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