Power exhaust in fusion plasmas

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 13
1 Introduction......Page 15
1.1 Fusion reactor operating criteria......Page 16
1.2 Plasma stability limits on fusion reactor performance......Page 20
1.3 Power exhaust limits on fusion reactor performance......Page 22
1.4 Chapter summary......Page 25
1.5 Units and notation......Page 28
1.6 Further reading......Page 29
2.1 What is a plasma?......Page 30
2.1.1 Plasma parameter......Page 31
2.1.2 Magnetization parameter......Page 32
2.2 Charged particle motion......Page 33
2.2.1 Guiding centre drifts......Page 34
2.2.2 Canonical (angle-action) variables......Page 41
2.3 Kinetic description......Page 47
2.3.1 Phase space conservation laws......Page 48
2.3.2 Guiding centre kinetic theory......Page 50
2.3.2.1 Drift-kinetic equation......Page 52
2.3.2.2 Gyro-kinetic equation......Page 55
2.3.2.3 MHD-kinetic equation......Page 57
2.4 Fluid description......Page 58
2.4.1 Co-ordinate space conservation laws......Page 59
2.4.2 Guiding centre fluid theory......Page 64
2.4.2.1 Gyro-tropic tensors......Page 66
2.4.2.2 Magnetization law......Page 68
2.4.2.3 Diamagnetic cancellation......Page 70
2.4.2.4 Diamagnetic energy flow......Page 73
2.4.2.5 Gyro-viscous stress tensor......Page 74
2.4.2.6 MHD-ordered fluid equations: magneto-hydrodynamics......Page 75
2.4.2.7 Drift-ordered fluid equations: the drift-fluid model......Page 79
2.4.2.8 Simplified drift-fluid models......Page 84
2.5 The relation between MHD- and drift-ordered dynamics......Page 86
2.6 Further reading......Page 87
3 Magnetized plasma equilibrium......Page 88
3.1 Magnetic geometry and flux co-ordinates......Page 89
3.2 Plasma current in MHD equilibrium......Page 98
3.2.1 Hamada co-ordinates......Page 100
3.2.2 Symmetry co-ordinates......Page 102
3.3.1 General screw pinch......Page 106
3.3.3 Large aspect ratio (small ) tokamak......Page 109
3.4 Further reading......Page 114
4.1 Hydrodynamic waves and instabilities......Page 115
4.2.1 Ideal MHD waves in a uniform plasma......Page 121
4.2.3 Ideal MHD waves and instabilities in a confined plasma......Page 123
4.2.4 Ideal MHD waves and instabilities in a general screw pinch......Page 129
4.2.5 Flute-reduced MHD......Page 131
4.2.6 Non-homogeneous shear Alfvén waves......Page 136
4.2.7 Current-driven ideal MHD instabilities: kink modes......Page 137
4.2.8 Pressure-driven ideal MHD instabilities: ballooning modes......Page 141
4.2.9 Resistive MHD instabilities: tearing modes......Page 156
4.3 Drift-waves and instabilities......Page 165
4.4 Kinetic waves and instabilities......Page 171
4.5 Further reading......Page 175
5 Collisional transport in magnetized plasmas......Page 176
5.1.1 Maxwell–Boltzmann collision operator......Page 177
5.1.2 Chapman–Enskog expansion......Page 180
5.1.3 Fokker–Planck collision operator......Page 184
5.2.1 Coulomb collision operator......Page 186
5.2.1.1 Fokker–Planck coefficients and Rosenbluth potentials......Page 187
5.2.1.2 Landau–Boltzmann collision operator......Page 189
5.2.1.3 Balescu–Lenard collision operator......Page 191
5.2.2 Test particle dynamics in a plasma......Page 192
5.2.3 Collisional momentum exchange......Page 193
5.2.4 Collisional energy (heat) exchange......Page 196
5.3.1 Collisional transport in an unmagnetized plasma......Page 198
5.3.2 Collisional transport in a cylindrical plasma......Page 202
5.3.2.1 Strongly collisional limit (…): Braginskii equations......Page 206
5.3.2.2 Weakly collisional limit (...): ZNC equations......Page 209
