An Introduction to the Physics of Intense Charged Particle Beams

355 Pages·1982·10.024 MB·English

by  R. B. Miller (auth.)

An Introduction to the Physics of
INTENSE CHARGED
PARTICLE BEAMS
An Introduction to the Physics of
INTENSE CHARGED
PARTICLE BEAMS
R. B. Miller
Sandia Laboratories
Albuquerque, New Mexico
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Miller, R. B.
An introduction to the physics of intense charged particle beams.
Bibliography: p.
Includes index.
1. Particle beams. I. Title.
QC793.3B4M54 539.7'3 82-557
ISBN-13: 978-1-4684-1130-0 e-ISBN-13: 978-1-4684-1128-7 AACR2
DOl: 10.1007/978-1-4684-1128-7
© 1982 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1982
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N. Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
Preface
An intense charged particle beam can be characterized as an organized
charged particle flow for which the effects of beam self-fields are of major
importance in describing the evolution of the flow. Research employing
such beams is now a rapidly growing field with important applications
ranging from the development of high power sources of coherent radiation
to inertial confinement fusion. Major programs have now been established
at several laboratories in the United States and Great Britain, as well as in
the USSR, Japan, and several Eastern and Western European nations. In
addition, related research activities are being pursued at the graduate level
at several universities in the US and abroad.
When the author first entered this field in 1973 there was no single
reference text that provided a broad survey of the important topics, yet
contained sufficient detail to be of interest to the active researcher. That
situation has persisted, and this book is an attempt to fill the void. As such,
the text is aimed at the graduate student, or beginning researcher; however,
it contains ample information to be a convenient reference source for the
advanced worker.
Most of the phenomena involving the transport of charged particle
beams can be understood within the framework of a macroscopic fluid
model based on moments of the Vlasov and Maxwell equations; this
description is used throughout the book. In certain important situations,
however, which depend on the detailed momentum space structure, a
plasma kinetics approach based on the Vlasov equation is introduced. I
have also adopted the Gaussian system of units, except as specifically noted
in a few isolated instances.
The book is divided into two main sections. In the basic chapters 1-5,
much of the essential material pertaining to the generation and transport of
intense beams has been assembled into a logical format and presented in a
v
vi Preface
consistent fashion. In general, this material is relatively well understood,
and in its description I have strived to maintain a balance between physical
clarity and mathematical development; the basic physics of each important
situation or concept is described in detail before proceeding with the
analysis.
In contrast, the material covered in the special topics chapters 6-8, is
generally less well understood, and the treatment more descriptive, reflect
ing the fact that these areas are in a state of rapid development. In some
cases there is considerable debate concerning the important physical mecha
nisms, and it is more difficult to formulate a methodical presentation that is
both complete and well-balanced. The selection of special topics is based on
the author's interests, as well as practical time constraints. It is anticipated
that individual monographs will be forthcoming on these, as well as several
other special topics requiring a knowledge of intense beam phenomena.
The problems given at the end of each chapter are arranged in the
order of presentation of the chapter material, and not according to the
degree of difficulty. Some of the problems are relatively trivial, but are
included because they demonstrate important physical concepts. On the
other hand, a few problems are quite difficult, and will require some tedious
algebra.
I have been aided by several colleagues in the preparation of this work.
I especially wish to thank B. Godfrey, R. Adler, J. Poukey, T. Genoni, J.
Freeman, C. Olson, K. Prestwich, S. Humphries, M. Widner, D. Straw, C.
Clark, T. Martin, G. Kuswa, G. Yonas, A. Mondelli, P. Sprangle, W.
Barletta, B. Newberger, S. Putnam, L. Sloan, K. Brueckner, and N. Rostoker
for comments on specific questions, and/or reviews of portions of the
manuscript. I also wish to thank D. Woodall (for the opportunity to teach a
graduate level course based on this work at the University of New Mexico),
and my hardworking students. Finally, I am pleased to acknowledge Karen
Adler, Carla Barela, and Nancy Lee for typing the manuscript, and Cindy
Miller and Margaret Clark for assistance with the figures and other last
minute details.
