# Plasma Electrodynamics

## 1st Edition

### Linear Theory

**Authors:**A. I. Akhiezer I. A. Akhiezer R. V. Polovin

**Editors:**D. Ter Haar

**eBook ISBN:**9781483152158

**Imprint:**Pergamon

**Published Date:**1st January 1975

**Page Count:**432

## Description

Plasma Electrodynamics, Volume 1: Linear Theory is a seven-chapter book that begins with a description of the general methods of describing plasma, particularly, kinetic and hydrodynamic methods. Chapter 2 discusses the linear theory of magneto-hydrodynamic waves. Chapter 3 describes the non-linear magneto-hydrodynamic waves, both simple waves and shock waves. Subsequent chapters explain the high-frequency oscillations in an unmagnetized plasma; oscillations of a plasma in a magnetic field; and interaction between charged particle beams and a plasma. The last chapter details the oscillations of a partially ionized plasma.

## Table of Contents

Preface

Preface to the English Edition

Chapter 1. Kinetic and Hydrodynamic Methods of Describing a Plasma

1.1. Kinetic Equations Hierarchy

1.1.1. Screened Coulomb Interaction and the Existence of Plasma Oscillations

1.1.2. Many-Particle Distribution Functions and Correlation Functions

1.1.3. Chain of Equations for Many-Particle Functions

1.2. The Vlasov Equation

1.2.1. The Plasma Parameter

1.2.2. The Self-Consistent Field

1.2.3. Set of Kinetic Equations with Self-Consistent Fields for a Multi-Component Plasma

1.3. The Pair Correlation Function of an Equilibrium Plasma and the Landau Collision Integral

1.3.1. The Pair Correlation Function

1.3.2. Landau Collision Integral

1.4. Relaxation of a Plasma

1.4.1. Relaxation Time of a Plasma

1.4.2. The Equalization of the Electron and Ion Temperatures

1.4.3. Boitzmann's H-Theorem for a Quiescent Plasma

1.5. The Hydrodynamical Description of a Plasma

1.5.1. The Hydrodynamical Description

1.5.2. The Equations of Magneto-Hydrodynamics

1.5.3. Transition from the Kinetic to the Hydrodynamical Description

1.5.4. Two-Component Hydrodynamics

1.5.5. Generalized Ohm Law

Chapter 2. Small Amplitude Magneto-Hydrodynamic Waves

2.1. Magneto-Sound and Alfvén Waves

2.1.1. Phase Velocities and Polarization

2.1.2. Polars

2.1.3. Conical Refraction

2.1.4. Damping of Magneto-Hydrodynamic Waves

2.1.5. Excitation of Magneto-Hydrodynamic Waves

2.1.6. Evolution of a Perturbation

2.2. Characteristics of the Magneto-Hydrodynamical Equations

2.2.1. Characteristic Lines

2.2.2. Characteristic Surfaces

2.2.3. Characteristics of Stationary Flow

Chapter 3. Simple Waves and Shock Waves in Magneto-Hydrodynamics

3.1. Simple Waves

3.1.1. The Connection between Simple Waves and Small Amplitude Waves

3.1.2. Kinds of Simple Waves

3.1.3. Distortion of the Profile of a Simple Wave

3.1.4. Integration of the Equations for Simple Waves

3.1.5. Riemann Invariants

3.1.6. Friedrichs' Theorem

3.2. Discontinuities

3.2.1. Boundary Conditions

3.2.2. Classification of Discontinuities

3.2.3. Zemplén's Theorem

3.2.4. Simple and Shock Waves in Relativistic Magneto-Hydrodynamics

3.3. Stability and Structure of Shock Waves

3.3.1. Evolutionarity of Shock Waves

3.3.2. Structure of the Shock Waves

3.3.3. Oscillatory Structure of a Shock Wave When There is a Magnetic Field Present

3.3.4. Cases of Degeneracy

3.3.5. Exothermic and Endothermic Discontinuities

3.3.6. Sweeping-out Conditions

3.4. Study of Discontinuities

3.4.1. Discontinuities in Various Quantities

3.4.2. Order of Sequence of Waves

3.4.3. The Piston Problem

3.4.4. Splitting-up of a Discontinuity

