Table Of ContentPhysics and Chemistry in Space
Volume 10
Edited by
J. G. Roederer, Fairbanks
J. T. Wasson, Los Angeles
Editorial Board:
H. Elsasser, Heidelberg . G. Elwert, Tiibingen
L. G. Jacchia, Cambridge, Mass.
J. A. Jacobs, Cambridge, England
N. F. Ness, Greenbelt, Md .. W. Riedler, Graz
A. V. Gurevich
Nonlinear Phenomena
in the Ionosphere
Translated by J. George Adashko
With 76 Figures
Springer-Verlag
New York Heidelberg Berlin
A. V. Gurevich
P. N. Lebedev Physics Institute, USSR Academy of Sciences/
Moscow, USSR
The illustration on the cover is adapted from Figure 63
ISBN 978-3-642-87651-6 ISBN 978-3-642-87649-3 (eBook)
DOI 10.1007/978-3-642-87649-3
All righ ts reserved.
No part of this book may be translated or reproduced in any form without
written permission from Springer-Verlag.
©1978 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1978
The use of registered names, trademarks, etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from
the relevant protective laws and regulations and therefore free for general use.
9 8 7 6 5 4 3 2 I
Library of Congress Cataloging in Publication Data. Gurevich, A1eksandr
Viktorovich. Nonlinear phenomena in the ionosphere. (Physics and chemistry
in space ; 10) Translation of Nelineinye Iavleniiil v ionosfere. Added t.p.:
Nelineinye Iavlenila v ionosfere. Includes bibliographical references. I.
Ionospheric radio wave propagation. 2. Non-linear theories. 3. Plasma
(Ionized gases) I. Title. II. Title: Nelineinye Iavlenila v ionosfere. III.
Series. QC801.P46 vol. 10 [QC973.4.16) 523.01',8 [551.5'27)78-7280
Preface
Nonlinear effects in the ionosphere (cross modulation of radio waves)
have been known since the 1930s. Only recently, however, has the
rapid increase in the power and directivity of the radio transmitters
made it possible to alter the properties of the ionosphere strongly and
to modify it artificially by applying radio waves. This has revealed a
variety of new physical phenomena. Their study is not only of scien
tific interest but also undisputedly of practical interest, and is presently
progressing very rapidly. This monograph is devoted to an exposition
of the present status of theoretical research on this problem. Particular
attention is paid, naturally, to problems in the development of which
the author himself took part.
It is my pleasant duty to thank V. L. Ginzburg, L. P. Pitaevskii,
V. V. Vas'kov, E. E. Tsedilina, A. B. Shvartsburg, and Va. S. Dimant
for useful discussions and for valuable remarks during various stages
of the work on the problem considered in this book.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . .
1.1. Data on the Structure of the Ionosphere. 1
1.2. Features of Nonlinear Phenomena in the Ionosphere 4
1.2.1. Nonlinearity Mechanisms. . . . . . . . . . . . 4
1.2.2. Qualitative Character of Nonlinear Phenomena. 7
1.2.3. Brief Historical Review. . . . . . . . . . . . . . . 11
2. Plasma Kinetics in an Alternating Electric Field . . . . . . . .. 14
2.1. Homogeneous Alternating Field in a Plasma
(Elementary Theory). . . . . . . . . . . . . . . . . . . . 14
2.1.1. Electron Current-Electronic Conductivity and
Dielectric Constant. . . . . . . . . . . . . . . 15
2.1.2. Electron Temperature . . . . . . . . . . . . . 19
2.1.3. Ion Current-Heating of Electrons and Ions 29
2.2. The Kinetic Equation . . . . . . . . . . . . . . . . . 34
2.2.1. Simplification of the Kinetic Equation for