Albuquerque, New Mexico R. B. Miller
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Pulsed Power Technology ................................... 2
1.2.1. Marx Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
1.2.2. Pulse-Forming Lines .................................. 6
1.2.3. Switching ......................................... 12
1.2.4. Vacuum Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3. Qualitative Behavior of Charged Particle Beams ................... 19
1.3.1. Solenoidal Field Transport in Vacuum ..................... 22
1.3.2. Charge and Current Neutralization by a Background Plasma ..... 24
1.4. The Macroscopic Fluid Description ........................... 26
2. Intense Electron and Ion Beam Generation . . . . . . . . . . . . . . . . . . . . . . . . . .31
2.1. Introduction ............. , .............................. 31
2.2. Electron Emission Processes ................................. 33
2.2.1. Thermionic Emission and Photoemission ................... 33
2.2.2. Field Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3. Explosive Electron Emission ............................ 37
2.3. Electron Flow in High-Power Diodes .......................... 41
2.3.1. The Relativistic Planar Diode ........................... 42
2.3.2. Parapotential Flow ................................... 45
2.3.3. Foilless Diodes ..................................... 50
2.4. Ion Flow in High-Power Diodes .............................. 54
2.4.1. Bipolar Space-Charge-Limited Flow ....................... 55
2.4.2. The Reflex Triode ................................... 57
2.4.3. Magnetically Insulated Ion Diodes ........................ 63
2.4.4. Time-Dependent Electron and Ion Flow in Pinched
Electron Beam Diodes ................................ 67
2.5. Summary .............................................. 70
vii
viii Contents
3. Propagation of Intense Beams in Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . .77
3.1. Introduction ............................................ 77
3.2. General Equations for Laminar Flow Equilibria ................... 78
3.3. Space-Charge-Limiting Current .............................. 84
3.3.1. Thin Annular Beam in an Infinitely Long Drift Space .......... 85
3.3.2. Infinite One-Dimensional Drift Space ..................... 87
3.3.3. Iterative Procedure for the Litniting Current in a Long
Drift Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.4. Upper Bound for the Litniting Current in Arbitrary Geometry .... 90
3.3.5. Wave Spectrum for a Nonrelativistic Beam in a
One-Dimensional Drift Space ........................... 92
3.4. Virtual Cathode Formation .................................. 97
3.4.1. Classical Static Theory ................................ 98
3.4.2. Prediction of Unstable Flow ........................... 100
3.4.3. Single Charge Sheet Model ............................ 100
3.4.4. Time-Dependent Virtual Cathode Behavior ................. 103
3.5. Laminar Flow Equilibria of Unneutralized Relativistic
-" Electron Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.5.1. Relativistic Rigid Rotor Equilibrium ..................... 106
3.5.2. Relativistic Hollow Beam Equilibrium .................... 107
3.5.3. General Laminar Flow Beam Equilibria ................... 108
3.6. Electron-Neutralized Transport of Intense Ion Beams in Vacuum ...... 116
3.6.1. Collinear Electron Neutralization ........................ 116
3.6.2. Transverse Electron Injection .......................... 118
3.7. Electrostatic Stability of Intense Relativistic Electron Beams ......... 120
3.7.1. Stability of the Rigid Rotor Equilibrium .................. 123
3.7.2. Stability of the Hollow Beam Equilibrium
(Diocotron Instability) ............................... 126
3.7.3. An Electron-Electron Two-Stream Instability ............... 129
3.8. Summary ............................................. 132
4. Propagation of Intense Beams in Plasma .......................... 139
4.1. Introduction ........................................... 139
4.2. Current Neutralization .................................... 140
4.3. Macroscopic Beam-Plasma Equilibria ......................... 148
=
4.3.1. Warm Fluid Equilibria with Bo O. ...............•....•. 149
4.3.2. Warm Fluid Equilibria in a Discharge Channel .............. 151
4.3.3. Cold Fluid Equilibria with an Axial Magnetic Field ........... 152
4.4. Macroscopic Beam-Plasma Instabilities ........................ 154
4.4.1. Resistive Hose Instability ............................. 155
4.4.2. Sausage Instability .................................. 164
4.5. Microscopic Instabilities ................................... 169
Contents ix
4.5.1. Stability of a Charge-Neutralized Electron Beam (Buneman
Instability) ........................................ 170
4.5.2. Electron Beam Stability in a Dense Plasma (Two-Stream and
Cyclotron Instabilities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.5.3. Electromagnetic Filamentation (Weibel) Instability ........... 177
4.6. Plasma Heating by Linear Relativistic Electron Beams ............. 180
4.6.1. Return Current Interaction ............................ 182
4.6.2. Beam-Electron-P1asma-Electron Streaming Interaction ........ 184
4.7. Summary ............................................. 187
S. Propagation of Intense Beams through Neutral Gas . . . . . . . . . . . . . . . . . . . 193
5.1. Introduction ........................................... 193
5.2. Beam-Induced Neutral Gas Ionization Processes .................. 194
5.2.1. Electron Impact Ionization ............................ 194
5.2.2. Electron Avalanche ................................. 195
