High-Pressure Shock Compression of Condensed Matter

Editor-in-Chiej Robert A. Graham

Editorial Board Roger Cheret, France Godfrey Eden, Great Britain Jing Fuqian, China Vitalii 1. Goldanskii, Russia James N. Johnson, USA Malcolm F. Nicol, USA Akira B. Sawaoka, Japan

Springer Science+Business Media, LLC

High-Pressure Shock Compression of Condensed Matter

L.L. Altgilbers. MD.J. Brown. L Grishnaev. B.M Novae. LR. Smith. L Tkach. and Y. Tkach: Magnetocumulative Generators

J. Asay and M Shahin poor (Eds.): High-Pressure Shock Compression of Solids

A.A. Batsanov: Effects of Explosion on Materials: Modification and Synthesis Under High-Pressure Shock Compression

R. Cheret: Detonation of Condensed Explosives L. Davison. D. Grady, andM Shahinpoor(Eds.): High-Pressure Shock

Compression of Solids II L. Davison. Y. Horie, and M Shahinpoor (Eds.): High-Pressure Shock

Compression of Solids IV L. Davison andM Shahinpoor (Eds.): High-Pressure Shock

Compression of Solids III A.N. Dremin: Toward Detonation Theory R. Graham: Solids Under High-Pressure Shock Compression J.N. Johnson and R. Cheret (Eds.): Classic Papers in Shock

Compression Science M Sueska: Test Methods for Explosives J.A. Zukas and w.P. Walters (Eds.): Explosive Effects and Applications

Larry L. Altgilbers Igor Grishnaev 1 vor R. Smith Yuriy Tkach

Mark D.J. Brown Bucur M. Novac Iaroslav Tkach

Magnetocumulative Generators

With a Foreword by C.M. Fowler

With 203 Illustrations

, Springer

Larry L. Altgilbers Mark DJ. Brown Advanced Technology Directorate Missile Defense and Space

Technology Center U.S. Army Space and Missile

Defense Command Huntsville, AL 35807, USA

Igor Grishnaev Peter the Great Military

Engineering Academy Moscow K-47, Russia

Editor-in-Chief Robert A. Graham Director of Research The Tome Group 383 Entrada Road Los Lunas, NM 87031, USA

Bucur M. Novac Ivor R. Smith Department of Electronic and Electrical

Engineering Loughborough University Loughborough, Leicestershire LE II 3TU, U.K.

YuriyTkach Iaroslav Tkach Institute of Electromagnetic Research Pravdi av.5 Kharkov 31022, Ukraine

Library of Congress Cataloging-in-Publication Data Magnetocumulative generators I Larry L. Altgilbers ... [et al.]

p. cm. - (High pressure shock compression of condensed matter)

Inc1udes bibliographical references and index. ISBN 978-1-4612-7053-9 ISBN 978-1-4612-1232-4 (eBook) DOI 10.1007/978-1-4612-1232-4 1. Pulsed power systems. 2. Magnetic flux compression.

1. Altgilbers. Larry L. II. Series. TK2986.M34 1999 621.3--dc21 99-13257

Printed on acid-free paper.

© 2000 Springer Science+Business Media New York Originally published by Springer-Verlag New York in 2000 Softcover reprint of the hardcover 1 st edition 2000

Ali rights reserved. This work may not be translated or copied in whole or in part without the written permission ofthe publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage .and retrievaI, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especiaIly identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely byanyone.

Production managed by Terry Komak; manufacturing supervised by Erica Bresler. Photocomposed copy prepared by the authors.

