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Plasma Kinetic Theory




ISBN 9781420075809
Published May 13, 2008 by Chapman and Hall/CRC
344 Pages 39 B/W Illustrations

 
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Book Description

Developed from the lectures of a leading expert in plasma wave research, Plasma Kinetic Theory provides the essential material for an introductory course on plasma physics as well as the basis for a more advanced course on kinetic theory. Exploring various wave phenomena in plasmas, it offers wide-ranging coverage of the field.

After introducing basic kinetic equations and the Lenard–Balescu equation, the book covers the important Vlasov–Maxwell equations. The solutions of these equations in linear and quasilinear approximations comprise the majority of kinetic theory. Another main topic in kinetic theory is to assess the effects of collisions or correlations in waves. The author discusses the effects of collisions in magnetized plasma and calculates the different transport coefficients, such as pressure tensor, viscosity, and thermal diffusion, that depend on collisions.

 

With worked examples and problem sets that enable sound comprehension, this text presents a detailed, mathematical approach to applying plasma kinetic theory to diffusion processes in plasmas.

Table of Contents

INTRODUCTION
Overview
Plasma frequency
Debye length
Plasma parameter
Distribution functions
Cyclotron frequencies
Collisions
Particle drifts
Waves
Plasma radiation
BASIC KINETIC EQUATIONS
The Klimontovich equation
The Liouville equation
System ensembles
THE LENARD–BALESCU EQUATION
Bogolyubov’s hypothesis
Solution via Fourier and Laplace transforms
The Fokker–Planck equation
Dynamic friction and diffusion
THE VLASOV-MAXWELL EQUATIONS
Electrostatic waves in an unmagnetized plasma
Effects of collisions on Landau damping
The Debye potential
WAVES IN A MAGNETIZED HOT PLASMA
The hot plasma dielectric tensor
Electrostatic waves
Velocity space instabilities
Conservation of energy and power flow
Collisional effects
Relativistic plasma effects
MOMENT EQUATIONS AND FLUID PLASMAS
Moments of the distribution function
The fluid equations
Low frequency waves
High frequency waves
TRANSPORT IN A NONUNIFORM GAS
Boltzmann equation
Collision symmetries
Collision theorems
The equilibrium state
The mean free time theory
The formal theory of kinetic processes
Results of the variational procedure
TRANSPORT IN A NONUNIFORM BINARY GAS
The Boltzmann equations
The equations of hydrodynamics
The collision terms
The equilibrium state
The formal theory of kinetic processes
The variation method
Results
TRANSPORT WITH A FINITE MAGNETIC FIELD
Boltzmann equations
The magnetohydrodynamic (MHD) equations
The formal theory of kinetic processes
Solutions for the electrical conductivity
Thermal conductivity and diffusion
The pressure tensor
Summary of results
APPENDIX A: MATHEMATICAL FUNCTIONS
APPENDIX B: COLLISION INTEGRALS
APPENDIX C: NOTATION AND LIST OF SYMBOLS
Bibliography
Index

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