Classical Transport Theory (eBook)

Front Cover 1
Classical Transport Theory 4
Copyright Page 5
Table of Contents 14
Preface 6
Introduction 18
Chapter 1. Motion of a charged particle in an electromagnetic field 22
1.1. Introduction 22
1.2. Hamiltonian mechanics. Canonical and pseudo-canonical transformations 24
1.3. Magnetic field and magnetic field lines. Intrinsic local reference frame 33
1.4. Equations of motion of a charged particle in an inhomogeneous stationary electromagnetic field. Particle variables 41
1.5. Motion of a charged particle in simple electromagnetic fields 47
1.6. The drift approximation: The method of the average 56
1.7. The drift approximation: The averaging pseudo-canonical transformation 67
1.8. The drift approximation: The averaging pseudo-canonical transformation 75
1.9. The drift approximation: The averaging pseudo-canonical transformation 86
References 93
Chapter 2. The microscopic description of a plasma 96
2.1. Statistical description of a plasma 96
2.2. Liouville equation for independent particles in stationary external fields 101
2.3. Liouville equation for independent particles in time-dependent external fields 108
2.4. The BBGKY equations and the kinetic equation for interacting charged particles 115
2.5. The Vlasov kinetic equation 121
2.6. The Landau kinetic equation 124
2.7. Conservation properties of the collision term 131
2.8 The "Lorentz process" 135
Appendix 2A.1. Derivation of the collision term 140
References 147
Chapter 3. The macroscopic description of a plasma 150
3.1. Local distribution functions 150
3.2. Macroscopic quantities of a plasma 153
3.3. Kinetic equation revisited 161
3.4. Equations of evolution of the macroscopic quantities 163
3.5. The entropy balance 172
References 178
Chapter 4. The Hermitian moment representation 180
4.1. Characteristic time scales. The quasi-neutrality approximation 180
4.2. The local plasma equilibrium state 184
4.3. The Hermitian moment expansion 187
4.4. Classification of the moments 194
4.5. Equations of evolution for the moments. I. General form 198
Appendix 4A.1. Derivation of the moment equations 219
Appendix 4A.2. Proof of the results of table 6.1 222
References 226
Chapter 5. The classical transport theory 228
5.1. The linear transport regime 228
5,2, Solution of the linearized moment equations, Asymptotics and Markovianization, Moment description and thermodynamics 234
5.3. The classical transport coefficients 245
5.4. Numerical values of the transport coefficients. Convergence of the approximation scheme 252
5.5. Discussion of the transport equations 260
5.6. Limiting values of the transport coefficients in a very strong magnetic field 275
5.7. Comparison with other treatments 281
References 292
Chapter 6. Entropy and transport 294
6.1. Entropy balance and H-theorem 294
6.2. Entropy and Hermitian moments. The kinetic form of the entropy production 298
6.3. The thermodynamic form of the entropy production 303
6.4. The transport form of the entropy production 306
References 310
Chapter 7. Magnetohydrodynamics 312
7.1. The classical hydrodynamical equations. Dissipative magnetohydrodynamics 312
7.2. Resistive magnetohydrodynamics 316
7.3. Ideal magnetohydrodynamics 322
7.4. Magnetohydrodynamics, astrophysics and fusion. The strategy of fusion theory 328
References 332
Appendix Gl: Basis functions in velocity space 334
Gl.l. Expansions around the reference distribution function 334
G1.2. Reducible tensorial Hermite polynomials 335
G1.3. Spherical harmonics, Laguerre-Sonine polynomials, Burnett functions 337
G 1.4. Irreducible tensorial H ermite polynomials 342
References 347
Author index 350
Subject index 356
Index of Notations 362