5.3.2.3 Radial flows in a cylindrical plasma......Page 212
5.3.3.1 Guiding centre orbits in axis-symmetric, toroidal geometry......Page 214
5.3.3.2 Radial flows in an axis-symmetric, toroidal plasma......Page 218
5.3.3.3 Radial flows in the collisional (Pfirsch–Schlüter) regime......Page 224
5.3.3.4 Radial flows in the collisionless (banana-plateau) regime......Page 228
5.3.3.5 Flux surface flows in axis-symmetric geometry......Page 230
5.4 Further reading......Page 233
6.1 Hydrodynamic turbulence......Page 234
6.1.1 Transition to turbulence in hydrodynamics......Page 236
6.1.2 HD turbulence in 3D......Page 238
6.1.2.1 Fluid frame, temporal correlations: passive scalar diffusion......Page 241
6.1.2.2 Laboratory frame, spatial correlations: direct energy cascade......Page 243
6.1.2.3 Probability distribution functions (PDFs): intermittency......Page 249
6.1.3 HD turbulence in 2D......Page 253
6.2 MHD turbulence......Page 257
6.2.1 MHD turbulence in 3D......Page 259
6.2.2 MHD turbulence in 2D......Page 265
6.3 DHD turbulence......Page 266
6.3.1 Drift-fluid turbulence......Page 267
6.3.1.1 Global drift-fluid model......Page 268
6.3.1.2 Mean field approximation......Page 272
6.3.1.3 Local drift-fluid models......Page 279
6.3.1.4 Numerical simulations of drift-fluid edge plasma turbulence......Page 282
6.3.2 Gyro-fluid turbulence......Page 289
6.3.3 Drift-kinetic and gyro-kinetic turbulence......Page 294
6.4 Comparison of collisional and turbulent diffusivities......Page 297
6.5 Further reading......Page 299
7 Tokamak plasma boundary and power exhaust......Page 300
7.1.1 Plasma–surface interactions......Page 301
7.1.2.1 Plasma–hydrogen interactions......Page 309
7.1.2.2 Plasma–impurity interactions......Page 312
7.1.2.3 Source and sink terms for plasma fluid equations......Page 313
7.1.3 SOL geometry: limiter, divertor and ergodic SOL......Page 314
7.1.3.1 Limiter SOL......Page 316
7.1.3.2 Divertor SOL......Page 317
7.1.3.3 Ergodic SOL......Page 320
7.1.4.2 SOL transport......Page 321
7.1.4.3 Radial SOL transport......Page 322
7.1.4.4 Diamagnetic SOL transport......Page 324
7.1.4.5 Parallel SOL transport......Page 326
7.1.5 SOL modelling approaches......Page 332
7.2 L-mode power exhaust: edge-SOL turbulence......Page 336
7.2.1 Experimental observations......Page 337
7.2.2.1 Interchange motions of plasma filaments......Page 342
7.2.2.2 Edge-SOL 2D electrostatic drift-fluid simulations......Page 350
7.2.2.3 Edge-SOL 3D electromagnetic gyro-fluid simulations......Page 353
7.3.1.1 ETB formation: the L–H transition......Page 367
7.3.1.2 ETB evolution: the H-mode pedestal......Page 369
7.3.1.3 ETB relaxation: edge localized modes (ELMs)......Page 374
7.3.2 Power exhaust in between ELMs......Page 381
7.3.2.1 Extension of ETB into the near-SOL: (neo)classical transport......Page 382
7.3.2.2 Marginal stability of near-SOL radial pressure gradient......Page 387
7.3.2.3 Combination of collisional and turbulent transport in the near-SOL......Page 388
7.3.3 Power exhaust during ELMs......Page 390
7.3.3.1 ELM heat loads on divertor tiles......Page 391
7.3.3.2 ELM heat loads on the limiter tiles......Page 396
7.3.4.1 Inter-ELM heat load control techniques......Page 402
7.3.4.2 ELM heat load control techniques......Page 403
7.4 Further reading......Page 408
8.1 ITER......Page 409
8.2 DEMO......Page 415
8.3 PROTO and beyond......Page 417
8.4 Further reading......Page 418
Appendix A Maxwellian distribution......Page 419
Appendix B Curvilinear co-ordinates......Page 421
References......Page 424
Index......Page 440