987654321

ISBN 978-1-4612-7053-9

Foreword

Devices that convert explosive energy into electromagnetic energy are often called Flux Compression Generators (FCGs) in the United States, whereas the term Magnetocumulative Generators (MCGs) is more com­monly used in Russia. Since the Russian literature is accessed more heavily in this book, the latter term is used here. In any event, the basic process involves using explosives to force an initial magnetic flux into a region of smaller inductance in such a manner that loss of flux is minimized. In the event that no flux is lost, the magnetic energy associated with the flux, inversely proportional to the inductance, must increase. Flux loss is min­imized by confining it with good conductors which, in turn, are driven rapidly by the explosive to reduce the system inductance. The magnetic energy is increased by the work the conductors do as they are forcibly moved against the magnetic field, the energy, in turn, being supplied by the explosive driving them. As the reader may infer, there are different kinds of generators, some of which might be difficult to recognize as MCGs. Nonetheless, they all possess the features outlined above.

Explosives have some unique features as energy sources. They have very high available energy densities; they release energy rapidly, or at high power; they can develop very high pressures. Different exploitation of these features has led, historically, to MCG development and use along two differ­ent lines: as generators of ultrahigh magnetic fields and as compact energy sources for devices that require very high pulsed power levels. Some peak performance levels achieved with these devices include the following: mag­netic fields in excess of two-thousand Teslas have been reported recently; pulsed power bursts of some hundred megajoules at multi-terawatt levels have been achieved; rocket launched experiments in the ionosphere have been performed that were only possible by using compact explosive pow­ered electromagnetic sources.

The understanding, and thus the design and construction, of these de­vices requires knowledge in many disciplines such as equation of state of materials, frequently under extreme conditions of pressure, temperature, and magnetic field, shock-wave physics, many aspects of electromagnetic

vi Foreword

theory, including magnetic field diffusion, the behavior of explosives, and other topics. A number of monograms that unite some of these disciplines have been written over the years, but only one comprehensive treatment of the subject has been available-the well-known book by H. Knoepfel, Pulsed High Magnetic Fields (North-Holland, Amsterdam-London, 1970). The main thrust of this book was the production and use of high magnetic fields and the design of the systems that produce them. Some treatment was made of pulsed power supplies, but it was necessarily limited since contributions from the large government weapons laboratories, the source of most of these devices, were withheld.

In is probable that m~re than 80% of the publications in the field have been published since Knoepfel's book appeared nearly 30 years ago. Of the eight "Megagauss Conferences," the major forum for this field, several were held since the book appeared. The proceedings of the first conference contained only 26 papers, while well over 800 papers were given at the subsequent seven conferences. The present volume has successfully undated the field, particularly in the treatment of MCGs designed for pulsed power sources. Of necessity, in a field so broad, the authors have had to limit the scope of the book. They have omitted treatment of high magnetic fields, have restricted the treatment of pulsed power MCGs mainly to a class called helical generators, and have restricted discussion of applications to only a few devices. These restrictions, however, have allowed a more complete discussion of the topics treated.

The first two chapters of the book present a review of disciplines nec­essary for a good understanding of t'he subject. Included here are a fairly comprehensive background in the electrodynamics involved in the opera­tion of MCGs as well as a brief survey of explosives, the properties, and effects. Several types of generators, among the many used in various appli­cations, are next described, followed by a discussion of various techniques used to shape the generator output pulses so that they are suitable for various applications. Chapter 5 contains one of the most comprehensive collections of lumped parameter solutions to various generator-load config­urations, a number of the solutions being reduced to closed form in terms of known functions. The preceding chapters are used somewhat as a prolog to now lead the reader, in Chapter 6, through a complete design of a heli­cal generator, thus putting to use much of the preceding material. Various experimental techniques are discussed in the penultinale chapter, among other things, giving the reader insight into various diagnostics employed in the field. The final chapter discusses use of MCGs as power supplies for var­ious devices, primarily laser and microwave sources. The book, enhanced by the generous use of figures, some 200 of them, is a useful and timely addition to the field.

