Preface to the Third Edition .................................. vii
Preface to the Second Edition .................................. ix
Preface to the First Edition ................................. xiii
Acknowledgement ................................................ xv
List of Figures ............................................. xxiii
Chapter 1 Toroidal Configuration ............................... 1
1.1 INTRODUCTION ............................................... 1
1.2 GENERAL COORDINATES ........................................ 6
1.3 BASIS VECTORS, METRIC TENSOR ............................... 7
1.4 VECTOR OPERATORS ........................................... 9
1.5 MAGNETIC FIELD REPRESENTATION ............................. 10
1.6 MAGNETIC SURFACES ......................................... 11
1.7 MAGNETIC SURFACE DESTRUCTION .............................. 13
1.8 THE STANDARD MAP .......................................... 22
1.9 Problems .................................................. 29
1.10 References ................................................ 31
Chapter 2 Equilibrium ......................................... 33
2.1 INTRODUCTION .............................................. 33
2.2 THE VIRIAL THEOREM ........................................ 34
2.3 FIELD LINE CURVATURE ...................................... 35
2.4 GENERAL 3-D EQUILIBRIA .................................... 36
2.4.1 Hamada coordinates ................................. 40
2.4.2 Boozer coordinates ................................. 41
2.4.3 Cylindrical coordinates ............................ 42
2.4.4 Zakharov coordinates ............................... 42
2.5 STELLARATORS .............................................. 43
2.6 AXISYMMETRIC EQUILIBRIA ................................... 46
2.7 TOKAMAK ORDERING .......................................... 48
2.8 THE SHAFRANOV EQUILIBRIUM ................................. 49
2.9 CYLINDRICAL TOKAMAK EQUILIBRIA ............................ 55
2.10 HIGH BETA EQUILIBRIUM ..................................... 58
2.11 FLUX CONSERVING EQUILIBRIA ................................ 60
2.12 EQUILIBRIUM SCALING ....................................... 61
2.13 EQUILIBRIUM TYPES ......................................... 62
2.14 STEPPED PRESSSURE EQUILIBRIA .............................. 63
2.15 Problems .................................................. 69
2.16 References ................................................ 70
Chapter 3 Guiding Center Motion ............................... 73
3.1 INTRODUCTION .............................................. 73
3.2 LAGRANGIAN AND HAMILTONIAN FORMULATION .................... 77
3.3 ORBIT TYPES IN AXISYMMETRIC EQUILIBRIA .................... 82
3.4 INTEGRAL INVARIANTS ....................................... 93
3.5 TOROIDAL PRECESSION ....................................... 96
3.6 LARGE ASPECT RATIO ........................................ 98
3.7 DIAMAGNETIC CURRENT ...................................... 102
3.8 CONFINEMENT OF FUSION ALPHA PARTICLES .................... 104
3.9 MAGNETIC PERTURBATIONS ................................... 104
3.9.1 Toroidal field ripple ............................. 104
3.9.2 Flute modes ....................................... 105
3.9.3 Ideal MHD modes ................................... 110
3.9.4 Kinetic Poincare plots ............................ 111
3.10 SCATTERING AND ENERGY DIFFUSION .......................... 115
3.11 Problems ................................................. 118
3.12 References ............................................... 119
Chapter 4 Linear Ideal Modes ................................. 121
4.1 INTRODUCTION ............................................. 121
4.2 PLASMA KINETIC AND POTENTIAL ENERGY ...................... 126
4.3 SELF ADJOINTNESS OF THE POTENTIAL ENERGY ................. 127
4.4 THE ENERGY PRINCIPLE ..................................... 128
4.5 CONVENIENT FORM FOR SW ................................... 129
4.6 CYLINDRICAL GEOMETRY ENERGY PRINCIPLE .................... 133
4.7 MHD INSTABILITIES IN LOW Я TOKAMAKS ...................... 137
4.8 KINK MODE ................................................ 139
4.9 THE M = 1 EXTERNAL KINK .................................. 144
4.10 THE INTERNAL KINK MODE ................................... 145
4.11 BALLOONING INSTABILITIES ................................. 148
4.12 MAGNETIC WELL ............................................ 154
4.13 BALLOONING, SIMPLE EQUILIBRIA ............................ 155
4.14 MERCIER, SUYDAM CRITERIA ................................. 158
4.15 BALLOONING EQUATION MODIFICATION ......................... 162
4.16 TAE MODES ................................................ 163
4.17 AXISYMMETRIC MODES ....................................... 164
4.18 NUMERICAL MHD SPECTRUM ................................... 167
4.19 SHAPE AND ASPECT RATIO ................................... 168
4.20 Problems ................................................. 172
4.21 References ............................................... 173
Chapter 5 Linear Resistive Modes ............................. 177
5.1 INTRODUCTION ............................................. 177
5.2 THE TEARING MODE ......................................... 182
5.2.1 The tearing mode, т ≠ 1 ........................... 191
5.2.2 The m = 1 tearing mode ............................ 194
5.3 THE SKIN CURRENT PROFILE ................................. 201
5.4 TOROIDAL AND SHAPING EFFECTS ............................. 202
5.5 THE RESISTIVE SURFACE KINK MODE .......................... 204
5.6 OPTIMIZED PROFILES ....................................... 206
5.7 THE RIPPLING MODE ........................................ 208
5.8 THE RESISTIVE INTERCHANGE MODE ........................... 209
5.9 RESISTIVE BALLOONING ..................................... 209
5.10 DIAMAGNETIC ROTATION ..................................... 211
