NON-STATIONARY ELECTROMAGNETICS: an integral equations approach

474 Pages·2018·417.442 MB·English

by  Nerukh, Alexander

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E(x) E (x')+ dx'(x x')E(x')
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Taylor & Francis
Taylor & Francis Group
http:// taylorandfrancis.com
Non-Stationary Electromagnetics
An Integral Equations Approach
Second Edition
Alexander Nerukh
Trevor Benson
1rrr
PAN STANFORD PUBLISHING
Published by
Pan Stanford Publishing Pte. Ltd.
Penthouse Level, Suntec Tower 3
8 Temasek Boulevard
Singapore 038988
Email: [email protected]
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Non-Stationary Electromagnetics: An Integral Equations Approach
(Second Edition)
Copyright© 2019 Pan Stanford Publishing Pte. Ltd.
All rights reserved. This book, or parts thereof may not be reproduced in any
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ISBN 978-981-4774-95-6 (Hardcover)
ISBN 978-0-429-02773-4 ( eBook)
Contents
Preface xiii
Introduction 1
1. Basic Relations for an Electromagnetic Field in a Medium
with Time-Varying Parameters and/or Moving Boundaries 9
1.1 Generalized Wave Equation for an Electromagnetic
Field in a Time-Varying Medium 10
1.1.1 Generalized Derivatives 10
1.1.2 Initial and Boundary Conditions for
Electromagnetic Fields in a Time-Varying
Medium 12
1.1.3 Maxwell's Equations in a Generalized
Derivatives Representation 16
1.1.4 Generalized Wave Equation for the Case of
a Non-Dispersive Background 18
1.1.5 Generalized Wave Equation for the Case of a
Dispersive Background 19
1.2 Fundamental Solutions to Maxwell's Equations 21
1.2.1 The Non-Dispersive Background 21
1.2.2 The Dispersive Background 23
1.2.3 A Rectangular Waveguide with Perfectly
Conducting Walls 24
1.3 Causal Time-Spatial Interpretation of Electromagnetic
Field Interaction with Time-Varying Objects 27
1.3.1 The Volterra Integral Equation for the
Electromagnetic Field in a Non-Dispersive
Background 27
1.3.2 Influence of a Dispersive Background on the
Integral Equation Form 32
I
vi Contents
1.3.3 Spatial-Temporal Interpretation of the Volterra
Integral Equation 34
1.3.4 Three Stages of Development of
Electromagnetic Transients in a Bounded
Medium with Time-Varying Parameters 35
1.3.5 Three Stages of Solution of a Non-Stationary
Problem 39
1.4 The Resolvent Method for Solving the Integral
Equation 40
1.4.1 Operator Form of an Integral Equation
Representation 40
1.4.2 Kernels of the Integral Equations for Typical
Media 44
1.4.3 The Resolvent Method 49
2. Transformation of an Electromagnetic Field in an
Unbounded Medium with Time-Varying Parameters 59
2.1 Transformation of an Electromagnetic Wave in a
Non-Dispersive Time-Varying Medium 60
2.1.1 The Resolvent for an Unbounded Medium
with a Jump Change in Its Properties 61
2.1.2 Splitting of a Plane Harmonic Wave by a
Time Jump in Medium Parameters 63
2.1.3 Transformation of Extrinsic Source Radiation
by a Jump in Medium Parameters 68
2.2 Evolution of a Harmonic Wave in a Medium
Modulated by Repetitive Identical Pulses 76
2.2.1 Electromagnetic Waves in a Linear
Modulated Medium 76
2.2.2 "Intermittency" in Electromagnetic Wave
Transients in a Time-Varying Linear Medium 82
2.3 Wave Chaotic Behavior Generated by Linear
Time-Varying Systems 90
2.3.1 Complexity of the Signals 90
2.3.2 Dependence of Electromagnetic Pulse Form
on a Modulation Cycle Number 92
I
Contents vii
2.3.3 Wave Chaotic Behavior Generated by Linear
Time-Varying Systems 94
2.4 Electromagnetic Wave in Isotropic Plasma with
Step-Wise Change of Plasma Density 99
2.5 Plane Wave in Gyrotropic Plasma with "Switching On"
of a Magnetizing Field 102
2.5.1 Basic Equations 103
2.5.2 The Resolvent for the Integral Equation 104
