ISBN-10:
9814261696
ISBN-13:
9789814261692
Pub. Date:
04/28/2010
Publisher:
World Scientific Publishing Company, Incorporated
Methods of Wave Theory in Dispersive Media

Methods of Wave Theory in Dispersive Media

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Product Details

ISBN-13: 9789814261692
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 04/28/2010
Pages: 272
Product dimensions: 6.60(w) x 9.80(h) x 0.80(d)

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

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