C.M. Fowler Los Alamos National Laboratory

March 20, 1999

Preface

In the 1950s, several groups of researchers proposed the use of explo­sives to reduce rapidly the volume occupied by a magnetic field, thereby generating a very high magnetic field. Perhaps the most prominent among these was Andrei Sakharov, an original thinker widely known and well re­spected fro his many important contributions across a wide spectrum of theoretical work on atomic science and technology. Subsequently, exper­imentalists at both the All-Russian Institute of Experimental Physics at Sarov (Russia) and the Los Alamos National Laboratory (USA) very suc­cessfully exploited the basic concepts that had emerged from these initial studies, as they designed, built, and tested the first working forms of the devices widely known as either magneto cumulative generators (MCGs) or flux compression generators (FCGs).

Over the years, generators with many widely differenct and often highly ingenious geometrical forms have appeared, as they have found applications in increasing front-line areas of basic and applied research. Nowadays, they are primarily use for the production of either very strong magnetic fields or very high-energy and high-current electric pulses. Although the basic science involved of course remains the same, whatever the applicatio, those applications considered in this book describe mainly the use of MCGs as sources of pulsed power. Typical examples are found in areas such as high­power lasers and microwave generators; in detonator arrays and railguns; in ion, electron, and neutron radiation sources; and in many others besides.

In order to ensure a full appreciation of the science and technology that is involved, this book reviews the basic physics that is necessary, before considering in detail some of the basic generator designs that have been built and tested. Consideration is also given to the construction and design of a typical generator for specific applications and the important role played by the load in the overall design process.

It should be noted that most of the material presented in this book arises from the personal experiences, views, and contributions of the various authors and that MCG work is ongoing in many laboratories in a number of other countries. It was not the intention of the authors to overlook the

viii Preface

valuable contributions of other researchers, but owing to limitations on the size of the volume, they decided to limit the material to that which they are most familiar.

To achieve the objective of this book and to present a coherent account of MCGs, Chapter 1 contains a thorough introduction to these devices. This chapter also provides the underlying electromagnetic and shock wave theory and the explosives technology that are required to appreciate the material of the later chapters. Chapter 2 describes the conditions that affect magnetic flux compression and the basic theory of how flux compression is achieved, and raises a number of important design issues. This is followed in Chapter 3 by a review of various basic MCG designs, including the cylin­drical coaxial, conical, helical, plate, disk, and semiconductor generators. This chapter concludes by discussing cascaded MCGs, built up from two or more of the basic designs, and special purpose short-pulse designs.

Chapter 4 describes the various ancillary circuit components that en­sure the MCG delivers its specified output pulse to the load, and includes novel switches, transformers, and transmission lines that have been devel­oped. The precise form these take depends on the characteristics of the load, and Chapter 5 therefore discusses a number of possible loads and the corresponding impact they have on the operation of the MCG.

Chapter 6 is devoted to an in-depth account of the design, construction, and testing of a particular helical MCG developed by Loughborough Uni­versity in the UK and termed the FLEXY I generator. This is followed in Chapter 7 by a description of the switches and conditioning circuits that were used with the FLEXY I, of the experimental techniques required to obtain its operating parameters, and of an explosive laboratory. This practical theme continues in Chapter 8, which describes the application of MCGs as power sources for high-power laser and microwave generators, topics selected because of the current high level of research and develop­ment interest in several countries.

As in any big undertaking, there are many people whom we need to acknowledge for their guidance and support provided over the three years or so that it has taken to produce this book. Particular thanks must be given to Dr. J. Richard Fisher (Director), Dr. Michael J. Lavan (Direc­tor, Advance Technology Directorate), and Dr. Ira Merritt (Chief, Concept Identification and Application Analysis Division), all of the US Army Mis­sile Defense and Space Technology Center. We should also acknowledge Mr. Phillip Tracy (Teledyne Brown Engineering, USA), Dr. Saulius Balevicius (Semiconductor Physics Institute, Lithuania), Dr. Kris Kristiansen (Texas Tech University, USA), Dr. Alexander Prishchepenko (High Mountain Geo­physical Institute, Russia), Drs. C.M. "Max" Fowler and Doug Tasker (Los Alamos National Laboratory, USA), Dr. Robert Hoeberling (Explosives Pulsed Power, Inc., USA), Dr. John M. Lyons (DERA, UK), and Prof. Michael J.Kearney (Loughborough University, UK). We would like to pay special attention to Dr. Lee Davison, Technical Editor for Springer-Verlag, who provided invaluable suggestions on the content and organization of this book.

