Fusion plasma physics
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Fusion plasma physics
（Physics textbook）
Wiley-VCH, c2005
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Description and Table of Contents
Description
Nuclear fusion has the potential to become the most important energy source of the new century. But still many problems, as e.g. the confinement of the plasma, are not yet solved. Thus they are subject to intense research which drives a rapid evolvement of this field of nuclear physics, and generates the need for an up-to-date textbook for graduate students.
This state-of-the-art textbook assembles the material for a modern course, and is aimed at graduate and advanced undergraduate students. It both introduces the fundamental principles and theories of fusion plasma physics, and presents the most recent topics from various sources in a systematic and concise way. Each chapter is rounded off with a set of exercises.
Table of Contents
1 Basic Physics 1
1.1 Fusion 1
1.2 Plasma 6
1.3 Coulomb Collisions 9
1.4 Electromagnetic Theory 15
2 Motion of Charged Particles 21
2.1 GyromotionandDrifts 21
2.1.1 Gyromotion 21
2.1.2 E B Drift 24
2.1.3 Grad-B Drift 25
2.1.4 PolarizationDrift 27
2.1.5 CurvatureDrift 28
2.2 ConstantsoftheMotion 31
2.2.1 Magnetic Moment 31
2.2.2 Second Adiabatic Invariant 32
2.2.3 Canonical Angular Momentum 34
2.3 Diamagnetism* 36
3 Magnetic Confinement 41
3.1 Confinement in Mirror Fields 41
3.1.1 SimpleMirror 41
3.1.2 Tandem Mirrors* 46
3.2 Closed Toroidal Confinement Systems 49
3.2.1 Confinement 49
3.2.2 Flux Surfaces 53
3.2.3 Trapped Particles 55
3.2.4 TransportLosses 59
4 Kinetic Theory 65
4.1 BoltzmannandVlasovEquations 66
4.2 DriftKineticApproximation 66
4.3 Fokker-Planck Theory of Collisions 69
4.4 PlasmaResistivity 76
4.5 Coulomb Collisional Energy Transfer 78
4.6 Krook Collision Operators 82
5 Fluid Theory 85
5.1 MomentsEquations 85
5.2 One-Fluid Model 89
5.3 Magnetohydrodynamic Model 93
5.4 Anisotropic Pressure Tensor Model* 96
5.5 Strong Field, Transport Time Scale Ordering 98
6 Plasma Equilibria 103
6.1 General Properties 103
6.2 Axisymmetric Toroidal Equilibria 105
6.3 Large Aspect Ratio Tokamak Equilibria 111
6.4 SafetyFactor 116
6.5 Shafranov Shift* 120
6.6 Beta 123
6.7 Magnetic Field DiffusionandFluxSurfaceEvolution* 125
6.8 Anisotropic Pressure Equilibria* 128
7 Waves 131
7.1 Waves in an Unmagnetized Plasma 131
7.1.1 Electromagnetic Waves 131
7.1.2 Ion Sound Waves 133
7.2 Waves in a Uniformly Magnetized Plasma 134
7.2.1 Electromagnetic Waves 134
7.2.2 Shear Alfven Wave 137
7.3 Langmuir Waves and Landau Damping 139
7.4 Vlasov Theory of Plasma Waves* 142
7.5 ElectrostaticWaves* 148
8 Instabilities 155
8.1 Hydromagnetic Instabilities 158
8.1.1 MHD Theory 159
8.1.2 Chew-Goldberger-Low Theory 160
8.1.3 Guiding Center Theory 162
8.2 EnergyPrinciple 165
8.3 Pinch and Kink Instabilities 169
8.4 Interchange (Flute) Instabilities 173