3.4.5. The Chapman-Jouguet Theorem

3.4.6. Oblique Shock Waves

Chapter 4. High-Frequency Oscillations in an Unmagnetized Plasma

4.1. Hydrodynamical Theory of High-Frequency Oscillations of an Unmagnetized Plasma

4.1.1. Electromagnetic Waves in a Plasma

4.1.2. Langmuir Oscillations

4.1.3. Ion-Sound Oscillations

4.2. Kinetic Theory of Longitudinal Plasma Oscillations

4.2.1. Evolution of an Initial Perturbation

4.2.2. Frequency and Damping of Langmuir Oscillations

4.2.3. The Meaning of Landau Damping

4.2.4. Kinetic Theory of Ion-Sound Oscillations

4.3. Kinetic Theory of Electromagnetic Waves in a Plasma

4.3.1. The Dielectric Permittivity Tensor and the Dispersion Equation for Electromagnetic Waves in a Uniform Plasma

4.3.2. Polarization of Plasma Waves

4.3.3. Excitation of Waves in a Plasma

4.3.4. The Dielectric Permittivity Tensor in the Case of an Isotropic Particle Distribution

Chapter 5. Oscillations of a Plasma in a Magnetic Field

5.1. Hydrodynamical Theory of Oscillations of a Plasma in a Magnetic Field

5.1.1. Dielectric Permittivity Tensor of a Cold Plasma in a Magnetic Field

5.1.2. Plasma (Hybrid) Resonances in a Cold Plasma

5.1.3. General Picture of the Spectra of the Oscillations of a Cold Magneto-Active Plasma

5.1.4. High-Frequency (Electronic) Branches of the Oscillations in a Cold Magneto-Active Plasma

5.1.5. Low-Frequency Branches of the Oscillations of a Cold Magneto-Active Plasma

5.1.6. Propagation of Electromagnetic Waves in a Cold Magneto-Active Plasma Parallel to the Magnetic Field

5.1.7. Transverse Propagation of Electromagnetic Waves in a Cold Magneto-Active Plasma

5.2. Kinetic Theory of Plasma Oscillations in a Magnetic Field

5.2.1. Dielectric Permittivity Tensor in a Magneto-Active Plasma in the Kinetic Approximation

5.2.2. The Dielectric Permittivity Tensor of a Plasma with a Maxwell Distribution

5.2.3. Kinetic Theory of Plasma Resonances

5.3. Damping of High-Frequency Electromagnetic Waves in a Magneto-Active Plasma

5.3.1. Electron-Cyclotron Absorption of the Extra-Ordinary Wave in a Hot Low-Density Plasma

5.3.2. Electron-Cyclotron Absorption of the Slow Extra-Ordinary Wave and of the Ordinary Wave in a High-Density Plasma

5.3.3. Electron-Cyclotron Resonance At Higher Harmonics and Electron Cherenkov Damping of High-Frequency Waves

5.3.4. Damping of Waves Near Plasma Resonances

5.4. Absorption of Alfvén and Fast Magneto-Sound Waves

5.4.1. Cherenkov Absorption of Alfvén and Fast Magneto-Sound Waves in a Low-Pressure Plasma

5.4.2. Ion-Cyclotron Resonance

5.5. Low-Frequency Oscillations of a Hot Plasma in a Magnetic Field

5.5.1. Longitudinal Oscillations of a Plasma with Hot Electrons and Cold Ions

5.5.2. Low-Frequency Electromagnetic Waves in a Plasma with Finite Pressure and To » Ti

5.5.3. High-Frequency Electron Sound

5.5.4. Low-Frequency Electron Sound

5.6. Cyclotron Waves in a Plasma for the Case of Quasi-Transverse Propagation

5.6.1. Longitudinal Ion-Cyclotron Oscillations in a Plasma for Quasi-Transverse Propagation

5.6.2. Non-Potential Ion-Cyclotron Waves in an Isothermal Low-Pressure Plasma for the Case of Quasi-Transverse Propagation

5.7. Cyclotron Waves in the Case of Transverse Propagation

5.7.1. Ordinary Cyclotron Waves

5.7.2. Longitudinal Electron-Cyclotron Oscillations

5.7.3. Longitudinal Ion-Cyclotron Oscillations

5.7.4. Extra-Ordinary Electron-Cyclotron Waves

5.7.5. Extra-Ordinary Ion-Cyclotron Waves

Chapter 6. Interaction between Charged Particle Beams and a Plasma. Stable and Unstable Particle Distributions in a Plasma