Contents

Foreword v C.M. Fowler

Preface vii

1 Explosive-Driven Power Sources 1 1.1 Introduction. . . . . . . . . . . . ....... 1 1.2 Overview of Explosive-Driven Power Sources 2 1.3 Magnetocumulative Generator History . . 5 1.4 Electromagnetic Theory ............ 7

1.4.1 Field Theory: Maxwell's Equations .. 7 1.4.2 Circuit Equations: Kirchhoff's Equations 14

1.5 Electromagnetic Phenomena. . . . . . . 16 1.5.1 Magnetic Pressure and Diffusion 16 1.5.2 Magnetic Force . . 17 1.5.3 Magnetic Pressure .. 19 1.5.4 Electric Fields .... 19

1.6 Shock and Detonation Waves 20 1.7 Explosives and Explosive Components 25

1.7.1 Categories of Explosives 25 1.7.2 Explosive Components . 27

1.8 Introduction to MCGs .. 28 1.8.1 Circuit Equations. . . . 28 1.8.2 Field Equations. . . . . 30 1.8.3 Magnetocumulative Generator Performance 31

References 33

2 Magnetocumulative Generator Physics and Design 35

x Contents

2.1 Conditions That Affect Magnetic Field Compression 35 2.1.1 Field Diffusion . . . . 36 2.1.2 Liner Compressibility 38 2.1.3 Conductivity Change. 41 2.1.4 Surface Instability . . 42

2.2 Theory of Magnetocumulative Current Generators 45 2.3 Current Generator Design Issues . . . . . . . . . . 49

2.3.1 Eliminating Electric Breakdown ...... 49 2.3.2 Increasing the Energy Amplification Factor 50 2.3.3 Delivering the Maximum Possible Energy to the Load 51 2.3.4 Attaining the Maximum Possible Gain . 51 2.3.5 Unconstrained Energy Amplification 52

References

3 Magnetocumulative Generators 3.1 Introduction....... 3.2 Classifications of MCGs 3.3 Coaxial MCGs ..... 3.4 Spiral (Helical) MCGs . 3.5 Plate MCGs . 3.6 Loop MCGs ..... . 3.7 Disk MCGs ..... . 3.8 Semiconductor MCGs

3.8.1 Theory of Operation 3.8.2 SWMCG Working Substances . 3.8.3 SWMCG Designs.

3.9 Cascaded MCGs 3.10 Short-Pulse MCGs

References

4 Pulse-Forming Networks 4.1 High-Speed Opening Switches .

4.1.1 Explosive Opening Switches . 4.1.2 Electroexplosive Switches 4.1.3 Explosive Plasma Switches

4.2 Pulsed Transformers 4.3 Spark Gap Switches .... 4.4 Pulse-Forming Lines . . . . 4.5 High-Voltage MCG Systems

4.5.1 Magnetic Flux Trapping . 4.5.2 Flux Trapping and No Transformer. 4.5.3 Flux Trapping and Transformers ..

55

57 57 58 60 68 76 84 88 93 94 99

101 107 109

121

125 126 128 129 135 139 148 153 158 161 165 166

Contents xi

References 171

5 Electrical Loads 175 5.1 Direct Connection to a Load ........ 175

5.1.1 Case 1: Rc = 0, L(t) = Lo exp( -at) 176

5.1.2 Case 2: Rc = 0, L = Lo(1 - at) 5.1.3 Case 3: Rc i= O,L = Lo(l- at) 5.1.4 Case 4: CL = a ........ . 5.1.5 Case 5: C L = 0, Rc = a ... .

