s, solid areas correspond to the statistical method, and points to the Monte-Carlo method.

Vth

Figure 5. Comparisons between Monte-Carlo and Particle-In-Cell codes (the boundary of the solid area corresponds to that calculated with the Monte-Carlo algorithm, and points correspond to the results of calculations with the PIC code).

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bands. This result is confirmed by numerical simulations with very low values of VT VZ . For finite velocity spread, the value of Vth increases within the resonant bands, but decreases outside of them. For higher values of the velocity spread, Vth becomes relatively small for any value of the parameter O . This indicates a possibility for the multipactor zones to overlap, provided that the secondary emission coefficient of the material exceeds the threshold value of Vth within a continuous region of O . At the second stage, realistic multipactor charts have been obtained using an approximation of the secondary emission coefficient according to Vaughan’s formula 21 with variable parameters: V m (maximum value of the secondary emission coefficient) and Wm (electron impact energy corresponding to V m ). It was found that depending on V m and the ratio mVT2 2Wm , the multipactor charts can contain some finite number of separated multipactor zones only, or a combination of separated and overlapping multipactor zones. Some results of these calculations with a fixed value mVT2 2Wm 10 2 are shown in Fig. 6.

Vm=1.2

Vm=2.0

Vm=1.5

Vm=1.7

Vm=2.5

Figure 6. Multipactor charts with different values of secondary emission coefficient.

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The parameter p

VZ

2W m m .

Some Monte-Carlo simulations were performed with real material data (Fig.7). Material: Copper etched surface Material: Alodine Thomson Treatment + Bake 4.5h in vacuum, Vaughan’s formula only, Vaughan’s formula is is used, V1 corresponds to 54 eV, Vmax used, V1 corresponds to 25 eV, Vmax corresponds to 225 eV, corresponds to 303 eV, electrons have electrons have Maxwellian Maxwellian distribution of initial distribution of initial velocities velocities with VT corresponding to 3 eV, with VT corresponding to 3 eV, Vmax = 1.75 Vmax=2.25

Log-log plot of breakdown voltage as a function of fL

Log-log plot of breakdown voltage as a function of fL

Figure 7. Plot of Multipactor charts: gap voltage versus f*d product.

To conclude the single carrier case, comparisons have been made between the Monte-Carlo method, the statistical method, and measurements performed at ESTEC. The squares represent ESTEC measurements. The light triangles correspond to the limits of the Multipactor zones obtained by the statistical code. The Monte-Carlo results, shown in black diamonds in Fig. 8, are computed at steps of the f*d product and of the power P:

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aluminium

90 80 70

P (dB)

60 50

monte carlo mesures ESTEC

statistical mat code2 semenov

40 30 20 10 0 0,1

1

10

100

1000

f*d (GHz.mm)

Figure 8. Multipactor chart: comparisons between the Monte-Carlo code, the statistical code and measurements at ESTEC.

There is good agreement between the results of the Monte-Carlo code, the statistical code, and the ESTEC measurements for Aluminum.

4.

MULTIPACTOR IN MULTI-CARRIER OPERATION

4.1

ECSS: The 20 Cycles Rule 15

In the case of multi-carrier operation (which is the common situation in telecommunication systems), new parameters must be taken into account, such as amplitude, phase and frequency of the different carriers. A rule defined by the ECSS (European Cooperation for Space Standardisation) is aimed at helping designers handle the problem of Multipactor in multi-carrier operations: it is called the 20-cycle rule. According to this rule, Multipactor discharges can only occur if the time envelope of the signal is above the Multipactor threshold during a time corresponding to 20 gap-crossings of the electrons, for a given order. Consequently, when a frequency multiplex is given, it is necessary to find the worst-case phase distribution in order to have the highest level of the signal envelope, during the time corresponding to 20 cycles. Once this worst-case phase law has been determined, it is possible to

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compute the margin between the level of the signal envelope and the Multipactor threshold, as predicted by the chart. Software called WCAT has been developed in order to facilitate these calculations. The different parameters which can be taken into account are the number of carriers, amplitude of each carrier, number of gap crossings, the multipactor order to be considered, the “frequency” * “gap” size product, the material in question, and the model to be used for the secondary emission coefficient. The software finds the worst-case phase law of the frequency multiplex, which gives rise to the maximum value of the voltage during 20 cycles (the worst case from the Multipactor point-of-view). It can also compute the maximum voltage during an arbitrary number of cycles and the duration of the cycle depending on the order. The optimisation program is based on a genetic algorithm. Let’s consider the following example. 12 carriers of 130 W each are analysed. These carriers have frequencies between 10, 7 and 13 GHz. The metal is Alodine. The f*d product equals: f*d=13, 91 GHz. mm:

Figure 9. WCAT: optimisation of the phase law of the frequency multiplex.

The maximum of the signal envelope threshold is 390 V. The threshold computed by the Multipactor chart is at 1210 V. Thus, we can deduce the margin from the above computations: 20*log (1210/390) = 9,83 dB.

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Computation of Electron Dynamics in Multi-Carrier Operation

The Multipactor effect is very sensitive to variations of the different parameters described above. To illustrate this point, the Multipactor effect can occur if all carriers have fixed frequencies and the same initial phases, but do not occur when frequencies and phases are different. 2D tests were performed to show the discharge’s dependence on initial phase and frequency ranges. Parameters corresponding to silver plated copper are used, secondary emission is approximated by Vaughan’s formula, V1 and Vm correspond to 30 eV and 215 eV respectively, Vm=1.99, electrons have a distribution of initial velocities, which depend on the emission angle and the initial velocity V0 corresponds to 3 eV. 4.2.1

Test Sets

The first test set was made by using carriers with different phases. The control parameter is the initial phase range between the first and the last carrier. The choice of phases for the other carriers is done randomly within the phase range. The initial phase sets are shown in Table 2. The results of the test are shown in Fig. 10. The second test set was made using different frequency ranges of the carriers. The control parameter is the frequency range between the first and the last carrier. Other carriers’ frequencies are equally spaced within this frequency range. The frequency ranges are shown in Table 3. The results of the test are shown in Fig.11. For both tests, the initial number of electrons was 105. The tests were executed until the number of electrons were greater than 106 or less than 1 and until time exceeded 3·10-8 sec. The time step was 10-13 sec. The amplitudes were chosen to obtain a total oscillatory velocity VZ (when all frequencies are the same) close to Vm. Even when all of the frequencies are fixed, and the initial phase range is differs from test to test, the electron number growth is hardly predictable (Fig.10). It shows that initial phases of carriers are very important parameters to take into account in order to obtain a reliable prediction of multipactor. A similar result is obtained for varying frequency range: even if initial phases of all carriers are the same (or fixed) but the frequency range is different from test to test, the results of multipactor development are also quite different (Fig.11). The fact that a variation in the carrier amplitudes can also lead to different types of possible electron dynamics, is even more obvious. To conclude, all the carrier parameters should be taken into account, together.

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Table 2. Parameters for the first and the second test sets 7

8

9

10

5.652

5.024

4.396

3.768

3.141

2.512

1.884

1.256

0

Frequencies set 2: 10.9 GHz, 10.92 GHz, 10.94 GHz, 10.96 GHz, 10.98 GHZ, 11.01 GHz Amplitudes: 281.17 V, 279.67 V, 278.25 V, 276.9 V, 275.62 V, 274.41 V

Figure 10. Multipactor effect in multi-carrier operation: influence of initial phases range.

4.2.2

Frequency set number Frequency range

1

2

3

4

5

6

0.55 GHz

6

0.44 GHz

5

0.33 GHz

4

0.22 GHz

3

0

2

0.628

Maximum difference between 2 initial phases

1

0.11 GHz

Initial phases set number

Initial phases: all phases are equal 0 Amplitudes:

281.17 V, 279.67 V, 278.25 V, 276.9 V, 275.62 V, 274.41 V

Figure 11. Multipactor effect in multicarrier operation: influence of frequency separation.

Conclusion

Multipactor in multi-carrier operation has been analysed with respect to the dependence on amplitude, frequency and phase separation. An example using six carriers between two parallel-plates with silver-plated copper has been analysed. The results have shown that all parameters must be taken into account in order to obtain a reliable prediction of multipactor. Consequently, it implies that Multipactor charts for the Multi-carrier case cannot be drawn without properly defined parameters.

5.

THE MULTIPACTOR EFFECT IN WAVEGUIDES16

In the previous studies, the only case considered was the two parallelplate model. When the case of a waveguide is analysed, the difficulty lies in the fact that two lateral metallic planes must be added in the analysis. In order to analyse this situation, a code based on the Monte-Carlo algorithm has been developed.

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319

Algorithm used in the Waveguide Theory

When the electron collides with the metallic wall, the probability to give a reflected electron or to give secondaries is computed to have the number of electrons after the collision. If the primary electron creates secondary electrons, the number of secondary electrons emitted is computed depending on the energy and on the incidence angle of the primary electron. One single, randomly selected trajectory is followed after each impact. With this approach, many trials are computed to cover numerous cases. If, after one trial, the number of electrons is above 106, Multipactor may occur.

Emitted electron

e-

eProbability law of the secondary electrons

Reflected electron

Secondary electron

e-

D

D

Figure 12. Electron collision with the metallic wall: secondary and back-scattered electrons.

A back-scattered electron will leave the metallic wall with the same angle as the incident one (compared to the normal to the metallic wall). To be more precise, the electron will stay inside a probability cone whose main component is the symmetrical angle relative to the normal. If secondary electrons are emitted, they are emitted following a cosine probability law. Finally, we assume that all secondary or reflected electrons have the same behaviour as the chosen one. The Monte-Carlo algorithm is performed at each f*d product step, for a given power and for a given initial angle. The computation stops if the Multipactor effect occurs (i.e. if the number of created electron is larger than 106) or if the Multipactor effect will have not occur (i.e. if the number of created electrons is below 10-6) or if the number of trajectories, during which we follow the electron, has reached a limit. Four loops are considered: loop on the f*d product, on the power, on the initial phase, on the number of trajectories. Different formulas can be used for the secondary electron coefficient.

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In order to take into account the dependence on the angle of the incident electron, the above equations must be multiplied by the following coefficient: exp [1.55(1-cos D)] 17. The probability of reflection is given by: (1  cos D )

9 Z atom

and depends on the arrival angle of the incident electron, 17.

In the simulations, all three components of the TE10 electromagnetic field mode are considered. The variables linked with the electron are the position, the time and the velocity. Impact is possible with the four walls of the waveguide. It is important to notice that the magnetic field has a tendency to modify the trajectory of the electron--it moves toward the lateral walls.

5.2

Illustration for a Standard Waveguide

The waveguide used for the illustration is WR75 (19,05 x 9,525 mm). The frequency is 12 GHz and the metal considered is Aluminium. The result is shown in Fig.13:

No Multipactor for high fxd

Multipactor zones

Figure 13. Multipactor chart in the case of a waveguide.

6.

CONCLUSION AND PERSPECTIVES

The parallel plate model has been extensively studied during the research project performed by Chalmers, IAP and CNES. The main feature of the discharge is its resonance property, which is manifested in the Multipactor charts as resonant bands. The influence of parameters such as the initial velocity spread and the secondary emission coefficient has been evaluated.

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An important point is that the effects of these parameters are not independent. As a matter of fact, depending on the value of the secondary emission yield, the resonant bands are narrower or wider. The existence of hybrid modes has made it possible to explain the continuous region in the multipactor charts in cases of high secondary emission coefficients. These modes can be found in the parameter space between the well-known resonant zones and can be considered as a combination of the classical resonant modes. In the multi-carrier case, the phenomenon is not very easy to describe, because the signal envelope has a very complex variation in time. The most accurate way to solve the problem is to couple the time evolution of the envelope with the electron trajectories between the metallic walls. Results coming from the code realising such a coupling have demonstrated that, as the multi-carrier character of the signal is taken into account, the Multipactor effect becomes very sensitive to parameters such as frequency separation between carriers, phase distribution and amplitude. In the case of the Multipactor effect in single carrier operation in a waveguide, the two lateral walls play an important role in the simulation. The two main phenomena are taken into account are secondary emission and reflection. The charts have shown that for high values of the f*d product, Multipactor does not occur. Concerning perspectives for the future, one of the main points is the simulation of the effect inside complex microwave components such as corrugated filters, cavity filters, etc. A first step towards solving such problems could be to predict the Multipactor effect in the presence of fringing fields, which occur in irises. Another interesting issue would be to use the Particle-In-Cell code for microwave geometries like waveguides. This could make it possible to evaluate the influence of a complex geometry also within the context of multi-carrier operation. Finally, it is important to be aware of the importance of e.g. Solid State Power Amplifiers (SSPA) in applications such as active antennas in new telecommunications systems. The power level at the output of such components increases more and more, and SSPAs are rapidly becoming competitive relative to the Travelling Wave Tube. As a consequence, new questions arise such as e.g. the Multipactor effect in the presence of dielectric walls. A project involving Chalmers University, IAP and CNES has been granted to study the Multipactor effect at or close to the walls of dielectric materials.

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8. 9. 10.

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REFERENCES P. T. Farnsworth, Television by electron image scanning, J. Franklin Inst., vol. 218, pp. 411-444, 1934 A. J. Hatch and H. B. Williams, The secondary electron resonance mechanism of lowpressure high-frequency gas breakdown, Journal of Applied Physics vol. 25 n°4, pp. 417-423, 1954. E. Chojnacki, Simulations of a multipactor-inhibited waveguide geometry, Physical Review, ST Accel. Beams vol. 3, 032001, 2000 V. D. Shemelin, Existence zones for Multipactor discharges, Sov. Phys. Tech. Phys. Vol. 31 (9), pp. 1029-1033 R. L. Geng, H. S. Padamsee, V. Shemelin, Multipacting in a rectangular waveguide, Proc. 2001, Particle Accelerator Conf., Chicago, pp. 1228-1230 V. Semenov, A. Kryazhev, D. Anderson, M. Lisak, Multipactor suppression in amplitude modulated radio frequency fields, Phys. Plasmas vol. 8, No. 11, pp. 5034-5039 C. Bourat, J.-M. Joly, On Multipactor effect in a 600 MHz RF cavity used in electron linear accelerator, IEEE Trans., Electrical Insulation, vol. 24, No. 6, pp. 10451048,1989 A. J. Hatch, H. B. Williams, Multipacting modes of high-frequency gaseous breakdown, Phys. Rev., v. 112, No. 3, pp. 681-685, 1958 A. Woode, J. Petit, Investigations into Multipactor Breakdown in satellite Microwave Payloads, ESA Journal, v. 14, No. 1, pp. 467-478, 1990. A. Kryazhev, M. Buyanova, V. Semenov, D. Anderson, M. Lisak, J. Puech, L. Lapierre, J. Sombrin, Hybrid resonant modes of two-sided Multipactor and transition to the polyphase regime, Phys. Plasmas vol. 9, No. 11, November 2002. G. Francis, A. von Engel, The growth of the High-Frequency Electrodeless discharge, Proc. Roy. Soc. London, Ser. A, V. 246, pp. 143-180, 1953 J. Sombrin, Effet Multipactor, CNES Report No. 83/DRT/TIT/HY/119/T A. L. Gilardini, Multipacting Discharges : constant –k theory and simulation results, J. Appl. Phys., v. 78, No. 2, pp. 783-795, 1995 D. Anderson, A. Sazontov, N. Vdovicheva, M. Buyanova, V.Semenov, J. Puech, M. Lisak, L. Lapierre, Simulations of Multipactor zones taking into account realistic properties of secondary emission, ESA Conference MULCOPIM 2003, September 2003 Space Engineering: Multipaction design and test, ECSS E-20-01, 5 May 2003 J. Sombrin, Claquage hyperfréquence et effet Multipactor dans les satellites, OHD conference, June 1993 F. Maurice, L. Meny, R. Tixier, Microanalyse et Microscopie Electronique à balayage, Ecole d’été de Saint-Martin d’Hères, Les éditions de Physique subventionnées par le CNRS, 11-16 September 1978 W. Henneburg, R. Orthuber, and E. Steudel, Z. Tech. Phys., vol. 17, p. 115, 1936. J.R.M. Vaughan. Multipactor. IEEE Trans. Electr. Dev., v. 35, No. 7, pp. 1172-1180, 1988.

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20. A. J. Hatch and H. B. Williams, The secondary electron resonance mechanism of lowpressure high-frequency gas breakdown, J. Appl. Phys. V. 25, No. 4, pp. 417- 423, 1954. 21. J.R.M. Vaughan. A new formula for secondary emission yield.Trans. Electr. Dev., v. 36, No. 9, pp. 1963-1967, 1989.

