SERIES IN PLASMA PHYSICS High Power Microwaves Third Edition James Benford John A. Swegle Edl Schamiloglu CRC Press Taylor & Francis Group High Power Microwaves Third Edition Series in Plasma Physics Other recent books in the series: Waves and Oscillations in Plasmas Hans L Pécseli Complex and Dusty Plasmas: From Laboratory to Space V E Fortov and G E Morfill Applications of Laser–Plasma Interactions Shalom Eliezer and Kunioki Mima Plasma Kinetic Theory D G Swanson High Power Microwaves, Second Edition J Benford, J A Swegle and E Schamiloglu Controlled Fusion and Plasma Physics K Miyamoto Plasma Electronics: Applications in Microelectronic Device Fabrication T Makabe and Z Petrović An Introduction to Inertial Confinement Fusion S Pfalzner Aspects of Anomalous Transport in Plasmas R Balescu Non-Equilibrium Air Plasmas at Atmospheric Pressure K H Becker, R J Barker and K H Schoenbach (Eds) Magnetohydrodynamic Waves in Geospace: The Theory of ULF Waves and their Interaction with Energetic Particles in the Solar-Terrestrial Environment A D M Walker Plasma Physics via Computer Simulation (paperback edition) C K Birdsall and A B Langdon Plasma Waves, Second Edition D G Swanson Microscopic Dynamics of Plasmas and Chaos Y Elskens and D Escande Plasma and Fluid Turbulence: Theory and Modelling A Yoshizawa, S-I Itoh and K Itoh The Interaction of High-Power Lasers with Plasmas S Eliezer Introduction to Dusty Plasma Physics P K Shukla and A A Mamun Series in Plasma Physics High Power Microwaves Third Edition James Benford Microwave Sciences, Lafayette, California John A. Swegle J-Two, Aiken, South Carolina Edl Schamiloglu University of New Mexico, Albuquerque, New Mexico CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20151002 International Standard Book Number-13: 978-1-4822-6060-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com For Hilary and Eloise Benford Al, Gerry, and Jennifer Swegle Elmira and Selin Schamiloglu Contents List of Acronyms xiii Preface xv Authors xvii 1 Introduction 3 1.1 Origins of HPM 3 1.2 HPM Operating Regimes 5 1.3 Future Directions in HPM 12 1.3.1 Previous Trends 12 1.3.2 New Trends 13 1.4 Further Reading 14 References 14 2 Designing High Power Microwave Systems 17 2.1 Systems Approach to High Power Microwaves 17 2.2 Looking at Systems 19 2.3 Linking Components into a System 20 2.3.1 Prime Power 21 2.3.2 Pulsed Power 23 2.3.3 Microwave Sources 24 2.3.4 Mode Converter and Antenna 26 2.4 Systems Issues 27 2.5 Scoping an Advanced System 29 2.5.1 NAGIRA: Prototype for the SuperSystem 30 2.5.2 Constructing a SuperSystem 31 2.5.3 Antenna and Mode Converter 32 2.5.4 Backward Wave Oscillator 33 2.5.5 Pulsed Power Subsystem 34 2.6 Conclusion 39 Problems 39 References 39 3 High Power Microwave Applications 41 3.1 Introduction 41 3.2 HPM Weapons 41 3.2.1 General Aspects of HPM Weapons 43 3.2.2 E-Bombs 48 3.2.3 First-Generation HPM Weapons 49 3.2.3.1 Active Denial 49 3.2.3.2 Neutralizing Improvised Explosive Devices 50 3.2.3.3 Vigilant Eagle 51 3.2.4 Missions 52 3.2.5 Electromagnetic Terrorism 53 3.2.6 Coupling 55 3.2.7 Counter-DEW 56 3.2.8 HPM Effects on Electronics 57 3.2.9 Conclusion 61 3.3 High-Power Radar 61 3.4 Power Beaming 62 3.5 Space Propulsion 67 3.5.1 Launch to Orbit 67 3.5.2 Launch from Orbit into Interplanetary and Interstellar Space 71 3.5.3 Control of Large Space Structures 73 3.5.4 Power Beaming Systems Cost 75 3.5.5 Economies of Scale 77 3.6 Plasma Heating 77 3.6.1 Sources for ECRH 81 3.7 Particle Accelerators 81 Problems 86 References 87 4 Microwave Fundamentals 93 4.1 Introduction 93 4.2 Basic Concepts in Electromagnetics 93 4.3 Waveguides 95 4.3.1 Rectangular Waveguide Modes 97 4.3.2 Circular Waveguide Modes 101 4.3.3 Power Handling in Waveguides and Cavities 104 4.4 Periodic Slow-Wave Structures 110 4.4.1 Axially Varying Slow-Wave Structures 110 4.4.2 Azimuthally Varying Slow-Wave Structures 113 4.4.3 Metamaterials for Dispersion Engineering 117 4.5 Cavities 119 4.6 Intense Relativistic Electron Beams 122 4.6.1 Space-Charge-Limited Flow in Diodes 123 4.6.2 Beam Pinching in High-Current Diodes 125 4.6.3 Space-Charge-Limited Electron Beam Flow in a Drift Tube 125 4.6.4 Fedosov’s Solution for the Current Limit from a Magnetically Insulated Coaxial Diode 127 4.6.5 Beam Rotational Equilibria for Finite Axial Magnetic Fields 128 4.6.6 Brillouin Equilibrium of a Cylindrical Electron Beam 129 4.7 Rotating Magnetically Insulated Electron Layers 130 4.8 Microwave-Generating Interactions 132 4.8.1 Review of Fundamental Interactions 132 4.8.2 O-Type Source Interactions 133 4.8.3 M-Type Source Interactions 137 4.8.4 Space-Charge Devices 138 4.9 Amplifiers and Oscillators, High- and Low-Current Operating Regimes 140 4.10 Phase and Frequency Control 141 4.10.1 Phase Coherent Sources 143 4.11 Multispectral Sources 143 4.12 Summary 144 Problems 145 References 146 5 Enabling Technologies 151 5.1 Introduction 151 5.2 Pulsed Power 151 5.2.1 Explosive Flux Compressors 156 5.2.2 Linear Induction Accelerators 159 5.2.3 Magnetic Stores 160 5.2.4 Summary 161 5.3 Electron Beam Generation and Propagation 161 5.3.1 Cathode Materials 161 5.3.2 Electron Beam Diodes and Electron Beam Propagation 165 5.4 Microwave Pulse Compression 166 5.5 Antennas and Propagation 170 5.5.1 Mode Converters 170 5.5.2 Antenna Basics 172 5.5.3 Narrowband Antennas 175 5.5.3.1 Compact High-Power Narrowband Antennas 178 5.5.4 Wideband Antennas 179 5.6 Diagnostics 180 5.6.1 Power 181 5.6.2 Frequency 181 5.6.2.1 Heterodyne Detection 181 5.6.2.2 Time–Frequency Analysis 182 5.6.3 Phase 182 5.6.4 Energy 183 5.6.5 Mode Imaging 184 5.6.6 Plasma Diagnostics 185 5.7 Computational Techniques 187 5.8 HPM Facilities 189 5.8.1 Indoor Facilities 189 5.8.2 Outdoor Facilities 190 5.8.3 Microwave Safety 192 5.8.4 X-Ray Safety 194 5.9 Further Reading 194 Problems 194 References 196 6 Beamless Systems 201 6.1 Introduction 201 6.2 UWB Systems 201 6.2.1 UWB Defined 201 6.2.2 UWB Switching Technologies 204 6.2.2.1 Spark Gap Switches 204 6.2.2.2 Solid-State Switches—Non-Photoconductive 206 6.2.2.3 Photoconductive Switches 207 6.2.3 UWB Antenna Technologies 210 6.2.4 UWB Systems 213 6.2.4.1 Mesoband Systems 213 6.2.4.2 Subhyperband Systems 214 6.2.4.3 Hyperband Systems 215 6.3 Nonlinear Transmission Lines 217 6.3.1 NLTL Historical Overview 218 6.3.2 Simplified Soliton Theory 218 6.3.2.1 Derivation of the KdV Equation for LC Ladder Circuit 219 6.3.3 Gyromagnetic Lines 221 6.3.4 Nonlinear Dielectric Material 221 6.3.5 Nonlinear Magnetic Material 222 6.3.6 BAE Systems’ NLTL Source 223 6.3.7 Hybrid NLTLs 226 6.4 Conclusion 226 Problems 226 References 227 7 Relativistic Magnetrons and MILOs 231 7.1 Introduction 231 7.2 History 232 7.3 Design Principles 233 7.3.1 Cold Frequency Characteristics of Magnetrons and CFAs 236 7.3.2 Operating Voltage and Magnetic Field 241 7.3.3 Characteristics of Magnetrons 243 7.3.4 Summary of Magnetron Design Principles 247 7.4 Operational Features 247 7.4.1 Fixed-Frequency Magnetrons 248 7.4.2 Tunable Magnetrons 251 7.4.3 Repetitive High-Average-Power Magnetrons 252 7.5 Research and Development Issues 255 7.5.1 Peak Power: Phase Locking Multiple Sources 256 7.5.1.1 Efficiency: Transparent Cathode and Other Novel Cathode Topologies 257 7.5.1.2 Efficiency: Limiting Axial Current Loss and Radial versus Axial Extraction 258 7.5.2 Frequency Agility and Mode Switching 261 7.6 Fundamental Limitations 262 7.6.1 Power Limits 262 7.6.2 Efficiency Limits 264 7.6.3 Frequency Limits 266 7.7 MILOs 267 7.8 Crossed-Field Amplifiers 271 7.9 Summary 271 Problems 273 References 274 8 BWOs, MWCGs, and O-Type Cerenkov Devices 281 8.1 Introduction 281 8.2 History 282 8.3 Design Principles 284 8.3.1 Slow-Wave Structure: Dimensions and Frequencies 287 8.3.2 Addition of the Beam: Resonant Interactions for Different Device Types 289 8.3.3 Start Current and Gain 293 8.3.4 Peak Output Power: Role of Computer Simulation 296 8.4 Operational Features 299 8.4.1 BWOs 301 8.4.2 SUSCOs 303 8.4.3 KL-BWOs 306 8.4.4 TWTs 307 8.5 Research and Development Issues 309 8.5.1 Pulse Shortening 310 8.5.2 BWO Operation at Lower Magnetic Fields 312 8.5.3 Axially Varying Slow-Wave Structures to Enhance Efficiency 313 8.5.4 Phase Locking Multiple Devices 313 8.5.5 Other O-Type Sources: DCMs, PCMs, and Plasma-Filled BWOs 314 8.6 Fundamental Limitations 315 8.7 Summary 317 Problems 317 References 321 9 Klystrons and Reltrons 327 9.1 Introduction 327 9.2 History 328 9.3 Design Principles 330 9.3.1 Voltage, Current, and Magnetic Field 330 9.3.2 Drift Tube Radius 331 9.3.3 Klystron Cavities 331 9.3.4 Electron Velocity Modulation, Beam Bunching, and Cavity Spacing 334 9.3.5 Beam Bunching in Low-Impedance Relativistic Klystrons 337 9.3.6 Circuit Modeling of Klystrons 338 9.3.7 Reltron Design Features 341 9.4 Operational Features 342 9.4.1 High-Impedance, Near-Relativistic Klystrons 342 9.4.2 High-Impedance, Relativistic Klystrons 345 9.4.3 Low-Impedance Klystrons 347 9.4.4 Reltrons 352 9.5 Research and Development Issues 355 9.5.1 High Power Multibeam and Sheet-Beam Klystrons 356 9.5.2 Low-Impedance Annular-Beam Klystrons—Triaxial Configuration 357 9.5.3 Low-Impedance Annular-Beam Klystrons—Coaxial Configuration 360 9.6 Fundamental Limitations 363 9.6.1 Pencil-Beam Klystrons 363 9.6.2 Annular-Beam Klystrons 365 9.6.3 Reltrons 366 9.7 Summary 366 Problems 367 References 370 10 Vircators 375 10.1 Introduction 375 10.2 Vircator History 375 10.3 Vircator Design Principles 376 10.4 Operational Features 381 10.5 Double-Anode Vircators 384 10.5.1 Reditrons 385 10.6 Cavity Vircators 387 10.7 Feedback Vircators 389 10.8 Coaxial Vircators 390 10.9 Phase Locking Vircators 391 10.10 Applications and Limitations of Vircators 393 Problems 394 References 395 11 Gyrotrons, Electron Cyclotron Masers, and Free-Electron Lasers 399 11.1 Introduction 399 11.2 Gyrotrons and ECMs 399 11.2.1 History of Gyrotrons and ECMs 400 11.2.2 Gyrotron and ECM Design Principles 401 11.2.3 Gyrotron and ECM Operational Features 407 11.2.3.1 High-Average-Power Gyrotrons 407 11.2.3.2 Relativistic Gyrotrons 408 11.2.3.3 CARMs 411 11.2.3.4 Gyroklystrons 412 11.2.4 Outlook for ECMs 415 11.3 Free-Electron Lasers 416 11.3.1 History 416 11.3.2 Free-Electron Laser Design Principles 417 11.3.3 Operational Features of Free-Electron Lasers 424 11.3.4 Outlook for Free-Electron Lasers 424 11.4 Summary 426 Problems 427 References 428 Appendix: High Power Microwave Formulary 435 Index 447 List of Acronyms ADS Active Denial System AFOSR Air Force Office of Scientific Research AFRL Air Force Research Laboratory AFWL Air Force Weapons Laboratory A-K Anode-Cathode ANSI American National Standards Institute ARL Army Research Laboratory ARM Antiradiation Missile ASAT Antisatellite BASS Bulk Avalanche Semiconductor Switches BINP Budker Institute of Nuclear Physics BWG Beam Waveguide BWO Backward Wave Oscillator CAEP Chinese Academy of Engineering Physics CARM Cyclotron Autoresonance Maser CERN European Center for Nuclear Research CFA Crossed-Field Amplifier CHAMP Counter-electronics High-powered Microwave Advanced Missile Project CIAS Carbon-Impregnated Aluminosilicate CLIC Compact Linear Collider CONOPS Concept of Operation COTS Commercial-off-the-Shelf CSG Competitive Strategies Group CSR Cost Savings Ratio CVD Chemical Vapor Deposition CW Continuous Wave DCM Dielectric Cerenkov Maser DEW Directed Energy Weapon DSRD Drift Step Recovery Diode EAST Experimental Advanced Superconducting Tokamak ECCD Electron Cyclotron Current Drive EC H&D Electron Cyclotron Heating and Current Drive ECM Electron Cyclotron Maser ECM Electronic Countermeasure ECRH Electron Cyclotron Resonance Heating EED Electro-Explosive Device EIRP Effective Isotropic Radiated Power EMC Electromagnetic Compatibility EMI Electromagnetic Interference EMP Electromagnetic Pulse EPFL Ecole Polytechnique Federale de Lausanne ERP Effective Radiated Power ETA Experimental Test Accelerator FCC Federal Communications Commission FCG Flux Compression Generator FEL Free Electron Laser FLAPS Flat Parabolic Surface FWHM Full-Width-at-Half-Maximum FZK Forschungszentrum Karlsruhe GmbH GA General Atomics GMBK Gigawatt Multibeam Klystron GPS Global Positioning