 | Weiland J. Stability and transport in magnetic confinement systems. - New York: Springer, 2012. - x, 227 p.: ill. - (Springer series on atomic, optical, and plasma physic; 71). - Incl. bibl. ref. - Ind.: p.225-227. - ISBN 978-1-4614-3742-0; ISSN 1615-5653
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1 Introduction ................................................. 1
1.1 Principles for Confinement of Plasma by a Magnetic
Field ................................................... 1
1.2 Energy Balance in a Fusion Reactor ...................... 4
1.3 Magnetohydrodynamic Stability ........................... 7
1.4 Transport ............................................... 8
1.5 Scaling Laws for Confinement of Plasma in Toroidal
Systems ................................................. 9
1.6 The Standpoint of Fusion Research Today ................. 9
References .................................................. 10
2 Different Ways of Describing Plasma Dynamics ................ 11
2.1 General Particle Description, Liouville and
Klimontovich Equations ................................. 11
2.2 Kinetic Theory as Generally Used by Plasma
Physicists ............................................. 13
2.3 Gyrokinetic Theory ..................................... 14
2.4 Fluid Theory as Obtained by Taking Moments of the
Vlasov Equation ........................................ 15
2.4.1 The Maxwell Equations ........................... 16
2.4.2 The Low Frequency Expansion ..................... 16
2.4.3 The Energy Equation ............................. 18
2.5 Gyrofluid Theory as Obtained by Taking Moments of the
Gyrokinetic Equation ................................... 20
2.6 One Fluid Equations .................................... 21
2.7 Finite Larmor Radius Effects in a Fluid Description .... 22
2.7.1 Effects of Temperature Gradients ................ 25
References .................................................. 26
3 Fluid Description for Low Frequency Perturbations in an
Inhomogeneous Plasma ........................................ 27
3.1 Introduction ........................................... 27
3.2 Elementary Picture of Drift Waves ...................... 29
3.2.1 Effects of Finite Ion Inertia ................... 32
3.2.2 Drift Instability ............................... 34
3.2.3 Excitation by Electron-Ion Collisions ........... 35
3.3 MHD Type Modes ......................................... 36
3.3.1 Alfvén Waves .................................... 37
3.3.2 Interchange Modes ............................... 37
3.3.3 The Convective Cell Mode ........................ 40
3.3.4 Electromagnetic Interchange Modes ............... 40
3.3.5 Kink Modes ...................................... 43
3.3.6 Stabilization of Electrostatic Interchange
Modes by Parallel Electron Motion ............... 45
3.3.7 FLR Stabilization of Interchange Modes .......... 45
3.3.8 Kinetic Alfve'n Waves ........................... 47
3.4 Quasilinear Diffusion .................................. 49
3.5 Confinement Time ....................................... 52
3.6 Discussion ............................................. 53
References .................................................. 55
4 Kinetic Description of Low Frequency Modes in
Inhomogeneous Plasma ........................................ 57
4.1 Integration Along Unperturbed Orbits ................... 57
4.2 Universal Instability .................................. 63
4.3 Interchange Instability ................................ 65
4.4 Drift Alfve'n Waves and β Limitation ................... 67
4.5 Landau Damping ......................................... 70
4.6 The Magnetic Drift Mode ................................ 71
4.7 The Drift Kinetic Equation ............................. 72
4.8 Dielectric Properties of Low Frequency Vortex Modes .... 73
4.9 Finite Larmor Radius Effects Obtained by Orbit
Averaging .............................................. 76
4.10 Discussion ............................................. 80
4.11 Exercises .............................................. 80
References .................................................. 81
5 Kinetic Descriptions of Low Frequency Modes Obtained
by Gyroaveraging ............................................ 83
5.1 The Drift Kinetic Equation ............................. 83
5.1.1 Moment Equations ................................ 87
5.1.2 The Magnetic Drift Mode ......................... 88
5.1.3 The Tearing Mode ................................ 89
5.2 The Linear Gyrokinetic Equation ........................ 90
