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Klystrons, Traveling Wave Tubes,
Magnetrons, Crossed-Field Amplifiers,
and Gyrotrons
A. S. Gilmour, Jr.
A R T E C H H O U S E B O S T O N | L O N D O N
a r t e c h h o u s e . c o m
Contents
PREFACE xvii
CHAPTER 1 INTRODUCTION 1 1.1 The Microwave Spectrum 1 1.2 The Domain of Microwave Tubes 2 1.3 Classical Microwave Tube Types 3 1.4 Overview of This Book 8 References 9
CHAPTER 2 STATIC FIELDS PRODUCED BY ELECTRONS 11 2.1 Electric Field 11 2.2 Magnetic Field 17
CHAPTER 3 ELECTRON MOTION IN STATIC ELECTRIC FIELDS 19 3.1 Motion Parallel to Field 19 3.2 Relativistic Velocity Corrections 20 3.3 Electric Lenses 22 3.4 Universal Beam Spread Curve 26
CHAPTER 4 INFLUENCE OF MAGNETIC FIELD ON ELECTRON MOTION 31
4.1 Electron Motion in a Static Magnetic Field 31 4.2 Electron Motion in Combined Electric and Magnetic Fields 33
4.2.1 Perpendicular Fields in Rectangular Coordinates 33 4.2.2 Axially Symmetric Fields 35
CHAPTER 5 THERMIONIC CATHODES 39 5.1 Emission Mechanisms 41
5.1.1 Thermionic Emission 41 5.1.2 Schottky Effect 45 5.1.3 Field Emission 47 5.1.4 Space Charge Limitation 49
5.2 Evolution of Thermionic Cathodes 54
V
vi Klystrons, TWTs, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons
5.3 Impregnated Dispenser Cathodes 60 5.3.1 Fabrication 60 5.3.2 Operation 63 5.3.3 Miram Curves 63 5.3.4 Work Function Distribution 65
5.4 Life Considerations 70 5.4.1 Grant and Falce Life Prediction Model 74 5.4.2 Longo Life Prediction Model 76
5.5 Dispenser Cathode Surface Physics 79 5.6 Heaters 85
5.6.1 Conventional Heater Assemblies 85 5.6.2 Fast Warm-Up Heaters 88 5.6.3 Heater Testing 89 5.6.4 Effect of Filament Magnetic Field 90
References 92
CHAPTER 6 ELECTRON GUNS 95 6.1 Pierce Guns 95
6.1.1 Focus Electrodes for Parallel Flow 96 6.1.2 Focus Electrodes for Convergent Flow 98 6.1.3 Defocusing Effect of Anode Aperture 103 6.1.4 Formation of Minimum Beam Diameter 107 6.1.5 Thermal Velocity Effects 109 6.1.6 Effects of Patchy Emission and Cathode Roughness 113
6.2 Beam Control Techniques 114 6.2.1 Cathode Pulsing 114 6.2.2 Control Focus Electrodes 114 6.2.3 Modulating Anode 116 6.2.4 Grids " 116 6.2.5 Summary of Beam Control Electrode Characteristics 128
References 130
CHAPTER 7 ELECTRON BEAMS 133 7.1 Overview of Uniform-Field Focusing 134
7.1.1 Brillouin Flow 135 7.1.2 Scalloping 136 7.1.3 Confined (Immersed) Flow 140
7.2 Uniform-Field Focusing and Laminar Flow 142 7.2.1 The Beam Equation 142 7.2.2 Brillouin Flow 145 7.2.3 Confined (Immersed) Flow 149
7.3 Uniform-Field Focusing and Nonlaminar Flow 153
Contents VII
7.4 Focusing with Permanent Magnets 155 7.4.1 Overview 155 7.4.2 Laminar Flow, No Cathode Flux 157 7.4.3 Laminar Flow with Cathode Flux 163 7.4.4 Nonlaminar Flow 167
7.5 Ion Effects in Electron Beams 173 7.5.1 Examples of Ion Effects 174 7.5.2 Gas Sources 178 7.5.3 Ionization 180 7.5.4 Potential Depression in an Electron Beam 182 7.5.5 Steady State Effects of Ionization 185 7.5.6 Low-Frequency Instabilities 189 7.5.7 High-Frequency Instabilities 192
References 197
CHAPTER 8 BEAM-GAP INTERACTIONS 201 8.1 Beam Modulation 201
8.1.1 Gridded (Planar) Gaps 202 8.1.2 Gridless (Nonplanar) Gaps 204
8.2 Current Induction 206 8.2.1 Gridded (Planar) Gaps 206 8.2.2 Gridless (Nonplanar) Gaps 214
8.3 Beam Loading 214 References 216
CHAPTER 9 ELECTRON BUNCHING PRODUCED BY A GAP 217 9.1 Ballistic Bunching 217 9.2 Bunching with Space Charge Forces 220 9.3 Large Signal Levels 228 References 235