System GPU Graphics Processing Unit HAT High-Power Amplifier Transmitter HDL Harry Diamond Laboratories HE High Explosive HEMTT Heavy Expanded Mobile Tactical Truck HPM High Power Microwaves HPPA High Pulsed Power Antenna HUD Heads-up Display IAE Institute of Applied Electronics IAP Institute of Applied Physics ICHE Institute of High-Current Electronics ICRH Ion Cyclotron Resonance Heating IED Improvised Explosive Device IHCE Institute of High-Current Electronics ILC International Linear Collider INPE National Institute for Space Research IRA Impulse Radiating Antenna IREB Intense Relativistic Electron Beam IREE Institute of Radio Engineering and Electronics ITER International Thermonuclear Experimental Reactor JCTD Joint Concept Technology Demonstration JDAM Joint Direct Attack Munition JIEDDO Joint Improvised Explosive Device Defeat Organization JINR Joint Institute of Nuclear Research JNLWD Joint Nonlethal Weapons Directorate JSOW Joint Standoff Weapon KdV Korteweg de Vries KE Kinetic Energy KEK High Energy Accelerator Research Organization KIT Karlsruhe Institute of Technology KL-BWO Klystron-Like Backward Wave Oscillator LANL Los Alamos National Laboratory LBNL Lawrence Berkeley National Laboratory LEO Low Earth Orbit LEP Large Electron-Positron LHC Large Hadron Collider LHH Lower Hybrid Heating LIA Linear Induction Accelerator LLNL Lawrence Livermore National Laboratory LNA Low Noise Amplifier LTD Linear Transformer Driver MANPADS Man-Portable Air Defense System MCG Magnetocumulative Generator MDO Magnetron with Diffraction Output MIG Magnetron Injection Gun MILO Magnetically Insulated Line Oscillator MIT Massachusetts Institute of Technology MITL Magnetically Insulated Transmission Line MOPA Master Oscillator/Power Amplifier MPM Medium Power Microwaves MWCG Multiwave Cerenkov Generator MWDG Multiwave Diffraction Generator MWS Missile Warning System NAGIRA Nanosecond Gigawatt Radar NINT Northwest Institute of Nuclear Technology NKCE Nonkinetic Counter-Electronics NLC Next Linear Collider NRL Naval Research Laboratory NUDT National University of Defense Technology OC Open Circuit Pasotron Plasma-Assisted Slow-Wave Oscillator PCM Plasma Cerenkov Maser PCSS Photoconductive Solid State PDA Personal Digital Assistant PFL Pulse Forming Line PFN Pulse Forming Network PI Physics International PIC Particle-In-Cell PPM Periodic Permanent Magnet PRF Pulse Repetition Frequency PRR Pulse Repetition Rate PV Photovoltaic RCS Radar Cross Section RDG Relativistic Diffraction Generator REICO Relativistic Extended-Interaction-Cavity Oscillator RF Radiofrequency RKA Relativistic Klystron Amplifier RKO Relativistic Klystron Oscillator RMS Root Mean Square RPD Receiver Protection Device RPM Recirculating Planar Magnetron RR-BWO Resonant Reflector Backward Wave Oscillator RWR Radar Warning Receiver S&T Science and Technology SAM Surface to Air Missile SAR Specific Absorption Rate SBK Sheet Beam Klystron SCO Split Cavity Oscillator SDI Strategic Defense Initiative SES Switched Energy Storage SLAC Stanford Linear Accelerator Center SLC Stanford Linear Collider SLED SLAC Energy Development SLR Sidelobe Ratio SNL Sandia National Laboratories SOS Semiconductor Opening Switch SPS-ALPHA Solar Power Satellite by means of an Arbitrarily Large Phased Array SUSCO Sectioned Un-Severed Cerenkov Oscillator SWO Surface Wave Oscillator SWS Slow-Wave Structure TB-NLC Two-Beam Next Linear Collider TBA Two-Beam Accelerator TE Transverse Electric TEM Transverse Electromagnetic TFA Time-Frequency Analysis TKA Triaxial Klystron Amplifier TM Transverse Magnetic TPI Tomsk Polytechnic Institute TR Transmitter/Receiver TTU Texas Tech University TWT Traveling Wave Tube UAS Unmanned Aerial System UAV Unmanned Aerial Vehicle UCAV Unmanned Combat Air Vehicle UESTC University of Electronic Science and Technology UM University of Michigan UMD University of Maryland UNM University of New Mexico USAF United States Air Force UWB Ultrawideband VEPP Russian Electron-Positron Collider Concept VMD Voltage Modulation Depth Preface This third edition has the following revisions compared to the second edition published in 2007: • Every chapter has been significantly updated. • The chapter previously called Ultrawideband Systems is titled Beamless Systems and includes nonlinear transmission lines. • Chapter 10 now focuses entirely on vircators due to a resurgence of interest in them. • Chapter 11 is a new chapter that covers gyrotrons, electron cyclotron masers, and free electron lasers. As with previous editions, this book is meant to communicate a wide-angle, integrated view of the field of high power microwaves, or HPM. Our treatment of HPM is actually rather brief; by limiting the book’s length to a manageable number of pages, we hope to encourage the reader to further explore the field, rather than skip to select sections of narrower interest, which often happens with lengthier tomes. Our presentation is broad and introductory with the flavor of a survey; however, it is not elementary. For the reader seeking greater detail, we have provided an extensive set of references and guidance to the literature with each chapter. We anticipate that our readers will include researchers in this field wishing to widen their understanding of HPM; present or potential users of microwaves who are interested in taking advantage of the dramatically higher power levels that are being made available; newcomers entering the field to pursue research; and decision makers in directed energy weapons acquisitions and related fields, such as radar, communications, and high-energy physics, who must educate themselves in order to determine how developments in HPM will affect them. This book has its origins in many short courses we have taught in the United States and western Europe. Over time, as we have continued to update and widen the scope of our classes, our outlook in the field of HPM has expanded considerably. Although we approached the field by initial investigations with particular HPM sources, we found ourselves asking questions with increasingly more global implications, which this book addresses: • How does HPM relate historically and technically to the conventional microwave field? • What applications are possible for HPM, and what key criteria will HPM devices have to meet in order to be applied? • How do high power sources work? Are there really as many different sources as the nomenclature seems to indicate? What are their capabilities, and what limits their performance? • Across the wide variety of source types, what are the broad fundamental issues to be addressed in the future? We believe that addressing these questions has profited us—and ultimately the reader—and that our perspectives are largely complementary: our primary research interests lie with different source types. While James Benford works largely as an experimentalist, John Swegle is a theorist. The new coauthor since the Second Edition, Edl Schamiloglu, describes himself as an applied theorist. The reader is encouraged to read Chapter 1, the introductory chapter, where we outline the historical trends that have led to the development of HPM and compare the capabilities of HPM with those of other domains, such as conventional microwaves and THz sources. A premise of this book is that the field can be divided into two sectors, which sometimes overlap: one applications-driven and the other technology-driven. Chapter 2 is entirely new and deals with both perspectives. Chapter 3 directly treats the applications of HPM. The other chapters are focused on technologies. Chapter 4 on microwave fundamentals is a guide to the major concepts used in later chapters. Chapter 5 on enabling technologies describes the equipment and facilities surrounding the sources in which microwaves are generated. These are the elements that make the system work by supplying electrical power and electron beams to the source, radiating microwave power into space, and measuring microwave properties. Chapter 6 deals with the ultrawideband or beamless technologies. Chapters 7 through 11 deal in detail with the major source groups. The Appendix contains the High Power Microwave Formulary. Finally, in the frontal matter we have included a List of Acronyms to assist the reader. We thank our colleagues for helping in the preparation of this book: Gregory Benford, Steven Gold, John Luginsland, Dominic Benford, Bill Prather, David Price, Edward Goldman, Keith Kato, David Giri, Carl Baum, William Radasky, Jerry Levine, Douglas Clunie, David Price, John Mankins, Kevin Parkin, Richard Dickinson, Bob Forward, Bob Gardner, George Caryotakis, Daryl Sprehn, Mike Haworth, Sid Putnam, Yuval Carmel, Joe Butler, Sonya Looney, Michael Petelin, Ron Gilgenbach, Larry Altgilbers, Mike Cuneo, James McSpadden, and Mats Jansson. Special thanks go to Charles Reuben (University of New Mexico), who tirelessly handled the figures, and to Weihua Jiang (Nagaoka University of Technology, Japan), whose corrections and requests for clarification when translating the second edition into Chinese improved this third edition significantly. We also thank John Luginsland (Air Force Office of Scientific Research, AFOSR) for his support of this project. Finally, we thank Francesca McGowan of Taylor & Francis Group for shepherding us through this third edition. Very special thanks go to our wives for their patience. James Benford Microwave Sciences, Lafayette, California John A. Swegle J-Two, Aiken, South Carolina Edl Schamiloglu University of New Mexico, Albuquerque, New Mexico Authors James Benford is the president of Microwave Sciences, Inc., in Lafayette, California. He does contracting and consulting in high power microwaves. His interests include high power microwave systems from conceptual designs to hardware, microwave source physics, electromagnetic power beaming for space propulsion, experimental intense particle beams, and plasma physics. He earned his PhD in physics from the University of California San Diego. He is an IEEE fellow and an EMP fellow. He has taught 26 courses in high power microwaves in 10 countries. In 2013, he coedited Starship Century, dealing with the prospect of star travel. Visit jamesbenford.com for papers on these topics. John A. Swegle is currently employed at the Savannah River National Laboratory in Aiken, South Carolina, and also works as an independent consultant on high power microwaves. He began his career at Sandia National Laboratories in Albuquerque, New Mexico, where he was a member of the plasma theory group, and then moved to the Lawrence Livermore National Laboratory. He has obtained his PhD and MS degrees in plasma physics from Cornell University and BSEE and MSEE degrees from the University of Washington, Seattle. He has served two terms as an associate editor of The Physics of Plasmas, and as an editor of a special issue of the IEEE Transactions on Plasma Science, devoted to high power microwaves. He has conducted short courses or extended workshops on the subject of high power microwaves in the United States, Europe, and China. Edl Schamiloglu is a distinguished professor of electrical and computer engineering at the University of New Mexico. He earned his BS and MS degrees from Columbia University, New York, and his PhD from Cornell University in 1988. He is an IEEE fellow and an EMP fellow. His research interests are HPM source development and their effects on networked infrastructure. He is a recipient of numerous awards, most recently the 2013 IEEE NPSS Richard F. Shea Award and the 2015 IEEE NPSS Pulsed Power Science and Technologies’ Peter Haas Award. He conducts numerous short courses and lectures all over the world. CHAPTER 1: INTRODUCTION 1.1 Origins of HPM 3 1.2 HPM Operating Regimes 5 1.3 Future Directions in HPM 12 1.4 Further Reading 14 1 Introduction The first edition of High Power Microwaves was a technical monograph that reflected the research and trends up until that time. The second edition was a textbook that adopted a systems point of view, and so added chapters on the systems approach—ultrawideband sources—which introduced problems for students and included a high power microwaves (HPM) formulary. Therefore, it was substantially larger than the first edition. The field of HPM has since then moved forward in technologies and applications. HPM systems are being built, studied, and applied not only in the original centers, United States and Russia, but also more widely in Western European countries such as the United Kingdom, France, Germany, and Sweden, as well as in a broad program in China. Many other nations are participating, including Israel, Japan, India, Taiwan, South Korea, and Singapore. In the third edition, we have updated the material to the first half of 2015. We continue our emphasis on optimizing the entire system, that is, viewing HPM systems as integrated devices. One cannot separate the system into discrete constituent components and optimize them separately. In adopting a systems point of view, one begins with a basic understanding of the constraints imposed by the application. Then one identifies subsystem component classes and how they interact and properly takes into account the requirements of ancillary equipment. To get a flavor of this approach, we advise the reader to begin by reading the first two chapters before reading the specific technical chapters that follow. Chapter 2, on HPM systems, describes how to conceptualize an HPM system by making choices of components based on a standard methodology. Chapter 3, on HPM applications, sets out the requirements for such systems. This edition continues as a textbook to be used by students in HPM courses or for self-study by the technically trained. Therefore, we have updated and increased the number of problems following most of the chapters. (Readers who wish to acquire solutions for these problems, or additional problems, see jamesbenford.com.) Note that the chapter previously titled Ultrawideband Systems is now entitled Beamless Systems (Chapter 6) and includes nonlinear transmission lines (NLTLs). Chapter 10 now focuses entirely on vircators due to a resurgence of interest in them. Chapter 11 is a new chapter that covers gyrotrons, electron cyclotron masers, and free electron lasers. 1.1 ORIGINS OF HPM HPM has emerged in recent decades as a new technology allowing new applications and offering innovative approaches to existing applications. A mix of sources that either push conventional microwave device physics in new directions or employ altogether new interaction mechanisms has led to a quantum leap in microwave power levels. HPM generation taps the enormous power and energy reservoirs of modern intense relativistic electron beam technology. Therefore, it runs counter to the trend in conventional microwave electronics toward miniaturization, with solid-state devices intrinsically limited in their peak power capability. Our definition of HPM is as follows: • Devices that exceed 100 MW in peak power. • Devices that span the centimeter- and millimeter-wave range of frequencies between 1 and 300 GHz. This definition is arbitrary and does not cleanly divide HPM and conventional microwave devices, which have, in the case of klystrons, exceeded 100 MW. The HPM devices we consider here have reached power levels as high as 15 GW. 4 HIGH POWER MICROWAVES HPM is the result of the confluence of several historical trends, as shown in Figure 1.1. Microwaves were first generated artificially by Hertz in the 1880s. Radio came into use at lower frequencies in the early twentieth century with the advent of gridded tubes. In the 1930s, several investigators realized that higher frequencies could be obtained by using resonant cavities connected to electrical circuits, and the first cavity device, the klystron, was produced in 1937. This was followed by a burst of activity during World War II that included the extrapolation of the magnetron and the invention of the traveling wave tube (TWT) and the backward wave oscillator (BWO). Modulators that frequently used gridded power tubes powered all these sources. In the 1960s, the cross-field amplifier (CFA) was developed. Thereafter, the 1970s saw the strong emergence of lower-power, but extremely compact, solid-state-based microwave sources. By this time, microwave tube technology was oriented toward volume production, and research effort was curtailed. In the 1950s, efforts to control thermonuclear fusion for energy production led to a detailed understanding of the interaction between particles and waves, and ultimately to the requirement for new tube developments using gyrotrons for higher average power at frequencies that have climbed to over 100 GHz. In the 1960s, electrical technology was extended with the introduction of pulsed power, leading to the production of charged particle beams with currents in excess of 10 kA at voltages of 1 MV and more. These intense beams were applied to the simulation of nuclear weapons’ effects, inertial confinement fusion, and other studies of high-energy density physics. The availability of intense relativistic electron beams was the last piece in the puzzle, allowing the knowledge of wave–particle interaction gained in the study of plasma physics to be put to use in the generation of microwaves (Figure 1.2). As a consequence of this genealogy, the culture of the HPM community lies closer to those of the plasma physics and pulsed power communities than to that of the conventional microwave tubes. One result of this is that HPM technology was initially slow to adopt materials and surface and vacuum techniques that are well established in the microwave tube community and essential to resolving the pulse-shortening challenge that limits HPM to shorter pulses of hundreds of nanoseconds. That has now changed. FIGURE 1.1: Historical origins and emergence of high power microwaves. 1.2 HPM OPERATING REGIMES The first HPM sources were descendants of conventional microwave sources such as the magnetron, the BWO, and the TWT. In these devices, increased power comes from using higher operating currents and stronger beam–field couplings within the interaction region. Using high voltages to produce relativistic electron beams, meaning electron energies comparable to or greater than the 511-keV rest energy of an electron, has had several profound consequences for HPM. The most important is the introduction of new devices, such as the virtual cathode oscillator or vircator and the relativistic klystron, which depend fundamentally on the very high beam currents that accompany high voltages. Another is the further exploitation of devices based explicitly on relativistic effects, most prominently the gyrotron. Finally, there is the stronger energy-dependent tuning as opposed to velocity-dependent tuning of the output frequencies in devices such as the free-electron laser (FEL) and the cyclotron autoresonance maser (CARM). The domain of HPM also includes impulse sources, which are very short duration, high power generators of broad bandwidth radiation. Usually referred to as ultrawideband (UWB) devices, they typically generate ≈1 GW or so with a duration of about 1 ns, and only a few cycles of microwaves launched. In the third edition, we categorize these sources under the broader area of beamless sources. Bandwidth is therefore of the same order as the frequency, typically 1 GHz. Such pulses are generated by direct excitation of an antenna by a fast electrical circuit, instead of the earlier method of extracting energy from an electron beam. Although the peak output power levels of UWB sources can be comparable to narrowband sources, the energy content is considerably smaller because of very short pulse lengths. Recently NLTLs have emerged to generate narrowband radiation by taking an input rectangular voltage pulse and converting it to oscillations. These sources exploit nonlinearities in dielectric or magnetic materials and require neither electron beams nor a vacuum. The golden age of HPM, which lasted till the 1990s, had the character of a power derby, during which enormous strides were made in the production of high power levels at increasingly higher frequencies. Researchers in the erstwhile Soviet Union achieved their world-record successes using a series of new devices—the multiwave Cerenkov and diffraction generators (MWCGs and MWDGs) and the relativistic diffraction generator (RDG)—based on large interaction regions FIGURE 1.2: Plasma physicists dominated the development of HPM sources because of their understanding of wave–particle interactions when space charge is strong. 6 HIGH POWER MICROWAVES many microwave wavelengths in diameter. In the United States, relativistic magnetrons and klystrons at lower frequencies and FELs at higher frequencies generated high powers. A measure of the success of these efforts is the product of the peak microwave power and the square of the frequency, Pf^2. Figure 1.3 shows the general history of the development of microwave sources in terms of this factor. In the figure the points identify the year when the plotted value of Pf^2 was first achieved. Conventional microwave devices (tubes) made three orders of magnitude progress between 1940 and about 1970, but thereafter only minor improvements were made. Conventional devices, the klystron and gyrotron, in particular, continue to make advances, albeit slowly. HPM devices began at Pf^2 ~ 1 GW·GHz^2 and have progressed upward an additional three orders of magnitude in the ensuing 20 years. The device with the highest figure of merit produced to date is the FEL, with a radiated output power of 2 GW at 140 GHz, so Pf^2 is 4 × 10^4 GW·GHz^2. Figure 1.4 shows the peak power generated by a representative sample of high power sources as a function of the frequency. It appears that the peak power of many sources falls off roughly as f^(-2) at high frequencies; however, no clear trend emerges for lower frequencies below 10 GHz. Why Pf^2? This scaling for a given source type reflects the fact that power extracted from resonant cavity devices is proportional to their cross section, which scales with wavelength squared.* In addition, the power in a waveguide, which has a cross section proportional to λ^2, is limited by the breakdown electric field. Another meaning is that the power density on the target of a microwave beam transmitted is proportional to Pf^2 for a fixed antenna aperture (because the antenna gain is ~ f^2; see Chapter 5), so it is a good parameter to rank sources for directed energy and power beaming over a distance. The early golden age of HPM ended in the 1990s with a sobering realization that device development was stalling around 10 GW and 1 kJ of pulse energy. These parameters were achieved through considerable effort and without taking full advantage of sophisticated three-dimensional computational modeling tools that were only beginning to become more widely available. * This is because the power in a cavity is the integral of the electric field energy over the volume, which can be extracted in Q cycles, where Q is the quality factor. The number of modes possible in a cavity is proportional to the volume in units of wavelength cubed, λ^3. Therefore, the power extracted scales with λ^2. The electric field is limited by breakdown, so power can be increased by using larger cross sections while maintaining mode control: P = (ω / Q) ∫ (1/2) ε E_RF^2 dV, N ∝ V / λ^3, P ∝ (λ^2 E_RF^2 N) / Q FIGURE 1.3: Growth of microwave devices in terms of the figure of merit Pf^2. The points identify the year when the plotted value of Pf^2 was first achieved. 1 Introduction 7 Two points were perhaps lost in the focus on our original figure of merit, Pf^2; they are as follows: 1. On closer examination, the envelopes of the output from the highest-power experiments of the early 1990s—the multiwave devices, the RDG, and the relativistic klystron—were very irregular, evidence of a number of phenomena, including shifting between closely spaced modes during the pulse. 