5.11 Problems ................................................. 215
5.12 References ............................................... 217
Chapter 6 Mode-Particle Interaction .......................... 221
6.1 INTRODUCTION ............................................. 221
6.2 IDEAL DISPLACEMENT  AND POTENTIAL .................. 226
6.3 RESONANCE ................................................ 233
6.4 THE FIBONACCI SEQUENCE ................................... 236
6.5 LANDAU PHASE MIXING ...................................... 238
6.6 PHASE VECTOR ROTATION .................................... 241
6.7 MODE INDUCED AVALANCHE ................................... 246
6.8 MODE-PARTICLE ENERGY TRANSFER ............................ 251
6.9 MODE EVOLUTION ........................................... 253
6.9.1 Frequency determined by equilibrium ............... 253
6.9.2 Frequency determined by particle distribution ..... 257
6.9.3 Calculation of SWn ................................ 276
6.9.4 Monte Carlo evaluation ............................ 278
6.10 TAE MODE DRIVE AND SATURATION ............................ 280
6.11 TRAPPED PARTICLE RESONANCE ............................... 284
6.12 FISHBONE INDUCED LOSS .................................... 287
6.13 FISHBONE DESTABILIZATION ................................. 289
6.14 THE FISHBONE CYCLE ....................................... 299
6.15 RESISTIVE KINETIC INTERNAL KINK .......................... 302
6.16 STABILIZATION OF THE SAWTOOTH ............................ 303
6.17 BALLOONING DESTABILIZATION ............................... 308
6.18 ALPHA PARTICLE EFFECTS ................................... 309
6.19 Problems ................................................. 311
6.20 References ............................................... 312
Chapter 7 Cyclotron Motion ................................... 317
7.1 INTRODUCTION ............................................. 317
7.2 SUB CYCLOTRON HEATING .................................... 317
7.3 STOCHASTIC DOMAIN ........................................ 323
7.4 CYCLOTRON MOTION IN A TOROIDAL SYSTEM .................... 325
7.5 CYCLOTRON AND GUIDING CENTER ANALYSES OF RESONANCE ....... 328
7.6 PROFILE FLATTENING ....................................... 331
7.7 References ............................................... 333
Chapter 8 Nonlinear Behavior ................................. 335
8.1 INTRODUCTION ............................................. 335
8.2 THE REDUCED EQUATIONS .................................... 339
8.3 NONLINEAR EXTERNAL KINK .................................. 342
8.4 VACUUM BUBBLES ........................................... 345
8.5 NONLINEAR INTERNAL KINK .................................. 349
8.6 COMPLETE RESISTIVE RECONNECTION .......................... 352
8.7 NONLINEAR TEARING MODE ANALYSIS .......................... 352
8.8 SAWTOOTH OSCILLATIONS .................................... 360
8.9 DISRUPTIONS .............................................. 365
8.10 EMPIRICAL LIMITS ......................................... 370
8.11 THE GREENWALD DENSITY LIMIT .............................. 372
8.12 STABILIZATION OF TEARING MODES ........................... 374
8.13 Problems ................................................. 377
8.14 References ............................................... 378
Chapter 9 Transport .......................................... 383
9.1 INTRODUCTION ............................................. 383
9.2 THE DRIFT KINETIC EQUATION ............................... 389
9.3 CROSS FIELD DIFFUSION .................................... 392
9.4 BOOTSTRAP CURRENT ........................................ 396
9.5 NEOCLASSICAL TEARING ..................................... 401
9.6 WARE PINCH ............................................... 401
9.7 MAGNETIC FIELD RIPPLE TRANSPORT .......................... 402
9.8 DIFFUSION IN A STOCHASTIC FIELD .......................... 415
9.9 ISLAND INDUCED DIFFUSION ................................. 418
9.10 ANOMALOUS TRANSPORT ...................................... 421
9.11 CONFINEMENT SCALING ...................................... 426
9.12 NONLOCAL TRANSPORT ....................................... 428
9.12.1 Determination of the Levy flight distribution ..... 432
9.12.2 Two fluid Montroll equation ....................... 433
9.13 BURN CONTROL ............................................. 435
9.14 Problems ................................................. 438
9.15 References ............................................... 441
Chapter 10 The Lithium Wall Fusion Concept .................... 447
10.1 THE IDEA OF MAGNETIC FUSION .............................. 447
10.2 CONFINEMENT REGIME CONTROLLED BY THERMAL CONDUCTION ...... 449
10.3 DIFFUSION BASED CONFINEMENT REGIME ....................... 450
10.4 IMPLEMENTATION ........................................... 452
10.5 ALPHA PARTICLE CONFINEMENT ............................... 454
10.3 DIVERTOR PLATES .......................................... 455
10.7 References ............................................... 456
Chapter 11 Phase Integral Methods ............................. 457
11.1 INTRODUCTION ............................................. 457
11.2 CONNECTION FORMULAE ...................................... 460
11.3 CAUSALITY ................................................ 467
11.4 BOUND STATES - INSTABILITIES ............................. 468
11.5 OVERDENSE BARRIER - SCATTERING ........................... 472
11.6 UNDERDENSE BARRIER - SCATTERING .......................... 476
11.7 EIGENVALUE PROBLEMS ...................................... 479
11.8 Problems ................................................. 484
11.9 References ............................................... 487
Index ......................................................... 489
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