5.2 Connection Through Pulsed 'Iransformers 5.2.1 Case 1: Complex Loads ..... . 5.2.2 Case 2: Resistive and Inductive Loads 5.2.3 Case 3: Rl = a and 120 = a ..... 5.2.4 Case 4: Low-Resistance Loads. . . .

180 181 183 184 185 185 188 191 194

5.2.5 Case 5: Rl = 0, R2 = 0, and CL = a 197 5.2.6 Case 6: Active Load, When Rl = a . 202 5.2.7 Case 7: Pulse-Shaping 'Iransformers 204

5.3 Connecting Through an Electroexplosive Switch 208 5.3.1 Complex Load . . . . . . . . . . . . . . . 209 5.3.2 Active Load . . . . . . . . . . . . . . . . . 213 5.3.3 Effects of Switch Inductance on Energy Coupling Co-

efficient for an Inductive Load. . . . . . . 215 5.4 Pulsed 'Iransformer and Electroexplosive Switch 220

5.4.1 Complex Load 221 5.4.2 Active Load. . . . . . . . . . . . . . . . . 226

References 229

6 Design, Construction, and Testing 233 6.1 A Brief Description of FLEXY I . 233 6.2 Computer Models. . . . . . . . . . 234

6.2.1 Simple Zero-Order Model for a Helical MCG 235 6.2.2 Simple 2D Model for a Helical MCG 249 6.2.3 Comparison to Other Codes. 263

6.3 Helical Generator Design. . . . . 265 6.3.1 Basic Input Data . . . . . 265 6.3.2 Helical Coil Design Rules 267

6.4 Construction of the FLEXY I . . 270 6.5 Testing the FLEXY I. . . . . . . 275 6.6 Comparison of Theoretical and Experimental Results. 276 6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 277

References 279

xii Contents

7 Experimental Methods and Techniques 283 7.1 Experimental Methods . . . . . . . 283

7.1.1 Electromagnetic Techniques. 284 7.1.2 Detonic Techniques. . . . . . 289

7.2 Explosive Pulsed Power Laboratory. 296 7.3 Testing Fast Switches and Conditioning Circuits 299

7.3.1 Exploding Foil Empirical Model ..... 300 7.3.2 Magnetic Flux Compressor/Opening Switch Experi-

ments . . . . . . . . . . . . . . . . . . . . . . . 304 7.3.3 Opening and Closing Exploding Foil Switches. 308 7.3.4 Faster Switching Techniques. 315 7.3.5 Optimizing Exploding Foils 318

7.4 Magnetic Coupling between MCGs . 322 7.4.1 The FLUXAR System. . . . 323 7.4.2 FLUXAR Working Equations. 325 7.4.3 FLUXAR Techniques and Performance 329 7.4.4 A Case Study. . . . . 334

7.5 Limitations of Helical MCGs 337 7.6 Summary 338

References 339

8 Applications: Lasers and Microwaves 345 8.1 Lasers . . . . . . . . . . . . . . . . . . 346

8.1.1 Neodymium Solid-State Lasers 346 8.1.2 Photodissociation Iodine Laser 348

8.2 High-Power Microwave Sources . . . . 350 8.2.1 Autonomous Power Supplies for Microwave Sources 351 8.2.2 Virtual Cathode Oscillators . . . . . . . . 361

8.3

8.4

8.2.3 Multiwave Cerenkov Generators ..... 8.2.4 Magnetically Insulated Linear Oscillators 8.2.5 'fransition Radiation Generators Direct-Drive Devices . . . . . . . . . . . . . . . . 8.3.1 Types of EMAs . . . . . . . . . . . . . . . 8.3.2 Explosive Magnetic Generator of Frequency 8.3.3 Cylindrical Shock-Wave Source Summary ...................... .

References

Index

366 369 383 386 386 388 404 412

413

417