Electrons. . . . . . . . . . . . . . . . . . . . . 35
2.2.2. Transformation of the Electron Collision Integral. 40
2.2.3. Inelastic Collisions . . . . 50
2.3. Electron Distribution Function. 58
2.3.1. Strongly Ionized Plasma. 59
2.3.2. Weakly Ionized Plasma . 69
2.3.3. Arbitrary Degree of Ionization-Concerning the
Elementary Theory. . . . . . . . . . . . 82
2.4. Ion Distribution Function . . . . . . . . . . . 87
2.4.1. Simplification of the Kinetic Equation. 87
2.4.2. Distribution Function . . . . . 88
2.4.3. Ion Temperature, Ion Current. . . . . . 91
VIII Contents
2.5. Action of Radio Waves on the Ionosphere 94
2.5.1. Ionization Balance in the Ionosphere. . . 94
2.5.2. Effective Frequency of Electron and Ion
Collisions-Fraction of Lost Energy . . . 99
2.5.3. Electron and Ion Temperatures in the
Ionosphere . . . . . . . . . . . . . . . . . 106
2.5.4. Heating of the Ionosphere in an Alternating
Electric Field . . . . . . . . . . . . . . . . 108
2.5.5. Perturbations of the Electron and Ion
Concentrations. . . . . . . . . . . . . . . . 111
2.5.6. Artificial Ionization of the Ionosphere-
Heating of Neutral Gas . . . . . . . . . . 113
3. Self-Action of Plane Radio Waves . . . 125
3.1. Simplification of Initial Equations. 125
3.1.1. Nonlinear Wave Equation. . 125
3.1.2. Nonlinear Geometrical Optics of a Plane Wave. 127
3.2. Effect of Nonlinearity on the Amplitude
and Phase of the Wave . . . . . . . . 129
3.2.1. Self-Action of a Weak Wave . . . . 129
3.2.2. Self-Action of a Strong Wave. . . . l32
3.2.3. Self-Action of Waves in the Case of
Artificial Ionization . . 144
3.3. Change of Wave Modulation. . . . . . . . . 147
3.3.1. Weak Wave. . . . . . . . . . . . . . . 147
3.3.2. Change of Amplitude Modulation of
Strong Wave. . . . . . . . . . . . . . . 150
3.3.3. Phase Modulation . . . . . . . . . . . . 157
3.3.4. Nonlinear Distortion of Pulse Waveform 158
3.4. Generation of Harmonic Waves and Nonlinear
Detection . . . . . . . . . . . 161
3.4.1. Frequency Tripling. . . . . . . . . . . . . . 161
3.4.2. Nonlinear Detection. . . . . . . . . . . . . 164
3.5. Self-Action of Radio Waves in the Lower Ionosphere. 165
Contents IX
4. Interaction of Plane Radio Waves. 176
4.1. Cross Modulation. . . . . . . 176
4.1.1. Weak Waves. . . . . . 176
4.1.2. Strong Perturbing Wave. 183
4.1.3. Resonance Effects near the Electron
Gyrofrequency . . . . . . . . . 188
4.2. Interaction of Unmodulated Waves. . . . . 191
4.2.1. Interaction of Short Pulses . . . . . . 191
4.2.2. Change in the Absorption of a Wave Propagating in
a Perturbed Plasma Region . . . . . . . . 194
4.2.3. Generation of Waves with Combination
Frequencies. . . . . . . . . . . . . . . . . 196
4.3. Radio Wave Interaction in the Lower Ionosphere. 198
4.3.1. Cross Modulation . . . . . . . . . . . . . . . 198
4.3.2. Fejer's Method. . . . . . . . . . . . . . . . . 201
4.3.3. Nonstationary Processes in the Interaction
of Strong Radio Waves . . . . . . . . . . . . 204
5. Self-Action and Interaction of Radio Waves
in an Inhomogeneous Plasma . . . . . . . . . 207
5.1. Inhomogeneous Electric Field in a Plasma 207
5.1.1. Fundamental Equations . . . . . . . 207
5.1.2. Distribution of Density and Temperatures in
Plasma. . . . . . . . . . . . . . . . . . . . 216
5.2. Kinetics of Inhomogeneous Plasma. . . . . . . 221
5.2.1. Kinetic Coefficients. Elementary Theory. 221
5.2.2. Kinetic Theory . . . . . . . . . . . . . . . 225