QUASI-OPTICAL MODE CONVERTERS IN ADVANCED HIGH-POWER GYROTRONS FOR NUCLEAR FUSION PLASMA HEATING M. Thumm1,2, A. Arnold2, O. Drumm1, J. Jin1, G. Michel3, B. Piosczyk1, T. Rzesnicki1, D. Wagner4, X. Yang1 1

Karlsruhe Research Center, Association EURATOM-FZK, Institute for Pulsed Power and Microwave Technology, D-76021 Karlsruhe, Germany; 2University of Karlsruhe, Institute of High-Frequency Techniques and Electronics, D-76128 Karlsruhe, Germany; 3Max-PlanckInstitute for Plasma Physics, Ass. EURATOM-IPP, D-17491 Greifswald, Germany; 4MaxPlanck-Institute for Plasma Physics, Ass. EURATOM-IPP, D-85748 Garching, Germany Abstract:

Key words:

1.

The R&D activities at the Karlsruhe Research Center (FZK) on advanced highpower millimeter (mm)-wave gyrotrons for future use in electron cyclotron heating and current drive (EC H&CD) in magnetically confined fusion plasmas consist of: (1) Development of a 1 MW continuous wave (CW) gyrotron at 140 GHz for the stellarator W7-X, (2) Development of a coaxial cavity gyrotron capable of delivering 2 MW CW at 170 GHz for ITER, (3) Investigations on a 4 MW 170 GHz coaxial cavity gyrotron with a twobeam output (2x2 MW) for a future DEMO fusion reactor, and (4) Investigations on a tunable multi-frequency gyrotron (105 GHz to 140 GHz). The present paper discusses the different quasi-optical mode converter schemes employed in these various types of advanced gyrotrons. Conventional and coaxial high-power gyrotrons, quasi-optical mode converters, electron cyclotron plasma heating and current drive

INTRODUCTION

For increasing the collector’s electron beam interception area in long-pulse, high-power gyrotrons, an output coupler that separates the spent electron beam from the outgoing rf power, is required. It is the short wavelength, high output power and the rotating asymmetric high-order cavity mode of such tubes that have led to the need for novel mode conversion concepts [1]. The down-conversion of these high-order cavity modes with complicated field

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structure by using conventional waveguide mode transducers with highly oversized waveguide diameter is practically impossible due to the extreme mode competition involved. The higher the operating mode is, the more it is appropriate to employ an asymptotic procedure for its description, namely the method of geometrical optics (g.o.) (see e.g. [2], [3]). In the framework of this method, the initial mode is represented as a system of rays successively reflected from the waveguide walls (Brillouin-Keller concept). To directly convert the complicated field structure of rotating high-order asymmetric gyrotron cavity modes into a linearly polarized Gaussian beam, i.e. to modify the configuration of rays, one can use quasi-optical (q.o.) devices, a proper combination of a specific mode converting waveguide slot radiator (launcher) together with a few curved mirrors [4], [5], often called a Vlasov converter. This method is universal, but diffraction effects limit its efficiency to approximately 80%, which cannot be accepted for high-power gyrotrons.

Figure 1. Different output coupling schemes for high-power, high-frequency gyrotrons [1].

The present section summarizes the principles and advantages of q.o. mode converters and discusses the design of improved launchers and beam shaping reflectors with higher efficiency

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1.1 Advantages of Quasi-Optical Mode Converters The q.o. mode converter is a part of the internal electrodynamic system of the gyrotron like the cavity and the uptaper (Figure 1b). Radial output coupling of the RF power into the fundamental Gaussian (TEM0, 0) freespace mode has three significant advantages for high-power operation: a. The linearly polarized TEM00 mode is directly usable for low-loss transmission as well as for effective antenna feeding and no further mode converters are needed. Therefore, q.o. mode converters are also used for relatively modestly overmoded systems when a very compact mode converter to the TEM00 mode is required [6], [7]. b. The converter separates the electron beam from the RF-wave path (Figure 1b) so that the electron collector is no longer part of the output waveguide as in the case of a tube with an axial output (Figure 1a). Hence, the collector can be designed especially for handling the high electron-beam power. In addition, energy recovery with a depressed collector becomes possible. c. The harmful effects of rf power reflected from the output window are expected to be significantly reduced, especially if the window disk is slightly tilted.

1.2. Principles of Quasi-Optical Mode Converters The principal schemes of q.o. mode converters for (a) rotating asymmetric modes and (b) for circular symmetric modes are shown in Figure 2. TE- and TM-modes in a circular waveguide can be decomposed into a series of plane waves, each propagating at the Brillouin angle TB relative to the waveguide axis:

TB = arcsin (Xmn/koa) Xmn: ko: a:

root of Bessel function (or derivative) free-space wavenumber radius of the launcher waveguide

(1)

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Rc

m a Xmn

Figure 2. Principal schemes of quasi-optical mode converters and amplitude distribution at the launcher. The electric field orientation shown in b) applies only for TEon modes.

The requirement of a zero azimuthal electric field at the waveguide wall defines their relative phases. In the q.o. limit, a plane wave front is represented by one ray. Its transverse location is defined by the requirement that at a particular point of interest the ray direction must coincide with the direction of the Poynting vector of the original TE- or TM-mode field distribution. If the point of interest is located at the waveguide wall the ray has the distance: Rc =

m a X mn

(2)

from the waveguide axis. Hence, if all plane waves are represented by q.o. rays they form a caustic at the radius Rc (Figure 2). In an unperturbed circular waveguide, the density of the rays along the caustic is uniform [2].

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The distance that a ray has propagated in the axial direction between two subsequent reflections from the waveguide wall is LB

ª § m ·2 º 2a «1  ¨ ¸ » «¬ © X mn ¹ »¼

1/ 2

cot T B .

(3)

In the transverse direction a section of angle: 'M

2T

§ m · 2 arccos ¨ ¸ © X mn ¹

(4)

reflects all rays exactly once. Accordingly, for modes with mz0 the reflection points of each of the rays are placed on the waveguide surface in a helical line with the angle of inclination [3] \ = arctan (T tanTB/sinT)

(5)

and the distance (pitch) that a ray has propagated in the axial direction when it has completed a full turn is [3] H = 2S a cot \ 2

§ m · 1¨ ¸ ß © X mn ¹ 2S a 2 X mn § m · arccos ¨ ¸ © X mn ¹

= Lc = launcher cut length

(6)

which is the launcher cut length. Hence waveguide sections (wound parallelograms: "G region") with the length Lc and the transverse width defined by a'M reflect each ray once. Back scattering effects due to diffraction of the incident high-order mode by the helical and straight edges of the launcher have been estimated by using the method of equivalent currents [8]. For TB <70° the total reflected power is lower than –30 dB. The helical-cut launcher radiates the rf power via its straight cut onto the first phase correcting mirror of quasi-parabolic shape (Figure 2). The power reflected from the first mirror propagates as an astigmatic beam onto a series of two elliptical or hyperbolical reflectors where the astigmatism is removed

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and the output beam transverse dimensions are matched to the window size [3], [9].

1.3. Improved Quasi-Optical Mode Converters The wave beam produced by a conventional launcher differs essentially from a Gaussian beam, due to the fact that the field amplitude on the wall is constant. The coefficients of excitation of the Gaussian beam are about 0.8 (power) and depend slightly on the wave indices [5]. This cannot be accepted for high-power gyrotrons owing to the harmful diffracted radiation (stray radiation) in the tube. The following requirements for the q.o. mode converter should be satisfied: - low diffraction losses inside the tube (less than 5%) - matching of the output wave beam to the HE11 waveguide mode or the fundamental Gaussian beam with efficiencies higher than 95%. At the aperture of conventional Vlasov launchers there exists an approximately uniform field distribution in the axial and azimuthal directions (Figure 2), leading to these high diffraction losses. There are two general methods to provide low diffraction losses leading to a pencil-like wave beam: (1) Employing tailored aperture distributions at the radiating cut such that the sidelobes are reduced ([3] and references therein), which means preshaping of the wave beam before its launching. The shaped beam has weaker fields at the cut edges (low diffraction) and a nearly Gaussian angular spectrum. (2) Synthesis of mode converting, phase correcting mirrors [10]-[13]. This method allows one to synthesize a desired field structure of paraxial wavebeams. Both methods are described in the following sections. (1) Pre-shaping of the wave beam before launching a. Beam Shaping by a Flared Launcher Cut: To tailor the aperture field distribution and to reduce the side lobes caused by the straight launcher cut, flared radiation cuts (visors or wings) have been used. In the case of transformation of a whispering gallery mode (WGM) with a single radial field maximum (e.g. TE15,1) into a Gaussian beam one achieves a theoretical efficiency of 98% whereas the efficiency for the transformation of the TE15,2 mode [14] or the TE12,2 mode [15] is only 92-93%. In the case of higher order

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volume modes such as TE15, 4, this method gives a rather poor efficiency of only 87% [16]. b. Beam Shaping by Mode Converting Feed Waveguide: To achieve a sidelobe-free fundamental Gaussian beam as the output mode, the launcher must have feed waveguide deformations such that the incident rotating TE mode is converted to a mode mixture generating a Gaussian beam distribution [16]-[19]. A Gaussian aperture field distribution can be approximated by a raisedcosine field distribution, which can be obtained by means of a superposition of nine specific waveguide modes with matched amplitudes and relative phases [20]: § 1 j S M 1  j S M ·§ 1 j 2 S z 1  j 2 S z · f ( M ,z ) ¨1  e T  e T ¸ ¨1  e L  e L ¸ 2 2 2 2 ¹ © ¹©

(7)

The interference of the nine waveguide modes creates an RF-field bunching in the axial and azimuthal directions. Requirements for this bunching are: (a) longitudinal bunching: modes must have equal caustic radii and an interference length close to the launcher cut length Lc, (b) azimuthal bunching: modes must have equal caustic radii and similar Bessel zeros. This leads to the following mode selection rules:

'E

r

2S Lc

and

'm

r

S T

(8)

These wall distortions (scattering surface) transform the input eigenwave to an eigenwave of the weakly perturbed transmission line. By means of this principle, each required amplitude distribution can be approximated. Numerical optimization calculations include much more than nine coupled modes. The helical converter ("dimple-wall converter") is described by the following wall perturbation: a(M,z) = ao [1 + H1cos ('E1z - l1M) + H2cos ('E2z - l2M)]

where

'E1 = r (E1 -E2) 'E2 = r (E1 -E3)

l1 = r (m1 - m2) = 'm1 l2 = r (m1 - m3) = 'm2

(9)

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and E1 is the propagation constant of the operating mode and E2 and E3 propagation constants of modes, which fulfil the requirement of eq. (8). The required minimal launcher length is

Lmin

S 2 2 Emv  Em1,v  Em1,v

(10)

A shallow linear uptaper of the mean launcher radius ao reduces the danger of spurious gyrotron oscillations in the launcher [1], [21] due to an unintentional cavity introduced by the dimples. In the framework of geometrical optics, the performance of the dimplewall launcher can be explained in the following way. Among the rays composing the initial mode, let us define one to be the leader and find the points of its reflections from the waveguide wall. Then, we deform the inner waveguide surface to make it focusing near the reflection points of the leader ray and defocusing at the remaining area. Then, when successively reflected from the walls, the rays will converge to the leader and finally, will compose an eigenmode of an open mirror waveguide with the transverse distribution of the rf field depending on the mirror profile. (2) Mode Converting Phase Correcting Mirrors In cases where a simple Vlasov launcher or only a weakly beam preshaping launcher is used in connection with a large quasi-parabolic reflector, specific non-quadratic phase-correcting mirrors allow one to generate any desired amplitude and phase distribution of the wave beam. The amplitude distribution may be Gaussian [22], [23] but can also be flat or even ringshaped in order to optimize the power distribution for a given vacuum window geometry and material [24]. Advanced iterative computer algorithms have been developed to provide the optimized shapes of the mirrors [10]-[13] which are manufactured on numerically controlled milling machines. The computer codes are also used for the phase retrieval from amplitude measurements thus allowing detailed mode diagnostics and reconstruction of the overall fields [10]-[13], [25]-[29]. The knowledge of phase and amplitude at any point of the longitudinal axis of the beam makes a calculation of the field pattern at all other points possible.

Q-O Mode Converters ….

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333

1 MW, 140 GHZ, CW GYROTRON FOR W7-X

This section reports on the q.o. mode converter of the 1 MW, 140 GHz, CW prototype gyrotron, operating in the TE28, 8 cavity mode for the stellarator W7-X [30]. This operating mode belongs to a class of cavity modes for 1MW gyrotrons (TE22, 6, TE25, 10 and TE31, 8 ) for which the ratio of caustic to cavity radius is approximately 0.5. In this case, 'M = 2T |1200 and a 'm2 = 3 perturbation of the dimple-wall launcher provides perfect azimuthal focusing (Figure 3). The set of TE modes required to generate a Gaussian-like field distribution is given in Table 1.

Table 1. Set of TE modes to generate a Gaussian-like field distribution (with relative power)

TEm-2, n+1 (0.03)

TEm+1, n (0.11)

TEm+4, n-1 (0.03)

TEm-3, n+1 (0.11)

TEm, n (0.44)

TEm+3, n-1 (0.11)

TEm-4, n+1 (0.03)

TEm-1, n (0.11)

TEm+2, n-1 (0.03)

(a)

(b)

Figure 3. Geometrical optical description of ray propagation in a cylindrical waveguide: (a) side view; (b) top view.

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2.1 Design of the QO Mode Converter The current analysis method for these launcher systems is performed in two steps. First, the waveguide mode converter is analysed using coupledmode theory. Then, the radiated fields are calculated from the waveguide cut using the scalar diffraction integral. As described in section 1, the launcher employs an irregular cylindrical waveguide section (pre-bunching section) followed by a helical-cut launching aperture, as shown in Figure 4. In the pre-bunching section prior to the launcher, a Gaussian profile of the field intensity on the waveguide wall can be achieved by specific periodic 'm1 = 1 and 'm2 = 3 wall deformations (see eq (9)). There are two principal design criteria for the dimple-wall waveguide section. First, the section must convert the main mode to a mixture of modes such that 100% of the power in the waveguide is contained in a bundle with a Gaussian-like amplitude profile. Second, this profile must be achieved within a short distance, typically less than 200 mm, so that the launcher is short enough to avoid interception of the expanding spent electron beam. The design parameters for the launcher area are 21.9 mm for the input radius of the waveguide section and the mean radius of the launcher section is slightly up-tapered (R = a0 + 0.004 z). This configuration reduces the Q factor of the section between the cavity and the helical cut, and suppresses spurious oscillations generated by the spent electron beam of the gyrotron in the launcher section. As shown in Figure 2, The 'm1 = 1 and 'm2 = 3 wall perturbations for the longitudinal and azimutal field bunching, respectively, use the same amplitude of 0.041 mm and perturbation length of 70 mm (with 10 mm tapering), but they start at different positions along the z-axis of the launcher. The 'm1 = 1 perturbation is between z = 0 mm and z = 70 mm; the 'm2 = 3 is between z = 17 mm and z = 87 mm. The helical cut of the antenna is located at 5.027 rad and begins at z = 159.656 mm. The cut length is 54.688 mm, the Brillouin angle 1.130 rad, and the azimuthal spread angle T = 1.086 rad.

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Figure 4. Schematic drawing of the dimple-wall launcher and its wall deformations.

Figure 5 and 6 show analysis results of the coupled mode calculations of the helical mode converter for the TE28, 8 mode at 140 GHz. In Figure 5, the variation of the mode composition along the length of the converter is plotted. At z = 0, corresponding to the start of the wall variation, a pure rotating TE28, 8 mode is injected. As the radiation travels along the z-axis, power in the TE28, 8 mode is coupled into mainly eight satellite modes through the wall perturbations. There are strong couplings from the TE28, 8 mode to the four satellite modes TE27, 8, TE29, 8, TE25, 9 and TE31, 7. Because of symmetry with same perturbation, two satellite modes obtain almost the same coupling power from the TE28, 8 mode. 100

Conversion efficiency ( % )

90 80

TE28, 8

70 60 50 TE29,8

10 TE27,8 TE24, 9 TE26, 9 TE30, 7 TE32, 7

TE25,9

5

TE31,7

0 0

10

20

30

40

50

60

70

80

90

100

Z ( mm)

Figure 5. Mode composition (relative power) coefficients vary along the z-axis.

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5

Angle (rad)

4

3

2

1

0 0

20

40

60

80 100 120 140 160 180 200 220 240

Z (mm)

Figure 6. Contour map of the electrical field of a dimple-wall launcher on its unrolled waveguide wall. Normalized field contours are shown in linear at 0.1 increments from peak.