2. For shorter pulses (of the order of 100 ns, a value determined more accurately from electronic effect studies for offensive and defensive applications), the energy per pulse is a significant measure of system effectiveness. In this regard, the energy per pulse has been increasing slowly over the years. That number, for clean, reproducible power envelopes, is up by about an order of magnitude now to several hundred joules. In the 1990s, the term pulse shortening came into vogue, encompassing the various causes for the decrease in pulse length as peak power increases, with radiated energy staying roughly constant as power climbed into the mid-gigawatt range. This led to a reassessment of the way the HPM community was developing its sources. Today there is less attention paid to pulse shortening because high peak power applications have accepted using shorter pulses. Following the initial golden age, which focused almost solely on peak power, efforts were focused on improving existing source technologies rather than on new concepts. The following have been the trends: • Better surface cleanliness and vacuum environment and cathodes that deliver the requisite electron current densities at lower electric fields. • Lower cathode plasma temperatures and densities. • Designs to ensure that the intense electron beam impacted as little of the electrodynamic structure as possible before passing into the collector. FIGURE 1.4: Peak powers of types of pulsed HPM sources. Values of the quality factor Pf^2 vary over several orders of magnitude. 8 HIGH POWER MICROWAVES Up until about 2005, efforts were focused largely on refining existing concepts, rather than on developing new source configurations. With a heavy dose of empirical research mixed with computer modeling and simulation, Russian work on BWOs began to better integrate simulation and experiment. Chinese researchers looked more closely at field strengths in key regions of concentration to maintain power while eliminating breakdown. Building on original Russian designs, attention to pulsed power development in Russia and China has further led to longer, flatter voltage and current, and thus flatter microwave pulses. In the past decade, source development has become more prominent again with devices such as the triaxial relativistic klystron from the Naval Research Laboratory (NRL) and others; the transparent-cathode magnetron from the University of New Mexico (UNM); and the klystron-like BWO from China’s Northwest Institute of Nuclear Technology (NINT) making an appearance. While the magnetron takes advantage of innovations in both cathode design and microwave extraction to achieve remarkable efficiencies, in excess of 60%, the klystron and BWO offer the prospect of much higher power, albeit at the expense of added complexity. The development of the klystron-like BWO, as an example, involved an evolution that first featured an inductive cavity splitting the slow-wave structure (SWS) to sharpen up the bunches formed in the first section to more efficiently extract power in the second; this was followed by the addition of beam-decelerating output cavities to increase the field strength for extraction while managing the magnitudes of the fields at the walls to prevent breakdown. Both axial and coaxial microwave extraction were introduced to distribute the increased power to prevent field concentrations that could cause breakdown. Signal injection and bunching cavities upstream of the main interaction region initiate bunching earlier to allow phase locking of multiple devices. A 2013 paper described in Chapter 8 (Section 8.4.3) optimistically claimed that further measures could make power levels well in excess of 10 GW possible from a single device. Is the power race to begin again? We focus on the evolution of the klystron-like BWO to alert the reader to the tradeoffs between device complexity and output power. While ever-higher power levels from a single device may be possible, complexity offers its own intrinsic challenges. A competing approach is the coherent phasing of multiple sources, which offers redundancy and the prospect of graceful power decline, where power is reduced but not extinguished, rather than single-point total failure. Nevertheless, the use of multiple sources requires volume, and the demands of multiple support subsystems for beam generation, magnets, and X-ray shielding and cooling. Cutting-edge performance will require a consideration of such application- and operation-dependent tradeoffs. The ultimate limits on HPM source peak power are not well known. They are set by tradeoffs between the usual factors that limit conventional tubes, breakdown and mode competition, and factors unique to HPM, such as intense beam–field interactions and evolution of plasmas from surfaces and diodes. Electrical pulses with power up to about 10 TW are available from a single pulse generator, and one can buy 1-TW generators (a laboratory-based device, not suitable for mobile applications) for a few million dollars, commercially. At a moderate extraction efficiency of 10%, one could therefore expect a peak power of 100 GW. We expect that such powers can be achieved, but only if there is a need for the power and a willingness to accept the accompanying size, cost, and complexity. To do so requires substantial improvement in understanding the limitations of specific devices and overcoming pulse shortening and source-specific problems such as spurious mode generation. Another set of issues limits HPM average power achieved in repetitive operation. The convention in HPM has been to quote device efficiency in terms of the peak power efficiency of the source, defined as the ratio of the peak microwave power to the electron beam power at that moment. This is to be compared with the energy efficiency, which would be the ratio of the microwave pulse energy to the electron beam pulse energy. Aggressive research programs aimed at gaining a detailed understanding of large-signal behavior have been rewarded in certain cases with instantaneous power efficiencies of 40%–50% or more; under most circumstances, however, power efficiency is in the vicinity of 10%–30%. Energy efficiencies are usually much lower, due to the time the device and the pulsed power voltage and current take to come into resonance, the device falling out of resonance and pulse shortening at high power levels. Therefore, energy efficiencies are seldom quoted in the literature. 1 Introduction 9 A comparison of the peak and average power characteristics for conventional and HPM sources is given in Figure 1.5. The peak power of a device is plotted against its average power. While conventional devices span an enormous range in this parameter space, the HPM devices have not been developed to produce substantial average power levels. This is because conventional sources have been developed to be the workhorses for specific applications that, in certain cases, demand high average powers, such as radar and particle acceleration, while the HPM sources have not, as yet. The Stanford Linear Accelerator Center (SLAC) klystrons are the highest power devices of conventional origin (~100 MW peak, 10 kW average). The FEL is the highest average power HPM device (2 GW peak, 16 kW average). The duty factor for HPM sources—the product of the pulse length and the pulse repetition rate—is of the order of 10^(-6) (at most 10^(-5)), whereas for conventional devices it varies from 1 (continuous operation, called continuous wave, CW) to about 10^(-4). We expect that the impetus provided by HPM applications will spur advances in repetitive operation, and average powers will approach 100 kW. There are as yet no applications for both high peak and high average power. In military applications of HPM, one really is driven by a desire for high shot rates, rather than high average power per se. (Using an HPM system to get high average power combines the worst of both worlds, in terms of demands on the system. See Chapter 2 for more details on this topic.) Another comparison of conventional and HPM sources is shown in Figure 1.6. Considering only pulsed devices, that is, leaving out continuous operation, the conventional tubes typically produce ~1 MW for ~1 μs, giving a joule per pulse. Klystrons for accelerators produce energetic pulses at 1 to 10 MW. The SLAC klystron was developed to 67 MW, 3.5 μs, yielding 235 J. This borders on our definition of HPM (>100 MW). HPM sources produced tens of joules in the 1970s, hundreds of joules in the 1980s, and surpassed a kilojoule in the 1990s (MWCG and relativistic klystron amplifier [RKA]). These developments were achieved by increasing peak power at ~100-ns pulse duration. On further increasing pulse duration, the obvious route to higher energies faces pulse shortening. Most of the devices shown in Figure 1.6 are narrow bandwidth devices. The wideband impulse sources, with very short pulse durations, fall in the region of 100 MW, <1 J. The increasing use of HPM sources will also raise the issues of reliability and lifetime. With HPM sources predominantly functioning in a research environment to date, important reliability and lifetime issues have received very little attention. For example, the >10^(-6) torr vacuum levels of most HPM experiments contrast with the <10^(-7) torr levels of conventional tubes, where higher pressures are known to cause lifetime problems. Contemporary sophisticated issues are bandwidth, FIGURE 1.5: Peak versus average power for microwave sources with duty factors. 10 HIGH POWER MICROWAVES gain, linearity, phase and amplitude stability, and noise levels. These can be quite important in the context of a specific application. Parameter spaces of the current applications of HPM are shown in Figure 1.7. The power levels for directed energy and short-pulse radar vary widely. The highest power requirements are for earth-to-space power beaming (earth-to-space, space-to-space, and space-to-earth, primarily average power driven) and directed energy weapons. It is notable that first-generation FIGURE 1.6: Peak power and energy from continuous and pulsed (durations shown) microwave sources, narrow band, and wide band. FIGURE 1.7: Domains of HPM applications. Power is typically peak power, but in some cases, such as fusion heating and some directed energy weapons (DEW), is average power. Regions are schematic; specific schemes vary widely. 1 Introduction 11 HPM weapons approaching deployment, as described in the press and trade publications, are high in average power, operating continuously, not as a series of pulses in a burst (see Section 3.2.3). These are confined mostly to the frequency regime below 10 GHz, in part by atmospheric absorption. Linear colliders (particle accelerators) require higher frequencies (~30 GHz) at about 100 MW. Electron cyclotron resonance heating of plasmas is a much higher frequency application (over 100 GHz), with a continuous or average power requirement of 1–2 MW in single CW sources, and 20 MW in an array of tubes for ITER, the International Thermonuclear Experimental Reactor. Some of these applications are approaching maturity, as described in Chapter 3. The most stressful applications are military, because military platforms have severe requirements for onboard volumes and masses. Historically, the most comprehensive HPM weapon research programs were in the United States and Russia, especially during the Cold War era. There are now significant activities in Europe, with the United Kingdom, France, Sweden, and Germany being the most prominent. China has a large program, perhaps the world’s largest. The Chinese are investigating all source types, including some innovative configurations, at laboratories in, for example, Mianyang, Changsha, Chengdu, Beijing, and Xi’an. To accelerate its program, China has purchased HPM technology from Russia. The Chinese are pushing into new territory now, making source improvements based on strong interaction between simulation tools of increasing maturity and experiments. Over the past decade, HPM publication rates in Russia and the United States have slowed. The major increase in publication rates has been in China. Indeed, Chinese innovation has increased dramatically, bringing it to a world-leading position, particularly in the areas of relativistic BWOs, RKAs, vircators, and magnetically insulated line oscillators (MILOs). Innovations include the following: • Dual-mode BWOs, in which a mode-changing reflector at one end of the interaction region shifts the output power into a volume mode with much-reduced fields at the walls to allow higher power at reduced risk of breakdown. • Klystron-like BWOs with an added internal cavity to enhance beam bunching, as well as prebunching cavities at the input end and extraction cavities and multiple extraction outputs to raise efficiencies to well over 50% in computer simulations not yet verified by experiment. • Added idler cavities to increase the gain of RKAs to allow much lower input power levels that can be supplied by smaller solid-state devices. • Proposed use of an added modulator cavity in coaxial vircators, which raises efficiencies observed in computer simulations. • Introduction of cathode asymmetries in virtual cathode experiments to solve mode control issues involving azimuthally symmetric and asymmetric modes in favor of the latter (also done by Sweden). • Combined MILO–vircator configurations allowing independently controlled dual-frequency output at higher efficiencies allowed by the added conversion of electron energy in the downstream vircator. In Japan, interest is centered on gyrotrons for plasma heating, klystrons for accelerators, and FELs for a broad range of applications that span the frequency spectrum. In India, sources are being explored to build a national program. Note that applications fall below 300 GHz in Figure 1.7. That is partially because there exists at present a THz gap, as shown in Figure 1.8. Average power devices (P̄) are solid-state microwave and conventional vacuum devices, which in the past were referred to as tubes. High peak power devices (P̂) are HPM and solid-state lasers. Figure 1.4 shows the general 1/f^2 falloff of power of all devices whose dimensions scale with the operating wavelength. Lasers do not scale that way, so they are the only sources above the gap. The THz gap, between about 0.1 and 10 THz, is produced by limits on device fabrication. For more on this technological frontier, see the review articles by Booske. 12 HIGH POWER MICROWAVES FIGURE 1.8: Power versus frequency of microwave and THz devices. Average power devices (P̄) are solid-state microwaves and conventional vacuum devices; peak power devices (P̂) are HPM and solid-state lasers. Figure 1.4 shows the general 1/f^2 falloff of power of all devices whose dimensions scale with the operating wavelength. Lasers do not scale that way, so they are the only sources above the THz gap, which is produced by limits on device fabrication. (Adapted from Booske, J.H. et al., IEEE Trans. THz Sci. Tech., 1, 54, 2011. With permission.) 1.3 FUTURE DIRECTIONS IN HPM The field of HPM has matured. In the previous editions, we described the trends of the past two decades, the 1990s and 2000s. In this edition, newer technologies have been explored, while older problems continue to be addressed. 1.3.1 Previous Trends These trends were the high-power derby, mitigating pulse shortening and increasing power efficiencies, phase locking, the merging of HPM and conventional microwave technologies, and the move toward compactness in pulsed power and sources. • Progress is being made in lengthening pulses, mostly in linear beam devices and magnetrons. One group of significant improvements comes from the change in cathode technology, as described in Section 5.3.1. Researchers seem to have settled for 100 ns pulses as a good compromise between maintaining high electric fields, on the one hand, and the scaling of electronic vulnerability, on the other. This is described in Chapter 3. A second set of improvements in BWOs comes from the interactive use of simulation and experiment to actively reduce electric fields at the wall that cause breakdown, as described in Chapter 8. So the typical goal today might be 100 ns, 1 GW, which gives a 100 J pulse. • Power efficiencies have been improved on a spotty basis but have not received concentrated attention. An exception to this is continuous gyrotrons for the fusion application, which especially benefits from higher efficiency. This was achieved by applying depressed collectors. The present state of the art for them is about 50% efficiency but 60% has been achieved in some laboratories. Going beyond that will be difficult and appears unlikely. 1 Introduction 13 • HPM continues to enjoy the benefit of adopting conventional microwave device construction techniques. The two differing communities, technologies and traditions, have converged. The most important improvements have been clean environments, meaning improved surface and vacuum techniques. • There have been no substantial increases in repetition rates. Relativistic magnetrons and BWOs have demonstrated kilohertz rates. Average powers of up to 10 kW can be obtained and that is sufficient average power for applications. There appear to be no applications demanding repetition rates above about 100 Hz. One consequence of higher repetition rates would be the impact on prime and pulsed power. • In the 1990s, phase locking of both amplifiers and oscillators was demonstrated at high power with good phase stability. This has not been improved upon by extending to gangs of 10 sources. In principle, one could make a module of 10 sources and then gang together 10 such modules to reach 100 GW, but no application requires this, so it has not been done. However, recent Chinese research on RKAs supports moving to the next step of combining primed oscillators or commonly driven amplifiers, which requires higher gain, because a 30-dB amplifier will require a substantial master oscillator, while even an increase to 40 dB reduces the demand substantially (see Chapters 4 and 9). • Interest in explosive generators to power HPM devices appears to have waned; less work is being conducted around the world. • In the 1990s, virtual prototyping emerged as a powerful tool for designing HPM sources. Prior to the mid-1990s, experimentalists varied their apparatus and modeling by simulation sought to match experimental results. The situation is now reversed: no metal will be cut until simulation shows the exact configuration for optimal performance. Thus, particle-in-cell (PIC) codes have altered the basic paradigm of HPM source design. This trend will be reinforced by recent work in China on the construction of devices using metalized plastic. Furthermore, the huge advances in the so-called 3D printing provide another disruptive technology to alter the development paradigm. 1.3.2 New Trends As in previous decades, new trends have emerged. The new trends are as follows: • Multi-spectral sources, wherein a single source operates at two or more frequencies simultaneously, have been developed for relativistic magnetrons, MILOs, and BWOs (see Chapter 4). • Dispersion engineering may mean new kinds of sources will emerge. In electron beam-driven sources, metamaterials are being exploited to develop new slow wave structures with properties that are not achievable using traditional materials. In beamless sources NLTLs—ferrite lines or nonlinear LC networks—directly drive a radiating antenna with damped oscillations of a few cycles at a high repetition rate (see Chapters 4 and 6). • All solid-state pulsed power drivers are based on the semiconductor opening switch. • Linear transformer drivers, a compact pulser technology that will see applications (see Chapter 5). • Phase coherence is a technique used to combine two or more (N) sources driven by the same pulsed power generator. The fast rise time of the current from short-pulse generators using explosive electron emission cathodes ensures that the outputs are in phase between 20° and 30°, sufficient to yield N^2 scaling of the power density in the far field if each of the N sources radiates through its own antenna (see Chapter 4, Section 4.10.1). HPM systems will follow the demands of the applications. We expect that flatness of the driving voltage pulse may become more important in the future because it improves the overall energy efficiency of the device. Some devices will need broad tunable bandwidth, especially if HPM is coupled with electronic warfare. The fundamental properties of sources, such as phase stability, will have to be improved if electronic warfare systems are to be improved by using high power sources. 14 HIGH POWER MICROWAVES The use of modulations on the microwave power envelope will necessitate the development of amplifiers rather than oscillators. But amplifiers are usually larger, more complex, and more expensive. All applications will require reliability, a virtue little developed in HPM to date. For military applications, compact, low-mass, and transportable systems will be essential for deployments other than a fixed site. Mass and volume are largely driven by system elements ancillary to the source—such as magnets (including permanent magnets), beam collection and, in high average power applications, cooling—or prime and pulsed power on one end or antennas for high power radiation into air on the other. Ultimately, the ability of HPM to succeed will depend upon its ability to serve applications with a true market. These markets are only beginning to emerge and could include many defense applications, particle acceleration, industrial processes, or power beaming. Following the extraordinary technical successes achieved by HPM in the past 40 years, HPM is finding applications driven by real needs. We remain confident that the international effort to expand the HPM technology and its emerging applications will help this new domain of electromagnetics continue to flourish in the decades ahead. 1.4 FURTHER READING HPM is a broad enough field that finding the appropriate references is not simple. There are several books in English and an excellent review article by Gold and Nusinovich. The basic book on conventional tubes is by Gilmour. The best reference in the technical journals is IEEE Transactions on Plasma Science, especially the biennial special issues dealing with HPM sources, and there are special issues on pulsed power as well. Otherwise, papers on HPM appear primarily in the Journal of Applied Physics, Physics of Plasmas, Physical Review A, Laser and Particle Beams, China Physics B, Acta Physica Sinica (albeit, in Chinese), and the International Journal of Electronics. The Proceedings of the International Conferences on High Power Particle Beams, known popularly as, for example, BEAMS’12, contain state-of-the-art reports on HPM sources driven by pulsed power electron beam generators. UWB (beamless) work is chronicled in IEEE special issues and in Ultra-Wideband, Short-Pulse Electromagnetics, a continuing series from Kluwer Academic/Plenum Publishers. REFERENCES 1. Benford, J., Swegle, J., and Schamiloglu, E., High Power Microwaves, 2nd Edition, Taylor & Francis Group, Boca Raton, FL, 2007. 2. Benford, J. and Swegle, J., High Power Microwaves, Artech House, Norwood, MA, 1992. 3. Pond, N.H., The Tube Guys, Russ Cochran, West Plains, MO, 2008. 4. Booske, J.H., Plasma physics and related challenges of millimeter-wave-to-terahertz and high power microwave generation, Phys. Plasmas, 15, 1, 2008. 5. Booske, J.H. et al., Vacuum electronic high power terahertz sources, IEEE Trans. THz Sci. Tech., 1, 54, 2011. 6. Giri, D.V., High-Power Electromagnetic Radiators, Harvard University Press, Cambridge, MA, 2004. 7. Barker, R.J. and Schamiloglu, E., Eds., High-Power Microwave Sources and Technologies, IEEE Press, New York, 2001. 8. Barker, R.J. et al., Modern Microwave and Millimeter-Wave Power Electronics, IEEE Press, New York, 2005. 1 Introduction 15 9. Granatstein, V.L. and Alexeff, I., Eds., High Power Microwave Sources, Artech House, Norwood, MA, 1987. 10. Gaponov-Grekhov, A.V. and Granatstein, V.L., Applications of High Power Microwaves, Artech House, Norwood, MA, 1994. 11. Gold, S. and Nusinovich, G.S., Review of high-power microwave source research, Rev. Sci. Instrum., 68, 3945, 1997. 