5.2.3. Ion Ionization ..................................... 196
5.3. Neutral Gas Transport for Ib/I/ < 1 .......................... 196
5.3.1. Low-Pressure Limit ................................. 196
5.3.2. Intermediate-Pressure Regime .......................... 197
5.3.3. High-Energy Beam Transport in the High-Pressure Regime ...... 198
5.4. Neutral Gas Transport for 1/::5 Ib::5 IA ........................ 202
5.4.1. Low-Pressure Regime ................................ 202
5.4.2. Intermediate-Pressure Regime .......................... 205
5.4.3. High-Pressure Regime ................................ 208
5.5. Neutral Gas Transport for Ib > IA ........................... 210
5.6. Summary ............................................. 210
6. High-Power Sources of Coherent Radiation ........................ 213
6.1. The Relativistic Microwave Magnetron ........................ 214
6.1.1. Preoscillation Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.1.2. Anode Circuits ..................................... 219
6.1.3. Interaction of the Electron Space Charge and the rf Fields ...... 227
6.2. The Electron Cyclotron Maser (ECM) . . . . . . . . . . . . . . . . . . . . . . . . . 236
6.2.1. Physical Mechanism of the Electron Cyclotron Maser ......... 238
6.2.2. Linear Theory of the ECM Mechanism .................... 239
6.2.3. Nonlinear Saturation Mechanisms for the ECM Instability ...... 246
6.3. The Free Electron Laser (FEL) .............................. 248
6.3.1. Physical Mechanism of the Free Electron Laser .............. 249
6.3.2. Linear Theory of the Free Electron Laser in the Raman
Scattering Limit .................................... 256
6.3.3. Nonlinear Saturation Mechanism for the Free Electron Laser .... 261
6.4. Summary ...............................•............. 263
x Contents
7. CoUective Ion Acceleration with Intense Relativistic Electron Beams ....... 267
7.1. Introduction ........................................... 267
7.2. Summary of Results for the Neutral Gas and Vacuum Diode Systems ... 269
7.2.1. Collective Acceleration in a Neutral Gas-Filled Drift Tube ...... 269
7.2.2. Collective Acceleration in an Evacuated Drift Tube ........... 275
7.3. TheIonization Front Accelerator (IFA) ........................ 277
7.4. Wave Collective Ion Acceleration Mechanisms ................... 280
7.4.1. The Autoresonant Accelerator (ARA) ..................... 282
7.4.2. The Converging Guide Accelerator (CGA) ................. 286
7.5. Summary ............................................. 289
8. Particle Beam Fusion Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
8.1. Introduction ........................................... 293
8.2. Pellet Implosion Criteria .................................. 294
8.2.1. Charged Particle Energy Deposition ...................... 298
8.2.2. Pellet Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
8.2.3. Rayleigh-Taylor Instability ............................ 306
8.2.4. Target Designs for Charged Particle Beam ICF .............. 307
8.3. Electron Beam Fusion Concepts ............................. 314
8.3.1. Electron Beam Fusion in Vacuum Diodes .................. 314
8.3.2. Multiple Electron Beam Overlap Schemes .......•.......... 315
8.4. Ion Beam Fusion Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
8.4.1. Light Ion Fusion Approaches .......................... 319
8.4.2. Heavy Ion Fusion Approaches .......................... 327
8.5. Summary ............................................. 330
REFERENCES .....•................ , ..•.....•................ 335
INDEX ..................................................... 349
1
Introduction
1.1. Background
The rapid development since the early 1960s of a high-voltage pulsed
power technology has resulted in methods for generating very-high-current
pulses (;::; 10 kA) of electrons and ions with particle kinetic energies in the
range from - 100 ke V to ;;;:; 10 MeV. Although such techniques were
originally developed for materials testing, X-radiography, and nuclear
weapon effects simulation applications, they have since found widespread
use in such diverse fields as thermonuclear fusion, microwave generation,
collective ion acceleration, and laser excitation.
While the goals and objectives of such varied research areas may
necessarily differ, there is nonetheless a common need for understanding the
physical principles which govern the motion of intense charged particle
beams. The central aim of this book is to provide a basic description of
intense beam transport in a variety of situations ·of practical interest. In this
introductory chapter we first present a brief summary of the pulse power
technology that has made possible the remaining topics. In Section 1.3 we
present an elementary description of intense beam behavior with the use of
single-particle beam envelope equations, while the basic equations relevant
for a macroscopic fluid treatment are developed in Section 1.4.
Chapters 2-5 form the essential core of the book, with Chapter 2
presenting the various mechanisms for generating intense electron and ion
beams in high-voltage diodes. The important electron emission processes are
described in Section 2.2, while electron flow in high-power diodes is studied
in Section 2.3. As discussed in Section 2.4, the same high-voltage diodes are
also capable of generating very intense ion beams provided that the electron
distribution in the diode is suitably controlled or modified.
Chapter 3 deals with the transport of intense beams in vacuum. For
electron beams particular emphasis is placed on the equilibrium and stabil-