Foundations of Pulsed Power Technology

Jane Lehr is a Professor of Electrical and Computer Engineering at the University of New Mexico. Prior positions were at Sandia National Laboratories and the Air Force Research Laboratory's Directed Energy Directorate. She is a Fellow of the IEEE, past President of the IEEE Nuclear and Plasma Sciences Society, and currently serves as their Society Fellow Evaluation Chair. Pralhad Ron, PhD, is a scientist from the Bhabha Atomic Research Center (BARC), India. He retired as Head, Accelerator and Pulsed Power Division (APPD) of BARC. He served as Chairman, Steering Committee on Electron Beam Center, Kharghar, New Bombay, and Chairman, Safety Review Committee on Particle Accelerators in India constituted by the Atomic Energy Regulatory Board (AERB).

Preface xvii

About the Authors xxi

Acknowledgements xxiii

Introduction xxv

1 Marx Generators and Marx-Like Circuits 1

1.1 Operational Principles of Simple Marxes 1

1.1.1 Marx Charge Cycle 3

1.1.2 Marx Erection 4

1.1.2.1 Switch Preionization by Ultraviolet Radiation 5

1.1.2.2 Switch Overvoltages in an Ideal Marx 5

1.1.3 Marx Discharge Cycle 6

1.1.3.1 No Fire 7

1.1.3.2 Equivalent Circuit Parameters During Discharge 7

1.1.4 Load Effects on the Marx Discharge 10

1.1.4.1 Capacitive Loads 10

1.1.4.2 A Marx Charging a Resistive Load 14

1.2 Impulse Generators 15

1.2.1 Exact Solutions 15

1.2.2 Approximate Solutions 18

1.2.3 Distributed Front Resistors 19

1.3 Effects of Stray Capacitance on Marx Operation 19

1.3.1 Voltage Division by Stray Capacitance 20

1.3.2 Exploiting Stray Capacitance: The Wave Erection Marx 22

1.3.3 The Effects of Interstage Coupling Capacitance 23

1.4 Enhanced Triggering Techniques 26

1.4.1 Capacitive Back-Coupling 26

1.4.2 Resistive Back-Coupling 27

1.4.3 Capacitive and Resistively Coupled Marx 28

1.4.4 The Maxwell Marx 30

1.5 Examples of Complex Marx Generators 31

1.5.1 Hermes I and II 31

1.5.2 PBFA and Z 32

1.5.3 Aurora 33

1.6 Marx Generator Variations 33

1.6.1 Marx/PFN with Resistive Load 35

1.6.2 Helical Line Marx Generator 38

1.7 Other Design Considerations 39

1.7.1 Charging Voltage and Number of Stages 39

1.7.2 Insulation System 40

1.7.3 Marx Capacitors 41

1.7.4 Marx Spark Gaps 41

1.7.5 Marx Resistors 42

1.7.6 Marx Initiation 42

1.7.7 Repetitive Operation 44

1.7.8 Circuit Modeling 45

1.8 Marx-Like Voltage-Multiplying Circuits 45

1.8.1 The Spiral Generator 46

1.8.2 Time Isolation Line Voltage Multiplier 48

1.8.3 The LC Inversion Generator 49

1.9 Design Examples 54

References 57

2 Pulse Transformers 63

2.1 Tesla Transformers 63

2.1.1 Equivalent Circuit and Design Equations 64

2.1.2 Double Resonance and Waveforms 65

2.1.3 Off Resonance and Waveforms 66

2.1.4 Triple Resonance and Waveforms 67

2.1.5 No Load and Waveforms 68

2.1.6 Construction and Configurations 69

2.2 Transmission Line Transformers 71

2.2.1 Tapered Transmission Line 71

2.2.1.1 Pulse Distortion 71

2.2.1.2 The Theory of Small Reflections 72

2.2.1.3 Gain of a Tapered Transmission Line Transformer 77

2.2.1.4 The Exponential Tapered Transmission Line 77

2.3 Magnetic Induction 79

2.3.1 Linear Pulse Transformers 81

2.3.2 Induction Cells 81

2.3.3 Linear Transformer Drivers 83

2.3.3.1 Operating Principles 85

2.3.3.2 Realized LTD Designs and Performance 88

2.4 Design Examples 90

References 93

3 Pulse Forming Lines 97