12. Gilmour, A.S., Klystrons, Traveling Wave Tubes, Magnetrons, Cross-Field Amplifiers, and Gyrotrons, Artech House, Norwood, MA, 2011. CHAPTER 2: DESIGNING HIGH POWER MICROWAVE SYSTEMS 2.1 Systems Approach to High Power Microwaves 17 2.2 Looking at Systems 19 2.3 Linking Components into a System 20 2.4 Systems Issues 27 2.5 Scoping an Advanced System 29 2.6 Conclusion 39 2 Designing High Power Microwave Systems 2.1 SYSTEMS APPROACH TO HIGH POWER MICROWAVES One of our primary goals in writing this book is to develop in the reader a systems perspective toward HPM. This chapter describes that perspective for electron beam-driven sources, and its application to the design and construction of HPM systems. To illustrate some of the points in this chapter, we draw upon our experience in assembling systems for various applications. Our operational definition is that a system is an orderly working totality. Figure 2.1 shows that the subsystems making up the system are constrained by the mission it is to serve. (Figure 5.1 shows a subset of this.) Of course, there are constraints coming from the platform or the facility that the system is inside. Here platform is a military terminology for airplanes, vehicles, and ships. There are also issues about how the microwave beam reaches its target, which could be of an electronic system or fusion plasma, for example. Managing the heat generated by energy losses in the subsystems can be important, especially at high average powers. More concretely, HPM subsystems perform the following functions: 1. A prime power subsystem generates relatively low power electrical input in a long-pulse or continuous mode. 2. A pulsed power subsystem takes the low power/long-pulse electrical power, stores it, and then switches it out in high power electrical pulses of much shorter duration. 3. A microwave source transforms the short-duration, high power electrical pulses into electromagnetic waves. 4. A mode converter may be used to tailor the spatial distribution of electromagnetic energy to optimize transmission and coupling to an antenna. 5. An antenna, directs the microwave electromagnetic output, essentially compressing that output spatially into a tighter, higher-intensity beam. As presented, the arrows presented in Figure 5.1 depict the flow of power and energy within the system, from the prime power generator on the input end to the radiation of microwaves from the antenna on the output end. Note that while power flows to the right, in many instances requirements flow to the left, from an output requirement to a constrained input requirement. In assembling such a system, the selection of individual components is subordinate to the overall goal of optimizing the system as a whole for a chosen purpose. Note that this is the outline of a system; later diagrams will show much greater complexity. For example, power conditioning, which indeed is required for burst-mode operation, is shown later to be an important element for power and energy management. The need for adopting a systems approach stems from the nature of the process of designing and building a complex system that must meet the requirements posed by a user’s application within a set of sometimes competing constraints. In addressing complexity, while striving to meet requirements within a set of constraints, one must learn to step back and view the system from end to end, considering the effect that each subsystem has on the other subsystems, both upstream and downstream in the sense of the power flow depicted in Figure 2.1. Before we characterize our systems approach, let us consider these three motivating elements: complexity, 18 HIGH POWER MICROWAVES FIGURE 2.1: Elements of an HPM system. requirements, and constraints. The logical line of development is to follow a systems approach consisting of the following steps: • Determine the goals in terms of a clearly stated application, typically performance (as distinct from cost and schedule). • Define the objective criteria against which you will measure the achievement of your goals. • Analyze various candidate systems. • Select a system configuration and the subsystem configurations and component choices that realize that system. • Construct the subsystems and integrate into the final system. Unfortunately, these logical steps can rarely be performed in this order because, in practice, the system designer performs some or all of these functions simultaneously throughout the process. The reason for this is rather circular: problems cannot be adequately formulated until they are well understood, but they cannot be well understood until approximately solved. Thus, the two processes of understanding the problem and devising solutions are intertwined. Design of a system is extremely iterative. We can therefore see that systems thinking involves considerable art as well as science; it makes heavy use of intuition based on experience. System design must begin with a set of specifications, and close attention should be paid to them at the very beginning. It is important to not overspecify the system requirements or they may conflict with one another. In setting up specifications, there are a number of key questions to ask: will a system be mobile or stationary? Will it be single shot? A burst of shots? Multiple bursts? Will the antenna stare or steer? Will it operate in a laboratory or in a more demanding environment? To get an idea of the complicated nature of system design, consider a case in which the application provides a rather straightforward set of overall requirements that specify the following: (1) the peak energy per pulse to be delivered to a target at a given range, (2) the pulse repetition rate (PRR) within a burst of pulses, (3) the length of the burst of pulses, (4) the burst repetition rate, (5) the system volume, (6) the system mass, and (7) the maximum angular slew rate for redirecting the beam. To design a system to meet these seven requirements, we have a great deal of freedom. Return to the system block diagram of Figure 2.1, which has subsystems for prime power, pulsed power, a microwave source, mode converter, and antenna. We have multiple candidate technologies for each of those five block elements, and the realization of some of those choices may involve making component choices within the subsystem and individual part choices within the components as well. We will return to this hierarchy of system–subsystem–component–part later in the chapter. Each block element accepts certain input parameters from the subsystem upstream of it in the energy flow depiction of the figure and provides certain output parameters to the subsystem downstream. For example, a microwave source accepts electrical input characterized by the voltage, current, pulse length, and repetition rate from the pulsed power, and it provides microwave output 2 Designing High Power Microwave Systems 19 in the form of a certain power, pulse length, and repetition rate. It also provides additional parameters—mass and volume contributions, platform-relevant parameters such as form factor and center of mass, and operational restrictions such as operating temperature, humidity, and vibration level—that in sum characterize the system as a whole. Individual components and parts have their own input and output parameters, and they provide their individual contributions to system mass, volume, and linear dimensions. Further, there are constraints on voltage, current, frequency, and efficiency. Some of those constraints come from individual parts of each component, for example, you cannot buy an off-the-shelf gas thyratron switch for your pulsed power subsystem that handles over 40 kV. Viewing the whole system branching tree structure, under each subsystem there is a set of component choices and under each component its individual parts, some of which have subbranches for different part choices, all contributing input and output and system parameters to the design calculations. This compounded complexity is called combinatoric explosion. The optimization process is made even more difficult by two factors. First, the system designer will not be an expert in the design of every possible system element and component, so that, in effect, he runs the risk of ignoring certain design options out of ignorance. Therefore, there is a design team. Second, not every component exists as a well-characterized off-the-shelf product. Some have to be designed as custom items to the specifications set by the overall system designer. Thus, it is difficult to characterize in advance, because one is not entirely certain what items are going to be available. Considering the daunting complexity, one comes to see the value of the systems approach to design, which we will describe in this chapter. It is easier to begin by scoping the system with reduced scaling models, so that before going to the trouble of getting components designed, you can make choices about whether they are even in the ballpark. From an initial systems analysis, you can do a better job of setting requirements. Systems design involves optimization of the overall system, as distinct from piecemeal suboptimization of the elements of the system. Suboptimization is the common failure mode in systems, and it is a problem that occurs with high frequency. Common ways to suboptimize are as follows: • Win the battle/lose the war: You optimize a subsystem to the detriment of overall system performance. • Hammer looking for a nail: Your solution was decided in advance, so that all solutions employ your chosen subsystem or component. • A little knowledge is a dangerous thing: Operating with limited knowledge, you miss or mischaracterize a better solution. To avoid suboptimization, the system designer has to think one level up and one level down from his particular viewpoint at any step in the process. This is because the drivers he receives from above, at the system application level, and those he receives from below, from the component technologies, are never sufficiently well defined to make choices easy. Nevertheless, designing a system requires keeping both sets of requirements and constraints in mind simultaneously while integrating the full system. 2.2 LOOKING AT SYSTEMS The hope of the system designer is that the problem can be subdivided in such a way that the parts can be handled somewhat separately. Of course, a system can be described in many ways. For example, one can look at a system in terms of the phases of its chronological development and operation, a long timescale. Or one can look at only the short timescale of operation, the time sequence of system functioning, focusing on time evolution of quantities. Here we choose to describe systems in terms of the subsystems. The nomenclature we will use is shown in Figure 2.2. The entire system is made up of subsystems, by which we mean the technological subassemblies that comprise it. A common set of subsystems are prime power, pulsed power, and so on, as shown in Figure 2.1. Each subsystem is composed of components. For example, a microwave source can have a SWS and may require a magnet. In turn, components are made up of individual parts; a Marx generator’s parts would be capacitors, inductors, and resistors. In an antenna, the components are a pedestal, a dish, and a feed horn. 20 HIGH POWER MICROWAVES FIGURE 2.2: Nomenclature: Systems are made up of subsystems (pulsed power, etc.) that have components (Marx generator, etc.) composed of parts (capacitors, etc.). Existing system design methods and expert systems use this system–subsystem–component–part breakdown point of view. An excellent example of this is HEIMDALL, the expert system for HPM weapons, which calculates system concepts, meaning that it includes the subsystems but not all the ancillary equipment, such as vacuum pumps. In Figure 2.1, energy flows from prime power to higher-voltage, shorter-pulse-length pulsed power, and then to the HPM source. Here the energy is converted into microwaves; is extracted in a waveguide mode, which may be converted to another mode; and then radiates from an antenna. This diagram applies exactly to systems for power beaming and HPM weapons (see Chapter 3). In particle accelerators, the energy would not radiate, instead going directly to an accelerating cavity. 