Other additional modes that couple to the TE28, 8 mode through the waveguide wall deformations are also included in the analysis. These modes serve to increase the peak amplitude of the Gaussian field distribution and decrease the levels of sidelobes of power. Figure 6 shows the calculated contour map of the electrical field on the unrolled waveguide wall of the launcher. The shaped beam has weak fields (low diffraction losses) at the cut edge (indicated by the lines in Figure 6) and a nearly Gaussian angular spectrum. The Gaussian output pattern requires a certain amplitude and phase relation between the main mode and the satellite modes. The appropriate amplitude relation (Table 1) can be achieved with short perturbed sections of 70 mm. A longer smooth section follows and allows for the development of the optimum phase relation [31]. The radiation is launched from the prebunching section by cutting the waveguide wall around one Gaussian bundle where the wall currents are at a minimum. The scalar diffraction integral was used to simulate the radiation of the aperture fields and to examine the properties of the launched beam. With the scalar diffraction integral, the fields at an observation point are calculated by integrating the response to the point source Green’s function over all source regions. Due to the low fields along the edge of the helical cut, this advanced dimple-wall launcher generates a well-focused Gaussianlike radiation pattern with low diffraction. In this case, combined with a quasi-elliptical mirror, two toroidal mirrors can be used as the beam-forming mirror system to obtain a desired beam pattern on the gyrotron output

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window. Since calculations also show that toroidal mirrors are sufficient and, at the same time, they are inexpensive, easy to manufacture, and relatively easy to align.

2.2 Comparison with Measurements In order to compare the theoretical predictions with low power measurement results, the radiated field distribution of the launcher on a plane at the position of x = 100 mm away from the launcher axis, has been calculated as shown in Figure 7 (a). By using the beam-forming mirror system which is mentioned above, further calculation of the power conservation from the launching waveguide shows that an efficiency of more than 98% has been achieved to convert the high-order cavity TE28,8 mode at the frequency of 140 GHz into the fundamental Gaussian beam. A low power test facility has been built to check the performance of the q.o. mode converter system. The transmission measurement device consists of a network analyser, the low power TE28,8 mode generator, mode converter-system as device under test, and the pick-up antenna to measure the E-field distribution in a defined linear polarization (horizontal or vertical). The set-up and performance of the network analyser has been discussed in [32]. The pick-up antenna is fixed on a programmable 3dimensional movable table in order to scan the distribution at an arbitrary position. High power measurements were performed with a dielectric target plate and an IR camera.

1 5 0

1 4 0 1 2 0 1 0 0

Z (mm)

Z (mm)

1 0 0 8 0 6 0

5 0

4 0 2 0 0 -2 0 0

0 -2 0 0

-1 5 0

-1 0 0

-5 0

0

5 0

1 0 0

1 5 0

2 0 0

-1 5 0

-1 0 0

-5 0

0

5 0

1 0 0

1 5 0

2 0 0

Y (m m )

Y (m m )

(a) (b) Figure 7. Radiated field distribution on a plane at the position of 100 mm from the launcher axis. The contour map is shown at 3 dB increments from –30 dB to 0. (a) Calculation; (b) Cold measurement.

Figure 8 shows the comparison of the theoretical predictions with results of low power (cold) and high power (hot) measurements for three different distances from the gyrotron window. Calculations and cold test results are in

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40

Z (mm)

20

0

-20

-40

-40

-20

0

20

40

Y (mm)

40

40

20

20

Z (mm)

Z (mm)

336 mm

0

0

-20

-20

-40

-40

-40

-20

0

20

-40

40

-20

0

20

40

Y (mm)

Y (mm)

775 mm 100 80 60 40

Z (mm)

20 0 -20 -40 -60 -80 -100 -100 -80

-60

-40

-20

0

20

40

60

80

100

Y (mm)

1085 mm Figure 8. Comparison of calculations (left column), low power measurements (middle column), and high power measurements (right column) at three different distances from the window. The contour maps of calculations and cold measurements are shown in 3 dB increments from –30 dB to 0 dB.

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excellent agreement. The hot test shows a somewhat more astigmatic beam, which is probably due to minor mechanical tolerances of the built-in gyrotron mode converter. Nevertheless, after a series of two mirrors and a circular polarizer, high power calorimetric measurements reveal the very high fundamental Gaussian mode content.

3.

2 MW, 170 GHZ, CW COAXIAL CAVITY GYROTRON FOR ITER

Coaxial cavity gyrotrons operate in very high order modes like TE28, 16 at 140 GHz, TE31, 17 at 165 GHz or TE34, 19 at 170 GHz [23, 33]. Unfortunately, due to the ratio of caustic to cavity radius of approximately 0.3 for these modes, their transformation into a nearly Gaussian distribution in the dimple-wall launcher cannot be done as good as for the TE28,8 mode of the 140 GHz gyrotron with a ratio of caustic to cavity radius of approximately 0.5. From Eq. (8) one gets for the azimuthal focusing the selection rule 'm2 = 2.5 (Figure 9) instead of 'm2 = 3 (Figure 3) which means that 'm = 2 and 3 perturbations must be employed simultaneously.

Figure 9. Geometrical optical description of ray propagation of a coaxial cavity gyrotron mode in a cylindrical waveguide (top view): 360°/'M = 2.5.

The resulting calculated microwave field distribution at the inner surface of the dimple-wall launcher is shown in Figure 10. The edge of the cut is marked in the figure.

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6 5

Y / rad

4 3 2 1 0 0

50

100

150 200 z / mm

250

300

Figure 10. Calculated field distribution at the launcher surface. The edges of the launcher cut are indicated.

Since the field amplitude at the cut edge is reduced in comparison to a Vlasov-type launcher, lower diffraction losses and thus a decrease of the total stray radiation is expected. The microwave power radiated from the cut is collected by a quasi-elliptical mirror and then shaped by two nonquadratic phase correcting mirrors. In this case, simple smooth toroidal mirrors are not sufficient. 200

40 100

y / mm

Y / mm

20

0

0

-100

-20 -200

-40

-40

-20

0

x / mm

(a)

20

40

-300 -200

-100

0

100

200

x / mm

(b)

Figure 11. rf power distribution (contour lines in 3dB steps). (a) the window plane and (b) 1000 mm outside the window plane.

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The rf beam radiated out of the gyrotron has not an ideal Gaussian (TEM00) distribution. Because of limitations in the accuracy of mechanical fabrication of the surface structure of the non-quadratic phase correcting mirrors, a compromise must be made between the Gaussian content in the distribution of the rf output beam, and the amount of stray radiation captured inside the tube. Figure 11 shows the calculated power distribution in the window plane (a) and 1000mm outside the window plane (b). According to the calculations, it is expected that the total amount of stray losses will not exceed a value between 5% and 6% of the output power.

4.

4 MW, 170 GHZ COAXIAL CAVITY GYROTRON

Recent experiments at FZK and IAP Nizhny Novgorod suggest that coaxial cavity gyrotrons delivering in excess of 2 MW power at frequencies ranging from 140-170 GHz, operating with very high-order volume modes, can successfully be realized. In another next stage, the feasibility of a super power coaxial cavity gyrotron at 170GHz capable of giving power around 4MW, CW, operating in the ultra high volume modes for a future DEMO Fusion Reactor is presented as a step towards a big leap from 2 to 4 MW power levels. These modes are capable of giving a perfect dual-beam output through two CVD diamond windows with a suitable dimple-wall q.o. launcher. This will reduce the technical complexities connected with high diffraction losses (stray radiation) inside the tube. The realization of such an ultra high power gyrotron will drastically reduce the number of gyrotrons and corresponding superconducting magnets required in ECRH systems of fusion reactor installations. In the mode selection procedure, modes have been chosen which will give an ideal dual-beam focusing at the q.o. launcher (that is with helical 'm1 = 1 and 'm2 = 5 wall perturbations for which m2/2 = 360o/'M = 2.5. In this selection procedure, only three well-qualified modes, namely, TE44, 26, TE50, 30 and TE54, 32 have been picked out (Figure 12).

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2.52

m2 / 2 ( = 360 / M)

2.51

p

F F

2.50 F

2.49

2.48

m 100

120

140

160

180

200

Mode EigenvalueFmp ()

Figure 12. Mode eigenvalues and ray propagation for a dimple-wall launcher with azimuthal 'm2 = 5 perturbation.

Calculations with the FZK self-consistent multi-mode time-dependent code (SELFT) show that the TE54,32 mode is well capable delivering around 4.5 MW, CW power at 170 GHz [34,35]. The principle of the dual-beam q.o. mode converter is shown for the TE28, mode since a low power mode generator is available at FZK for this mode 16 at 140 GHz [32]. The wall perturbation of the dimple-type dual beam launcher is given by R (z,M) = RL + a cos (h1z - M) + a2 cos (h2z – 5 M) a1 = 0.030 mm, a2 = 0.027 mm, h1 = 0.093 mm, h2 = 0.005 mm Here the linear input taper of the deformation depths is not included.

with

R1 = 32.5 mm,

(11)

Q-O Mode Converters ….

343 1.000 0.9500 0.9000 0.8500 0.8000 0.7500 0.7000 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500 0.2000 0.1500 0.1000 0.05000 0

6

5

Angle/Rad

4

3

2

1

0 0

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100

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300

350

X/mm

1.000 0.9500 0.9000 0.8500 0.8000 0.7500 0.7000 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500 0.2000 0.1500 0.1000 0.05000 0

6

5

Angle/Rad

4

3

2

1

0 0

50

100

150

200

250

300

350

/ X/mm

Figure 13. Longitudinal 'm1 = 1 (upper) and azimuthal 'm2 = 5(lower) focusing in a dualbeam TE28, 16 quasi-optical mode converter (140 GHz, I.D. = 65 mm).

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6

5

Angle/Rad

4

3

2

1

0 0

50

100

150

200

250

300

350

X/mm

Figure 14. Contour map of the power of a dimple-wall dual-beam TE28, 16 quasi-optical mode converter (140 GHz, I.D. = 65 mm).

5.

QUASI-OPTICAL MODE CONVERTER FOR A MULTI-FREQUENCY GYROTRON (105–140 GHZ)

The availability of MW gyrotrons with fast frequency step tunability permits the use of a simple, fixed, non-steerable mirror antenna for local electron cyclotron resonance heating and current drive, as well as control of plasma instabilities such as neo-classical tearing modes. For plasma stabilization in the ASDEX-Upgrade tokamak, there is interest in steptunable gyrotrons operating at frequencies between 105 GHz (TE17, 6) and 140 GHz (TE22, 8) [36]. For this purpose, a multi-frequency gyrotron is under construction at Forschungszentrum Karlsruhe (FZK) in a cooperative parallel development with the Institute of Applied Physics in Nizhny Novgorod [37, 38]. In gyrotrons, the frequency can be varied in steps by changing the operating mode via variation of the cavity magnetic field [39, 40]. The rotating high-order cavity modes are converted to the linearly polarized Gaussian output beam by an improved q.o. mode converter [41]. For a frequency step-tunable high power gyrotron, in order to achieve a Gaussian distribution of the output beam with low diffraction losses and minimal frequency dependence for all design frequencies, both the launcher and the

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mirror system of the q.o. mode converter have to be optimized for all excited modes.

5.1 Optimization of the Launcher Calculations have been performed for different types of antennas and cuts. For the high-order modes of a long pulse high power gyrotron, the Vlasovtype launcher becomes impractical because of its moderate conversion efficiency (80%) and the requirement of large size focusing reflectors for a rapidly diverging beam. A dimple-wall launcher could both improve the conversion efficiency from a high-order cylindrical cavity mode to a free space Gaussian beam and reduce the dimensions of focusing reflectors, but it can be used only for limited modes. For this dimple-wall launcher, a Gaussian-like profile of the field intensity on the waveguide wall can be achieved by specific periodic wall deformations 'm1 = 1 and 'm2 = 3.

Figure 15. Calculated output patterns on a plane 50 mm behind a Vlasov antenna (left side) and a dimple-wall antenna (right side) shown for the TE22,8 mode at 140GHz.

As shown in Figure 15, comparing with the Vlasov-type launcher, the dimple-wall launcher produces a well-focused Gaussian radiation pattern with low diffraction. Further simulations show that by using a dimple-wall launcher, which is optimised for TE22, 8, the radiation pattern of the launcher presents an almost identical field shape for all nine considered modes between 105 GHz and 143 GHz (TE23, 8). Due to the different caustic radii, different mode has a different angle of emission. The design parameters for this launcher are a 21.0 mm input radius of the waveguide section, and a mean radius of the launcher section that is slightly up-tapered (R0 = a0 + 0.002 z). The 'm1=1 and 'm2 = 3 wall perturbations for the longitudinal and azimuthal field bunching, respectively, use the same amplitude of 0.05 mm

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and perturbation length of 183 mm (with 10 mm tapering), they start at z = 0 mm along the z-axis of the launcher. The helical cut of the antenna is located at 1.0 rad and begins at z = 115 mm, cut length 68 mm, Brillouin angle 1.025 rad.

5.2

Optimization of Phase Correcting Mirrors

The beam from the launcher is directed by the phase correcting mirror system in order to obtain a desired beam pattern. This transmits with low diffraction losses through the output window, which can be easily handled by the subsequent q.o. transmission line. For a frequency step tunable gyrotron, this mirror system will also guide the rf beam with minimal frequency dependence through the lateral output window of the gyrotron. The first mirror is a large quasi-elliptical one; it is used to focus the divergent beam from the launcher and to create plane phase fronts. The second and third mirrors are phase correcting mirrors with a non-quadratic shape of the surface, which are designed to produce the desired beam on the output window [10]. Since the antenna does not radiate a completely Gaussian distribution beam, the mirror system, in particular the phase correcting mirrors must be optimized for all modes to adjust the output beams. By means of the phase-correcting mirrors, the rf beam is adjusted in its phase distribution to model the field. There are small altitude changes of the surface on these phase forming non-quadratic mirrors, which modify the phase of the local plane wave and leave the amplitude of the reflected field at a plane mirror unchanged. Two numerical algorithms for generating an optimized contour on the surface of a non-quadratic phase-forming mirror have been introduced into the simulation: the gradient method and the wellknown Katsenelenbaum-Semenov algorithm. The gradient method is an iterative way to move from one point to another point in the direction of the searched optimum by adding a vector of progress. As an alternative, the Katsenelenbaum-Semenov algorithm, which is well known in optical applications, has been extended for the frequency step-tunable case. Detailed descriptions of a multi-mode optimization of a mirror with two different methods can be found in [42]. The simulation results show that they are both convergent and supply good results after only a few iteration steps. Figure 16 presents one example of the calculated field distribution on the output window plane with and without the optimized phase corrections. The left figure shows that the output beam has a Gaussian-like shape on the window. For the nine modes from TE17,6 to TE23,8, the simulations show that by using two optimized phase correcting mirrors, the q.o. mode converter has

Q-O Mode Converters ….

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achieved efficiencies of 94%--98% for converting the high-order cavity modes into the usable fundamental Gaussian mode. A new broadband mode generator has been designed and fabricated for the purpose of cold measurement [43, 44]. Two different manufacturers have manufactured two identical q.o. mode converter systems. The measurement results show that both mirror systems are in good agreement; identical beam patterns are formed on the output window [45]. Figure 17 shows one example of calculated (left) and measured (right) power density distribution at the gyrotron flange for the TE22, 8 mode at 140 GHz. It is obvious that the theoretical prediction agrees with the low power measurement. Measurement results show that the q.o. system with nonquadratic phase-correcting mirrors requires accurate alignment. Nevertheless, the use of such mirrors in frequency step-tunable gyrotron is undoubtedly possible.

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Figure 16. Calculated field distribution on the output window plane with (left) and without (right) the optimized phase corrections for the mode of TE22, 8 at 140GHz. Normalized field contours are shown in linear scale with 0.1 increments from the peak.

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Figure 17. Calculation (left) and cold measurement (right) of power density distribution on the gyrotron flange for the TE22, 8 mode at 140 GHz. The contour map is shown at 3 dB increments from –24 dB to 0.

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CONCLUSIONS

The R&D activities at the Karlsruhe Research Center (FZK) on advanced high-power millimeter (mm)-wave gyrotrons for future use in electron cyclotron heating and current drive (ECH & CD) in magnetically confined fusion plasmas consist of: (1) Development of a 1 MW continuous wave (CW) gyrotron at 140 GHz, operating in the TE28,8 cavity mode, for the stellarator W7-X, (2) Development of a coaxial cavity gyrotron, operating in the TE34,19 cavity mode, capable of delivering 2 MW CW at 170 GHz for ITER, (3) Investigations on a 4 MW 170 GHz coaxial cavity gyrotron, operating in the TE54,32 mode, with a two-beam output (2x2 MW) for a DEMO fusion reactor, and (4) Investigations on a tunable multi-frequency gyrotron, operating in nine modes from TE17,6 at 105 GHz to TE23,8 at 143 GHz. The present paper discusses the different q.o. mode converter schemes employed in these types of advanced gyrotrons for conversion of the very high rotating cavity mode into a linearly polarized fundamental Gaussian beam (TEM00). All the q.o. mode converters employ dimple-wall launchers in order to reduce diffraction losses and thus to avoid parasitic stray radiation inside the tubes. In the development lines (2) and (4), phase-correcting mirrors with non-quadratic shapes of the surfaces must also be used for efficiency enhancement and reduction of stray radiation.

