Table Of ContentReviews of Plasma Physics
VOPROSY TEORII PLAZMY
BOnPOCbl TEOPJ1l1 nJIA3Mbl
Translated from Russian by Dave Parsons
Translation Editor Herbert Lashinsky
University of Maryland
Reviews of
Plasma Physics
Edited by Acad. M. A. Leontovich
Volume
®SPRINGER SCIENCE+BUSINESS MEDIA, LLC
The Library of Congress cataloged the first volume of this title as follows:
Reviews of plasma physics. v. 1-
New York, Consultants Bureau, 1965-
/v. illus. 24 em.
Translation of Voprosy teorii plasmy.
Editor: v. 1 - M.A. Leontovich.
1. Plasma (Ionized gases)- Collected works. I. Leontovich, M. A., ed. II. Consul-
tants Bureau Enterprises, inc., New York. III. Title: Voprosy teorii plasmy. Eng.
QC718.V63 64-23244
The original text, published by Atomizdat in Moscow in 1974,
has been corrected and updated by the authors.
Library of Congress Catalog Card Number 64-23244
ISBN 978-1-4615-7816-1 ISBN 978-1-4615-7814-7 (eBook)
DOI 10.1007/978-1-4615-7814-7
© 1980 Springer Science+Business Media New York
Originally published by Plenum Publishing Corporation, New York in 1980
Softcover reprint of the hardcover 1st edition 1980
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,
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TRANSLATOR'S PREFACE
In the interest of speed and economy the notation of the orig-
inal text has been retained so that the cross product of two vectors
A and B is denoted by [AB], the dot product by (AB), the Laplacian
operator by ~. etc. It might also be worth pointing out that the
temperature is frequently expressed in energy units in the Soviet
literature so that the Boltzmann constant will be missing in various
familiar expressions. In matters of terminology, whenever pos-
sible several forms are used when a term is first introduced, e.g.,
magnetoacoustic and magnetosonic waves, "probkotron" and mirror
machine, etc. It is hoped in this way to help the reader to relate
the terms used here with those in existing translations and with
the conventional nomenclature. In general the system of literature
citation used in the bibliographies follows that of the American
Institute of Physics "Soviet Physics" series. Except for the cor-
rection of some obvious misprints the text is that of the original.
We wish to express our gratitude to Academician Leontovich
for kindly providing the latest corrections and additions to the
Russian text.
v
CONTENTS
Steady-State Plasma Flow in a Magnetic
Field
A. I. Morozov and L. S. Solov'ev
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 1. Acceleration Mechanisms , • • • • • • • • • • . 2
§1. Microscopic Picture of Plasma
Acceleration . . . . . . . . . . . . . . . . . . . 2
§2. Conditions for the Existence of an Electric
Field in a Plasma. , ••• , , , • , . . • • . • 5
§3. Basic Equations; the Replacement
Factor ~ . . . . . . . . . . . . . . . . . . . . . 8
§4. Perturbations of the Plasma Stream •.• , , 11
Chapter 2. Axisymmetric Flow of an Ideal Plasma
in a Magnetic Field with ~ = 0 , , , • • . • 18
§1. Conservation Laws and Equations for
the Stream Functions , • , . , • • . • • • • • 18
§2. Axisymmetric Flow across an Azimuthal
Magnetic Field. • • • • • • • • • • • • • • • • • 23
§3. Plasma Flow in a Narrow Flux Tube
(Hr!=O)....................... 26
§4. Integrable Flows Which Vary Slowly
along the z Axis. • • • • • • • • • • • • • • • • 35
§5. Flow Velocity Equal to Signal Velocity
at Some Point ••••• , .•••• , •• , •• , 43
§ 6, Current Eddies and Critical Surfaces, , , , • 45
vii
viii CONTENTS
Chapter 3. Flow in Axisymmetric Channel
with a Longitudinal Magnetic Field 54
§1. Integrated Characteristics •••••••••••• 54
§2. Flow in Narrow Axisymmetric Channel .•• 56
§3. Flow of Cold Plasma in Channel of Slowly
Varying Cross Section• ••••••••••.• 68
Chapter 4. Axisymmetric Hall Flow of an Ideal
Plasma . ...................... 70
§1. Conservation Laws and Integral
Parameters . ................... 70
§2. Qualitative Analysis of Equations (4.18)
and (4.19) ..................... 74
§3. Flow of a Two-Component Plasma
in Narrow Tube with H 1 = 0 . . . . . . . . . 81
§4. Flow in Smooth Channel with H 1 = 0 . . . . . 84
Appendix 1. Two-Parameter Steady-State Hydro-
magnetic Flow of Ideally Conducting Medium
in Arbitrary Curvilinear Coordinate System • • • • • 85
Appendix 2. Steady-State Symmetric Flow in
· Two-Fluid Magnetohydrodynamics . • . • • • • . • • • 94
§ 1. Flow of the Electron and Ion Fluids • • . • • • 94
§2. Symmetric Flows of Two-Fluid Magneto-
hydrodynamics with Slow Variation
along One of the Coordinates . • • • . • • . 100
References ........... ~ . . . . . . . . . . . . . . . . . . 102
C a 1 c u 1 at ion of Two-Dimension a 1 Plasma
Flows in Channels
K. V. Brushlinskii and A. I. Morozov
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Chapter 1. Formulation of the Problem and Method
of Analysis . • • • • . . • • . . . • • • . . . • • 108
§1.1. Physical Formulation of the Problem. • • • • 108
§1.2. Mathematical Models • • • • . • • . • . . • • • • 122