6.1. Interaction of Charged Particle Beams with the Oscillations of an Unmagnetized Plasma

6.1.1. Dispersion Equation for a Beam-Plasma System

6.1.2. Excitation of Longitudinal Plasma Oscillations by Resonance Beam Particles

6.1.3. Excitation of Longitudinal Oscillations by a Monoenergetical Beam

6.1.4. Instability of a Plasma in Which the Electrons Move Relative to the Ions

6.1.5. Excitation of Electromagnetic Waves in a Plasma by Charged Particle Currents

6.1.6. Instability of a Plasma with an Anisotropic Velocity Distribution

6.2. Interaction of a Charged Particle Beam with Plasma Oscillations in a Magnetic Field

6.2.1. The Dielectric Permittivity Tensor of a Beam-Plasma System in a Magnetic Field

6.2.2. Excitation of Longitudinal Oscillations of a Plasma in a Magnetic Field by an Electron Beam

6.2.3. Instability of a Magneto-Active Plasma in the Field of a Low-Frequency Electromagnetic Wave

6.2.4. The Excitation of Fast Magneto-Sound and Alfvén Waves by Electron and Ion Beams

6.3. Excitation of Electromagnetic Waves in a Plasma by Oscillator Beams

6.3.1. Dielectric Permittivity Tensor of an Oscillator Beam-Plasma System

6.3.2. Excitation of Longitudinal High-Frequency Oscillations by an Electron Oscillator Beam

6.3.3. Excitation of Fast Magneto-Sound Waves and Alfvén Waves by Oscillator Beams

6.4. Excitation of Electromagnetic Waves in a Plasma by Relativistic Charged Particle Beams

6.4.1. The Dielectric Permittivity Tensor of a Relativistic Plasma Beam

6.4.2. Excitation of Electromagnetic Waves in an Unmagnetized Plasma by a Relativistic Electron Beam

6.4.3. Dispersion Equation for "Oblique" Wave Propagation

6.4.4. Transverse Propagation

6.5. General Criteria for the Stability of Particle Distributions in a Plasma

6.5.1. Criteria for the Stability Or Instability of Particle Distributions in an Unmagnetized Plasma

6.5.2. Two-Stream Instability

6.5.3. Stability Criteria for Electron Distributions in a Plasma in a Magnetic Field

6.6. Absolute and Convective Instabilities

6.6.1. Criteria for Absolute and Convective Instability

6.6.2. The Traveling Waves Method

6.6.3. Criterion for Amplification and Blocking of Oscillations

6.6.4. Sturrock's Rules

6.6.5. Global Instability

6.6.6. Non-Invariant Nature of the Concepts of Absolute and Convective Instabilities

6.6.7. Nature of the Beam Instability

Chapter 7. Oscillations of a Partially Ionized Plasma

7.1. Electron Distribution Function and High-Frequency Electron Oscillations in an External Electrical Field

7.1.1. The Kinetic Equation

7.1.2. Stationary Electron Distribution Function

7.1.3. High-Frequency Electron Oscillations

7.2. Ion-Sound Oscillations in a Strong Electrical Field

7.2.1. Ion-Sound Oscillations in the Absence of an External Magnetic Field

7.2.2. Ion-Sound Oscillations in External Electrical and Magnetic Fields

7.3. Low-Frequency Oscillations of a Partially Ionized Plasma

7.3.1. Oscillations Involving Non-Conservation of the Numbers of Particles of the Different Components of the Plasma

7.3.2. Large Amplitude Uniform Low-Frequency Oscillations

References

Glossary

Index

Other Titles in the Series in Natural Phylosophy

Contents of Volume 2 Non-linear Theory and Fluctuations

Chapter 8. Non-Linear Waves in a Collisionless Plasma

8.1. Non-Linear High-Frequency Waves in a Cold Plasma

8.2. Non-Linear Waves in an Unmagnetized Two-Temperature Plasma

8.3. Non-Linear Waves in an Unmagnetized Non-Equilibrium Plasma

8.4. Non-Linear Waves in a Magneto-Active Plasma with Hot Electrons

8.5. Non-Linear Low-Frequency Waves in a Cold Plasma in a Magnetic Field

Chapter 9. Theory of Plasma Oscillations in the Quasi-Linear Approximation

9.1. Quasi-Linear Theory of the Oscillations of an Unmagnetized Plasma

9.2. Quasi-Linear Theory of the Oscillations of a Magneto-Active Plasma

Chapter 10. Non-linear Wave-Particle Interactions

10.1. Kinetic Equation for the Waves

10.2. Turbulent Processes in Which Langmuir Waves Take Part

10.3. Ion-Sound Turbulence

10.4. Interaction between Magneto-Sound and Alfvén Waves

Chapter 11. Fluctuations in a Plasma

11.1. Fluctuation-Dissipation Relation

11.2. Electromagnetic Fluctuations in an Equilibrium Plasma

11.3. Transformation of the Fluctuation-Dissipation Relation

11.4. Electromagnetic Fluctuations in a Non-Isothermal Plasma

11.5. Electromagnetic Fluctuations in a Non-Equilibrium Plasma

11.6. Kinetic Theory of Fluctuations

11.7. Fluctuations in a Partially Ionized Plasma in an External Electrical Field

Chapter 12. Scattering and Transformation of Waves in a Plasma

12.1. Scattering of Electromagnetic Waves in an Unmagnetized Plasma

12.2. Transformation of Transverse and Longitudinal Waves in a Plasma

12.3. Incoherent Reflection of Electromagnetic Waves from a Plasma

12.4. Scattering and Transformation of Waves in a Plasma in a Magnetic Field

12.5. Scattering and Transformation of Waves in a Partially Ionized Plasma in an External Electrical Field

12.6. Scattering and Transformation of Waves in a Turbulent Plasma

12.7. Echoes in a Plasma

Chapter 13. Scattering of Charged Particles in a Plasma

13.1. The Passage of Charged Particles Through an Unmagnetized Plasma

13.2. Dynamic Friction and Diffusion Coefficients in a Plasma

13.3. Passage of Charged Particles Through an Equilibrium Plasma in a Magnetic Field

13.4. The Interaction of Charged Particles with a Non-Equilibrium Plasma

## Details

- No. of pages:
- 432

- Language:
- English

- Copyright:
- © Pergamon 1975

- Published:
- 1st January 1975

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483152158