3.1 Transmission Lines 97

3.1.1 General Transmission Line Relations 99

3.1.2 The Transmission Line Pulser 101

3.2 Coaxial Pulse Forming Lines 102

3.2.1 Basic Design Relations 102

3.2.2 Optimum Impedance for Maximum Voltage 104

3.2.3 Optimum Impedance for Maximum Energy Store 105

3.3 Blumlein PFL 105

3.3.1 Transient Voltages and Output Waveforms 107

3.3.2 Coaxial Blumleins 109

3.3.3 Stacked Blumlein 111

3.4 Radial Lines 113

3.5 Helical Lines 116

3.6 PFL Performance Parameters 117

3.6.1 Electrical Breakdown 118

3.6.2 Dielectric Strength 119

3.6.2.1 Solid Dielectric 119

3.6.2.2 Liquid Dielectric 119

3.6.3 Dielectric Constant 126

3.6.4 Self-Discharge Time Constant 126

3.6.5 PFL Switching 127

3.7 Pulse Compression 128

3.7.1 Intermediate Storage Capacitance 129

3.7.2 Voltage Ramps and Double-Pulse Switching 129

3.7.3 Pulse Compression on Z 131

3.8 Design Examples 134

References 141

4 Closing Switches 147

4.1 Spark Gap Switches 148

4.1.1 Electrode Geometries 150

4.1.2 Equivalent Circuit of a Spark Gap 154

4.1.2.1 Capacitance of the Gap 154

4.1.2.2 Resistance of the Arc Channel 155

4.1.2.3 Inductance of Arc Channel 156

4.1.3 Spark Gap Characteristics 158

4.1.3.1 The Self-Breakdown Voltage and Probability Density Curves 158

4.1.3.2 Delay Time 160

4.1.3.3 Rise Time (tr) 163

4.1.3.4 Burst-Mode Repetitively Pulsed Spark Gaps 164

4.1.3.5 Shot Life 166

4.1.3.6 Electrode Erosion 167

4.1.4 Current Sharing in Spark Gaps 172

4.1.4.1 Parallel Operation 172

4.1.4.2 Multichanneling Operation 173

4.1.5 Triggered Spark Gaps 177

4.1.5.1 Operation of Triggered Spark Gaps 177

4.1.5.2 Types of Triggered Switches 179

4.1.6 Specialized Spark Gap Geometries 195

4.1.6.1 Rail Gaps 195

4.1.6.2 Corona-Stabilized Switches 197

4.1.6.3 Ultra-Wideband Spark Gaps 199

4.1.7 Materials Used in Spark Gaps 201

4.1.7.1 Switching Media 201

4.1.7.2 Electrode Materials 203

4.1.7.3 Housing Materials 204

4.2 Gas Discharge Switches 204

4.2.1 The Pseudospark Switch 204

4.2.1.1 Trigger Discharge Techniques 206

4.2.1.2 Pseudospark Switch Configurations 207

4.2.2 Thyratrons 209

4.2.3 Ignitrons 213

4.2.4 Krytrons 214

4.2.5 Radioisotope-Aided Miniature Spark Gap 216

4.3 Solid Dielectric Switches 216

4.4 Magnetic Switches 217

4.4.1 The Hysteresis Curve 218

4.4.2 Magnetic Core Size 220

4.5 Solid-State Switches 221

4.5.1 Thyristor-Based Switches 223

4.5.1.1 Silicon-Controlled Rectifier 223

4.5.1.2 Reverse Switch-On Dynister 226

4.5.1.3 Gate Turn-Off Thyristor 226

4.5.1.4 MOS Controlled Thyristor 227

4.5.1.5 MOS Turn-Off Thyristor 228

4.5.1.6 Emitter Turn-Off Thyristor 229

4.5.1.7 Integrated Gate-Commuted Thyristor 230

4.5.2 Transistor-Based Switches 230

4.5.2.1 Insulated Gate Bipolar Transistor 230

4.5.2.2 Metal–Oxide–Semiconductor Field-Effect Transistor 231

4.6 Design Examples 231

References 235

5 Opening Switches 251

5.1 Typical Circuits 251

5.2 Equivalent Circuit 253

5.3 Opening Switch Parameters 254

5.3.1 Conduction Time 255

5.3.2 Trigger Source for Closure 255

5.3.3 Trigger Source for Opening 256

5.3.4 Opening Time 256

5.3.5 Dielectric Strength Recovery Rate 256

5.4 Opening Switch Configurations 256

5.4.1 Exploding Fuse 257

5.4.1.1 Exploding Conductor Phenomenon 258

5.4.1.2 Switch Energy Dissipation in the Switch 260

5.4.1.3 Time for Vaporization 261

5.4.1.4 Energy for Vaporization 262

