Table of Contents
Synopsis v
Introduction vii
Chapter 1 Linear Harmonic Waves in Dispersive Systems. Initial-Value Problem and Problem with An External Source 1
1 Harmonic Waves in Dispersive Systems 1
2 Initial-Value Problem. Eigenmode Method 5
3 Characteristic Function of the State Vector. Dispersion Operator 8
4 Laplace Transform Method 11
Chapter 2 A Case Study of Linear Waves in Dispersive Media 19
5 Transverse Electromagnetic Waves in an Isotropic Dielectric 19
6 Longitudinal Electrostatic Waves in a Cold Isotropic Plasma. Collisional Dissipation of Plasma Waves 22
7 Transverse Electromagnetic Waves in a Cold Isotropic Plasma. Dissipation of Transverse Waves in a Plasma 26
8 Electromagnetic Waves in Metals 31
9 Electromagnetic Waves in a Waveguide with an Isotropic Dielectric 33
10 Longitudinal Waves in a Hot Isotropic Plasma. Electron Diffusion in a Plasma 35
11 Longitudinal Waves in an Isotropic Degenerate Plasma. Waves in a Quantum Plasma 39
12 Ion Acoustic Waves in a Nonisothermal Plasma. Ambipolar Diffusion 42
13 Electromagnetic Waves in a Waveguide with an Anisotropic Plasma in a Strong External Magnetic Field 45
14 Electromagnetic Waves Propagating in a Magnetized Electron Plasma along a Magnetic Field 51
15 Electrostatic Waves Propagating in a Magnetized Electron Plasma at an Angle to a Magnetic Field 58
16 Magnetohydrodynamic Waves in a Conducting Fluid 62
17 Acoustic Waves in Crystals 69
18 Longitudinal Electrostatic Waves in a One-Dimensional Electron Beam 72
19 Beam Instability in a Plasma 76
20 Instability of a Current-Carrying Plasma 83
Chapter 3 Linear Waves in Coupled Media. Slow Amplitude Method 87
21 Coupled Oscillator Representationand Slow Amplitude Method 87
22 Beam-Plasma System in the Coupled Oscillator Representation 95
23 Basic Equations of Microwave Electronics 99
24 Resonant Buneman Instability in a Current-Carrying Plasma in the Coupled Oscillator Representation 103
25 Dispersion Function and Wave Absorption in Dissipative Systems 105
26 Some Effects in the Interaction between Waves in Coupled Systems 108
27 Waves and Their Interaction in Periodic Structures 112
Chapter 4 Nonharmonic Waves in Dispersive Media 119
28 General Solution to the Initial-Value Problem 119
29 Quasi-Harmonic Approximation. Group Velocity 123
30 Pulse Spreading in Equilibrium Dispersive Media 135
31 Stationary-Phase Method 148
32 Some Problems for Wave Equations with a Source 151
Chapter 5 Nonharmonic Waves in Nonequilibrium Media 155
33 Pulse propagation in Nonequilibrium Media 155
34 Stationary-Phase Method for Complex Frequencies 160
35 Quasi-Harmonic Approximation in the Theory of Interaction of Electron Beams with Slowing-Down Media 162
Chapter 6 Theory of Instabilities 175
36 Convective and Absolute Instabilities. First Criterion for the Type of Instability 175
37 Saddle-Point Method. Second Criterion for the Type of Instability 186
38 Third Criterion for the Type of Instability 195
39 Type of Beam Instability in the Interaction with a Slowed Wave of Zero Group Velocity in a Medium 199
40 Calculation of the Green's Functions of Unstable Systems 206
Chapter 7 Hamiltonian Method in the Theory of Electromagnetic Radiation in Dispersive Media 213
41 Equations for the Excitation of Transverse Electromagnetic Field Oscillators 213
42 Dipole Radiation 217
43 Radiation from a Moving Dipole - Undulator Radiation 219
44 Cyclotron Radiation 224
45 Cherenkov Effect. Anomalous and Normal Doppler Effects 228
46 Application of the Hamiltonian Method to the Problem of the Excitation of Longitudinal Waves 236
Appendices
Appendix 1 Absorption of the Energy of a Localized Source 239
Appendix 2 On the Theory of Electromagnetic Wave Scattering by a Free Electron 243
Appendix 3 Problem with a Source for the Wave Equation in Spontaneous Emission Theory 247
References 257