CHAPTER 10 BASIC KLYSTRONS AND THEIR OPERATION 237 10.1 The Invention and Basic Operation of the Klystron 239 10.2 Klystron Cavities 244
10.2.1 Cavity Operation 244 10.2.2 Power Coupling 246 10.2.3 Tuners 248 10.2.4 Equivalent Circuits and Circuit Parameters 249 10.2.5 RF Cavity Losses 253
10.3 Small Signal Operation 254 10.3.1 Load Representation 256 10.3.2 Gain Calculation 256
viii Klystrons, TWTs, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons
10.4 Power Output Characteristics 260 10.4.1 Tuning of Conventional Klystrons 261 10.4.2 Transfer Characteristics 265
References 267
CHAPTER 11 SPECIAL-PURPOSE KLYSTRONS 269 11.1 High-Efficiency Klystrons 269 11.2 High-Power Klystrons 273
11.2.1 Limits on Beam Voltage 275 11.2.2 Limits on Beam Current 277 11.2.3 Estimate of Obtainable Power 278
11.3 Broadband Klystrons 281 11.3.1 Driver Sections 283 11.3.2 Output Sections 289
11.4 Multiple Beam Klystrons 294 11.5 Extended Interaction Klystrons 304 11.6 Reflex Klystrons 311 References 313
CHAPTER 12 TRAVELING WAVE TUBES 317 12.1 Introduction 317
12.1.1 Early History of the TWT 317 12.1.2 Basic Operation of the TWT 321
12.2 Traveling Wave Interaction 325 12.2.1 RF Current in a Beam 326 12.2.2 Circuit Equation 327 12.2.3 The Determinantal Equation 328 12.2.4 Synchronous Operation 328 12.2.5 Nonsynchronous Operation 331 12.2.6 Effect of Circuit Loss 332 12.2.7 Effect of Space Charge 332
12.3 High-Level Interaction 335 12.3.1 Discussion of Interactions 335 12.3.2 Estimates of Maximum Efficiency 338 12.3.3 Comment on Computer Modeling 339 12.3.4 Velocity Tapering 340
References 344
CHAPTER 13 WAVE VELOCITIES AND DISPERSION 347 13.1 Group and Phase Velocity 347 13.2 Dispersion 349
13.2.1 Coaxial Transmission Line 350
Contents ix
13.2.2 Rectangular Waveguide 350 13.2.3 Periodically Loaded Waveguide 358
CHAPTER 14 HELIX TWTS 363 14.1 Bandwidth 363
14.1.1 Dispersion 366 14.1.2 Dispersion Control 367
14.2 Gain 371 14.2.1 Transitions 372 14.2.2 Attenuators and Severs 375
14.3 Power 377 14.3.1 Peak Power 378 14.3.2 Average Power 383
14.4 Efficiency 389 14.5 Dual-Mode Operation 394 14.6 Microwave Power Modules 396 14.7 Ring Bar and Ring Loop TWTs 398 References 402
CHAPTER 15 COUPLED-CAVITY TWTS 405 15.1 Basic Operating Principles 406 15.2 Coupled-Cavity Structures 408
15.2.1 Waveguide Approach 408 15.2.2 Curnow-Gittins Equivalent Circuit Approach 412 15.2.3 Example of an Application of the Curnow-Gittins Circuit 415
15.3 Fundamental Backward Wave Operation 421 15.4 Fundamental Forward Wave Operation 429 15.5 Terminations and Transitions 430 References 435
CHAPTER 16 COLLECTORS 437 16.1 Power Dissipation 437 16.2 Power Recovery 441
16.2.1 Power Flow 441 16.2.2 Power Recovery with a Depressed Collector 444 16.2.3 Electron Energy Distribution 447 16.2.4 Spent Beam Power 450 16.2.5 Effect of Body Current 451 16.2.6 Multistage Depressed Collectors 453 16.2.7 Secondary Electrons in Depressed Collectors 458
16.3 Collector Cooling 462 16.3.1 Conduction Cooling 462
x Klystrons, TWTs, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons
16.3.2 Convection Cooling 462 16.3.3 Forced-Air Cooling 462 16.3.4 Forced-Flow Liquid Cooling 462 16.3.5 Vapor Phase Cooling 464 16.3.6 Radiation Cooling 465
References 467
CHAPTER 17 CROSSED-FIELD TUBES 469 17.1 Basic Configuration of Crossed-Field Tubes 470 17.2 Electron Flow with No RF Fields 471 Reference 475