5.4.1.5 Optimum Fuse Length 263

5.4.1.6 Fuse Assembly Construction 263

5.4.1.7 Multistage Switching 265

5.4.1.8 Performances of Fuse Switches 267

5.4.2 Electron Beam-Controlled Switch 267

5.4.2.1 Electron Number Density (ne) 269

5.4.2.2 Discharge Resistivity (ρ) 271

5.4.2.3 Switching Time Behavior 271

5.4.2.4 Efficiency of EBCS 274

5.4.2.5 Discharge Instabilities 276

5.4.2.6 Switch Dielectric 277

5.4.2.7 Switch Dimensions 278

5.4.3 Vacuum Arc Switch 280

5.4.3.1 Mechanical Breaker 280

5.4.3.2 Magnetic Vacuum Breaker 282

5.4.3.3 Mechanical Magnetic Vacuum Breaker 283

5.4.4 Explosive Switch 284

5.4.5 Explosive Plasma Switch 286

5.4.6 Plasma Erosion Switch 286

5.4.7 Dense Plasma Focus 287

5.4.8 Plasma Implosion Switch 289

5.4.9 Reflex Switch 290

5.4.10 Crossed Field Tube 291

5.4.11 Miscellaneous 293

5.5 Design Example 294

References 295

6 Multigigawatt to Multiterawatt Systems 303

6.1 Capacitive Storage 305

6.1.1 Primary Capacitor Storage 305

6.1.2 Primary–Intermediate Capacitor Storage 306

6.1.3 Primary–Intermediate–Fast Capacitor Storage 307

6.1.3.1 Fast Marx Generator 308

6.1.4 Parallel Operation of Marx Generators 308

6.1.5 Pulse Forming Line Requirements for Optimum Performance 309

6.1.5.1 Peak Power Delivery into a Matched Load 309

6.1.5.2 Low-Impedance PFLs 310

6.1.5.3 Pulse Time Compression 310

6.2 Inductive Storage Systems 311

6.2.1 Primary Inductor Storage 311

6.2.2 Cascaded Inductor Storage 311

6.3 Magnetic Pulse Compression 313

6.4 Inductive Voltage Adder 315

6.5 Induction Linac Techniques 317

6.5.1 Magnetic Core Induction Linacs 317

6.5.2 Pulsed Line Induction Linacs 319

6.5.3 Autoaccelerator Induction Linac 322

6.6 Design Examples 323

References 328

7 Energy Storage in Capacitor Banks 331

7.1 Basic Equations 331

7.1.1 Case 1: Lossless, Undamped Circuit ξ = 0 333

7.1.2 Case 2: Overdamped Circuit ξ > 1 334

7.1.3 Case 3: Underdamped Circuit ξ < 1 336

7.1.4 Case 4: Critically Damped Circuit ξ = 1 336

7.1.5 Comparison of Circuit Responses 337

7.2 Capacitor Bank Circuit Topology 338

7.2.1 Equivalent Circuit of a Low-Energy Capacitor Bank 339

7.2.2 Equivalent Circuit of a High-Energy Capacitor Bank 340

7.3 Charging Supply 342

7.3.1 Constant Voltage (Resistive) Charging 342

7.3.2 Constant Current Charging 344

7.3.3 Constant Power Charging 345

7.4 Components of a Capacitor Bank 345

7.4.1 Energy Storage Capacitor 346

7.4.1.1 Capacitor Parameters 347

7.4.1.2 Test Methods 349

7.4.1.3 Pulse Repetition Frequency 349

7.4.1.4 Recent Advances 349

7.4.2 Trigger Pulse Generator 350

7.4.3 Transmission Lines 352

7.4.3.1 Coaxial Cables 353

7.4.3.2 Sandwich Lines 355

7.4.4 Power Feed 356

7.5 Safety 357

7.6 Typical Capacitor Bank Configurations 361

7.7 Example Problems 363

References 366

8 Electrical Breakdown in Gases 369

8.1 Kinetic Theory of Gases 369

8.1.1 The Kinetic Theory of Neutral Gases 370

8.1.1.1 Maxwell–Boltzmann Distribution of Velocities 371

8.1.1.2 Mean Free Path 373

8.1.2 The Kinetic Theory of Ionized Gases 377

8.1.2.1 Energy Gained from the Electric Field 378

8.1.2.2 Elastic Collisions 378

8.1.2.3 Inelastic Collisions 379

8.1.2.4 Total Collisional Cross Section 383

8.2 Early Experiments in Electrical Breakdown 384

8.2.1 Paschen’s Law 384

8.2.2 Townsend’s Experiments 385

8.2.2.1 Region I: The Ionization-Free Region 386

8.2.2.2 Region II: The Townsend First Ionization Region 386

