Electrodynamics of Density Ducts in Magnetized Plasmas-The Mathematical Theory of Excitation and Propagation of Electromagnetic Waves in Plasma Waveguides

289 Pages·1999·13.103 MB·\289

by  I G Kondratiev (Author), A V Kudrin (Author), T M Zaboronkova (Author)

ELECTRODYNAMICS OF DENSITY DUCTS
IN MAGNETIZED PLASMAS

ELECTRODYNAMICS OF DENSITY DUCTS
IN MAGNETIZED PLASMAS
Igor G. Kondrat'ev
University ofNizhny Novgorod, Russia
Alexander V. Kudrin
University ofNizhny Novgorod, Russia
and
Tatyana M. Zaboronkova
Technical University ofNizhny Novgorod, Russia
CRC Press
Taylor & Francis Group
Boca Raton London New York
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First published 1999 by Gordon and Breach Science Publishers
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ISBN 13: 978-90-5699-200-2 (hbk)
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British Library Cataloguing in Publication Data
Kondrat'ev, Igor G.
Electrodynamics of density ducts in magnetized plasma
I .Electromagnetic waves - Mathematics 2.Plasma (Ionized gases) 3.Density matrices
I.Title 11.Kudrin, Alexander V. 111.Zaboronkova, Tatyana M.
539.2'0151
Contents
Preface ix
Chapter 1. Introduction
1.1. Density ducts in the earth's magnetosphere 1
1.2. Artificial density ducts created with strong electromagnetic fields
in magnetized plasmas 5
1.3. The results of model laboratory and active ionospheric experiments
on observation of artificial ducts 10
Chapter 2. The Basic Equations
2.1. Introduction 17
2.2. Maxwell's equations 17
2.3. The constitutive relations 19
2.4. The notations «, Je and H, Je 22
2.5. Dispersion properties of characteristic modes in a magnetoplasma 23
2.5.1. Dispersion equation 23
2.5.2. The functions p ,x and qi^ 27
0
2.6. The refractive index surfaces in some frequency bands 29
Chapter 3. Radiation from Given Sources in a Uniform
Unbounded Magnetoplasma
3.1. Introduction 37
3.2. General representation of source-excited fields 37
3.3. Power radiated 45
3.3.1. Integral formulation of the radiated power 45
3.3.2. Radiated power distribution over the spatial spectrum 48
3.4. Radiation from a linear electric current 49
3.4.1. Parallel orientation of a source 50
3.4.2. Perpendicular orientation of a source 57
3.5. Radiation from a ring electric current 60
3.5.1. Uniform current distribution 60
3.5.2. Nonuniform current distribution 64
3.6. Radiation from a ring magnetic current 69
3.7. On the definition of the radiation pattern 72
V
vi CONTENTS
Chapter 4. Modes in Axially Uniform Ducts
4.1. Introduction 79
4.2. The basic equations for modes of ducts 80
4.2.1. The field equations 80
4.2.2. The field solutions for a uniform plasma 85
4.2.3. The field solutions for a uniform duct 87
4.2.4. The dispersion equation for the modes of a uniform duct 91
4.3. Bound and leaky modes 94
4.4. Uniform duct without collision damping — the dispersion properties
of modes 100
4.4.1. The axisymmetric eigenmodes of a cylindrical enhancement 101
4.4.2. The axisymmetric leaky modes of a cylindrical enhancement 104
4.4.3. Some extension to the case of nonsymmetric modes 111
4.4.4. Modes of a plane duct with enhanced density 115
4.4.5. Modes of a cylindrical trough 116
4.5. Uniform duct without collision damping — field distribution 117
4.6. Mode synthesizing using Brillouin's concept 125
4.7. The effect of collisions on the characteristics of modes 130
4.8. Radially nonuniform duct with a monotonic density profile 135
4.9. Radially nonuniform duct with a nonmonotonic density profile 142
Chapter 5. Integral Representation of Source-excited
Fields on a Duct
5.1. Introduction 148
5.2. The field equations 149
5.3. Fields of ring currents, for a uniform duct 151
5.4. Analytic properties of the functions qi^ 157
5.5. Fields of ring currents, for a uniform duct (continued) 159
Chapter 6. Modal Representation of Source-excited
Fields on a Duct
6.1. Introduction. The boundary-value problem for a duct 167
6.2. The eigenfunction set for the nonuniform duct 170
6.2.1. Some mathematical developments 170
6.2.2. Field on the source-free duct 172
6.2.3. The eigenfunction expansion 179
6.3. The eigenfunction set for the uniform duct 183
CONTENTS vii
6.4. Mode orthogonality 185
6.5. Calculation of modal excitation coefficients 190
6.6. Analytic properties of the functions p (q) and q (q) 196
a a
6.7. Separation of leaky modes from the continuous spectrum 200
6.8. On the relation between alternative field representations 205
6.9. Note on the limiting transition to the case of a uniform plasma 206
6.10. The radiation field 207
6.11. The radiation pattern and the total radiated power 213
6.12. Radiated power distribution over the spatial spectrum of excited
waves 215
6.13. Some numerical results for ring currents 217
Chapter 7. Wave Propagation Along Axially Nonuni-
form Ducts
7.1. Introduction 221
7.2. The local field-structure. The method of local modes 222
7.3. Coupled local-mode equations 225
7.4. Alternative form of the coupling coefficients 227
7.5. The WKB solutions for guided modes 229
7.6. The use of successive approximations. Conditions for the validity
of the WKB solutions 230
Chapter 8. Wave Re-emission from a Density Duct
8.1. Introduction 235
8.2. Fields of local modes 236
8.3. The use of Huygens' principle and Kirchhoff's approximation 238
8.4. The distribution of fictitious sources on the radiating aperture 240
8.5. The characteristics of radiation re-emitted from the duct end 243
8.6. Some numerical examples 246
8.7. The use of artificial density ducts for increasing power radiated from
VLF/ELF sources 251
Bibliography 253
Index of definitions of the more important symbols 264
Author index 269
Subject index ill

