Transport processes in plasmas. Neoclassical transport theory (no pp.xxii-xxxiv)

Title page......Page 1
Date-line......Page 2
Preface......Page 3
Part I. Classical transport theory......Page Balescu R. Transport processes in plasmas. V.1. Classical transport theory (no pp.xxii-xxxiv)(NH, 1988)(ISBN 0444870911)(K)(T)(O)(351s)_PPl_.djvu#1
Part II. Neoclassical transport theory......Page 9
Contents......Page 11
Introduction......Page 15
8.1. Magnetic surfaces......Page 19
8.2 Magnetohydrodynamic equilibrium. Toroidal coordiante systems......Page 23
8.3 Surface quantities......Page 25
8.4. Natural coordinate systems......Page 28
8.5. Magnetic differential equations......Page 34
8.6. Surface averages......Page 39
8.7. The Clebsch representation......Page 41
8.8. Axisymmetric systems......Page 45
8.9. The standard model......Page 55
References......Page 60
9.1. Introduction. Qualitative description of the motion......Page 61
9.2. Exact equations of the charged particle motion in toroidal geometry......Page 65
9.3. Equations of the guiding centre motion in toroidal geometry......Page 73
9.4. The toroidal invariant of the motion......Page 77
9.5. Topological classification of the guiding centre orbits......Page 82
9.6. Shape of the guiding centre orbits......Page 86
9.7. Solution of the equations of motion......Page 93
9.8. Effects of electric drift and of non-axisymmetry......Page 98
References......Page 103
10.1. Characteristic parameters......Page 105
10.2. Kinetic equation and natural guiding centre variables......Page 108
10.3. The multiple time-scale perturbation expansion......Page 112
10.4. The drift kinetic equation......Page 114
10.5. The local equilibrium state for a magnetically confined plasma......Page 119
10.6. Ordering of the hydrodynamical quantities in a toroidally confined plasma......Page 123
References......Page 127
11.1. Test-particle collisions and field particle collisions......Page 129
11.2. Expansion of the linearized collision term......Page 134
11.3. Properties of the basis functions......Page 141
11.4. The approximate collision operator......Page 146
11.5. Explicit form of the drift kinetic equation......Page 150
Appendix 11A.1. Calculation of the like-particle collision frequencies......Page 153
References......Page 156
12.1. Short and long mean free path regimes......Page 157
12.2. The Hermitian moment expansion......Page 161
12.3. The Chew-Goldberger-Low (CGL) pressure tensor......Page 163
12.4. The vector moment equations......Page 168
12.5. The average parallel fluxes......Page 173
12.6. The quasi-transport equations......Page 177
12.7. The perpendicular fluxes......Page 180
12.8. The zero-divergence constraint. The "poloidal fluxes"......Page 183
12.9. Decomposition of the average radial fluxes......Page 191
12.10. The average parallel electric current......Page 198
12.11. Microscopic expression of the fluxes......Page 200
Appendix 12A.1. Proof of relation (9.3)......Page 203
References......Page 204
13.1. The electric drift fluxes and the modified drift fluxes......Page 205
13.2. The classical fluxes......Page 208
13.3. The Pfirsch-Schlueter fluxes......Page 214
13.4. Classical and Pfirsch-Schlueter transport......Page 221
Appendix 13A.1. Alternative derivation of the Pfirsch-Schlueter fluxes......Page 227
References......Page 231
14.1. Expansion of the distribution function according to the collision frequency......Page 233
14.2. Integration of the zeroth-order drift kinetic equation......Page 236
14.3. The integrability conditions of the first-order drift kinetic equation......Page 238
14.4. Solution of the integrability constraints......Page 244
14.5. The NGC variables: $x$, $\lambda$, $\phi$......Page 247
14.6. Expansion of the zeroth-order distribution function......Page 252
14.7. Relation between the zeroth-order distribution function and the macroscopic fluxes to order $\epsilon$......Page 256
14.8. The function $f_p$ and the neoclassical factor $\phi$......Page 258
14.9. Strategy for the solution of the first-order drift kinetic equation......Page 263
14.10. Three properties of the drift kinetic collision operator......Page 264
14.11. Relation between generalized stresses and poloidal fluxes......Page 267
14.12. The pseudo-viscosity coefficients......Page 272
Appendix 14A.1. Proof of the Alfven formula (2.9)......Page 274
Appendix 14A.2. Integrals involving the Chandrasekhar function $\mathcal{H}(x)$......Page 277
References......Page 280
15.1. Strategy of the derivation of the banana transport equations......Page 281
15.2. Derivation of the banana transport coefficients......Page 283
15.3. The transport equations in the long mean free path regime......Page 288
15.4. Numerical values of the transport coefficients. Limiting values. Convergence of the approximation procedure......Page 297
15.5. Discussion of the banana transport coefficients......Page 305
References......Page 321
16.1. Introduction......Page 323
16.2. The NGC variables $x$, $\xi$, $\phi$......Page 324
16.3. The plateau regime......Page 330
16.4. The pseudo-viscosity coefficients in the plateau regime......Page 334
16.5. The plateau transport equations......Page 338
16.6. Interpolation formulae for the diffusion coefficient......Page 346
16.7. Approximate transport equations for the entire collision frequency range......Page 350
16.8. Miscellaneous additional topics......Page 361
Appendix 16A.1. Some useful integrals......Page 368
References......Page 369
17.1. Introduction......Page 371
17.2. The unaveraged entropy production......Page 373
17.3. Entropy production and quadratic forms......Page 378
17.4. Decomposition of the parallel fluxes......Page 383
17.5. The surface-averaged entropy production......Page 388
17.6. The Pfirsch-Schlueter average entropy production......Page 394
17.7. The average banana entropy production......Page 398
17.8. Transport coefficients and en tropic coefficients......Page 403
17.9. Conclusions and comparison with other works......Page 414
Appendix 17A.1. Some properties of the collision matrix and of the parallel quasi-transport matrix......Page 416
Appendex 17A.2. Positivity of the entropic coefficient $p_{EE}$......Page 420
References......Page 421
18.1. The problem of one-dimensional toroidal plasmadynamics......Page 423
18.2. Toroidal plasmadynamics: fluid-dynamical aspects......Page 425
18.3. Toroidal plasmadynamics: electrodynamical aspects......Page 435
18.4. Discussion of the toroidal plasmadynamical equations......Page 445
18.5. The neoclassical confinement times......Page 448
References......Page 453
19.1. The conceptual framework of classical and neoclassical transport theories......Page 455
19.2. The runaway effect......Page 457
19.3. Microscopic aspects of the runaway effect......Page 463
19.4. The emergence of anomalous transport......Page 468
References......Page 470
G2.1. Non-orthogonal coordinate systems......Page 471
G2.2. Orthogonal coordinate systems......Page 478
G2.3. Concentric circular toroidal coordinates......Page 482
References......Page 485
Author index......Page 487