CHAPTER 18 CATHODES FOR CROSSED-FIELD TUBES 477 18.1 Introduction 477 18.2 Characteristics of Secondary Emission 478
18.2.1 Energy of Impacting Primary Electrons 479 18.2.2 Angle of Incidence of Primary Electrons 480 18.2.3 Secondary Emitting Properties of Surfaces 481 18.2.4 Energy Distribution of Secondary Electrons 484 18.2.5 Modeling of Secondary Emission Characteristics 485
18.3 Operation of Cathodes in Crossed-Field Devices 486 References 487
CHAPTER 19 MAGNETRONS 489 19.1 Types of Magnetrons 489
19.1.1 Cyclotron-Frequency Magnetrons 489 19.1.2 Negative-Resistance Magnetrons 490 19.1.3 Traveling Wave Magnetrons 491
19.2 Operation of the Traveling Wave Magnetron 494 19.2.1 Hub Formation 494 19.2.2 The Hartree Voltage 497 19.2.3 Spoke Formation 500 19.2.4 RF Circuit Operation 504
19.3 Moding 507 19.4 Coaxial Magnetrons 513 19.5 Inverted Magnetrons 516 19.6 Magnetron Tuning 516 19.7 Output Couplers and Transformers 518 19.8 Cathode and Heater Operation 520 19.9 Performance 522
19.9.1 Voltage-Current Characteristic 522 19.9.2 Frequency Pushing 522
Contents XI
19.9.3 Frequency Pulling 523 19.9.4 Thermal Drift 525
19.10 Applications of Magnetrons 526 19.10.1 Conventional Magnetrons 526 19.10.2 Frequency Agile Magnetrons 527 19.10.3 Signal Injected Magnetrons 529 19.10.4 Beacon Magnetrons 532 19.10.5 Microwave Oven Magnetrons 532 19.10.6 Industrial Heating Magnetrons 534 19.10.7 Low-Noise Magnetrons 535 19.10.8 Relativistic Magnetrons 538
19.11 Summary of Power Capabilities 539 References 540
CHAPTER 20 CROSSED-FIELD AMPLIFIERS 543 20.1 Introduction 543
20.1.1 Injected-Beam CFAs 543 20.1.2 Distributed Emission CFAs 544
20.2 CFA Operation 547 20.2.1 Electron Emission and Hub Formation 547 20.2.2 Spoke Formation and Growth 549
20.3 CFA Slow Wave Circuits 552 20.4 CFA Performance 557
20.4.1 Forward Wave CFAs 558 20.4.2 Backward Wave CFAs 559 20.4.3 DC Operation 562 20.4.4 Gain and Operating Limits 563 20.4.5 CFA Phase Characteristics 567 20.4.6 Weight and Size Considerations 570
20.5 Power Capabilities 571 20.6 Thermal Considerations 572 20.7 CFA Power Supply Considerations 580
20.7.1 DC-Operated Supplies 580 20.7.2 Cathode Pulsing Supplies 580
References 581
CHAPTER 21 GYROTRONS 583 21.1 Introduction 583 21.2 Basic Interaction Mechanism 584 21.3 MIG Configuration and Requirements 590
21.3.1 MIG Configurations 590 21.3.2 First-Order Design Procedure 593
xii Klystrons, TWTs, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons
21.3.3 MIG Performance 598 21.4 Beam-Wave Interaction 601
21.4.1 Hollow Cavities 601 21.4.2 Coaxial Cavities 604 21.4.3 Mode Converters 606 21.4.4 Harmonic Operation 609 21.4.5 Collectors 609
21.5 Gyro-Monotrons (Oscillators) 611 21.5.1 RF Output Coupling 611 21.5.2 Second-Harmonic Gyrotrons 613 21.5.3 Permanent Magnet Gyrotrons 613
21.6 Gyro-Amplifiers 615 21.6.1 Gyro-Klystrons 616 21.6.2 Gyro-Twystrons 617 21.6.3 Gyro-TWTs 617
21.7 Terahertz Gyrotrons 622 References 623
CHAPTER 22 WINDOWS 627 22.1 Background 627 22.2 Coaxial Windows 627 22.3 Waveguide Windows 629 22.4 Scaling of Windows 636 References 636
CHAPTER 23 NOISE 639 23.1 Thermal Agitation Noise 639 23.2 Definitions of Noise Figure 640 23.3 Overview of Noise Phenomena 641 23.4 Noise in Electron Guns 642 23.5 Noise Generation at the Cathode 644
23.5.1 Shot Noise 644 23.5.2 Velocity Noise 645 23.5.3 Other Noise Generation Mechanisms 645