7.

REFERENCES

[1]

Thumm M.K., Kasparek, W. Passive high power microwave components. IEEE Trans. on Plasma Science, 2002; 30:755-786 Weinstein L.A., Open Waveguides and Resonators, Golem Press, Boulder Colorado, 1969, 139 Möbius A., Thumm M., "Gyrotron output launchers and output tapers", in Gyrotron Oscillators – Their Principles and Practice, C. Edgcombe, Ed. London: Taylor & Francis, 1993, ch. 7, 179-222 Vlasov S.N., Orlova I.M. Quasi-optical transformer which transforms the waves in a waveguide having a circular cross-section into a highly-directional wave beam. Radio Phys. and Quantum Electronics 1974; 17:115-119 Vlasov S.N., Zagryadskaya L.I., Petelin M.I. Transformation of a whispering gallery mode, propagating in a circular waveguide into beam of waves. Radio Eng. and Electron Physics 1975; 20:14-17 Thumm M., "High-power microwave transmission systems, external mode converters and antenna technology", in Gyrotron Oscillators - Their Principles and Practice, C. Edgcombe, ed., London: Taylor & Francis, 1993, ch. 13, 365-401

[2] [3]

[4]

[5]

[6]

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[8] [9] [10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

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Kuzikov S.V., Petelin M.I. Conversion of paraxial waveguide mode to Gaussian beam., Proc. Int. Workshop on Strong Microwaves in Plasma, Nizhny Novgorod, 1996, ed. A.G. Litvak, Russian Academy of Sciences, 1997, vol. 2, 877-885 Wien A., Thumm M. Numerical analysis of quasi-optical mode converters. Part 1: Backscattering analysis of shaped-end radiators. Int. J. Electronics 1999; 86:739-745 Vlasov S.N., Shapiro M.A. Bievolvent mirror for transfer of caustic surfaces. Soviet Technical Physics Letters 1989; 15:374-375 Bogdashov A.A., Chirkov A.V., Denisov G.G., Vinogradov D.V., Kuftin A.N., Malygin V.I., Zapevalov V.E. Mirror synthesis for quasi-optical mode converters. Int. J. Infrared Millimeter Waves 1995; 16:735-743 Hirata Y., Mitsunaka Y., Hayashi K., Itoh Y. Wave-beam shaping using multiple phasecorrection mirrors: IEEE Trans. on Microwave Theory and Techniques 1997; vol. MTT45.72-77 Michel G., Sanchez E. Investigations on transmission lines with non-quadratic mirrors. Proc. 10th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Heating, Ameland, The Netherlands, 1997, ed. by T. Donne and A.G.A. Verhoeven, World Scientific, Singapoore, 1997 Denisov D.R., Chu T.S., Shapiro M.A., Temkin R.J. Gyrotron internal mode converter reflector shaping from measured field intensity. IEEE Trans. on Plasma Science 1999; PS-27:512-519 Vlasov S.N., Shapiro M.A., Sheinina E.V. Wave beam shaping on diffraction of a whispering gallery wave at a convex cylindrical surface. Radio Phys. Quantum Electronics 1988; 31:1070-1075 Iima M., Sato M., Amano J., Kobayashi S., Nakajima M., Hashimoto M., Wada O., Sakamoto K., Shiho M., Nagashima T., Thumm M., Jacobs A., Kasparek W. Measurement of radiation field from an improved efficiency quasi-optical converter for whispering-gallery mode. Conf. Digest 14th Int. Conf. on Infrared and Millimeter Waves, Würzburg. Proc. SPIE 1240, 405-406, 1989 Denisov G.G., Kuftin A.N., Malygin V.I., Venediktov N.P., Vinogradov D.V., Zapevalov V.E. 110 GHz gyrotron with built-in high efficiency converter. Int. J. Electronics 1992; 72:1079-1091 Denisov G.G., Petelin M.I., Vinogradov .V. Converter of high-mode of a circular waveguide into the main mode of a mirror line. 1990, WO90/0780 H01P1/16, PCT Gazette, 16:47-49 Denisov G.G., Petelin M.I., Vinogradov D.V. Effective conversion of high waveguide modes to eigenmodes of open mirror lines., Proc. 10th Summer-Seminar on Wave Diffraction and Propagation, Moscow, SRIRP, 96-128, 1993 Pretterebner J., Möbius A., Thumm M. Improvement of quasi-optical mode converters by launching an appropriate mixture of modes, Conf. Digest 17th Int. Conf. on Infrared and Millimeter Waves, Pasadena, SPIE 1929, 40-41, 1992 Thumm, M. "Modes and mode conversion in microwave devices", in Generation and Application of High Power Microwaves, R.A. Cairns and A.D.R. Phelps, eds., Bristol and Philadelphia: Institute of Physics Publishing, 1997 Alberti S., Arnold A., Borie E., Dammertz G., Erckmann V., Garin P., Giguet E., Illy S., LeCloarec G., Le Goff Y., Magne R., Michel G., Piosczyk B., Tran C., Tran M.Q., Thumm M., Wagner D. European high-power CW gyrotron development for ECRH systems. Fusion Eng. and Design 2001; 53:387-397 Denisov G.G. Development of 1 MW output power level gyrotrons for fusion systems., Proc. Int. Workshop on Strong Microwaves in Plasmas, Nizhny Novgorod, 1999, A.G. Litvak Ed., Russian Academy of Sciences, vol. 2, 967-986, 2000

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[23] Piosczyk B., Braz O., Dammertz G., Iatrou C.I., Illy S., Kuntze M., Michel G., Möbius A., Thumm M., Flyagin V.A., Khishnyak V.I., Pavelyev A.B., Zapevalev V.E. Coaxial cavity gyrotron with dual rf beam output. IEEE Trans. on Plasma Science 1998 PS26:393-401 [24] Mjasnikov V.E., Agapova M.V., Alikaev V.V., Borshchegovsky A.S., Denisov G.G., Flyagin V.A., Fix A.Sh., Ilyin V.I., Ilyin V.N., Keyer A.P., Khmara V.A., Khmara D.V., Kostyna A.N., Nichiporenko V.O., Popov L.G., Zapevalev V.E. Megawatt power level long-pulses 110 GHz and 140 GHz gyrotrons., Proc. Int. Workshop on Strong Microwaves in Plasmas, Nizhny Novgorod, 1996, ed. A.G. Litvak, Russian Academy of Sciences, vol. 2, 577-598, 1997 [25] Chirkov A.V., Denisov G.G., Aleksandrov N.L. 3D wavebeam field reconstruction from intensity measurements in a few cross sections., Optics Communications 1995 115;449452 [26] Empacher L., Gantenbein G., Kasparek W., Erckmann V., Laqua H. Matching of a nongaussian gyrotron beam to a transmission line using thermographic measurements. Proc. of the 21st Int. Conference on Infrared and Millimeter Waves, e.d M.v. Ortenberg and H.U. Mueller, AM-10, ISBN 3-00-000800-4, Berlin 1996 [27] Aleksandrov N.L., Chirkov A.V., Denisov G.G., Kuzikov S.V. Mode content analysis from intensity measurements in a few cross sections of oversized waveguides. Int. J. Infrared Millimeter Waves 1997, 18:1323-1334 [28] Chirkov A.V., Denisov G.G. Methods of wavebeam phase front reconstruction using intensity measurements. Int. J. Infrared and Millimeter Waves 2000, 21:83-90 [29] Michel G., Thumm M. Spectral domain techniques for field pattern analysis and synthesis. Surv. Math. Ind. 1999; 8:259-270 [30] Dammertz G., Alberti S., Arnold A., Borie E., Erckmann V., Gantenbein G., Giguet E., Hogge J.-P., Illy S., Kasparek W., Koppenburg K., Laqua H., Le Cloarec G., Le Goff Y., Leonhardt W., Lievin Ch., Magne R., Michel G., Müller G., Neffe G., Kuntze M., Piosczyk B., Schmid M., Thumm M., Tran M.Q. Development of a 140 GHz, 1 MW, continuous wave gyrotron for the W7-X stellarator. Frequenz 2001; 55:270-275 [31] Pretterebner, J. Kompakte quasi-optische Antennen im überdimensionierten Rundhohlleiter. Ph.D.Thesis, IPF, University Stuttgart, 2003 [32] Braz O., Arnold A., Kunkel H.-R., Thumm M. Low power performance tests on highly oversized waveguide components of high power gyrotrons. Proc. 22nd Int. Conf. on Infrared and Millimeter Waves, Wintergreen, Virginia, USA, 1997, 21-22 [33] Piosczyk B., Braz O., Dammertz G., Iatrou C.T., Illy S., Kuntze M., Michel G., Thumm M. 165 GHz, 1.5 MW-coaxial gyrotron with depressed collector. IEEE Trans. on Plasma Science 1999; PS-27:484-489 [34] Kartikeyan M.V., Pavelyev A.B., Piosczyk B., Thumm M. A step towards a 170 GHz, 5 MW coaxial super gyrotron, Proc. 4th IEEE Int. Vacuum Electronics Conference (IVEC2003), Seoul, Korea, 2003, 36-37 [35] Kartikeyan M.V., Borie E., Piosczyk B., Thumm M. In quest of a 170 GHz coaxial super gyrotron, Conf. Digest 28th Int. Conf. on Infrared and Millimeter Waves, Otsu, Japan, 2003, 169-170 [36] Leuterer F., Kirov K., Monaco F., Münich M., Schütz H., Ryter F., Wagner D., Wilhelm R., Zohm H., Franke T., Voigt K., Thumm M., Heidinger R., Dammertz G., Koppenburg K., Kasparek W., Gantenbein G., Hailer H., Mueller G.A., Bogdashov A., Denisov G., Kurbatov V., Kuftin A., Litvak A., Malygin S., Tai E., Zapevalov V. Plans for a new ECRH system at ASDEX Upgrade, Fusion Eng. and Design 2003; 66-68:537-542

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[37] Borie E., Drumm O., Illy S., Koppenburg K., Kartikeyan M., Piosczyk B., Wagner D., Yang X., Dammertz G., Thumm M. Possibilities for multifrequency operation of a gyrotron at FZK, IEEE Trans. on Plasma Science 2002; PS-30:828-834 [38] Zapevalov V.E., Bogdashov A.A., Chirkov A.V., Denisov G.G., Kufin A.N., Lygin V.K., Moiseev M.A. Optimizatiion of the frequency step tunable 105-170 GHz 1MW gyrotron prototype, Proc. 27th Int. Conf. on Infrared and Millimeter Waves, San Diego, USA, 2002; 1-2 [39] Thumm M., Arnold A., Borie E., Braz O., Dammertz G., Dumbrajs O., Koppenburg K., Kuntze M., Michel G., Piosczyk B. Frequency step-tunable (114-170 GHz) megawatt gyrotrons for plasma physics applications, Fusion Eng. and Design 2001; 53:407-421 [40] Koppenburg K., Dammertz G., Kuntze M., Piosczyk B., Thumm M. Fast frequencystep-tunable high-power gyrotron with hybrid-magnet-system, IEEE Trans. on Electron Dev. 2001; 48:101-107 [41] Thumm M., Michel G., Möbius A., Wagner D. Advanced quasi-optical mode converter for a step-tunable 118-162 GHz, 1 MW Gyrotron, Proc. 21st Int. Conf. on Infrared and Millimeter Waves, Berlin, Germany 1996; AT6-7 [42] Drumm O., Dammertz G., Thumm M. Design methods for mirrors in a quasi-optical mode converter for a frequency step-tunable gyrotron, Proc. 27th Int. Conf. on Infrared and Millimeter Waves, San Diego, USA, 2002; 193-194 [43] Wagner D., Thumm M., Arnold A. Mode generator for the cold test of step-tunable gyrotrons, Proc. 27th Int. Conf. on Infrared and Millimeter Waves, Proc. 27th Int. Conf. on Infrared and Millimeter Waves, San Diego, USA, 2002; 303-304 [44] Arnold A., Dammertz G., Wagner D., Thumm M. Measurements on a mode generator for cold tests of step-tunable gyrotrons, Proc. 27th Int. Conf. on Infrared and Millimeter Waves, Proc. 27th Int. Conf on Infrared and Millimeter Waves, San Diego, USA, 2002; 289-290 [45] Arnold, A., Dammertz G., Koppenburg K.,Wagner D., Thumm M. Low power measurements on a mode converter system of step-tunable gyrotrons, Proc. 28th Int. Conf. on Infrared and Millimeter Waves, Otsu, Japan 2003; 415-416

RADAR AND COMMUNICATION SYSTEMS: SOME TRENDS OF DEVELOPMENT Epigraph: Looking into the starry sky, do not forget to look underfoot (Folk aphorism)

A. A.Tolkachev(1), E. N.Yegorov (2), A.V. Shishlov(1) (1) - Joint-Stock Company Radiofizika, Moscow, Russia (2) - Joint-Stock Company REIS, Moscow, Russia

Abstract:

Presently, at frequencies up to X-band, advanced radar and communication systems use active phased array antennas based on efficient solid-state amplifiers integrated into monolithic circuits. However, at higher frequencies, beginning with Ka-band, such systems are able to operate only at moderate powers, and thus passive phased array antenna shifters are anticipated to be the only practical method to control high-power beams in the foreseeable future.

Keywords:

Radar system, communication system, active phased array antenna, high power amplifier, phase shifter

1.

INTRODUCTION

Progress of communication and radar technologies, along with using digital methods for signal synthesis and processing, is characterized by x expansion to higher-frequency ranges, and x using active phased-array antennas. The first method enhances the communication capacity and increases the radar resolution and selectivity, which is combined with opportunities to reduce overall dimensions and weights of the systems. As for radars, they are able to measure the range, two angles, and Doppler velocity of the target. Resolution and measurement accuracy on each of the coordinates are inversely proportional to the wavelength O, with all other factors being equal. Therefore, radar selectivity, which is defined as a product of resolutions on each of the coordinates, rises as O-3 - O-4. (Radar selectivity is an extremely important characteristic as it determines radar’s interference immunity). 353 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 353–370. © 2005 Springer. Printed in the Netherlands.

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Target data accuracy, in particular angle measurement accuracy, grows as well. That is especially important for far range targets, because linear errors caused by angle measurement are much larger than range measurement error. On the other hand, if requirements on target data accuracy and on interference immunity are fixed, using of higher frequencies allows reduction in the antenna’s overall dimensions, relative bandwidth and radiating pulse width. Phased array antennas (PAA’s) are of two types: active and passive (Fig. 1). Amplifiers of passive PAA are located behind the aperture phasecontrols (Fig. 1b). In active PAA’s (APAA), transmitting and receiving amplifiers of the APAA are located within the antenna and closer to the antenna aperture than phase-controls (Fig. 1a). Development of PAA has a long history but during recent decades, the main emphasis was given to APAA’s based on use of solid-state microwave elements and signal processing. The solid-state based APAA’s are characterized by enhanced efficiency and reliability. However, the cost of APAA’s grows rapidly with the increase of carrier frequency (wavelength reduction), so large high-power antennas at the shortcentimeter waveband are extremely expensive and at the millimeter-wave band, practically impossible at any rate in the foreseeable future.

2.