2.5.3 The Case of the Arbitrary Time-Varying
Magnetic Field Approximation 106
2.5.4 The Transformation of a Plane Wave by a
Jump of a Magnetic Field 108
2.5.5 The Transformation of the Plasma
Oscillations 112
3. Influence of Medium Plane Boundaries on
Electromagnetic Transients 119
3.1 A Resolvent for an Initial-Boundary-Value 1D
Problem in a Dielectric 121
3.2 Electromagnetic Field in a Half-Restricted
Time-Varying Medium 125
3.2.1 Transformation of a Plane Wave by a
Jump Change of a Dielectric Permittivity 125
3.2.2 Splitting of a Pulse in a Half-Space with
Time-Varying Conductivity 141
3.3 Jump Changes of Plasma Density in a Plasma
Half-Space with a Plane Boundary 146
3.3.1 Plasma Density's Jump Change in a
Half-Space 146
3.3.2 The Resolvent of the Second Stage of
Evolution with Two-Step Change of
Plasma Density 152
3.3.3 The Field after One Jump of Plasma Density 154
3.3.4 Transformation of an Electromagnetic Wave
by Two-Step Change of the Plasma Density 157
3.4 The Evolution of an Electromagnetic Field in the
Dielectric Layer after Its Creation 162
I
viii Contents
3.5 Electromagnetic Field in a Layer with Non-Linear
and Time-Varying Medium 168
3.5.1 Integral Equation Representation for
Numerical Calculation 169
3.5.2 Numerical Algorithm for Solving Integral
Equations 173
3.5.3 Numerical Results 180
3.5.4 Comparison of the FDTD and Volterra
Integral Equations in Time Domain
Approaches 185
3.6 Triple Asymmetry in Time-Spatial Structure of
an Airy Pulse in Non-Stationary Environment 189
3.6.1 The Problem Equations 191
3.6.2 Transformed Pulses 194
4. 3D+ T Problems with Electromagnetic Transients 209
4.1 The 3D Resolvent for a Problem with a Plane
Boundary of a Dielectric Half-Space 209
4.1.1 The Resolvent for the Inner Problem 212
4.1.2 The Resolvent for the External Problem 221
4.2 Fresnel's Formulae in Time-Domain for a Plane
Interface between Two Dielectrics 224
4.3 Inclined Incidence of a Plane Wave on a Plane
Boundary of the Time-Varying Medium 229
4.3.1 The Field Caused by the Permittivity Time
Jump 230
4.3.2 The Field Caused by the Boundary
Presence Only 235
4.3.3 The Evolution of the Refracted Field 237
4.3.4 The Field Outside the Non-Stationary
Medium 245
4.4 Re focusing of Point Source Radiation by the Plane
Boundary of a Time-Varying Dielectric 245
4.5 Formation of Point Source Image by Time Change
of Plasma 251
I
Contents ix
4.6 Frequency Change of Partial Spherical Waves
Induced by Time Change of Medium Permittivity 259
4.6.1 Field Representation 260
4.6.2 Analysis of the Inner Field 264
4.6.3 Analysis of the Exterior Field 266
4.7 Evolution of Waves after Plasma Ignition in a
Sphere 269
4.7.1 Solution to the Problem 269
4.7.2 The Evolutionary Process 271
5. Non-Stationarity of Electromagnetic Waves Caused by
the Movement of a Medium Boundary 277
5.1 Transformation of an Electromagnetic Wave by a
Uniformly Moving Boundary of a Medium 277
5.1.1 Discrepancy of Secondary Waves and
Boundary Conditions Numbers 279
5.1.2 Resolution of Moving Boundaries
"Paradoxes" 281
5.2 Evolution of an Electromagnetic Wave after the
Beginning of Medium Boundary Movement 288
5.3 Relativistic Uniform Accelerated Movement of a
Medium Boundary 292
5.4 Electromagnetic Field Energy Accumulation in a
Collapsing Dielectric Layer 302
5.4.1 Increase of the Wave Amplitudes in the
Collapsing Layer 302
5.4.2 The Energy Accumulation in the Layer 306
5.4.3 Generation of Electromagnetic Pulses by the
Collapsing Layer 308
6. An Electromagnetic Field in a Metallic Waveguide with a
Moving Medium 317
6.1 Expansion of an Electromagnetic Field by
Non-Stationary Eigen-Functions of a Waveguide 318
6.2 Equations for a Field in the Waveguide with a
Non-Stationary Insertion 324