8.2.2.3 Region III: Townsend Second Ionization Region 387

8.2.3 Paschen’s Law Revisited 387

8.2.4 The Electron Avalanche 391

8.3 Mechanisms of Spark Formation 393

8.3.1 The Townsend Discharge 394

8.3.1.1 Multiple Secondary Mechanisms 396

8.3.1.2 Generalized Townsend Breakdown Criterion 398

8.3.1.3 Townsend Criterion in Nonuniform Geometries 399

8.3.1.4 Modifications for Electronegative Gases 400

8.3.2 Theory of the Streamer Mechanism 400

8.3.2.1 Criterion for Streamer Onset 401

8.3.2.2 The Electric Field Along the Avalanche 406

8.3.2.3 A Qualitative Description of Streamer Formation 407

8.3.2.4 Streamer Criterion in Nonuniform Electric Fields 410

8.3.2.5 The Overvolted Streamer 411

8.3.2.6 Pedersen’s Criterion 412

8.4 The Corona Discharge 413

8.5 Pseudospark Discharges 415

8.5.1 The Prebreakdown Regime 415

8.5.2 Breakdown Regime 416

8.6 Breakdown Behavior of Gaseous SF6 417

8.6.1 Electrode Material 418

8.6.2 Surface Area and Surface Finish 418

8.6.3 Gap Spacing and High Pressures 419

8.6.4 Insulating Spacer 420

8.6.5 Contamination by Conducting Particles 420

8.7 Intershields for Optimal Use of Insulation 421

8.7.1 Cylindrical Geometry 421

8.7.1.1 Two-Electrode Concentric Cylinders 422

8.7.1.2 Cylindrical Geometry with an Intershield 423

8.7.1.3 Intershield Effectiveness 426

8.7.2 Spherical Geometry 426

8.7.2.1 Two Concentric Spheres 426

8.7.2.2 A Spherical Geometry with an Intershield 426

8.8 Design Examples 427

References 433

9 Electrical Breakdown in Solids, Liquids, and Vacuum 439

9.1 Solids 439

9.1.1 Breakdown Mechanisms in Solids 440

9.1.1.1 Intrinsic Breakdown 440

9.1.1.2 Thermal Breakdown 442

9.1.1.3 Electromechanical Breakdown 444

9.1.1.4 Partial Discharges 445

9.1.1.5 Electrical Trees 447

9.1.2 Methods of Improving Solid Insulator Performance 449

9.1.2.1 Insulation in Energy Storage Capacitors 449

9.1.2.2 Surge Voltage Distribution in a Tesla Transformer 449

9.1.2.3 Surface Flashover in Standoff Insulators 450

9.1.2.4 General Care for Fabrication and Assembly 452

9.2 Liquids 452

9.2.1 Breakdown Mechanisms in Liquids 452

9.2.1.1 Particle Alignment 452

9.2.1.2 Electronic Breakdown 453

9.2.1.3 Streamers in Bubbles 453

9.2.2 Mechanisms of Bubble Formation 455

9.2.2.1 Krasucki’s Hypothesis 455

9.2.2.2 Kao’s Hypothesis 455

9.2.2.3 Sharbaugh and Watson Hypothesis 456

9.2.3 Breakdown Features of Water 457

9.2.3.1 Dependence of Breakdown Strength on Pulse Duration 457

9.2.3.2 Dependence of Breakdown Voltage on Polarity 457

9.2.3.3 Electric Field Intensification 457

9.2.4 Methods of Improving Liquid Dielectric Performance 457

9.2.4.1 New Compositions 458

9.2.4.2 Addition of Electron Scavengers 458

9.2.4.3 Liquid Mixtures 458

9.2.4.4 Impregnation 458

9.2.4.5 Purification 459

9.3 Vacuum 459

9.3.1 Vacuum Breakdown Mechanisms 459

9.3.1.1 ABCD Mechanism 460

9.3.1.2 Field Emission-Initiated Breakdown 460

9.3.1.3 Microparticle-Initiated Breakdown 462

9.3.1.4 Plasma Flare-Initiated Breakdown 463

9.3.2 Improving Vacuum Insulation Performance 464

9.3.2.1 Conditioning 464

9.3.2.2 Surface Treatment and Coatings 467

9.3.3 Triple-Point Junction Modifications 467

9.3.4 Vacuum Magnetic Insulation 468

9.3.5 Surface Flashover Across Solids in Vacuum 471

9.3.5.1 Secondary Electron Emission from Dielectric Surfaces 471

9.3.5.2 Saturated Secondary Electron Emission Avalanche 473