MAIN FEATURES OF MULTIFUNCTIONAL RADARS AND COMMUNICATION SYSTEMS

Let us consider a multifunction radar with a PAA capable of carrying out at least two functions: x independent detection of targets within a specified volume of space and preparation of the necessary information for tracking of the detected targets; x tracking of a specified number of the detected targets. The requirements of power capabilities of radars operating in these two modes are quite diverse and different, depending upon the wavelength. It is known that the attainable velocity of surveillance ( :c rad/s) can be represented as follows [1]:

:c

Pa SV eff 1 u 2 4 4SR q kTeff

(1)

Radar and Communications Systems

355 Radiator Diplexer

M

M

¦

>>

LNA

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>>

Divider

LNA HPA >>

M

M

HPA

>>

>>

M

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>>

HPA

>>

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HPA

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Phase shifter

Combiner

¦

RX

TX

a) Block- diagram of active PAA Radiator M

M

M

M

¦

Phase shifter Combiner/ divider Diplexer

HPA

TX

LNA

RX

b) Block- diagram of passive PAA Figure 1. Active and passive PAA’s.

where: R -radar range, m, Pa - average radiated power, W, S - effective antenna area at reception, sq.m, Veff - radar cross-section (RCS) of the target, sq.m, q2 - signal-to-noise ratio, k - Boltsman's constant Teff - effective noise temperature of the receiving system. It is proportional to the average radiating power multiplied by the receiving antenna area, and does not depend on wavelength. Since the cost of producing the power and the cost of creating the antenna grows as wavelength decreases, it is expedient to develop exclusive

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surveillance radars operating at a relatively long-meter or decimeter-wave band. Interference immunity and target data accuracy of these radars are lower than aforementioned parameters of radars operating in short-wave bands. The required energy for single-target tracking depends on the singlepulse radiated energy E, in J [1]:

R4

E SV eff 1 u 2 2 4S q O kTeff

(2)

In that case, the range of coverage depends on the wavelength as O-1/2, i.e., it grows with the decrease of wavelength because of the higher concentrations of energy in space. Thus, radar coverage range, frequency selectivity, and interference immunity, increase. Consequently, it is desirable to develop target-track radars operating at the short centimeter waveband or at the long-wave part of the millimeter-wave band. Thus, the ratio of energy consumption per detection and per tracking grows with decreasing of wavelength. In real radar systems, energy consumption per tracking as a rule, is much less than the consumption per detection in S-band (O a 10 cm) systems, and is incomparably less in X-band (O a 3 cm) systems and, in particular, in Ka-band (O a 0.8 cm) systems. That is the reason for the 1972 Anti Ballistic Missile (ABM)-Defense Systems Treaty defining that excess of 3˜106 W˜sq.m value of radar average, radiated power multiplied by aperture area as an indication of the fact that the radar belongs to the strategic (anti-intercontinental ballistic missile) radar category:

Pa S d 3 u 10 6

W sq.m

(3)

Let us attempt now to estimate limitations on multifunction radars in high frequency bands, using as an example, ABM-defense radars and keeping in mind that these estimations are qualitatively valid for other high-power multifunction radars. The considerable troposphere attenuation of millimeter and sub-millimeter waves limits their application in radar and communication. The most favorable area of their application is the near-Earth space, where molecular absorption is absent and the influence of ionized clouds is insignificant.

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Millimeter waves can be effectively used both in cellular communication systems as well as in radar systems if a few tens of kilometers coverage range is acceptable (for example, anti-aircraft defense radar systems) or, in systems operating at high elevation angles (more than 20 deg, for example, anti-missile defense radars). The data rate of a communication system depends on the signal-to-noise ratio q of the front-end amplifier, which is expressed by the communication link equation [2]:

q

· 1 1 ¸˜ ˜ 2 2 ¸ © Teff ¹ O R kB §

Pa S t ˜ ¨¨ S r

(4)

where: Pa - average transmitting power, St - transmitting antenna aperture area, Sr - receiving antenna aperture area, Teff - effective noise temperature of the receiving system, R - distance of communication link, k - Boltsman's constant, B - bandwidth. From Equation (4), one can see that system capacity increases at higher frequencies due to the concentration of energy radiated by the transmitting antenna to space. On the other hand, the value of q is proportional to energetic efficiency Pa St of transmitting antenna and Sr /Teff -of receiving antenna.

3.

COMPARISON OF PASSIVE PAA AND ACTIVE PAA

Along with conditions of radio-wave propagation, the main limitation of using higher frequency ranges is the radar cost. Currently, the cost of a PAA and of a power amplifier, connected to the PAA or included in its structure, makes up 70-90% of total radar cost. Basing on our averaged, expert estimations, we make a qualitative assessment of PAA elements cost realizing radiation of 2 kW average power per one sq.m of passive or active PAA aperture, as a function of operational frequency.

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As applied to passive PAA, the cost consists predominantly of two components: cost of aperture phase-control elements (aperture phase shifters) and cost of a transmitter. Currently, semiconductor and ferrite elements are widely used for phase control in passive PAAs. Cost estimations for passive PAA elements implemented by leading R&D engineer Dr. Yu. B. Korchemkin, are presented in Tables 1, 2.

Table 1. The cost of a PAA element using ferrite phase shifters. Optimistic (pessimistic) estimate

1 2 3 4 5

The cost, USD PAA element O=10 cm 6 cm 3 cm 1 cm Phase-shifting section (ferrite, waveguide, coil) 100 40 20 15 Radiator (two dielectric rods) 60 30 15 5 Armature (cradle, body, radome) 40 20 10 5 Control circuit, supply, special-purpose 40 20 15 10 processor Mechanical construction 100 60 30 15 TOTAL 340(600) 170(300) 85(150) 50(90)

Table 2. The cost of a PAA element using semiconductor phase shifters. Optimistic (pessimistic) estimate The cost, USD PAA element O=10 cm 6 cm 3 cm 1 cm 1 Phase-shifting section (p-i-n diodes, plate, 200 180 170 160 tuner) 2 Radiator (two planes with stripline radiators) 60 30 15 5 3 Armature (cradle, body, radome) 40 20 10 5 4 Control circuit, supply, special-purpose 30 20 20 20 processor 5 Mechanical construction 80 70 60 50 TOTAL 340(600) 320(500) 275(400) 240(350)

Let us suppose that spacing of radiating element is 0.7O, which corresponds approximately to a 90-degree sector of electronic beam steering. From (1), the number of array elements N a O2. The cost of one square meter of the aperture for that case is shown in Fig. 2. The cost of high power amplifiers for radars with passive PAA using different microwave vacuum tubes can be found from expert evaluation as presented in the Figure 3.

Radar and Communications Systems

1 000

thou USD Ferriteelement antenna aperture

100

359

Semiconductorelement antenna aperture

O , cm 10 0,1

1

10

100

1

Figure 2. Cost of one sq.m of passive PAA aperture as a function of wavelength.

1000

thou USD

Pa= Generaluse devices

100

10

2 kW

Gyro devices

1 0,1

1

10

O, cm

100

Figure 3. Cost of power amplification by means of various types of microwave vacuum devices.

In an active PAA, cost is determined by the basic element of the semiconductor APAA module including the power amplifier. If the power flux density at the unit aperture surface is fixed, the cost of the module slowly depends on the frequency band and, according to expert estimations, is about USD 1000 - 2000 [3,4]. The cost of mechanical construction can be estimated equal roughly to one fourth of the module cost.

360

Tolkachev, Yegorov, Shishlov Figure 4 comprises cost estimates for both passive and active PAA’s .

10000

thou USD

Passive PAA using generaluse amplifiers

Thaad (USA)

1000

Semiconductorelement active PAA

Passive PAA using gyro devices Wavelength for expedient applying the semiconductorelement active PAAs

100

10 0,1

1

Wavelengths for possible applying the semiconductorelement active PAAs

Wavelengths for applying the passive PAAs microwave vacuum using devices

O, ɫm 10

100

ȿL/M-2080 (Israel)

1

Figure 4. Cost of one sq.m of PAA aperture radiating 2 kW average power as a function of wavelength.

It is necessary to mention that cost of any radio system consists of two components: initial cost of development, and cost of maintenance. From our experience, expenses for maintenance of radio-systems with passive PAA exceed expenses for fabrication of the systems. At the same time, our experience of handling with radio systems containing APAA shows that expenses for maintenance are about 10–25% of the initial expenses for fabrication. It is appropriate to mention that reliability of radar systems with passive PAA in many respects is defined by the reliability of a vacuum HPA with high-voltage power supply. As a rule, a lifetime of the HPA is much less than a specified life of the whole radar. For this reason, the HPA is substituted many times during the specified life of the radar. As for the transmitting APAA, it represents a system of many highreliability solid-state power-radiating sources working in parallel. In case of

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361

M channels failure of initial number N, energetic efficiency of the antenna changes as follows:

( Pa S ) N  M 2M | 1 N ( Pa S ) N

(5)

This means that 10% failure of modules leads to about 1 dB degradation of energetic efficiency. Similar relations are valid for receiving APAA. Maintenance statistics of radio systems with APAA is evidence of high reliability of receiving and transmitting solid-state modules. Mean time between failures is about 200 000 hours for receiving modules and about 100 000 hours for transmitting modules [3]. Similar data are obtained in our developments. This reliability of modules provides degradation of energetic efficiency of APAA of about 1 dB during 10 000 hours. Of course, such performance is achieved in case of optimal construction of antenna with appropriate cooling system, protection from mechanical and environment exposures. Trustworthy results of research and development the APG-77 radar for F22 fighter gave evidence of the fact that radars with active and passive PAA have similar cost of development. But the system with a passive PAA exceeded for about two times the available volume and weight, and had a power consumption that exceeded the capability of airborne power supply [5]. At the same time, Figures 2 and 3 allow one to propose the expedience of applying the general-use vacuum devices, in particular the gyrodevices packaged with permanent magnets, in large and powerful millimeter-wave radars [6].

4.

EXAMPLES OF PAA OF RADAR SYSTEMS

Let us consider several examples of radars with PAA. The EL/M-2080 radar recently developed in Israel is an example of the multifunctional L-band radar using solid-state APAA. Though there is very little information on the characteristics of the radar in publications, some indirect data allows supposition that the antenna area is about 25 sq.m, and the number of solid-state hybrid modules containing power bipolar transistors is about 600. It is possible to expect that the average power of each module is in the 30 to 60 W interval. Hence, PaS # 4.5˜105 - 106 W sq.m., that is the value of Pa S that complies with the restriction of the 1972 ABM-defense Systems Treaty. The cost of

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manufacturing the solid-state modules of the radar is probably about 1,000,000 USD. Several specimens of the radar have been manufactured [7]. The multifunctional X-band radar of THAAD system is the other interesting example of APAA with very large quantity of modules. The antenna area of the radar is 9.2 sq.m, the number of solid-state modules is 25 344, and antenna array spacing is 0.6 O. No information about the module average power is available from publications, however it is possible to suppose that it is between 1 and 10 W. Hence, Pa S = 2.5˜1052.5˜106 W sq.m. The cost of a solid-state module is about 1000 USD, that is the overall cost of modules for one APAA is about 25,000,000 USD [8], [9]. Thus, costs of these two radars differ roughly by 25:1, though the searching capabilities of the radars are approximately equal to one another. The cost difference of the radars is caused by higher measurement accuracy and interference immunity of the THAAD system. Whereas there exist no powerful radars with solid-state APAA in millimeter wave band currently, the radar “Ruza” (35 GHz) created in 1989 (Fig. 5) by JSC “Radiophyzika” (Moscow) in cooperation with other companies, is the most remarkable example of radar with PAA which is passive for transmission and active for reception [10,11]. The array antenna contains 120 large radiators with ferrite phase shifters. The total antenna aperture is about 40 sq.m. The radar uses gyroklystron power amplifiers. Average radiated power is 50 kW, hence, Pa S | 2˜106 W sq.m. Due to very large spacing of elements, the PAA has conical sector of electronic beam steering of about 1q. The PAA is installed on the positioner, which provides mechanical beam steering in the upper hemisphere.

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Figure 5. Radar “Rusa”.

For similar radar with a wide angle of electronical beam steering, the other passive PAA was developed by JSC “Radiophyzika” [12]. This reflective-type PAA developed on basis of ferrite phase shifter is shown in the Fig. 6. The PAA contains about 3600 phase shifters arranged over hexagonal grid with spacing 1.1O. Protruding waveguide-dielectric rod radiators form a flat-topped pattern that suppresses grating lobes. The PAA has a sector of electronic beam steering about r25q. The array has hexagonal aperture with diameter of its inscribed circle of 0.64 ɦ. Effective illumination of the aperture is provided by a quasi-optical exciter. In combination with a commercial klystron on TWT HPA with average output power of 2 kW, the system can provide Pa Seff | 5u102 W sq.m.

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Figure 6. Reflective PAA of Ka-band.

The described array can be used as not only a single antenna but as a subarray of a large “semi-active” PAA of hexagonal structure. For example, assembled with approximately 102 subarrays with HPA, such an antenna would have Pa Seff | 3u106 W sq.m.

5.

APAA FOR COMMUNICATION SYSTEMS

As to communications, the trends are partly similar to radar systems and partly different. On the one hand, it is necessary to note that the trend of using higher frequency bands is very attractive in communications because it ensures considerable advantage of system throughput rate, allows a reduction in power consumption, reduces the overall dimensions of hardware, and increases the system interference immunity. These advantages seem to be very valuable especially in the case of satellite antennas for communications. On the other hand, communication systems usually operate within the angular coverage, which is far less than required coverage of radar systems. Hence, requirements to the radiating power of communication systems are, in general, far easier than that of radars, and very small APAA containing a few hundreds or even a few tens of elements are widely used in this case. Applying of APAA in communication systems is extremely expedient in

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respect of serviceability, as it allows rejection of insufficiently reliable vacuum high-voltage microwave devices. Also, it permits an increase in efficiency and flexibility of communication systems. Very high reliability, possibility to form many beams with independent electronic scanning, broad capability of pattern shaping, make APAA a very attractive and reasonable technical solution in these systems despite the costs of the antenna systems being rather high. Apparently, the APAA replaces conventional antennas not only in microwave, but in millimeter-wave systems too, first of all, in satellite communication systems. As far as we know, the first APAA for mobile satellite communications through high elliptic satellite "Molniya" was developed in the Soviet Union in 1970 [13]. The airborne APAA of L-band (800/900 MHz), containing 64 elements providing one electronically steered beam near the upper hemisphere (r80q) is shown in Fig. 7. The system’s transmitting antenna has Pa Seff | 102 W sq.m.

Figure 7. L-band airborne APAA for communication system through the satellite “Molniya".

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Another APAA developed for geostationary communication satellite “Kupon” [14] (Ku-band) is shown in the Fig. 8. It contains 64 elements. The modules are arranged in nodes of a hexagonal grid with spacing about 3O , which provides a beam coverage area about r9q, which is enough to cover the earth from the geostationary orbit. The antenna has four independently steered and shaped beams. Maximum Pa Seff of the APAA is about 10 W sq.m.

Figure 8. Ku-band APAA of communication satellite “Kupon”.

The APAA developed by “Boeing” [15, 16] and used in mobile satellite communication system of millimeter wave band is shown in Fig. 9. The APAA consists of 91 elements. Hermetic active modules containing monolithic microwave integrated circuits (MMIC) are arranged in nodes of a hexagonal grid with spacing of approximately 0.6O , that provides r70qsector of electronical beam steering. Despite each channel containing rather

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Figure 9. APAA (f =44 GHz) for satellite communications.

powerful HPA (Pout = 0.6 W), the parameter Pa Seff | 10 -1 W sq.m is rather small. The most impressive example of Ku-band APAA for experimental high data rate (Gigabit) satellite is under development by CRL and MELCO (Japan) [17]. Both transmitting and receiving APAAs contain about 2800 elements with a 2.4 m aperture diameter for transmitting (18 GHz), and 1.6 m for receiving (28 GHz). Output power of the transmitting APAA must be about 400 W. Noise figure of receiving APAA will be less than 3.5 dB. The array consists of horn radiators spaced at about 2.2O, which provides r10qsector of electronical beam steering. Efficiency of the transmitting APAA Pa Seff | 2 ˜10 3 Wsq.m is very high for this frequency band. Transmitting (Fig. 10) and receiving antenna subarray units containing 64 channels each were already successfully developed and tested [17]. Use of APAA containing MMIC is supposed in many advanced Ka-band satellite communication systems [9]. To support space missions, communication systems in the frequency range from S-band to Ka-band are used, and the transmit power is from 200W to 400 kW. Future upgrades to navigation, command uplink and emergency recovery complexes will require still higher frequency and higher power

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transmitters. These specifications can be met with combinations of both solid-state and vacuum electronic devices [18].

a) Antenna Aperture (44 Subarray Unit)

b) Subarray Unit Figure 10. Antenna configuration of the transmitting APAA for Gigabit satellite.

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CONCLUSION Radar and communication systems with active phase arrays are superior to passive systems at relatively low frequencies, but lose their competitive edge when approaching the millimeter-wave band. Beginning with Ka-band, the highest powers can be employed in practice only with passive phased arrays.

6.