§1.3. Method for Numerical Solution
of the Problem. • . • • . • . • . • . . • . . . . 137
CONTENTS ix
Chapter 2. Flow of Fully Ionized Plasma •••••••.•. 145
§2.1. Establishment of Steady-State;
Stability of the Flow • • • • • • . • . • • • • • 145
§2.2. Quasi-One-Dimensional Flow •.•••••••• 148
§2.3. Two-Dimensional Flow of Ideal Plasma •.. 152
§2.4. Influence of a Finite Conductivity
on the Flow . • • • . • • • • . • • • • • . • • • . 157
§2 ,5. Hall Effect • • • • • • • • • • • • • . . • • • • • . . 161
§2.6. Compressional Plasma Flows • • • . • • • • • 172
Chapter 3. Flow of a Gas Which Is Ionized in the
Channel . . . • . . . . . . . . . . . . . . . . . . 182
§3.1. Ionization Process in the Flow Model 182
§3.2. Steady-State Flow with a Conductivity
Discontinuity in a Channel
of Constant Cross Section • • . . • • . • • . 184
§3.3. Calculations for the Flow of an Ionizing
Gas • . . • • • . . . • • . . . . . . • . . • . . . • 188
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Two-Dimensional Magnetohydrodynamic
Model for the Dense Plasma Focus
of a Z Pinch
V. F. D'yachenko and V. s. Imshennik
Introduction. . . • . . • . . . • • . . . • • . . • . . . . • . . . . . 199
Chapter 1. MHD Analysis of a Noncylindrical Z
Pinch ....................... . 202
§1. Description of Dissipative Processes ..•.. 202
§2. Two-Dimensional Magnetohydrodynami c
Equations (MHD Model) ••.•••••••.• 209
§3. Energy Conservation Law and Kirchhoff
Equation . . . . . . . . . . . . . . . . . . . . . . 215
§4. Initial Conditions and Boundary Conditions
for the MHD Problem ••....•••.•.. 223
§5. Dimensionless Form of the Equations;
Complete Formulation of the MHD
Problem. . . . . . . . . . . . . . . . . . . . . . 228
X CONTENTS
Chapter 2. Numerical Solution of the Two-Dimensional
MHD Problem • • • • • • • • • . • • . • • • • • • 233
§6. General Comments. . • . • . • • • • • • . • . • • • 233
§7. The Free-Point Method •••••.••.•••.•• 236
§8. The Selection of Points •••.••••••••••• 239
§9. Method for Finding the Difference
Equations • • . • • • • • • • • . . • • • • . • • • • 244
§10. Calculation Equations •.•.••••.••.•••• 248
§11. Difference Formulation of the Boundary
Conditions. • . . • . • . • • . • • • • • . • • • • • 258
§12. Formulation of the Calculation Problem •••• 261
Chapter 3. MHD Analysis of the Z Pinch • . • • • • • . • . • 2 63
§13. A Few Comments. • • • • • • • • . • • . . . • • . • 263
§14. Collapse of the Shock Wave and the Current
Sheet to the Axis of the System •••••••• 265
§15. First Plasma Compression •••••••••••. 268
§16. Second Plasma Compression •••••.••••• 273
§17. Instability of the Plasma Interface
with the Magnetic Field •••.••.••••.• 280
§18. Energy Balance and Neutron Yield
of the Plasma Focus •.••.•..••••••• 287
Conclusion 295
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 97
Plasma Optics
A. I. Morozov and S. V. Lebedev
Chapter 1. Introduction . ..................... . 301
§1. Basic Concepts of Plasma Optics •••••••• 301
§2. Electric Field in the Plasma for Te = 0 •.•• 308
§3. Analysis of Plasma-Optical Systems ••.••• 322
Chapter 2. Analysis of a Paraxial Beam
in the Single-Particle Approximation .••• 325
§1. Specification of the Magnetic Fields •••••• 325
§2. Paraxial Approximation •..••••••.•••• 330
§3. Incorporation of Aberrations in
the Grinberg Scheme. • • • • • • • • • • • • • • 342
CONTENTS xi
§4. Harmonic Systems with Equipotential Prin-
cipal Trajectory• ••••••••••••••••• 345
§5. The "Weak-Field Approximation"
for Lenses ..................... 353
§6. Variational Formulation of Particle-
Optical Problems ••••••••••••••••• 362
Chapter 3. Plasma Lenses . . . . . . . . . . . . . . . . . . . . 367
§1. Axial Plasma Lens • • • • • • • • • • • • • • • • • • 367
§2. Annular Magnetic Lens ••••••••••••••• 373
§3. Electrostatic Plasma Lens ••••••••••••• 377
§4. First-Order Aberrations of an Annular
Plasma Lens . . . . . . . . . . . . . . . . . . . . 382
§5. Multiple-Lens, Multiply Connected
Charged-Particle Accelerators •••••••• 386
§6. Toroidal Multiply Connected, Multiple-Lens
Accelerator . .................... 394
Chapter 4. Plasma-Optical Systems with Two-
Parameter Focusing • • • • • • • • • • • • • • • 400
§1. Systems with Stabilized Focus •••••••••• 400
§2. Focusing in Terms of the Radial and
Azimuthal Velocities (Whirler System) ••• 404
§3. Energy Recovery • • • • • • • • • • • • • • • • • • • 410
Chapter 5, Equilibrium Neutralized Ion Beams ••••••• 414
§1. Thermalized Potential• ••••••••••••••• 414
§2. Distributions of the Thermalized Potential
and the Electron Temperature in
a Steady-State Plasma System •••••••• 418
§3. Ion Dynamics ..................... 427
§4. Electron Sheath of a Neutralized Ion Beam
Detached from the Walls ••.••.••.•.. 439
§5. Grazing a Neutralized Ion Beam in an
Axial Lens ..................... 448
§6. Magnetic Fields Produced by the
Currents Flowing in a Multiply
Connected, Multiple-Lens Accelerator ••• 456
References ...............•............... 458
