Classical Transport Theory

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

References

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

References

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

References

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

References

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

References

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

References

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

References

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

References

Author index

Subject index

Index of notations