Electron Cyclotron Heating of Plasmas

Electron Cyclotron Heating of Plasmas......Page 5
Contents......Page 9
1 Introduction......Page 13
References......Page 17
2 Magnetic Fields......Page 19
2.1 Magnetic Mirrors: Field Calculations Using the Vector Potential......Page 20
2.2 Orthogonal Curvilinear Coordinates and Clebsch Representations......Page 23
2.3 Magnetic Mirrors: Field Calculations Using the Scalar Potential......Page 24
2.5 Tokamaks: Rotational Transform and the \"Safety Factor\"......Page 27
References......Page 29
3.1 Electron Gyromotion......Page 31
3.2 Electron Bounce Motion......Page 34
3.3 Electron Drift Motions......Page 35
3.4 Relativistic Electron Kinematics for ECH......Page 40
3.5 The Hamiltonian Approach......Page 41
3.6 Drift Orbits in Toroidal Magnetic Configurations......Page 44
References......Page 46
4 Wave Propagation and Cyclotron Damping in Magnetized Plasmas......Page 49
4.1 The Cold-Plasma Dispersion Relation......Page 50
4.2 Critical Conditions for Parallel Propagation......Page 53
4.4 Clemmow–Mullaly–Allis Diagrams......Page 54
4.5 The High-Field Regime......Page 55
4.6 The Low-Field Regime......Page 56
4.7 A Few Preliminary Implications for ECH Experiments......Page 60
4.8.1 A Collisional Model of Damping......Page 62
4.8.2 An Introduction to Collisionless Cyclotron Damping......Page 63
4.8.3 Cyclotron Damping of Whistler Waves......Page 65
4.8.4 Cyclotron Damping of Waves Propagating as O-Modes......Page 71
4.9 Electrostatic Plasma Waves......Page 73
4.10 Estimates of the Electric Field Amplitude......Page 74
4.11 Ray Tracing in Inhomogeneous Plasmas......Page 75
References......Page 77
5 Interaction of Electrons with Electromagnetic Fields at Resonance......Page 81
5.1 A Rudimentary Stochastic Model of ECH......Page 82
5.2 Dynamics of the Fundamental Resonance Interaction......Page 88
5.2.1 Dynamics of the Electron Interaction With X-Mode Waves......Page 89
5.2.2 Dynamics of the Electron Interaction With Parallel RF Electric Fields......Page 93
5.2.3 Dynamics of the Electron Interaction with O-Mode Waves......Page 94
5.3 Heating of Relativistic Electrons......Page 98
5.4 Limit Cycles......Page 99
5.5 Nonlinear Effects: Mapping Approaches......Page 101
References......Page 107
6.1 Charge Balance......Page 109
6.2 Particle and Power Balance......Page 111
6.2.1 Particle and Energy Balance for Group 1......Page 112
6.3 Breakdown and Start-up......Page 115
6.3.1 Breakdown by Heating on the Midplane of a Magnetic Mirror......Page 116
6.3.3 Breakdown with Heating near the Midplane......Page 118
6.4.1 Particle Balance for Electrons in Group 2......Page 120
6.4.2 Particle and Power Balance for Electrons in Group 3......Page 123
6.5 Fokker–Planck Models of Hot-Electron Equilibria......Page 124
6.6 Ad Hoc Velocity–Space Models of Anisotropic Hot-Electron Equilibria......Page 127
References......Page 131
7.1 Interchange Instabilities......Page 133
7.2 Electrostatic Velocity–Space Instabilities Driven by Wave-Particle Interactions......Page 138
7.3 Electromagnetic Velocity Space Instabilities......Page 145
References......Page 150
8.1 Hot-Electron Experiments in \"Physics Test Facility\" and EPA [1–3]......Page 153
8.2 High-Beta Experiments in ELMO [9]......Page 160
8.3 Unstable Electromagnetic Waves in the TPM [12]......Page 165
8.4 Heating Experiments in AMPHED [15]......Page 173
References......Page 177
9.1 Ordinary-Mode Fundamental ECH Absorption in PLT......Page 181
9.2 ECH-Assisted Start-up in Tokamaks......Page 184
9.3 ECH Suppression of Tearing Modes in Tokamaks......Page 189
9.4 Electron Cyclotron Current Drive......Page 194
References......Page 199
10 The ELMO Bumpy Torus......Page 201
10.1 The Canted Mirror Experiments......Page 203
10.2 Experiments in EBT-I......Page 208
References......Page 216
11.1 Active Experiments in Space......Page 219
11.2 Laboratory Experiments of Astrophysical Significance......Page 224
11.3 Nonlinear Dynamical Ambipolar Equilibria......Page 228
References......Page 233
12.1 Low-Frequency Technology: Sources......Page 235
12.3 Low-Frequency Coupling Techniques......Page 236
12.4 High-Frequency Power Sources......Page 237
12.5 High-Frequency Transmission Systems......Page 238
References......Page 240
13 Frequency Modulated Electron Cyclotron Heating (FMECH)......Page 241
13.1 Achievable Values of Toroidal Asymmetry......Page 242
13.2 An Estimate of I/P......Page 246
13.3 Generation of the Energetic \"Source\" Electrons......Page 249
References......Page 251
Appendix A: Some Useful Physical Constants......Page 253
Appendix B: Formulas from Vector Calculus......Page 255
Appendix C: Properties of Some Mathematical Functions......Page 257
Index......Page 259