23.6 The Space Charge Minimum Region 647 23.6.1 Rack Noise Invariance 647 23.6.2 Shot Noise Reduction 647 23.6.3 Other Noise Effects 649
23.7 Low-Velocity Correlation Region 650 23.8 High-Voltage Acceleration Region 653
23.8.1 Noise Space Charge Waves 653 23.8.2 Impedance Transformation for Low-Noise Tubes 655
Contents хш
23.8.3 Lens Effects 657 23.9 RF Section Noise Phenomena 659
23.9.1 Circuit Loss 659 23.9.2 Partition Noise 659 23.9.3 Secondary Electron Interactions 664 23.9.4 Noise Growth 661 23.9.5 Magnetic Noise Suppression 661
23.10 Other Noise Sources 663 23.11 Minimum Noise Figure of a TWT 664 References 664
CHAPTER 24 NONLINEARITIES AND DISTORTION 667 24.1 Distortion Resulting from Saturation Effects 667
24.1.1 AM/AM Conversion 667 24.1.2 AM/PM Conversion 669 24.1.3 Harmonic Generation 671 24.1.4 Intermodulation Products 673
24.2 Digital Communications 678 24.2.1 QPSK and 16QAM 680 24.2.2 Data Characteristics 682 24.2.3 Amplifier Design to Reduce Distortion 683
24.3 Signal Capturing 686 24.4 Variations with Frequency 687
24.4.1 Broadband Gain Variations 688 24.4.2 Narrowband Gain Variations 688 24.4.3 Phase Nonhnearities or Time Delay Distortion 689
24.5 Pushing and Pulling 690 24.5.1 Amplitude Pushing 691 24.5.2 Phase Pushing 694 24.5.3 Pulling 698
References 699
CHAPTER 25 BREAKDOWN AND PROTECTION 701 25.1 Field Enhancement 703 25.2 DC Breakdown in Vacuum 705
25.2.1 Electrode Phenomena Leading to Breakdown 706 25.2.2 Avoiding Breakdown 719 25.2.3 Vacuum Arcs 722
25.3 DC Breakdown on Insulator Surfaces 726 25.4 RF Breakdown in Vacuum 729
25.4.1 Two-Surface Multipactor with No Magnetic Field 730 25.4.2 Two-Surface Multipactor in Combined Fields 733
xiv Klystrons, TWTs, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons
25.4.3 Single-Surface Multipactor with No Magnetic Field 735 25 A A Single-Surface Multipactor in Combined Fields 736
25.5 RF Breakdown of Insulators 737 25.6 DC Breakdown in Gas 738 25.7 RF Breakdown in Gas 742 25.8 Fault Detection and Tube Protection 751
25.8.1 Excess Body Current 751 25.8.2 Excess Reflected RF Power 753
References 753
APPENDIX A USEFUL CONSTANTS AND CONVERSIONS 757
APPENDIX В VACUUM TECHNOLOGY 759 B.l Units of Measurement 759 B.2 Ranges of Operation 760 B.3 Sources of Gas 761
B.3.1 Backstreaming 762 В.3.2 Permeation 763 B.3.3 Diffusion 764 B.3.4 Desorption 764 B.3.5 Vaporization 764 B.3.6 Virtual Leaks 764 B.3.7 Real Leaks 765
B.4 Vacuum Systems 765 B.5 Roughing Pumps 767
B.5.1 Oil-Filled Mechanical Pumps 767 B.5.2 Scroll Pumps 768 B.5.3 Sorption Pumps 768 B.5.4 Venturi Pumps 771
B.6 High-Vacuum Pumps 771 B.6.1 Diffusion Pumps 771 B.6.2 Ion Pumps 773 B.6.3 Turbomolecular Pumps 776 B.6.4 Cryogenic Pumps 777 B.6.5 Nonevaporable Getters 779
B.7 Vacuum Gauges 780 B.7.1 Thermocouple Gauge 780 B.7.2 Ionization Gauge 781
B.8 Bakeout 781 B.9 Microwave Tube Materials 783 B.10 Joining Techniques 786
B.l 0.1 Brazing 787
Contents XV
В. 10.2 Welding 790 References 793
APPENDIX С MAGNETICS 795 C.l Magnetic Quantities 795 C.2 Magnetic Circuits 796 C.3 Magnetic Materials 799
C.3.1 Ferromagnetic Materials 799 C.3.2 Normal and Intrinsic Hysteresis Curves 802 C.3.3 Energy Product 805 C.3.4 Rare Earth Magnet Materials 806
C.4 Permanent Magnets 807 C.4.1 Straight Field Magnets 807 C.4.2 Periodic Permanent Magnets 808 С.4.3 Double-Period and Long-Period Focusing 810
C.5 Pole Pieces 812 C.6 Electromagnets 814
References 819
GLOSSARY 821
About the Author 835
Index 837