REFERENCES

1. M.I. Skolnik, Radar Handbook, McGRAW-HILL, 1970. 2. L.Kantor at al, Handbook on Satellite Communications and Broadcasting. - Radio i Svyaz, Moscow, 1988. 3. Nicolas Fourikis. Phased Array-Based Systems and Applications. John Willey & Sons, Inc.1996. 4. Eliot D. Cohen, Trends in the Development of MMICs and Packages for Active Electronically scanned Arrays. - IEEE International Symposium on Phased Array Systems and Technology, Boston, 1996, ɪ.p. 1 - 4. 5. John A. Malas. F-22 Radar Development. NAECON - 97, p.831 - 839. 6. A.V. Gaponov-Grekhov, V.L. Granatshtein. Application of High-Power Microwaves. Boston-London, Artech House, 1994. 7. S. Dryer at al. EL/M 2080 ATBM Early Warning and Fire Control Radar System. IEEE International Symposium on Phased Array Systems and Technology 1996, ɪ 11-16. 8. M. Sarcione at al. The Design, Development and Testing of the THAAD Solid State Phased Array. IEEE International Symposium on Phased Array Systems and Technology. Boston, 1996, ɪ. 260-265. 9. E. Brookner. Phased Array for the New Millennium. 2000 IEEE International Conference on Phased Array Systems and Technology, 2000, ɪ.3-13. 10. A.A. Tolkachev at al. A Megawatt Power Millimeter-Wave Phased-Array Radar. IEEE Aerospace and Electronic Systems Magazine, July 2000 ISSN 0885-8985, v 15, ʋ 7, ɪ. 25-31. 11. A.A. Tolkachev, at al. Large Apertured Radar Phased Array Antenna of Ka-band , Proceedings of the XVIII Moscow International Conference on Antenna Theory and Technology, Moscow, 1998, p.p.15-23. 12. A.A. Tolkachev, at al. High Gain Antenna Systems for Millimeter Wave Radars with Combined Electronical and Mechanical Beam Steering. IEEE International Symposium on Phased Array Systems and Technology. Boston, 1996, ɪ.p. 266-271. 13. E.N. Yegorov, A.L. Epshtein, G.Ya. Guskov, B.A. Levitan, G.V. Sbitnev, A.V. Shishlov. New Technologies in Multibeam and Scanning Antennas for Communication Systems. Proceedings of the APSCC'94 Workshop, Seoul, Korea,1994, p.p. 211 - 221. 14. E.N. Yegorov, V.V. Likhtenvald, G.V. Sbitnev. The system of Active Phased Array Antennas for satellite relay "Kupon". Proceedings of the XVIII Moscow International Conference on Antenna Theory and Technology, Moscow, 1998, p.p 55-61. 15. G.W. Fitzsimmons, B.J. Lamberty, D.T. Harvey, D.E. Riemer, E.J. Vertatschitsch, J.E. Wallace, A connectorless Module for an EHF Phased Array Antenna. Microwave Journal., 1994, vol. 37, No 1, p.114-126.

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16. D.E. Riemer, Packaging Design of Wide-Angle Phased-Array Antenna for Frequencies Above 20 GHz, IEEE Trans., 1995, v. AP-43, No.9, p. 915-920. 17. T. Sakura, H. Aruga, S. Kitao, H. Nakaguro, A. Akaishi, N, Kadowaki, T. Araki. Development of Ka-band Multibeam Active Phased Array Antenna for Gigabit Satellite. Proceedings of the Fifth Ka-band Utilization Conference, Taormina, Italy, 1999, p.p. 515 522. 18. M. A. Kodis, D.S. Abraham D.D. Morabito Deep space C3: High Power Uplinks, AIP Conf. Proceedings 691, High Energy Density and High Power RF, Ed. S. H. Gold, G. S. Nusinovich, 2003, pp. 47-53.

ON ANTENNA SYSTEMS FOR SPACE APPLICATIONS Scientific and Remote Sensing Satellite Applications

Kees van ’t Klooster ESA Estec, Noordwijk, The Netherlands Abstract:

Examples of satellite projects accomplished by the European Space Agency (ESA) are broadly summarized with references and with attention to antenna aspects. Antennas are discussed for scientific or remote sensing applications. Limited power resources onboard the satellite, mass constraints and harsh space environmental factors dictate requirements, which often can only be satisfied after accurate efforts for design, realization and testing processes of antennas. Gain, coverage or pattern properties and polarization requirements must be satisfied for antennas. Requirements can be more demanding for microwave instrument antennas since instruments must measure accurately in absolute sense. Accurate knowledge of radiation behavior (vector behavior) is needed. High power transmission and very low power reception can dictate requirements for passive intermodulation (PIM). Multipaction aspects must be addressed to assure that no breakdown occurs because it might jeopardize antenna functionality. Quasi-optical techniques for high power applications are addressed in these proceedings. This paper describes with references, that there is some synergy in antenna development with the field of quasi-optics and high power rf-engineering; that there are developments and application scenarios for tools and techniques for antennas, which could be used for other applications discussed elsewhere in these proceedings and vice-versa.

Key words:

Satellite Antenna, Instrument Antenna, High Performance Antennas

1.

INTRODUCTION

Antenna system aspects are described after a review of a number of ESA satellite projects, in particular for (planetary) scientific missions and remote sensing applications. Antennas are needed for any satellite, telecom or microwave instrument functionality. Power resources onboard the satellites are limited and launch costs impose stringent requirements on several aspects for satellite sub-systems. Requirements for antennas are stringent for low mass, for environmental aspects related to exposure to harsh space conditions (temperature, radiation aspects, etc.) and survival of demanding launch-loads.

371 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 371–392. © 2005 Springer. Printed in the Netherlands.

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It makes a realisation of space antennas to an intriguing and demanding field of work. Satellite-antenna applications call for high accuracy, effective use of accurate design tools, specialised manufacturing and dedicated rf and environmental testing. When telecommunication antennas are used by satellites to transmit and receive client data geostationary or while orbiting the Earth, they must satisfy requirements for coverage. This often comes with a minimum gain requirement to be met within certain angular directions as seen from the satellite (coverage zone), while side-lobe control with maximum allowed levels is needed in directions outside the coverage. Alternatively, a number of independent beams might be required with sufficient isolation to serve different user areas. High power signals on transmission can co-exist simultaneously on the satellite with very weak signals in receive bands. This imposes a requirement for the antenna to be free of inter-modulation effects (PIM). When more transmitting carrier signals are used (serving different channels), passive intermodulation signals (weak signal) can be generated due to non-linear behaviour caused by physical hardware properties. Such a weak signal can appear as noise in one or more receiving bands at harmonic frequencies related to the different transmit signals. Such a situation is critical, when an antenna is used for both transmission and reception at the same time. In remote sensing applications, the antenna acts as microwave instrument sensor. It needs to be characterised sometimes in an absolute vector sense (amplitude, polarisation-state and phase) with requirements for stability over a long time, in different temperature situations in space. It leads to a necessity of accurate knowledge of absolute levels with minimum and maximum boundary constraints for complex radiation behaviour. Testing aspects can become very demanding and an example is given below with an antenna system for Cryosat. An example of results is presented to indicate progress in assessment of antenna performances, to indicate the accurate comparison between prediction and test results for phase measurements [8]. Other instrument sensor antennas are described in [8], are worth reading. High power concentration points may occur within antenna sub-systems. It could under certain conditions lead to voltage breakdown or multipaction, which may jeopardise functioning or even lead to damage. It requires careful design and testing if needed, to guarantee a multipaction-free antenna subsystem. Standards are developed [15] and dedicated workshops are organised by ESA in collaboration with national agencies [9]. Quasi optical techniques are employed by antenna systems operating at millimetre and sub-millimetre frequencies. Passive radiometers are an example where accuracy and coverage of certain frequency bands may call for

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channel de-multiplexing with reflecting and/or dichroic mirrors that act on Gaussian beams in, for example, a focal region of larger reflector systems. We introduced an application of polarisation considerations, using Laguerre expansions to represent vectorial field behaviour in a beam waveguide for millimetre wave radio-meters with a distinct set of modes [11]. The use of such methods is adopted in radio telescopes or ground-station antennas (beam-waveguides for instance). Alternative tools, based on general applicable and versatile physical optics analyses, have been made more and more accessible [12, 13], with clear progress shown in [14], using tools as described in [12]. The impact of reflection loss is important in radiometer antennas, in which small deviations in noise temperature must be determined. Examples are discussed of recent test results for samples related to the high performance, advanced composite reflector technology for the Planck project. The results have been obtained by the test facility at the Applied Physics Institute in Nizhny Novgorod. The latter facility was developed for testing reflection losses of mirrors and (diamond) windows for high power applications. Low reflection loss is very important in high power applications. We used the facility for measuring the reflection loss of reflector samples for extremely low power applications: the determination of reflection properties of advanced new composite and coated antenna materials for application in a radiometer antenna, for which a low reflection loss is mandatory. The application requires the receipt of extremely weak signals of cosmic background, which must be measured by the Planck project [6, 7]. The use of comparable tools and techniques for different applications is of interest, for example: analyses of beam-waveguides, multiband capabilities, and high accuracies in a determination of low reflection losses.

1.1

European Space Agency

Fifteen European countries work together in an inter-governmental organisation to provide and promote, for exclusively peaceful purposes, good boundary conditions for Space Science, Research and Technology and Space Applications. Space activities and programmes are elaborated with a long-term space policy and an industrial policy. Coordination takes place with national programmes. Certain directions are obligatory for participating members, for example, Space Science. There are also optional program elements, for telecommunications, for Earth remote sensing and for space transportation for example. It supports priorities within member-states. Successful developments can, after initial implementations, be transferred to new, specially established organisations, like Eumetsat for meteorological

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satellites, Eutelsat for telecommunication applications, Arianespace (rockets, launchers), Inmarsat for maritime telecommunication applications. ESA headquarters are located in Paris, France and the main technical centre, ESTEC is located in Noordwijk, The Netherlands. Other ESA establishments are ESOC for operation of satellites in Darmstadt in Germany, ESRIN in Frascati in Italy and VILSPA in Villafranca in Spain. More extensive information about ESA, its programmes and implementation is found on the website www.esa.int with various informative links to program elements, ESA establishments, ongoing satellite projects, (whether in preparation or in orbit), and information about educational programs [ref 1, 2, 3]. Several conferences and workshops, related to different technical topic areas, are organised. See [10] for a variety of subjects.

2.

ESA’S SCIENTIFIC SATELLITES

2.1

Past and Ongoing Satellite Missions

A number of ESA scientific satellites have been launched (more than 25), and an increasing amount of applications calling for data communication over larger distances [2], because several satellites are being sent much farther out into the planetary system. The first interplanetary satellite for ESA was Giotto, which was guided close to the comet Halley with dedicated navigation procedures, based on very long baseline interferometry (VLBI). Extensive international collaboration (Russia, NASA, and ESA) within the so-called pathfinder project allowed precise navigation of Giotto close to Halley’s comet. This was based on interferometric data processing of data received from satellites, which passed by Halley before Giotto did this (for instance the Russian Vega mission). Other ESA scientific satellite missions included Hipparcos for accurate astrometry and the Infrared Space Observatory (ISO), both orbiting the Earth in dedicated elliptical orbits. Hipparcos completed its astrometry mission in an orbit, which was not planned (due to a failure of an engine). The mission’s success was made possible thanks to dedicated ESOC orbit analyses. Antennas on-board these satellites are used for telecommanding and telemetry and for data down linking. Antennas for such tasks on such scientific spacecraft – in a near-Earth orbit and for the required data volume – have been often realised with a wide angular coverage: low-gain and broad radiation patterns are of interest in order to access the satellites under a variety of satellite orientations during such elliptical orbits. A wide radiation pattern also implies, that the effects of scattering and/or reflections of the satellite

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structure must be analysed in advance, in order to know the radiation performance of antennas, once they are placed on the satellite. It is important to understand the angular volume, in satellite coordinate frame, within which access for a link with the ground station on the Earth is possible. Such analysis task comes often back for every new satellite, because structures are different in configuration (with impact on the scattering). The interplanetary mission Ulysses was sent into a polar orbit around the Sun by means of gravity assistance from the planet Jupiter. Ulysses is now, in 2004, once again approaching Jupiter. Ulysses has a high gain S-X band antenna on-board and low gain antennas with cardioids-type of patterns. Power on-board the satellite is generated by a thermal-nuclear generator, because the distance to the Sun is too high to make efficient use of solar generators. The high gain S-X (dual) band antenna has a coaxial feed for S band with the X-band feed located in the central configuration of the coaxial S-band feed, slightly ex-centric located. The antenna permits finding information about pointing aspects, using information at S- and X-band assisted (almost like conical scanning. A picture and some other details are found in [16]. SOHO is the name of a satellite, which is navigated around the equilibrium point between the Earth and the Sun. The satellite monitors the Sun continuously and provides several first discoveries of comets plunging into the Sun. The link with the ground-station on the Earth is provided with an S-band mechanically moving reflector antenna. Cassini-Huygens is a NASA mission, jointly with ESA and the Italian Space Agency. Today, at the actual time of writing, Cassini entered into a Saturn orbit. The ESA provided element to the mission is a probe with instrumentation. This probe is expected to land on the moon Titan (on 14 Jan 2005). Some aspects are discussed below. There is collaboration with other agencies, in particular NASA. The Deep Space Network of NASA is used in a several cases for telecommunication and data-downlink of scientific data as recorded by the instruments on-board the satellites. Efforts are discussed between agencies worldwide for standard approaches for Deep Space telecommunications within committees like the CCSDS [4] to elaborate well-engineered, standardised approaches for space data handling systems (reduced cost/risk and permitting interoperability). Another ongoing satellite mission related to investigation of the space radiation environment is Cluster, a group of four satellites within Earth’s orbit with reception capability of low frequency signals. Long wire antennas are characteristic as receiving antennas on-board each satellite. The Newton mission (formerly called XMM) and the Integral mission are operating from a highly elliptical orbit around the Earth. Instrumentation on-

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board provides observation capacity at ultra-short wavelengths in the X-ray regime. Newton has been the heaviest scientific satellite so far launched by ESA (Ariane V). The dedicated developed technology for the high precision X-ray lens system on XMM has found derived applications for ultra high precision millimetre and sub-millimetre wave radio telescopes. The reflecting surface of a prototype for the ALMA radio telescopes was realised with ‘XMM-derived’ panel technology [17]. New technologies for potential future applications are investigated on dedicated small satellites. For instance, electric propulsion is expected for a future mission to Mercury (Bepi-Colombo mission). Electric propulsion is currently functioning and provides an early demonstration on the SMART-I satellite. This satellite SMART-1 is currently spiralling away from the Earth with the Moon as its destination, using an electro-propulsion engine. A new topic area related to antennas is being studied: if the radio frequency signal as generated by the electro-propulsion engine can be controlled, such an engine can be used as RF- beacon in space. This subject has been initiated by ESA and is being studied under General Study program. The first dedicated planetary mission of ESA is Mars-Express, currently orbiting the planet Mars and providing regularly high-resolution images. The telecommand and telemetry, as well as data downlinking are fully controlled by ESOC with the new ESA Deep Space Antenna, which was realised in Australia (New Norcia). The realisation of the latter ESA Deep Space Antenna was needed, because of the increased number of (inter-) planetary missions and with the NASA Deep Space Network more and more loaded.

Figure 1. High Gain Antenna for the Rosetta Satellite.

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Also the ESA mission Rosetta l, launched in early 2004, calls for the use of this Deep Space Antenna. Rosetta is expected to encounter a comet, to send a lander to the comet and to perform in-situ investigations, and this would be accomplished at a distance of several millions of kilometres away from the Earth. Fig.1 shows the high gain antenna for the Rosetta satellite. It operates in the allocated Deep Space telecommunication bands near 2 GHz (front-fed parabola) and near 8 GHz (Cassegrain configuration, with a dichroic sub reflector). The ground station antenna is an important element for such distant satellites and must perform with high reliability. The 35-meter antenna as constructed in Australia, provides accessibility for such distant satellite missions during several (about 6 to 8) hours a day. Optimum coverage for deep space missions requires antennas roughly spaced 120˚ apart over the globe, as is seen by NASA Deep Space Network with facilities in California (Goldstone USA), Spain and Australia. Currently ESA has a second ground station under construction near Madrid, Spain and a third station is under discussion.

Figure 2. ESA's first Deep Space Ground station Antenna in New Norcia in Australia.

Fig.2 shows a picture of the ESA 35 meter antenna. The schematic layout is shown in Fig.3. The dual reflector configuration is shaped for optimum efficiency and is fed by an S-X band beam-waveguide system inside the supporting tower. The beam-waveguide permits a rotation about elevation and azimuth axes with the rf radiation guided through the rotating junctions without little rf impact. Such beam-waveguide system can be optimised and analysed with dedicated tools, comparable to tools as applied elsewhere with quasi-optical

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techniques. Consultants from JPL have carried out initial design-studies for the antenna erected in Australia. They have been involved in support to the antenna contractor. Detailed analyses under ESA supervision have been carried out also in Europe, results of which have been published in a number of occasions [14, 19, and 20]. The structural design of the antenna was realised by German specialists of the Vertex team, who were formerly involved in the design of the millimetre wave radio telescope at Pico Veleta in Spain. A turning head antenna with very good and stabile properties resulted, capable to operate at S and X-band deep space frequencies. It has also been prepared in part for later operation at Ka-band (also an allocated deep space frequency band). AZIMLITH AXIS SUBREFLECTOR

MAIN REFLECTOR

ELEVATION PORTION

F1

M2, Paraboka

M1 ELEVATION AXIS

AZIMUTH PORTION

ELEVATIONBEARNGS

Kaband M4a, Dichroic M3, Paraboka M1, moves with Bard Az M4b, plane M2, M3, M4 move with Az M5, M6, M7 are not moving

F3

AZIMUTHEEAFINGS F2

NOTTOSCALE

M8, Dichroic

M7, plane M5, Elipse

X-band S-band

PEDESTAL

Figure 3. Schematic Layout of the Deep Space Antenna of fig.2.