2.3 LINKING COMPONENTS INTO A SYSTEM Conceptually, think of systems as collections of subsystems in the way that, although an atom has a complicated internal structure, for the study of chemistry one needs to know only an atom’s valence. The building blocks of a system, the subsystems, can be described as shown in Figure 2.3. Input parameters combine with features of the subsystem to produce the output parameters, which in turn become input parameters for the next subsystem. The output parameters flow to the next subsystem, providing it essential input information. System features such as the total weight, total size, and total electrical energy consumed can be calculated by summing those quantities for each subsystem. Each subsystem in Figure 2.1 has many parameters. They vary from simple physical parameters such as sizes and weights, to electrical parameters such as current, voltage, and impedance, to microwave parameters such as frequency, bandwidth, and waveguide mode. To assemble components into FIGURE 2.3: Interface parameters knit the components together. For examples of linking parameters, see Figure 2.4. 2 Designing High Power Microwave Systems 21 FIGURE 2.4: Energy flow between component classes in an HPM system. Quantities between component classes are those needed for linking them into a system. Optional branches are for an additional stage of electrical pulse compression (e.g., Marx to PFL) and pulse compression of microwaves after their generation. a system, some choice of sets of parameters must be made. In this section, we describe a particular linking parameter set of input and output parameters and how to use them in designing conceptual systems. Choosing to take some parameters as independent variables to describe components means that other parameters are then dependent, being derived from independent parameters. (Choice of independent variables may not be the same for all systems, selecting which parameters are to be independent, which dependent, is central to the art of system design.) To capture a description of the components in terms of major parameters, the particular linking parameter set for each component class, such as pulsed power components, has its own particular characteristics. We show a well-tested set in Figure 2.4. These are one useful way to consistently connect component classes to operate with other component classes. This is the energy flow direction. However, for system design efforts, there is no intrinsic direction of flow for the exchange of information or parameters between subsystems. Note that there usually are several stages of electrical pulse compression, called power conditioning. It is less common to use an additional stage of compression of the microwave pulse itself. Although it is quite common to see microwave pulse compression in conventional radar systems, it is less commonly used in the HPM world, although it was considered at the level of 100 MW for the next linear collider (NLC) (see Chapter 3 and Section 5.4). The advantage of microwave pulse compression allows use of lower-power, and therefore lower-voltage, pulsed power components. Compatibility, that is, which other technologies a subsystem can or cannot be mated to, is important to linking components together into a system. Beyond compatibility are preferences, the typical best design practice in linking subsystems. For example, each microwave source will produce radiation in a specific waveguide mode. That mode will influence the type of antenna with which a microwave source can operate. Whether available hardware can handle the mode via commercial availability or easy fabrication influences the design choice. Therefore, one must consider and specify which modes a source will produce and which modes an antenna can accept and radiate. 2.3.1 Prime Power For linking prime power to pulsed power (Figure 2.5), whether for electron beam-driven sources or beamless sources, the important parameters are the average power, the repetition rate—which together define the energy per pulse—and the output voltage. There are many technology choices for prime power. In Figure 2.6, we show a set of options that could be employed to provide continuous prime power output to a number of pulsed power options mentioned at the right of the figure, which would ultimately drive a microwave source. Our use of the term continuous is somewhat guarded, because the subsystem at the bottom of the figure, which involves an explosively driven magnetocumulative generator (MCG), is purely a single-shot subsystem. For clarity, we emphasize that the diagram is not the connection diagram for a prime power subsystem, but rather a presentation of possible component choices within a prime power subsystem. A common choice for many 22 HIGH POWER MICROWAVES FIGURE 2.5: Linking parameters for connecting prime power to pulsed power. FIGURE 2.6: Prime power component connections for continuous power. systems is to use a generator powered by an internal combustion engine, such as the diesel alternator or the turbo alternator, but it is also possible to drive systems with batteries for long periods. In either case, the common feature of these subsystem options is that either an alternating current (AC) internal combustion generator or a direct current (DC) battery provides long-pulse or continuous power that is converted to a DC output that functions as input to the pulsed power. For firing a system in burst mode so that the energy store is exhausted over the course of firing a burst of pulses, then replenished between bursts, other alternatives exist, as shown in Figure 2.7. Note that each option within this set of subsystem options has four components: an internal combustion prime power producing an AC output; an interface component followed by an energy store and electrical source that, depending on the option, operates at either AC or DC; and a converter, the output of which provides a series of switched DC pulses to the pulsed power. To better understand the operation, consider the timing diagram of Figure 2.8. The upper plot shows the power pulses delivered by the burst-mode prime power store to the input of a pulsed power system, with power pulses of duration τ_B separated by an interburst period of length τ_IB. Below, we see the timing for the individual pulses of duration τ_P delivered by the pulsed power during the period τ_B. The prime mover component delivers power continuously to the energy store and electrical source, which stores it over the interburst period and then delivers it at a higher power over the course of a burst. The pulsed power in turn stores the power during the burst and delivers it at much higher power during each pulse. For example, it is possible to store the energy in a flywheel or pulsed alternator and then convert it to AC or DC. Thus, the key difference between the continuous and burst-mode systems is the added energy storage in the latter. Average power is much higher in continuous mode, so thermal management becomes a larger issue. In the burst mode, the system has four operational states: firing, charging, charged and waiting, or off. 2 Designing High Power Microwave Systems 23 FIGURE 2.7: Prime power component connections for burst-mode power. FIGURE 2.8: States of burst-mode operation. The repetition rate for peak power selects the switching technologies available to the system. For example, pulsed power repetition rates above 150 Hz suggest a preference for spark gap, magnetic, or solid-state switches. For airborne systems with stringent requirements to limit size and weight, the prime power is a major driver because it is heavy, or the system must tap the platform power system, usually coming from the engine. Ground-based systems can use more conventional prime power, such as internal combustion engines. The designer of airborne systems tries to avoid adding another internal combustion engine, so will prefer tapping the system power. 2.3.2 Pulsed Power Pulsed power is used in most applications, with the major exceptions being continuous power beaming and plasma heating. The existing types of pulsed power (see Chapter 5) are modulators, Marx generators, pulse-forming lines (PFLs), pulse-forming networks (PFNs), inductive energy storage in combination with opening switches, all solid-state modulators based on the semiconductor opening switch, and linear transformer drivers. With the input voltage, average power, and repetition rate taken 24 HIGH POWER MICROWAVES FIGURE 2.9: Linking parameters for connecting pulsed power to the microwave. from prime power, the output of pulsed power components can be characterized by three classes of possible downstream elements: (1) another pulsed power component for further pulse compression, (2) directly to a microwave source, or (3) an impedance and voltage transformer. In the last case, the pulsed power component may produce the correct pulse length, but not the voltage or impedance, in which event one could use a pulse transformer, voltage adder (linear induction accelerator; see Chapter 5), or a tapered transmission line, which is another kind of impedance transformer. The most typical case is connecting a series of pulsed power components. A component, such as a Marx generator, provides the input to a further stage of electrical pulse compression, such as a PFL. The other, less typical, case is that the output of the first pulsed power component is connected to a microwave source, such as a Marx directly driving an antenna. For both cases, the output qualities that must be specified are output voltage, impedance (therefore current, the ratio of voltage to impedance), and pulse length (Figure 2.9). It is also important to specify rise and fall times because of resonance conditions that must be met for the source to generate microwaves. Electrical energy sent into the source before and after the resonance is met is useless, and unused electrical energy passed through the source must eventually be handled by the cooling system. A complex issue at the pulsed power–microwave source interface comes from the dynamic impedance of the microwave source, making impedance matching a serious design issue. Source impedance almost always varies in time and is voltage dependent as well (see Sections 4.6 and 5.3). High average power applications and high peak power applications place different demands on the technology base. High peak power means high voltage or high current or both; to get substantial average power, the system must operate continuously or at high repetition rates for a short period of time. High average power systems place the maximum demand on the prime power, while high peak power focuses the demand on the pulsed power. Using high peak power to get high average power for an application is an error. Mixing these two very different technology classes produces the worst of both worlds. An example: Two applications that require high average power are electron cyclotron resonance heating (ECRH) and the active denial system (ADS) for nonlethal antipersonnel use, as described in Chapter 3. Plasma heating using ECRH makes good use of efficient continuously-operating gyrotrons. As described in Chapter 11, these are generally at frequencies around 150 GHz, whereas the ADS is at 94 GHz because there is an atmospheric window at that frequency. The experimental test accelerator (ETA) system at Lawrence Livermore National Laboratory (LLNL) used a FEL for plasma heating at 140 GHz. The system was huge, much bigger, and more complex than gyrotrons that do the same job. The ETA experiments had to operate at kilohertz to get high average power. The operation was extremely expensive and inefficient. Using high peak powers to get high average powers is a losing proposition (Table 2.1, with Z denoting impedance). 