9.4 Composite Dielectrics 479

9.5 Design Examples 481

References 486

10 Pulsed Voltage and Current Measurements 493

10.1 Pulsed Voltage Measurement 493

10.1.1 Spark Gaps 493

10.1.1.1 Peak Voltage of Pulses (>1 μs) 494

10.1.1.2 Peak Voltage of Pulses (<1 μs) 495

10.1.2 Crest Voltmeters 496

10.1.3 Voltage Dividers 498

10.1.3.1 Resistive Divider 498

10.1.3.2 Capacitive Dividers 507

10.1.4 Electro-optical Techniques 511

10.1.4.1 The Kerr Cell 511

10.1.4.2 The Pockels Cell 515

10.1.5 Reflection Attenuator 518

10.2 Pulsed Current Measurement 519

10.2.1 Current Viewing Resistor 519

10.2.1.1 Energy Capacity 519

10.2.1.2 Configurations 520

10.2.1.3 Tolerance in Resistance 521

10.2.1.4 Physical Dimensions 523

10.2.1.5 Frequency Response 523

10.2.2 Rogowski Coil 523

10.2.2.1 Voltage Induced in the Rogowski Coil 524

10.2.2.2 Compensated Rogowski Coil 525

10.2.2.3 Self-Integrating Rogowski Coil 527

10.2.2.4 Construction 529

10.2.3 Inductive (B-dot) Probe 529

10.2.4 Current Transformer 530

10.2.5 Magneto-optic Current Transformer 530

10.2.5.1 Basic Principles 531

10.2.5.2 Intensity Relations for Single-Beam Detector 532

10.2.5.3 Intensity Relations for Differential Split-Beam Detector 532

10.2.5.4 Light Source 533

10.2.5.5 Magneto-optic Sensor 533

10.2.5.6 Frequency Response 533

10.2.5.7 Device Configurations 533

10.3 Design Examples 535

References 538

11 Electromagnetic Interference and Noise Suppression 547

11.1 Interference Coupling Modes 547

11.1.1 Coupling in Long Transmission Lines 548

11.1.1.1 Capacitive Coupling 548

11.1.1.2 Radiative Coupling 550

11.1.1.3 Inductive Coupling 550

11.1.2 Common Impedance Coupling 550

11.1.3 Coupling of Short Transmission Lines over a Ground Plane 551

11.1.3.1 Voltages Induced by Transients 553

11.1.3.2 Modification of Inductances by the Ground Plane 556

11.2 Noise Suppression Techniques 559

11.2.1 Shielded Enclosure 559

11.2.1.1 Absorption Loss (A) 561

11.2.1.2 Reflection Loss (R) 561

11.2.1.3 Correction Factor (β) 563

11.2.1.4 Shielding Effectiveness for Plane Waves 563

11.2.1.5 Shielding Effectiveness for High-Impedance E and Low-Impedance H Fields 564

11.2.1.6 Typical Shielding Effectiveness of a Simple Practical Enclosure 565

11.2.1.7 Twisted Shielded Pair 565

11.2.2 Grounding and Ground Loops 566

11.2.2.1 Low-Impedance Bypass Path 567

11.2.2.2 Single-Point Grounding 568

11.2.2.3 Breaking Ground Loops with Optical Isolation 568

11.2.3 Power Line Filters 569

11.2.3.1 Types of Filters 569

11.2.3.2 Insertion Loss 570

11.2.4 Isolation Transformer 571

11.3 Well-Shielded Equipment Topology 572

11.3.1 High-Interference Immunity Measurement System 574

11.3.2 Immunity Technique for Free Field Measurements 575

11.4 Design Examples 575

References 581

12 EM Topology for Interference Control 585

12.1 Topological Design 586

12.1.1 Series Decomposition 587

12.1.2 Parallel Decomposition 588

12.2 Shield Penetrations 589

12.2.1 Necessity for Grounding 590

12.2.2 Grounding Conductors 591

12.2.3 Groundable Conductors 592

12.2.4 Insulated Conductors 592

12.3 Shield Apertures 595

12.4 Diffusive Penetration 597

12.4.1 Cavity Fields 599

12.4.1.1 Frequency Domain Solutions 600

12.4.1.2 Time Domain Solutions 601

12.4.2 Single Panel Entry 603

12.4.3 Voltages Induced by Diffusive Penetration 604

12.5 Design Examples 604

References 606

Index 609