Fig.4 shows the pattern predictions for S- band frequency derived with GRASP8 antenna software, based on physical optics. Fig. 5 shows results for X-band. The influence of the complex response of the dichroic sub-reflector

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is included in the analysis. In general, the offset geometry of the larger elliptically shaped reflector in the bottom of the beam-waveguide system, leads to some cross-polarisation level. The dichroic reflector is all-metal for low-loss and power handling reasons.

Figure 4. Deep Space Antenna Performance Prediction (S-band) [20].

It separates S- and X-bands and has a certain transfer/reflection response as a function of the angle of incidence. The overall cross-polarisation of a beam-waveguide depends on this. Final performances have been analysed and show an increase in cross-polar level, within specifications [19, 20]. Final performances are functional for the application and with the robust mechanical construction a reliable ground station antenna has been realised.

Figure 5. Deep Space Antenna Performance Prediction (X-band).

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Early July 2004, the Cassini satellite will be put into orbit around Saturn. A few months later, orbit insertion around the moon Titan will follow. The ESA provided probe named Huygens, will be detached from the Cassini spacecraft and land on the moon Titan. The probe will carry out several measurements during the landing, whilst hanging under its parachute, if it survives the landing, and if there is battery power left after the landing. The measured data are transmitted to the Cassini spacecraft in orbit around Titan. Cassini receives the data with its high gain telecommunication antenna and stores it in its on-board memory. After the landing of Huygens on Titan, the Cassini spacecraft will be reoriented towards the Earth and will relay the data from its mass memory towards the Earth, using the NASA Deep Space Network. Huygens transmit power is about 10 watts and a residual carrier will have a strength of several watts. If it were possible to receive this weak signal on Earth in a narrow bandwidth of 1 Hz, this weak signal would require a very large aperture (>70 m). ESA, under its General Study program, has requested investigation of the feasibility of the signal reception using Very Long Baseline Interferometry (VLBI) techniques. The study results indicated such feasibility [5]. Following this, proposals have been submitted by JIVE for observation time at radio telescopes to the necessary supervising radio-astronomical entities (NRAO, EVN, and Australia). The receiving and recording capacity at the observing stations during the landing of Huygens on Titan needs some adaptation, (as of June 2004), but the initial plan is nearing completion. ESA is discussing with the Joint VLBI Institute (JIVE) in Europe in such a way, that JIVE oversees and elaborates the implementation of such unique experiment to receive the weak residual carrier. JIVE operates the most advanced 20-channel correlator (www.jive.nl), capable also to handle Mark 5 data recording systems based on disks. This Huygens VLBI tracking experiment is in interesting contrast (extremely low power) with the subject of the NATO Advanced Study Institute on Quasi Optical Techniques for High Power Applications. The mentioned VLBI experiment will first demonstrate a recording of very low power flux density (the low watt carrier signal of Huygens, which is controlled in the Huygens probe by an ultra stabile oscillator). Furthermore, using VLBI techniques, very low signal to noise levels are possible at the different radio telescopes. Correlation processing provides an increase in dynamic range, it permits to subdivide the reception band in very narrow frequency bins, this with the reception band sampled at the Nyquist sampling rate. The predicted scientific result is, as indicated in the feasibility study under the ESA General Study Programme, that the landing trajectory of Huygens can be determined with a resolution close to a kilometre, when

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Huygens is hanging on its parachute and carried by the winds possibly present in the Titan atmosphere. As there is no telecommunication with the Cassini spacecraft during the landing, the reception of this carrier signal (on Earth) by means of radio telescopes, permits detection of activity by the Huygens probe, This is the only sign received by other means than by the Cassini spacecraft. A resolution of 1 kilometre at 1200.000.000 kilometres distance is two orders better than achievable with the Hubble Space Telescope. Such record resolution is possible thanks to a radio astronomical technique, called phase referencing. For the subject under investigation, usually an unknown radio-astronomical source, the weak Huygens signal is mapped against a celestial background, using so-called calibration sources within the angular field near the signal under observation. Such a technique permits observation with high (record) angular accuracy, thanks to the transfer of phase accuracy to the processing of the signal of interest. For details, one can consult the General Study Report on the ESA website www.esa.int.

2.2

Planned ESA Scientific Missions and Antenna Related Subjects

There are ESA planetary missions planned, like Venus Express and Bepi Colombo and possibly more to come. A second Deep Space Antenna, similar to the one discussed above, is under construction now in Spain. Its planned use is for data downlink in X-band for Venus Express. S-band is not implemented in this new ground-station antenna, only X-band, and in the future--Ka-band. The Venus Express mission relies on recurrent use of technologies as developed for the Mars Express mission. The high-gain antenna for Venus Express is different in size (thus in gain) and material properties. Venus is closer to the Sun, therefore, the thermal constraints imposed different resins for the reflector and dichroic sub-reflector. A dual frequency band operation with dedicated dichroic, associated optimisation processes, low loss, and technology implementations are of generic interest. Details about the Mars-Express and Venus Express high gain antenna are found in [21]. For the Bepi-Colombo satellite planned for launch towards Mercury, requirements are more demanding, being so close to the Sun, at 30% of the Earth to Sun distance, thus a factor 9 increase in radiation intensity from the Sun, compared to near-Earth orbits. The environmental temperatures can be high (or low during planet occultation) and dedicated processes, technologies and mechanisms are needed for such high gain antenna. Additional stringent

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requirements include high accurate rf-performances for radio science experiments (amplitude and phase stability), which will permit accurate ranging data. The antenna is therefore investigated to develop necessary technologies. Bepi-Colombo is an international co-operation, based on the reciprocity of information and data exchange, and no exchange of funds between ESA and JAXA [22]. The Huygens experiment mentioned earlier (VLBI-tracking of the carrier signal coming from the probe), leads to novel and interesting navigation capabilities for planetary missions. This is important when it comes to accurate determination of angular windows for insertion into planetary orbits. Current recommendations (ǻ-DOR) to derive navigation data are described in [4]. Strong signals are transmitted with dedicated tones modulated on the carrier signal by the spacecraft and strong radio astronomical sources are used as celestial reference during interferometric observation with a number of Earth station antennas. The weak calibration sources employed during the Huygens experiment call for broadband observation of celestial reference sources for calibration purposes and so, a weak signal coming from the probe is compared in angular position with such reference sources. It may result, in the future, that monitoring of weak systematic signals of for instance, small satellites, probes or planetary landers permit accurate navigation, using VLBI techniques and phase referencing, and using celestial sources as a reference. Alternatively, exploiting the range of other parameter settings within the chain, potentially low-bit rate data links may be established and exploited. By using such interferometric techniques, in such a case one might use low gain antennas potentially, which is obviously convenient on-board a small satellite. In this context, an initial study deserves to be mentioned by the University of Toronto within ESA’s Aurora program. [35]. A number of radio astronomy satellites worldwide are being prepared for a mission in an orbit location close to the Sun-Earth equilibrium point L2 (Lagrange point). The L2-point is located about 1500000 kilometres away from the Earth in the direction away from the Sun. The location would permit un-obscured observation capability during the whole year of a celestial angular volume directed away from the Sun. This angular volume of observation moves with the Earth-Sun direction around the Sun during the year. Cosmic background radiation is measured today by the NASA mission MAP [23]. ESA has the mission Herschel (near-infrared sub-mm observatory) and Planck in a realisation phase for launch in 2007. Herschel will carry a Cassegrain telescope-antenna, realised with CSIC technology. It has a primary mirror (3.5 m diameter) [24] and in the secondary focus cooled detectors operating at -271 Kelvin. It is the largest telescope of its type ever

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built and is realised in Europe within a contract activity between ESA and Atrium in Toulouse (France). The Planck satellite will measure cosmic

Figure 6. (left) Planck Satellite Configuration with radio-telescope antenna inside a baffle.

Fig. 6 shows the Planck satellite configuration with the dual reflector antenna subsystem with an effective aperture diameter of about 1.5 meters. The surface accuracy of the Planck telescope antenna is below 10 µm and the antenna system is located within a baffle to have very low impact of stray radiation. For more details, consults [25]. We have carried out highly accurate measurements of reflection loss on samples of both Planck reflector and baffle material. The conclusions of the tests were that there could be interesting phenomena: a baffle material well suited for optical applications, appeared to have two times higher reflection loss at millimetre wave frequencies than the expected losses (a type of

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aluminum). For instance, the backside of the baffle material, also aluminum but not very pretty, appeared to be very good. It had very low reflection losses, almost comparable to values as expected from pure aluminum (fig.7). The Planck reflector is realised with dedicated composite materials (resins and carbon fibre), coated with dedicated materials and vacuum deposited aluminium. The finishing layer (plasil), deposits in vacuum, and protects the aluminium from corrosion. (Fig.9) The measurements have been carried out in the Applied Physics Institute (Fig.7, 8) in a band (100 – 200 GHz).

Figure 7. Schematic Description of Highly Accurate Reflection Loss Measurement Facility of Applied Physics Institute, Nizhny Novgorod, courtesy V. Parshin.

Reflectivity testing of composite materials with surface coatings is important to demonstrate actual values of the reflection losses. Extrapolation from tests carried out in a particular frequency band to expected results in another frequency band cannot be guaranteed, so testing in other frequency bands is therefore recommended [6,7]. For further details concerning ESA’s satellite missions within the scientific satellite program, the reader is (again) referred to the website www.esa.int under the science projects.

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Figure 8. Quasi-Optical Test Facility at Applied Physics Institute in Nizhny Novgorod.

Figure 9. Results of reflection loss measurement of two samples (picture left) of Planck telescope reflector material (indicated with x and +) and baffle material (squares, backside of sample) and three curves for aluminum and silver as calculated and measured with calibration mirrors of Applied Physics Institute, courtesy V. Parshin, N. Novgorod.

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EXAMPLES OF ANTENNAS FOR REMOTE SENSING SATELLITES

A few sophisticated Earth Observation satellites have been into space, starting with meteorological satellites like the spinning Meteosat satellites (MOP - Meteosat Operational and its successor Meteosat Second Generation or MSG) [26]. A cylindrical electronically despun antenna keeps an antenna beam pointed towards the Earth, while the satellite is spinning at 100 revolutions per minute. (With every revolution one line is recorded, for an image of the Earth to be built up). For MSG one has expanded on imaging and spectral capability, compared to earlier MOP satellites. The electronically despun antenna mentioned, has been used in Europe for more than 25 years in Meteosat satellites. Moreover, for MSG, the UHF data collection function has also been realised with a cylindrical-switched UHF cylindrical antenna with crossed dipoles as elements. Electronically despinning doesn’t disturb the acquisition of the image; it has no mechanical movement in the antenna. The L-band antenna transmits the raw measured data towards the Earth and transmits processed images (which are up linked for re-distribution) to users. The antennas are described in [27]. Active remote sensing has seen strong developments in Europe with satellite missions like ERS-1 and ERS-2, which provided synthetic aperture radar data over a period more than 10 years. The active microwave instrument (AMI) on-board the ERS satellites can be connected to either the Wind-Scatterometer Antennas (WSA-mode) or to a Synthetic Aperture Radar antenna (SAR-mode), using a microwave-switching matrix. The latter switch-matrix routes the pulsed high-power (5.2 kilowatt peak) to the WSA or SAR antennas as necessary. During the development phase, a lot of attention has been spent to multipactor issues for components, for the switching matrix and for the antennas. With at that time novel technologies for the antenna, the critical locations for multipactor were investigated by analysis and by testing. One example is the main coupling slot in the slotted waveguide SAR antenna. The radiation characteristics of the 10 m long SAR antenna have been thoroughly tested before launch, even in full polarisation sense, although the antenna is polarised linearly (vertically). The planar near-field (ESA-Ericsson) facility has been used. ERS exploits only a single, vertical polarisation [16, 28]. Subsequent studies have allowed investigating limited multi-beam capabilities of SAR antennas, using low-loss, slotted waveguide approaches, as described in [29, 30, 31, 32, 33]. Although accurate tools were developed for passive slotted waveguide antennas [31], the passive antenna was abandoned. An active SAR antenna was developed for the next SAR missionENVISATof ESA. Slotted waveguide design tools 31]were used

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within the SAR instrument for the Cassini mission by Alenia and slotted waveguide developments [32] and derived configurations contributed to very early developments for the dual-polarised slotted waveguide antenna configuration currently implemented in the active phased array configuration for TerraSAR-X [34]. A recent development for SAR antennas is based on an interesting hybrid type of approach. A reflector antenna is realised with a limited, dedicated set of beams to cover about 80 to 100 km wide strip in scansar mode, or 20 km in high-resolution strip map mode. Rolling of the satellite permits access to a range of incidence angles on the ground. Again, multipaction is an issue to be taken into account. Such type of approach permits to arrive at a simple satellite configuration, which can possibly be launched by a small (cheap) launcher [40]. A recent example of highly accurate prediction, manufacturing and realisation is presented with the antenna sub-system for the interferometric radar altimeter (SIRAL instrument) for Cryosat mission [8].

Figure 10. Cryosat SIRAL Antenna Configuration (Courtesy Saab-Ericsson).

The reader is referred to www.esa.int for background information about Earth observation missions. Accurate prediction results and verification by measurement have been presented, with some examples in [8] and are repeated here in part (courtesy Saab-Ericsson).

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phase diff 0.6 0.5 0.4 0.3 0.2 0.1 -0.8

-0.6

-0.4

0 -0.2 -0.1 0

0.2

0.4

0.6

0.8

-0.2

Figure 11. SIRAL Antenna System Phase Distribution, predicted with GRASP (left) and Measurement (along Horizontal line) [8].

Progress in both modelling and antenna testing is reflected by such results (fig.11, 12). Note that accurate antenna measurements of phase distributions require additional verification techniques to determine effects of the test range. Also. the modelling of the antenna performances requires accurate assessment of all necessary details to be included in the antenna model (analysed with GRASP [12]). Requirements placed on phase response of the antenna sub-system have been several times more stringent than what is normally encountered for telecommunication applications. Thus, SIRAL antenna technology (fig.10) is of interest for telecommunication applications at higher frequency bands (Ka-band and above like Q and V band).

Figure 12. SIRAL Antenna System Phase Difference Distribution as Measured [8].

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Correcting mirrors are discussed elsewhere in this paper. An approach is discussed, based on phase retrieval from a set of amplitude measurements. In antenna testing, phase retrieval is pursued for accurately setting the reflector panels of (sub) millimeter wave radio telescopes. We have explored the implementation of a technology based on a flexible membrane, for correcting the wave front of a (sub) millimeter wave radiometer antenna and demonstrated this in a laboratory test configuration. Artificial assumptions were made for a main-reflector assembly, which could suffer deformations based on in orbit thermal situations. A correctable sub reflector was introduced to correct for such deformations. It has been demonstrated that such approach can assist in correcting (compare to correcting mirrors in a gyrotron). For antenna applications, such technique can also be useful for applications as shaping of the beam and/or pointing correction or high accurate pointing of the beam. Correction of deformation errors has been demonstrated and thus it contributed to a better behavior of the dual reflector radiometer antenna. The necessary surface shape for the correcting mirror was derived with standard antenna synthesis techniques and we know that in this situation, there are more methods to derive the surface. A further optimization in the process was made, using Zernicke polynomial expansion, to arrive at convenient sample point settings for actuators for a set of deformation configurations to be corrected. The technological implementation includes considerations of membrane material and thickness aspects and adaptability for a set of different deformation cases. The result shows flexibility and a controllability of the membrane [39, 41, 42]. The nickel electroforming technique has been used for a prototype, sub-millimeter wave radio telescope in the ALMA project, as reported in [38]. Such new, advanced technologies are of generic interest. In [36] other complimentary references are found for antennas for remote sensing applications. This topic is too broad to include in this discussion. Rf instruments are as accurate as their calibration. Calibration is very important. For calibration in orbit of SAR instruments, one uses active calibrators or passive corner-reflectors. We did elaborate with investigations the use of reflector antennas (a deviating type of target) for calibration of radar cross section for SAR. In [37] these passive reflector antennas are discussed as potential calibrator and as shown recently, a relatively interesting result has been obtained. ERS SAR observations have assisted us to receive better knowledge of the properties of such calibrators.