2.3.3 Microwave Sources Microwave sources are usually the most complex element of the system, as Figure 2.10 shows. Simply put, for purposes of connecting to downstream elements (most typically a direct connection to the antenna), the essential features of the source can be taken as the peak microwave power, frequency, pulse length, and output waveguide mode. The bandwidth can also influence the choice of downstream components. Sources also have substantial supporting equipment: a vacuum pump, a magnet in many cases, a cooling system (as do other subsystems), and a collector or dump to capture the beam. There may be a master oscillator if the source is an amplifier. Its power, frequency, pulse duration, and pulse width describe this oscillator. The magnetic field will be specified by the physics of the source. There may also be a need for an X-ray shield to protect personnel. 2 Designing High Power Microwave Systems 25 TABLE 2.1: Advantages and Disadvantages of Pulsed Power Subsystems - Pulse-forming line (PFL): • Pros: Integrates well with cylindrical switches, Simplicity, Lower Z • Cons: Low optimum Z, Length scaling with pulse length - Pulse-forming network (PFN): • Pros: Shorter at long pulse length, Modularity allows variable pulse length, Higher Z matches more sources • Cons: Cost: labor-intensive, Can be heavy - Blumlein PFL: • Pros: Twice the voltage compared to PFL • Cons: Greater complexity, Greater size, mass - PFL with double-resonant transformer: • Pros: Compact • Cons: Transformer failure is catastrophic - Voltage adder: • Pros: Relatively compact, High voltage appears only in the diode, High repetition rates, to >kHz • Cons: Complex, Massive, Expensive FIGURE 2.10: Linking parameters for connecting prime power to pulsed power and on to the antenna. The source will have ancillary equipment: vacuum pumps, cooling. A master oscillator will be required for amplifiers. Perhaps the most important interface in an HPM system is between the pulsed power and microwave source. Electrically, it can be characterized as shown in Figure 2.11, where the pulsed power is represented by an equivalent circuit with a specified open-circuit voltage, V_OC (voltage produced in an open circuit by the pulsed power), and a pulsed power output impedance, Z_PP, while the microwave source is characterized by its impedance, Z_SOURCE. The importance of this interface comes from the need for the impedances of the pulsed power and the microwave source to be well matched, or serious energy and power efficiency losses will occur (see Section 5.2). This in turn affects the size, mass, and cost of the system. Impedance matching is made complex by the fact that typically the source impedance varies with time. It usually falls from an initial value because of gap closure in the beam-generating diode. For a Child–Langmuir and foilless diodes (see Section 4.6.1), which many sources have, the impedance varies with the anode–cathode gap d, but weakly with voltage. For Child–Langmuir diodes, Z_SOURCE ~ d^2 / V^(1/2) (2.1) so plasma generated at the cathode or anode and moving to close the gap can change impedance steadily. Therefore, the time when peak microwave power should occur (when the microwave resonance is reached) is the best time for impedance match to occur (Table 2.2, with B denoting magnetic field). 26 HIGH POWER MICROWAVES FIGURE 2.11: Circuit for the vital pulsed power/microwave source interface. The combination of impedances determines electrical input to the source. I_beam = V_oc / (Z_pp + Z_diode) V_beam = I_beam * Z_diode = V_oc * (Z_diode / (Z_pp + Z_diode)) TABLE 2.2: Features of Microwave Sources - Vircator: • Pros: Compact and simple, low-voltage/low-impedance operation • Cons: Low efficiency in basic configuration, frequency chirps upward during pulse • Magnet?: N | Tunable?: Y - Relativistic klystron: • Pros: Highest powers, high-current/low-voltage reduces size, wide frequency range • Cons: Large, complex configuration required to raise power further • Magnet?: Y | Tunable?: N - Reltron: • Pros: Compact, lightweight, tunable • Cons: Current configurations not operated above 0.5 GW, limited screen lifetime and repetition rate • Magnet?: N | Tunable?: Y - Magnetrons: • Pros: Compact, extensively explored, operated in arrays, widely tunable • Cons: Anode erosion limits lifetime at high power, high-voltage operation requires large B • Magnet?: Y | Tunable?: Y - MILOs: • Pros: No magnetic field, low-voltage/low-impedance operation • Cons: Low efficiency, low repetition rates, not tunable • Magnet?: N | Tunable?: N - BWOs: • Pros: Extensively explored, compact, multi-GW, relatively efficient, mechanically tunable • Cons: Source size currently tied to output wavelength, small size raises power-handling issues, mode control, and electric field management as diameters increase • Magnet?: Y | Tunable?: Y - Multiwave devices: • Pros: Large cross section (D >> λ), high-power, high energy/pulse • Cons: Large interaction region creates large magnet power-supply demand, output mode complex • Magnet?: Y | Tunable?: N - Gyroklystrons: • Pros: Amplifier, operates X-band and above • Cons: Relatively complex design, frequency <34 GHz • Magnet?: Y | Tunable?: Y - Gyrotrons: • Pros: High frequency continuous power to MW, wide range of frequency, high efficiencies, step-tunable • Cons: High frequencies require careful control of operating mode • Magnet?: Y | Tunable?: Y 2.3.4 Mode Converter and Antenna The output parameters of the source determine the connection to the antenna (Figure 2.12). The most crucial factor is a waveguide mode, which must be made compatible with the desired antenna. The characteristics of the output of the antenna are the power, frequency, and antenna gain or angular beam width. They determine the output beam propagation characteristics (Figure 2.13). Antennas are discussed in Section 5.5 (Table 2.3). 2 Designing High Power Microwave Systems 27 FIGURE 2.12: Linking parameters for connecting the microwave source to the antenna. FIGURE 2.13: Antenna output parameters determine propagation of the microwave beam. TABLE 2.3: Advantages and Disadvantages of Antenna Subsystems - Pyramidal horn: • Pros: Simple, Inexpensive • Cons: — - Conical horn: • Pros: Simple • Cons: Cost: labor-intensive, Can be heavy - Parabolic dish: • Pros: Steerable • Cons: Greater complexity, High power density at feed - Vlasov: • Pros: Compact, Simple • Cons: Gain limited by waveguide size - Helical: • Pros: Relatively compact, Easy steering • Cons: Complex, High power density at feed, Beam direction changes with frequency, Expensive - Array of horns: • Pros: High gain, Reduces air breakdown, Mechanical steering, Compatible with rapid electronic tracking by phase control of elements • Cons: Complex, Expensive, Must pack densely to avoid grating lobes, Limited steering - Array of dishes: • Pros: High gain, Reduces air breakdown, Mechanical steering, Compatible with rapid electronic tracking by phase control of elements • Cons: Complex, Expensive, Must pack densely to avoid grating lobes 2.4 SYSTEMS ISSUES It is frequently thought that the factor that drives selection of components for sources is efficient transfer of energy from electricity to microwaves. While this is a factor, it is actually a stalking horse for the truly important factors. Various applications have different driving factors. In Chapter 1, we described the early years of HPM, when peak power was the driving factor. But more recently, the 28 HIGH POWER MICROWAVES compatibility of sources with the other elements in the system has become more important. There are also other factors, such as complexity, maintainability, affordability, tunability, reliability, fragility, transportability, mobility, and the ability to withstand accelerations. It has been said that we are now in a new era of -ilities. For military applications, which typically require a mobile system, the driving parameters for the system are usually the volume and on-board average power requirement of the system. Weight is less important, which may seem counterintuitive. For example, airborne usually means lightweight. An HPM weapon will usually be fitted onto an existing platform in the space previously reserved for another weapon. Such weapons are usually denser than HPM devices. For example, if an HPM system, with some vacuum volume, substitutes for an explosive warhead with high density, the weight actually drops. So, often the real constraint is volume. Power-beaming applications are usually limited by the available antenna apertures at either the transmitting antenna or the receiving rectenna. For particle accelerators, on the other hand, one major driving factor is the cost of the source when manufactured in quantity. This is true because of very stringent performance requirements on lifetime, average power, and energy per pulse. Another is reliability, which stems from the complexity of the system: when there are so many microwave sources, frequent breakdowns would be intolerable. This requirement argues in favor of more conservative technology choices. The key distinguishing electrical parameters of the system components are the voltage and current and their ratio, impedance. Impedance is a quite general quantity, as it also relates to appropriate components of the electric field vector E and magnetic field vector B through the component geometry and to particle drifts in the source, which are proportional to local electric and magnetic fields, E/B. Impedance also relates to antennas through the complex impedance, including both the real part, resistance, and the imaginary part, reactance. Antenna design frequently consists of reducing the reactive component, making impedance matching simpler. The voltage–impedance parameter space into which HPM source technologies fall is shown in Figure 5.2. With voltages of <100 kV and impedances of >1 kΩ, conventional microwave applications (radar, electronic countermeasures, communications) lie at the low power end (power = V^2 / Z) for voltage V and impedance Z. Most, but not all, present-day HPM devices cluster at impedances Z = 10–100 Ω. Voltages generally span the range of 0.1–1 MV, but some sources have been operated up to several megavolts. The implication is that efficient transfer of electrical energy to microwave sources that span a broad range of impedances will require pulsed power technologies that similarly span a substantial impedance range. When adjoining circuit elements do not have the same impedance, voltage, current, and energy transferred to the downstream element can be very different (Figure 5.3). Efficient energy transfer suffers if impedance mismatch exists, especially if the downstream component is of lower impedance than the circuit driving it. Nevertheless, there are exceptions: mismatching upward to higher-load impedance is sometimes used as an inefficient means of increasing load voltage. As an example of the effect of system considerations, consider the case of the use of flux compression generators (FCGs, see Section 5.2.2), also known as explosive generators and MCGs, to drive single-shot HPM weapons. These devices have been extensively developed in Russia and the United States and are now being widely studied. FCGs operate at time-varying impedances well below 1 Ω, producing very high currents at low voltages. As a consequence, workers use transformers, in part to get better rise times for inductive loads. Because of the very high currents, the preferred pulsed power system for such devices is inductive energy storage with an opening switch (see Section 5.2). The impedance transformation required to couple FCGs to ~100 Ω sources would be very inefficient. In the 1990s, the search for high power, low-impedance microwave sources to better match FCGs led to interest in the magnetically insulated line oscillator (MILO) (Chapter 7), which has an impedance of ~10 Ω. But the MILO is not easily tunable, is heavy, and requires a more complex antenna to radiate in a useful pattern. Consequently, the Russians chose to use both a vircator (Chapter 10), whose impedance, although higher, is lower than that of other Russian sources, and the BWO (Chapter 8). The vircator’s other advantages are its small size and simple, inexpensive construction. And like the MILO it requires not external magnetic field. Its very low efficiency is made up for by the very high energies available from FCGs and low mass due to the very high energy density of high explosives as a source