Classical Transport Theory

Classical Transport Theory

1st Edition - January 1, 1988

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  • Author: R. Balescu
  • eBook ISBN: 9781483294551

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Transport Processes in Plasmas, Vol. 1: Classical Transport Theory focuses on problems on the transport of matter, pressure and velocity gradients combined with external electric, magnetic fields, and momentum and energy in a plasma submitted to temperature. The publication first ponders on the motion of a charged particle in an electromagnetic field and microscopic description of a plasma. Discussions focus on Liouville equation for independent particles in stationary external fields, Landau kinetic equation, conservation properties of the collision term, motion of a charged particle in simple electromagnetic fields, drift approximation, and Hamiltonian mechanics. The text then examines the macroscopic description of a plasma and Hermitian moment representation. Topics include local plasma equilibrium state, classification of the moments, local distribution functions, macroscopic quantities of a plasma, equations of evolution of the macroscopic quantities, and entropy balance. The manuscript reviews magnetohydrodynamics, entropy and transport, and classical transport theory. Concerns include linear transport regime, classical transport coefficients, entropy and Hermitian moments, transport form of the entropy production, and resistive magnetohydrodynamics. The book is a valuable source of data for researchers interested in the classical transport theory.

Table of Contents

  • Preface v

    Introduction 1

    Chapter 1. Motion of a Charged Particle in an Electromagnetic Field

    1.1. Introduction

    1.2. Hamiltonian Mechanics. Canonical and Pseudo-Canonical Transformations

    1.3 Magnetic Field and Magnetic Field Lines. Intrinsic Local Reference Frame

    1.4. Equations of Motion of a Charged Particle in an Inhomogeneous Stationary Electromagnetic Field. Particle Variables

    1.5. Motion of a Charged Particle in Simple Electromagnetic Fields

    1.6. The Drift Approximation: The Method of the Average

    1.7. The Drift Approximation: The Averaging Pseudo-Canonical Transformation. I. Stationary, Homogeneous Fields

    1.8. The Drift Approximation: The Averaging Pseudo-Canonical Transformation. II. Stationary, Spatially Inhomogeneous Fields

    1.9. The Drift Approximation: The Averaging Pseudo-Canonical Transformation. III. Slowly Time-Dependent, Inhomogeneous Fields


    Chapter 2. The Microscopic Description of a Plasma

    2.1. Statistical Description of a Plasma

    2.2. Liouville Equation for Independent Particles in Stationary External Fields

    2.3. Liouville Equation for Independent Particles in Time-Dependent External Fields

    2.4. The BBGKY Equations and the Kinetic Equation for Interacting Charged Particles

    2.5. The Vlasov Kinetic Equation

    2.6. The Landau Kinetic Equation

    2.7. Conservation Properties of the Collision Term

    2.8. The "Lorentz Process"

    Appendix 2A.1. Derivation of the Collision Term


    Chapter 3. The Macroscopic Description of a Plasma

    3.1. Local Distribution Functions

    3.2. Macroscopic Quantities of a Plasma

    3.3. Kinetic Equation Revisited

    3.4. Equations of Evolution of the Macroscopic Quantities

    3.5. The Entropy Balance


    Chapter 4. The Hermitian Moment Representation

    4.1. Characteristic Time Scales. The Quasi-Neutrality Approximation

    4.2. The Local Plasma Equilibrium State

    4.3. The Hermitian Moment Expansion

    4.4. Classification of the Moments

    4.5. Equations of Evolution for the Moments. I. General Form

    4.6. Equations of Evolution for the Moments. II. The Generalized Frictions

    Appendix 4A.1. Derivation of the Moment Equations

    Appendix 4A.2. Proof of the Results of Table 6.1

    Appendix 4A.3. Collisional Contributions to the Moment Equations


    Chapter 5. The Classical Transport Theory

    5.1. The Linear Transport Regime

    5.2. Solution of the Linearized Moment Equations. Asymptotics and Markovianization. Moment Description and Thermodynamics

    5.3. The Classical Transport Coefficients

    5.4. Numerical Values of the Transport Coefficients. Convergence of the Approximationscheme

    5.5. Discussion of the Transport Equations

    5.6. Limiting Values of the Transport Coefficients in a Very Strong Magnetic Field

    5.7. Comparison with Other Treatments


    Chapter 6. Entropy and Transport

    6.1. Entropy Balance and H-Theorem

    6.2. Entropy and Hermitian Moments. The Kinetic Form of the Entropy Production

    6.3. The Thermodynamic Form of the Entropy Production

    6.4. The Transport Form of the Entropy Production


    Chapter 7. Magnetohydrodynamics

    7.1. The Classical Hydrodynamical Equations. Dissipative Magnetohydrodynamics

    7.2. Resistive Magnetohydrodynamics

    7.3. Ideal Magnetohydrodynamics

    7.4. Magnetohydrodynamics, Astrophysics and Fusion. The Strategy of Fusion Theory


    General Appendix G1. Basis Functions in Velocity Space

    G1.1. Expansions Around the Reference Distribution Function

    G1.2. Reducible Tensorial Hermite Polynomials

    G1.3. Spherical Harmonics, Laguerre-Sonine Polynomials, Burnett Functions

    G1.4. Irreducible Tensorial Hermite Polynomials


    Author index

    Subject index

    Index of notations

Product details

  • No. of pages: 364
  • Language: English
  • Copyright: © North Holland 1988
  • Published: January 1, 1988
  • Imprint: North Holland
  • eBook ISBN: 9781483294551

About the Author

R. Balescu

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