Preface
This book is intended to provide a systematic, self-contained treatment of excita-
tion, propagation and re-emission of electromagnetic waves guided by density ducts
in magnetized plasmas. Its object is to set out the theoretical basis of electrody-
namics of ducts as fully as possible. In this book, the classical dielectric-waveguide
theory is generalized to the case of open guiding systems in a magnetoplasma and
the conceptual physical and mathematical aspects of the theory, together with its
applications to problems encountered in actual practice, are emphasized.
The book is partly based on lectures delivered by the authors at the Radiophysics
Department of the Nizhny Novgorod University and is mainly supported by original
works of the authors in the subject matter. It is therefore hoped that this book
will serve both as a textbook for a novice theorist, and as a reference source for
more experienced research workers. The reader is assumed to be familiar with
calculus, vectors analysis, the theory of complex variables, and some background in
electromagnetic theory.
To assist in understanding, especially for those comparatively new to the subject,
we begin with a discussion of the underlying physical phenomena and then provide
relevant theoretical fundamentals. This material is presented in Chapters 1, 2 and 3
which have three principal objectives: (i) to offer an outline of some of the results
of observations and formation mechanisms of natural and artificial density ducts;
(ii) to give some of the basic theory for electromagnetic waves in plasmas needed
throughout the remainder of the book; and (iii) to discuss a few specialized topics,
primarily concerning radiation from given sources in a magnetoplasma, which may
not be familiar to all readers, but are crucial to an understanding of the further
material. Chapter 4 deals with the theory of guided wave propagation along axi-
ally uniform ducts. It also serves to furnish the reader with sufficient references in
relevant areas of study. The purpose of Chapters 5 and 6 is to show how to find
the field excited by a given source in the presence of a duct. The theory of these
two chapters is set out very fully because the authors know of no other complete
treatment on that topic. The emphasis is placed on excitation of guided modes
discussed earlier. Chapter 7 is concerned with the asymptotic theory of wave prop-
agation along axially nonuniform ducts. In Chapter 8 mode re-emission from a duct
is considered.
IX