The Plasma State

1st Edition - January 1, 1971
Editor: Juda Shohet
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 4 9 9 - 4

The Plasma State discusses the fundamental principles that describe plasma occurrence. The book reviews the plasma state, collisions, collisional processes, diffusion, mobility,… Read more

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The Plasma State discusses the fundamental principles that describe plasma occurrence. The book reviews the plasma state, collisions, collisional processes, diffusion, mobility, Rutherford scattering, and the collision cross-section. The motion of isolated charged particles occurs in electrical, magnetic, or gravitational fields. During low plasma density and low background gas pressure, the collision frequency is also low. It is during this time that the single particle approach can be studied using a fundamental equation of motion. The text also discusses the problems encountered in the presence of extremely large numbers of particles, moving and interacting with one another. Other topics related to the statistics of collisions and fluid behavior are the collisionless Boltzmann equation, inclusion of collisional processes in statistical descriptions, and the "integrate out" of velocity dependence of the collisionless Boltzmann equation which gives a fluid model of a plasma. The book also describes the different acceleration processes, such as Coulomb collisions, electron or ion-neutral collisions, collective or wave phenomena, that all produce radiation. The text is suitable for students of physics, engineering, atomic physics.

Preface

1 The Plasma State

Suggested Reading

2 Collisions and Collisional Processes

A. Elementary Concepts

B. Conservation of Energy, Momentum, and Angular Momentum

C. The Collision Cross Section

D. Rutherford Scattering

E. Diffusion and Mobility

Suggested Reading

Problems

3 The Motion of Isolated Charged Particles

A. The Motion of a Charged Particle in a Magnetic Field

B. Crossed Electric and Magnetic Fields

C. Gravitational Fields

D. Magnetic Field Gradients—Magnetic Mirrors and Cusps

E. The Effects of AC Electric Fields

Suggested Reading

Problems

4 The Beginnings of Collective Phenomena—Plasma Statistical Mechanics

A. Fundamental Definitions

B. Conservation Laws for Systems

C. Density and Distribution Functions and Averages

D. Liouville's Theorem

E. The Microcanonical Ensemble

F. Development of the Distribution Laws

G. Velocity, Speed, and Energy Distribution Functions

H. Application of Ensemble Theory to a Plasma

Suggested Reading

Problems

5 Further Aspects of Collective Phenomena: Statistics of Collisions and Fluid Behavior

A. Adiabatic Invariants and Constants of the Motion

B. Hamilton-Jacobi Theory

C. Collisions in the Boltzmann Equation: Fokker-Planck Methods

D. Diffusion and Mobility from the Boltzmann Equation

E. The Moments of the Boltzmann Equation

Suggested Reading

Problems

6 Simple Applications of the Fluid and Statistical Models of a Plasma

A. Hydromagnetics (Magnetohydrodynamics)

B. Hydromagnetic Equilibrium

C. Plasma Diamagnetism

D. Magnetic Confinement

E. Hydromagnetic Wave Motion and Diffusion

F. Plasma Parameters

G. Wave Propagation in Plasmas—Introductory Remarks

Suggested Reading

Problems

7 Waves in Cold Plasmas

A. Waves and the Wave Equation

B. Eigenvalues of the RLC Circuit (Ordinary Differential Equations)

C. Eigenvalues of the Wave Equation (Partial Differential Equations)

D. Eigenvalues of Waves in Cold Plasmas—The Dispersion Relation

E. Representations of the Eigenvalues

F. Nonzero Temperature Effects

Suggested Reading

Problems

8 Waves (Stable and Unstable) in Hot Plasmas

A. Transform Theory

B. Applications of Transform Theory to the Wave Equation and Boltzmann Equation

C. The Electrostatic and Long- Wavelength Approximation

P. The Dispersion Relation for Longitudinal Electrostatic Waves, I

E. Complex Contour Integration and Analytic Continuation

F. The Dispersion Relation for Longitudinal Electrostatic Waves, II

G. The Nature of the Eigenmodes—Landau Damping

H. Waves and Instabilities—Criteria

I. Branch Lines

J. Position-Space Damping

K. Confinement and Equilibrium of a Plasma—Hydrodynamic and Microinstabilities

Suggested Reading

Problems

9 Plasma Kinetic Theory—Nonequilibrium Statistical Mechanics

A. Collisional Velocity Averages

B. Validity of Collisional Models

C. Development of the Bogoliubov, Born, Green, Kirkwood, Yvon (BBGKY) Hierarchy

D. Cluster Expansion

Suggested Reading

Problems

10 Radiation Processes and Correlation Functions

A. Generalized Emission and Absorption Processes

B. Radiation Fields from a Charged Particle

C. The Radiation Spectra

D. Bremsstrahlung

E. Cyclotron Emission

F. Fluctuations and Correlations in Plasmas

Suggested Reading

Problems

Appendix

A. Frequently Used Physical Constants

B. Useful Vector Identities

C. Units and Dimensions

Index