Classical transport theory

Title page......Page 1
Date-line......Page 2
Preface......Page 3
Contents......Page 11
Part I. Classical transport theory......Page 9
Introduction......Page 15
1.1. Introduction......Page 19
1.2. Hamiltonian Mechanics. Canonical and pseudo-canonical transformations......Page 21
1.3 Magnetic field and magnetic field lines. Intrinsic local reference frame......Page 30
1.4. Equations of motion of a charged particle in an inhomogeneous stationary electromagnetic field. Particle variables......Page 38
1.5. Motion of a charged particle in simple electromagnetic fields......Page 44
1.6. The drift approximation: The method of the average......Page 53
1.7. The drift approximation: The averaging pseudo-canonical transformation. I. Stationary, homogeneous fields......Page 64
1.8. The drift approximation: The averaging pseudo-canonical transformation. II. Stationary, spatially inhomogeneous fields......Page 72
1.9. The drift approximation: The averaging pseudo-canonical transformation. III. Slowly time-dependent, inhomogeneous fields......Page 83
References......Page 90
2.1. Statistical description of a plasma......Page 93
2.2. Liouville equation for independent particles in stationary external fields......Page 98
2.3. Liouville equation for independent particles in time-dependent external fields......Page 105
2.4. The BBGKY equations and the kinetic equation for interacting charged particles......Page 112
2.5. The Vlasov kinetic equation......Page 118
2.6. The Landau kinetic equation......Page 121
2.7. Conservation properties of the collision term......Page 128
2.8. The \"Lorentz process\"......Page 132
Appendix 2A.1. Derivation of the collision term......Page 137
References......Page 144
3.1. Local distribution functions......Page 147
3.2. Macroscopic quantities of a plasma......Page 150
3.3. Kinetic equation revisited......Page 158
3.4. Equations of evolution of the macroscopic quantities......Page 160
3.5. The entropy balance......Page 169
References......Page 175
4.1. Characteristic time scales. The quasi-neutrality approximation......Page 177
4.2. The local plasma equilibrium state......Page 181
4.3. The Hermitian moment expansion......Page 184
4.4. Classification of the moments......Page 191
4.5. Equations of evolution for the moments. I. General form......Page 195
4.6. Equations of evolution for the moments. II. The generalized frictions......Page 204
Appendix 4A.1. Derivation of the moment equations......Page 216
Appendix 4A.2. Proof of the results of table 6.1......Page 219
Appendix 4A.3. Collisional contributions to the moment equations......Page 221
References......Page 223
5.1. The linear transport regime......Page 225
5.2. Solution of the linearized moment equations. Asymptotics and Markovianization. Moment description and thermodynamics......Page 231
5.3. The classical transport coefficients......Page 242
5.4. Numerical values of the transport coefficients. Convergence of the approximation scheme......Page 249
5.5. Discussion of the transport equations......Page 257
5.6. Limiting values of the transport coefficients in a very strong magnetic field......Page 272
5.7. Comparison with other treatments......Page 278
References......Page 289
6.1. Entropy balance and $H$-Theorem......Page 291
6.2. Entropy and Hermitian moments. The kinetic form of the entropy production......Page 295
6.3. The thermodynamic form of the entropy production......Page 300
6.4. The transport form of the entropy production......Page 302
References......Page 307
7.1. The classical hydrodynamical equations. Dissipative magnetohydrodynamics......Page 309
7.2. Resistive magnetohydrodynamics......Page 313
7.3. Ideal magnetohydrodynamics......Page 319
7.4. Magnetohydrodynamics, astrophysics and fusion. The strategy of fusion theory......Page 325
References......Page 329
G1.1. Expansions around the reference distribution function......Page 331
G1.2. Reducible tensorial Hermite polynomials......Page 332
G1.3. Spherical harmonics, Laguerre-Sonine polynomials, Burnett functions......Page 334
G1.4. Irreducible tensorial Hermite polynomials......Page 339
References......Page 344
Part II. Neoclassical transport theory......Page Balescu R. Transport processes in plasmas. V.2. Neoclassical transport theory (no pp.xxii-xxxiv)(NH, 1988)(ISBN 044487092X)(K)(T)(O)(491s)_PPl_.djvu#1
Author index......Page 347