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CONCLUDING REMARKS

Some antenna applications and related developments have been discussed in the context of mission applications. The subject is too extensive to be complete in a short exposition such as this. Only scientific and remote sensing satellite applications have been dealt with. References indicate a way to further information. It is shown, that several interesting antennas have been realised within ESA activities and that there is more to come. The use of comparable tools and techniques for different applications (antenna field or high-power applications) is of interest, like for instance (crosspolarisation) analyses of beam-waveguides, multiband aspects, and high accuracies in determination of low reflection losses.

5.

REFERENCES

[1]

ESA General Information: http://www.esa.int

[2]

ESA General Information on Scientific Satellites: http://www.esa.int/esaSC/index.html

[3] [4] [5]

ESA Education Programme: http://www.esa.int/esaED/index.html. http://www.ccsds.org/ In ESA Scientific Publication SP-544, obtainable from ESA, 2004. ‘VLBI Tracking of the Huygens Probe in the Atmosphere of Titan’, S.V. Pogrebenko, L.I. Gurvits, R. M. Campbell, I. M. Avruch, J.-P. Lebreton, C.G.M. van’t Klooster. Proceedings of ICATT 2003, September 2003, Conference Proceedings,, Sebastopol

[6]

‘Reflectivity of Antenna and Mirror Reflectors between 110 and 200 GHz’, Svetlana E. Myasnikova, Vladimir V. Parshin, Kees van ‘t Klooster, G.Valsecchi, [7] Proceedings of Antennas and Propagation Symposium, Columbus, USA June 2003, ‘Reflectivity of Antenna Reflectors: Measurements at Frequencies between 110 and 200 GHz’, C.G.M. van ‘t Klooster, V.V.Parshin, S.E.Myasnikova, [8] Proceedings EUSAR 2004, 25-27 May, Ulm Germany, ‘SIRAL Antenna Design and Performance of the SAR Interferometer Radar Altimeter Antenna Subsystem for CRYOSAT Mission’, M. Baunge, H. Ekstrom, M. Lindholm, M. Petersson, V. Sohtell, K. Woxlin, (Saab Ericsson), J.C.Angevain, P.deChateau-Thierry, J.David, L.Phalippou, L. Rey (Alcatel Space). [9] http://www.estec.esa.nl/conferences/03C26/index.html [10] http://www.estec.esa.nl/conferences/past_events.html [11] Proceedings Journees Internationales de Nice sur les Antennes (JINA), France, 1990. ‘Analysis of a Reflector Antenna with Quasi-Optical Front-End using Gaussian Beams’, G.A. van Dooren, C.G.M. van ‘t Klooster. [12] http://www.ticra.com and find information about software like GRASP for antennas.

[13] Proceedings of IEEE Antennas and Propagation Symposium, San Jose, 1990, ‘Physical Optics Analysis of a Beam Waveguide with Six Reflectors’, P.S.Kildal, J.Kuhnle, C.G.M. van ‘t Klooster, R. Graham.

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[14] Proceedings of IEEE AP Symposium, Salt Lake City, July 2000, USA, ‘Analysis of Beam Waveguides for Reflector Antenna Systems’, M. Lumholt, K. Pontoppidan, K. van ‘t Klooster. [15] Proceedings of ESA Workshop on Multipactor and PIM, Sept. 2003, Estec, Noordwijk The Netherlands (http://www.estec.esa.nl/conferences/03C26/index.html), ‘An ECSS-E-20-01A Compatible Software Tool for the Evaluation/Prediction of Multipactor Breakdown for Single- and Multi-Carrier Signals’, S. Strijk (ESA/Estec). [16] Proceedings Journees Internationales de Nice sur les Antennes (JINA), France, 1990. ‘Antennas for Remote Sensing and Scientific Satellites’, C.G.M. van ‘t Klooster, N.E.Jensen, (invited paper). [17] Proceedings of the ICATT2003 Antenna Conference, Sebastopol, Ukraine, 2003, ‘A Spin-Off of Space Technology: Highly Accurate Reflector Panels for a Prototype ALMA Radio Telescope’, Kees van ‘t Klooster, Giuseppe Valsecchi, Josef Eder. [18] Proceedings of IEEE Antennas and Propagation Symposium, Columbus, 2003, USA. ‘A Reconformable Reflector for a Sub-Millimetre Wave Reflector Antenna’, C.G.M. van ‘t Klooster, F. Zocchi, P. Binda, H.H. Viskum. [19] Proceedings of ESA Workshop on TT&C, Estec 29-31 October 2001, Noordwijk. ‘Analysis of Frequency Selective Surfaces in Beam-waveguide Antenna’, M. Lumholt, K. Pontoppidan, K. van ‘t Klooster, P. Besso. [20] ESA Contract Report S-1005-03, ESA-Contract 13400/98, by Ticra. ‘Extended Analyses of the 35 m ESA Deep Space Antenna’, M. Lumholt. [21] Proceedings of 27th ESA Antenna Workshop on Innovative Periodic Antennas, Santiago de Compostela, 9-11 March 2004. ‘Mars Express and Venus Express High gain Antennas’, Caballero, R ; Palacios, C; Encinar, J. [22] http://www.esa.int/export/esaSC/120391_index_0_m.html or http://www.esa.int/science/bepicolombo and http://www.stp.isas.jaxa.jp/mercury/ [23] http://map.gsfc.nasa.gov/m_mm.html [24] http://www.esa.int/science/herschel [25] http://www.esa.int/science/planck

[26] http://www.eumetsat.de [27] Proceedings Conference Mathematical Methods in Electromagnetic Theory (MMET), ‘The Antenna Sub-System for Meteosat Second Generation Satelliktes, Modelling Tools and Needs’, C.G.M van ‘t Klooster, M. di Fausto, I. Florio, A.Rosa, B.Robert, VIIIth MMET, Kharkov, Ukraine, 2000, invited paper. [28] Proceedings Journees Internationales de Nice sur les Antennes (JINA), France, 1992. ‘ ERS-1 Antenna Performances in Orbit’, C.G.M. van ‘t Klooster, F.O. Aidt. [29] Proceedings of IEE – ICAP Conference, York, UK, 1991. ‘ A Dual-Beam Slotted Waveguide Array Antenna for SAR Applications’, M. Bonnedal, I. Karlsson, C.G.M. van ‘t Klooster. [30] Proceedings of IEEE Antennas and Propagation Symposium, London, Canada, 1991. ‘Multiple Beam Slotted Waveguide Antenna for Spaceborne Synthetic Aperture Radar’ C.G.M. van ‘t Klooster, M. Bonnedal, I.Karlsson, N.Chr. Albertsen. [31] Proceedings of PIERS Conference, 1994, Noordwijk, The Netherlands, ‘A Compound Slot Waveguide Array’, N. Chr. Albertsen, e.a. [32] Proceedings of IEEE Antennas and Propagation Conference, Chicago, USA, 1992. ‘Dual polarised Slotted Waveguide SARantenna’, L.Josefsson, C.G.M. van ‘t Klooster. [33] ESA Technology Quarterly, Preparing for the Future, Nr.1, September 1991. ‘Dual Beam Slotted Waveguide Antenna’, C.G.M. van ‘t Klooster.

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[34] Proceedings EUSAR 2004, 25-27 May, Ulm Germany, ‘The TerraSAR-X Mission’, R. Werninghaus, e.a. [35] University of Toronto, General Studies, www.esa.int/GS http://www.utias-sfl.net/SpecialProjects/ARTEMISIndex.html [36] Proceedings of Conference, 12-14 April 1999, ‘Perspectives on Radio Astronomy: Technologies for Large Antenna Arrays’ edited by A.B. Smolders, M.P.van Haarlem, www.astron.nl [37] In Proc. JINA Conference, Nice 1998, ‘On the Use of Ground-Based Parabolic Reflector Antennas for External Calibration of Space-borne SAR’, van ‘t Klooster, C., Zherdev, P.A., Borisov, M, Gusevski, V, Zakharov, A.I., Buck, C.H. [38] In: Proc. of IEEE Antennas and Propagation Conf., ’High Precision Electroformed Nickel Panel Technology for Submillimetre Radio Telescope Antennas’, G. Valsecchi, J. Eder, G. Grisoni, C. van ‘t Klooster, L. Fanchi, 2003, Columbus, Ohio, USA. [39] In: Proc. of IEEE Antennas and Propagation Conf., ‘A Reconformable Reflector for a Sub-mmwave Reflector Antenna’, F.Zocchi, P.Binda, H.H.Viskum, van ‘t Klooster, K. [40] Proceedings EUSAR 2004, 25-27 May, Ulm Germany, ‘A Low Cost Mutlifeed Antenna’, Chr.Heer, B. Grafmueller, L. Kanderhag, M.Viberg, Kees van ’t Klooster. [41] Proceedings of 25th ESA Antenna Workshop Estec, 18-20 September 2002, Noordwijk. “Reconformable Sub-reflector for Sub-Millimetre Wave Radiometer”, F.Zocchi, G.Valsecchi, H. Viskum, K. van ‘t Klooster. [42] In AIAA Proceedings, Yokoma, April, 2003, Japan, “Corrective Sub Reflector for Millimetre and Sub-Millimetre Wave Appplications”, H.H. Viskum, C. van ‘t Klooster, F. Zocchi, P.Binda, R. Wagner.

INTENSE MICROWAVE PULSE TRANSMISSION THROUGH ELECTRICALLY CONTROLLED FERRITE PHASE SHIFTERS

N. Kolganov1, N. Kovalov1, V. Kashin2, E. Danilov2 1

Institute of Applied Physics, Nizhny Novgorod, Russia; Special Design Bureau “Almaz”, Moscow, Russia.

2

Abstract:

Transmission of X-band ~1 MW pulses through a Faraday phase shifter is followed by (a) distortion of the RF envelope if pulse is longer than ~ 10 ns, and (b) reduction of the phase shifter effective electric length after a series of pulses. The ferrite degradation is reversible: after a cycle of magnetization, the pulse form is reproduced. These effects should be taken into account at designing ferrite lenses for high-power microwave pattern control.

Key words:

high power microwaves, beam scanning, phase shifter, ferrites, pulse energy limitation.

Electrically controlled ferrite phase shifters usually operate with the RF magnetic field H small compared with the coercive field H c . However in high power pulsed microwave systems the latter condition may be violated. This paper describes results of an experiment [1] with a Faraday phase shifter that operated under condition H !! H c . The phase shifter is represented by a section of circular cross section waveguide filled with a ferrite 3C418. The input RF pulse (shown in Fig. 1) had a carrier frequency of 10 GHz, a peak power up to 1 MW, and a duration near 20 ns; however, because of intra-pulse modulation, the bandwidth was ~100 MHz.

393 J. L. Hirshfield and M. I. Petelin (eds), Quasi-Optical Control of Intense Microwave Transmission, 393–398. © 2005 Springer. Printed in the Netherlands.

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Figure 1. Envelope of pulse incident onto the phase shifter.

Figure 2. Envelope of pulse transmitted through phase shifter with I = 0q.

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Figure3. Envelope of pulse transmitted through phase shifter with I = 650q.

For these tests, the residual magnetization direction coincided with the direction of wave propagation. The H11 wave mode was circular polarized, but at the ends of the phase shifter it was converted into the H 10 mode of rectangular cross section waveguide. Before injection of the microwave pulse, the ferrite was magnetized by means of a procedure shown in Fig. 4: x at first a negative sufficiently-large external field H 0 put the ferrite from a previous state BS ' to the saturated state 1; x then a positive external field H 0 put the ferrite into state 2; x finally the external magnetic field was put to zero and the ferrite came to the operating state B S . During RF pulse transmission, the external magnetic field was absent.

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2 BS

BS '

1

Figure 4. Ferrite magnetization procedure within the saturated magnetization loop. (Hc = 0.9 Oe, Br = 1.4 kG).

The dependence of the effective electric length of the phase shifter on the residual magnetization was measured by means of a special low power microwave scheme, before and after a sequence of RF pulses, with the switching and measurements performed during 3-4 minutes. For definiteness, the length I 0 was attributed to the residue magnetization B0  Br | 1400 Gs . Correspondingly, the residual magnetizations B0 Br | 1400 Gs and B0 Br 0 resulted in I 650q and I 360q lengths. The measurement precision was within r 2q . Compared to the input pulse, the output pulse was shortened and distorted, as shown in Figs. 2 and 3, presumably owing to excitation of ferrite spin waves. After re-magnetization of the ferrite to its primary state, the pulses were reproducible. After transmission of a sequence of microwave pulses through the phase shifter, its electric length changed, as shown in Figs. 5 and 6; but later, i.e., after a few days, it remained constant. After transmission of a train of pulses, the larger the initial magnetization of the ferrite, the larger was found

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to be the defect in the electric length. After a magnetization cycle (see Fig. 4) the ferrite returned to its primary state.

Figure 5. Dependence of defect in electric length for I

'I

on the number of pulses in a train N

90 q ; curves 1-5 correspond to peak powers of 50; 100; 200; 400 and 800 kW respectively.

Figure 6. The same as as Figure 5, but for I

0q .

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Thus, the ferrite degradation after high power microwave pulse transmission is seen to be reversible. To reduce the degradation, it is necessary to limit the RF pulse energy. For instance, a lens composed of the above described phase shifters might scan wave flows of ~1 MW/cm2 density, if the pulse duration were in the range 5-8 ns.

REFERENCE 1.

E.A.Danilov, V.A.Kashin, N.F.Kovalev, H.G.Kolganov, Electronika (In Russian). 2001. v.46, N8, pp. 1007-1010.

Radiotechnika

and

INDEX OF AUTHORS

Kalynova, G, 3, 15 Kapilevich, B. 25 Kashin, V. 393 Kasparek, W. 115, 241 Katsenelenbaum, B. 65 Kharchev, N. 115 Kinkead, A. 199 Kirilenko, A. 41 Koldanov, V. 199 Kolganov, N. 393 Kolik, L. 115 Korchemkin, Yu. 165 Korovin, S. 131 Kovalev N. 95, 177, 393 Kulik, D. 41 Kumric, H. 241 Kusyi, O. 65 Kuzikov, S. 147, 199 Lapierre, L. 305 LaPointe, M. 147, 199 Laqua, H. 241 Leuterer, F. 241 Likin, K. 115 Lisak, M. 305 Litvak, A. 147 Lobaev, M. 199 Lukovnikov, D. 147 Lurie, Y. 253 Malygin, V. 3, 147 Martín, R. 115 Mesiats, G. 283 Michel, G. 241, 325 Milevsky, N. 165 Neilson, J. 55 Nezhevenko, O. 147, 199 Petelin, M. 147, 185, 283 Petrov, A. 115 Phelps, A. 105, 131

Abubakirov, E. 95 Anderson, D. 305 Arnold, A. 325 Batanov, G. 115 Belousov, V. 3 Blyakhman, A. 273, 283 Bogdashov, A. 15, 147 Bratman, V. 105 Bruns, W. 73 Buyanova, M. 305 Caryotakis, G. 185 Chirkov, A. 3, 147 Clunie, D. 283 Cross, A. 105 Dammertz, G. 241 Danilov, E. 393 Denisenko, V. 165 Denisov, G. 3, 15, 105, 147 Drumm, O. 325 Erckmann, V. 241 Fedorov, V. 165 Fernández, A. 115 Fix, A. 147 Gantenbein, G. 241 Ginzburg, N. 131 Gold, S. 199 Golubiatnikov, G. 297 Gorbachev, A. 199 Grünert, M. 241 Harris, R. 283 Henke, H. 73 Hirshfield, J. 147, 199 Holzhauer, E. 241 Ilin, V, 3 Isaev, V. 199 Ivanov, O. 199 Jin, J. 325 Jordan, U. 305

399

400 Pinhasi, Y. 219, 253 Piosczyk, B. 325 Plaum, B. 241 Popov, L. 3 Postoenko, G. 185, 283 Puech, J. 305 Rodin, Yu. 147 Rostov, V. 131 Rud, L. 41 Rzesnicki, T. 325 Samsonov, S. 105 Sarksyan, K. 115 Sazontov, A. 305 Schamiloglu, E. 177 Scheitrum, G. 185 Schwörer, K. 241 Semenov, V. 305 Serdobintsev, G. 147 Shishlov, A. 353 Shmelyov, M. 147

Index of Authors Sombrin, J. 305 Thumm, M. 325 Tkachenko, V. 41 Tolkachev, A. 353 Tulpakov, V. 95 Turchin, I. 185 Udiljak, R. 305 van’t Klooster, K. 371 Vdovicheva, N. 305 Vikharev, A. 199 Voitovich, N. 65 Wacker, R. 241 Wagner, D. 241, 325 Wardrop, B. 283 Weissgerber, M. 241 Yahalom, A. 219, 253 Yakovlev, V. 147 Yalandin, M. 131 Yang, X. 325 Yegorov, E. 353