5.2.3. Fully Ionized Plasma. . . . . . . . . . . . 234
5.3. Modification of the F Region of the Ionosphere
by Radio Waves. . . . . . . . . . . . . . . . . . . 235
5.3.1. Modification of the Electron Temperature and
of the Plasma Concentration . . . . . . . . . 235
5.3.2. Radio Wave Reflection Region. . . . . . . . 245
5.3.3. Growth and Relaxation of the Perturbations 253
x
Contents
5.4. Focusing and Defocusing of Radio Wave Beams. 258
5.4.1. Nonlinear Geometrical Optics 259
5.4.2. Defocusing of Narrow Beams. . . . . . . . 264
5.4.3. Mutual Defocusing. . . . . . . . . . . . . . 275
5.4.4. Thermal Focusing in the Lower Ionosphere. 278
6. Excitation of Ionosphere Instability . 282
6.1. Self-Focusing Instability . . . . 283
6.1.1. Spatial Instability of a Homogeneous Plasma. 283
6.1.2. Instability in the Wave-Reflection Region. . . 291
6.2. Resonant Absorption and Resonance Instability. . . 298
6.2.1. Langmuir Oscillations in an Inhomogeneous
Plasma. . . . . . . . . . . . . 299
6.2.2. Excitation of Plasma Waves. . . . . . . 305
6.2.3. Resonance Instability . . . . . . . . . . 311
6.2.4. Absorption of Ordinary Radio Waves. 315
6.3. Parametric Instability. . . . . . . . . . . . . . 321
6.3.1. Langmuir Oscillations of a Plasma in
an Alternating Field . . . . . . . . . . . 322
6.3.2. Parametric Excitation of Langmuir Oscillations. 329
6.3.3. Parametric Instability in the Ionosphere. 335
6.3.4. Dissipative Parametric Instability. 340
References . . . . 353
Principal Symbols 363
Subject Index. . . 367
1. Introduction
1.1. Data on the Structure of the Ionosphere
The ionosphere is a part of the earth's upper atmosphere, extending in
height from 60 to about 1000 km. In this region, the atmosphere is a
partly ionized gas or plasma. The processes that occur in the ionospheric
plasma are closely connected with the wave and corpuscular radiation of
the sun, with events in the magnetosphere and variation of the earth's
magnetic field, with motion of the upper atmosphere, and so on. This is
why the ionosphere varies so greatly with time (with the time of day,
with the season of the year, with the II-year cycle of solar activity) and
with geographic latitude.
The ionosphere is a transition layer between the nonionized upper
atmosphere and the fully ionized hydrogen plasma of the magnetosphere.
The structure and properties of the ionosphere, therefore, vary rapidly
with height.
The lower region of the ionosphere, at heights z = 50 to 80 km, is
usually called the 0 layer. This layer is ionized in day time. The region
at heights from 80 to 130 km is called the E layer, and that above 150 km
the F layer. A distinction is sometimes made between the F layer, up to
1
approximately 250 km, and the F 2 layer, above 250 km.
A model of the ionosphere at medium latitudes and at average solar
activity is represented in Tables 1 and 2 (Harris et aI., 1962; Al'pert et aI.,
1967). This model will be used here in estimates and numerical calculations.
The density of the upper atmosphere, as seen from Table 1, decreases
rapidly with height. The molecular composition varies little up to 100-
110 km°. In the 100-120 km region, dissociation of the oxygen molecule,
O2 -> + 0, takes place. The nitrogen dissociates at ~ 300 km. At 500-
600 km, the relative helium concentration increases rapidly, and the same
occurs for hydrogen at z ~ 1000 km. At z ~ 1500 km, the hydrogen atoms
H are in the majority.