5.2.1 Applications .................................... 94
5.3 The Nonlinear Gyrokinetic Equation ..................... 96
5.4 Gyro-Fluid Equations ................................... 99
References ................................................. 100
6 Low Frequency Modes in Inhomogeneous Magnetic Fields ....... 101
6.1 Anomalous Transport in Systems with Inhomogeneous
Magnetic Fields ....................................... 101
6.2 Toroidal Mode Structure ............................... 103
6.3 Curvature Relations ................................... 107
6.4 The Influence of Magnetic Shear on Drift Waves ........ 110
6.5 Interchange Perturbations Analysed by the Energy
Principle Method ...................................... 113
6.6 Eigenvalue Equations for MHD Type Modes ............... 116
6.6.1 Stabilization of Interchange Modes by
Magnetic Shear ................................. 116
6.6.2 Ballooning Modes ............................... 119
6.7 Trapped Particle Instabilities ........................ 128
6.8 Reactive Drift Modes .................................. 131
6.8.1 Ion Temperature Gradient Modes ................. 132
6.8.2 Electron Temperature Gradient Mode ............. 135
6.8.3 Trapped Electron Modes ......................... 136
6.9 Competition Between Inhomogeneities in Density and
Temperature ........................................... 139
6.10 Advanced Fluid Models ................................. 140
6.10.1 The Development of Research .................... 141
6.10.2 Closure ........................................ 144
6.10.3 Gyro-Landau Fluid Models ....................... 146
6.10.4 Nonlinear Kinetic Fluid Equations .............. 147
6.10.5 Comparisons with Nonlinear Gyrokinetics ........ 148
6.11 Reactive Fluid Model for Strong Curvature ............. 150
6.11.1 The Toroidal η1 Mode ........................... 151
6.11.2 Electron Trapping .............................. 154
6.11.3 Transport ...................................... 156
6.11.4 Normalization of Transport Coefficients ........ 158
6.11.5 Finite Larmor Radius Stabilization ............. 159
6.11.6 The Eigenvalue Problem for Toroidal Drift
Waves .......................................... 160
6.11.7 Early Tests of the Reactive Fluid Model ........ 163
6.12 Electromagnetic Modes in Advanced Fluid Description ... 164
6.12.1 Equations for Free Electrons Including Kink
Term ........................................... 165
6.12.2 Kinetic Ballooning Modes ....................... 167
6.13 Resistive Edge Modes .................................. 168
6.13.1 Resistive Ballooning Modes ..................... 170
6.13.2 Transport in the Enhanced Confinement State .... 173
6.14 Discussion ............................................ 175
References ................................................. 176
7 Transport, Overview and Recent Developments ................ 181
7.1 Stability and Transport ............................... 181
7.2 Momentum Transport .................................... 181
7.2.1 Simulation of an Internal Barrier .............. 183
7.2.2 Simulation of an Edge Barrier .................. 184
7.3 Discussion ............................................ 187
References ................................................. 187
8 Instabilities Associated with Fast Particles in Toroidal
Confinement Systems ........................................ 191
8.1 General Considerations ................................ 191
8.2 The Development of Research ........................... 192
8.3 Dilution Due to Fast Particles ........................ 193
8.4 Fishbone Type Modes ................................... 194
8.5 Toroidal Alfvén Eigenmodes ............................ 195
8.6 Discussion ............................................ 197
References ................................................. 198
9 Nonlinear Theory ........................................... 199
9.1 The Ion Vortex Equation ............................... 199
9.2 The Nonlinear Dielectric .............................. 207
9.3 Diffusion ............................................. 208
9.4 Fokker-Planck Transition Probability .................. 212
9.5 Discussion ............................................ 215
References ................................................. 215
General References ............................................ 219
Answers to Exercises .......................................... 221
Index ......................................................... 225
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