The electron and ion densities increase up to 300-400 km (Table 2)
and then decrease quite slowly at z > 400 km. The degree of plasma
ionization, which is very low at small heights (N/Nm = 10-8 - 10-4 at
2 Introduction
Table 1. Molecular composition of the ionosphere
Day-time (12:00 noon), concentration Nm, cm-3
z, Total
km N2 O2 He 0 H Nm T,K
60 5.5· 1015 1.5· 10'5 7.0.10'5 270
70 1.6.10'5 4.2 . 1014 2.0· lO'S 200
80 2.3· 10'4 6.2· 1013 2.9· 10'4 180
90 3.1 . 1013 8.2.10'2 3.9· 1013 190
100 7.7· 10'2 1.9· 1012 5.7· 107 2.0.10" 6.2.104 9.6· 10'2 210
110 1.4 . 10'2 3.5 . 1011 3.8· 107 1.4.1011 5.3 . 104 1.9.10'2 270
120 5.8· 1011 1.2· 1011 2.5· 107 7.6· 10'0 4.3· 104 7.8· 1011 360
130 2.0.10'1 3.8. 10'0 1.7 . 107 3.7· 10'0 3.2 . 104 2.8· 1011 460
150 4.8· 10'0 7.2· 109 1.0· 107 1.35· 10'0 2.1 . 104 6.9.1010 670
200 4.8· 109 5.9· 108 4.9.106 3.0· 109 1.3 . 104 8.4· 109 1070
250 1.1 . 109 1.2· 108 3.4· 106 1.3 . 109 1.0 . 104 2.5· 109 1250
300 3.2· 108 2.7· 107 2.7· 106 5.9· 108 9.3· 103 9.3· 108 1330
400 3.5· 107 2.2 . 106 1.9 . 106 1.6· 108 8.3· 103 2.0· 108 1390
500 4.4 . 106 2.1 . 105 1.4· 106 5.0· 107 7.6· 103 5.6· 107 1400
600 5.9· 105 2.1.104 1.0· 106 1.6· 107 7.1 . 103 1.7 . 107 1400
700 8.5· 104 2.3· 103 8.0· 105 5.2· 106 6.6· 103 6.0· 106 1400
800 1.3 . 104 2.7· 102 6.1 . 105 1.8· 106 6.2 . 103 2.4· 106 1400
900 2.1 .103 3.3.10' 4.7· 105 6.2· lOS 5.8· 103 1.1 . 106 1400
1000 3.5· 102 4.3 3.7· 105 2.2· 105 5.4 . 103 6.0· 105 1400
Night-time (midnight), concentration N m' em -3
z, Total
km N2 O2 He 0 H Nm T,K
60 5.5· 1015 1.5 . 1015 7.0.10'5 270
70 1.6· 1015 4.2.10'4 2.0· 1015 200
80 2.3· 10'4 6.2· 1013 2.9· 10'4 180
90 3.1 . 1013 8.2· 10'2 3.9· 1013 190
100 7.7.10'2 1.9· 1012 5.7· 107 2.2· 1011 6.2· 104 9.6· 1012 210
110 1.4.1012 3.5· 1011 3.8· 107 1.4.1011 5.3· 104 1.9.10'2 270
120 5.8.10" 1.2 . 1011 2.5· 107 7.6· 10'0 4.3· 104 7.8 . 10" 360
130 2.0· 1011 3.7· 10'0 1.7 . 107 3.7· 10'0 3.2. 104 2.7· lO" 470
150 4.8· 10'0 7.0· 109 1.0· 107 1.4· 10'0 2.2 . 104 6.9· 10'0 650
200 4.7· 109 5.6· 108 5.9· 106 3.2· 109 1.6· 104 8.4 . 109 850
250 7.7· 108 7.1 . 107 4.3 . 106 1.2· 109 1.4· 104 2.0.109 910
300 1.4· 108 1.0· 107 3.3 . 106 4.4.108 1.3 . 104 5.9· 108 930
400 6.0.106 2.8· 105 2.1 . 106 7.0· 107 1.1 . 104 7.8· 107 940
500 2.8· 105 8.6· 103 1.3 . 106 1.2· 107 1.0· 104 1.3 . 107 950
600 1.5· 104 2.9· 102 8.7· 105 2.3· 106 9.0· 103 3.2· 106 950
700 8.4 . 102 1.1 . 10' 5.8· 105 4.4 . 105 8.1 . 103 1.0· 106 950
800 5.1 . 10 4.6 ·10-1 3.9· 105 8.9· 104 7.3 . 103 4.8.105 950
900 3.4 2.1.10-2 2.6· 105 1.9· 104 6.7· 103 2.8· 105 950
1000 2.4 . 10-1 1.0.10-3 1.8· 105 4.2· 103 6.1 . 103 1.9 . 105 950