8.5 Ballooning Instabilities 179
8.6 Drift Wave Instabilities 183
8.7 Resistive Tearing Instabilities* 186
8.7.1 Slab Model 186
8.7.2 MHDRegions 187
8.7.3 Resistive Layer 189
8.7.4 Magnetic Islands 190
8.8 Kinetic Instabilities* 192
8.8.1 Electrostatic Instabilities 192
8.8.2 Collisionless Drift Waves 193
8.8.3 Electron Temperature Gradient Instabilities 195
8.8.4 Ion Temperature Gradient Instabilities 196
8.8.5 Loss-Cone and Drift-Cone Instabilities 197
8.9 Sawtooth Oscillations* 201
9 Neoclassical Transport 205
9.1 Collisional Transport Mechanisms 205
9.1.1 ParticleFluxes 205
9.1.2 HeatFluxes 207
9.1.3 MomentumFluxes 208
9.1.4 FrictionForce 210
9.1.5 ThermalForce 210
9.2 ClassicalTransport 212
9.3 Neoclassical Transport - Toroidal Effects in Fluid Theory 215
9.4 MultifluidTransportFormalism* 221
9.5 ClosureofFluidTransportEquations* 224
9.5.1 Kinetic Equations for Ion-Electron Plasma 224
9.5.2 TransportParameters 228
9.6 Neoclassical Transport - Trapped Particles 231
9.7 Chang-Hinton Ion Thermal Conductivity* 237
9.8 Extended Neoclassical Transport - Fluid Theory* 238
9.8.1 RadialElectricField 239
9.8.2 ToroidalRotation 240
9.8.3 TransportFluxes 240
9.9 ElectricalCurrents* 242
9.9.1 BootstrapCurrent 242
9.9.2 TotalCurrent 243
9.10OrbitDistortion 244
9.10.1 ToroidalElectricField-WarePinch 244
9.10.2 PotatoOrbits 245
9.10.3 Orbit Squeezing 246
9.11TransportinaPartiallyIonizedGas* 247
10 Plasma Rotation* 251
10.1 Neoclassical Viscosity 251
10.1.1 Rate-of-StrainTensorinToroidalGeometry 251
10.1.2 Viscous Stress Tensor 252
10.1.3 Toroidal Viscous Force 253
10.1.4 Parallel Viscous Force 257
10.1.5 Neoclassical Viscosity Coefficients 258
10.2RotationCalculations 260
10.2.1 PoloidalRotationandDensityAsymmetries 260
10.2.2 Radial Electric Field and Toroidal Rotation Velocities 262
10.3 Momentum Confinement Times 264
10.3.1 Theoretical 264
10.3.2 Experimental 265
11 Turbulent Transport 267
11.1ElectrostaticDriftWaves 267
11.1.1 General 267
11.1.2 IonTemperatureGradientDriftWaves 270
11.1.3 Quasilinear Transport Analysis 270
11.1.4 SaturatedFluctuationLevels 272
11.2 Magnetic Fluctuations 273
11.3 Candidate Microinstabilities 275
11.3.1 Drift Waves and ITG Modes 276
11.3.2 Trapped Ion Modes 276
11.3.3 Electron Temperature Gradient Modes 277
11.3.4 Resistive Ballooning Modes 277
11.3.5 Chaotic Magnetic Island Overlap 277
11.4Wave-WaveInteractions* 278
11.4.1 ModeCoupling 278
11.4.2 DirectInteractionApproximation 279
11.5 Drift Wave Eigenmodes* 280
11.6 Gyrokinetic and Gyrofluid Simulations 282
12 Heating and Current Drive 285
12.1 Inductive 285
12.2AdiabaticCompression* 288
12.3FastIons 291
12.3.1 NeutralBeamInjection 291
12.3.2 FastIonEnergyLoss 293
12.3.3 FastIonDistribution 296
12.3.4 NeutralBeamCurrentDrive 298
12.3.5 Toroidal Alfven Instabilities 299
12.4 Electromagnetic Waves 301
12.4.1 Wave Propagation 301
12.4.2 WaveHeatingPhysics 304
12.4.3 Ion Cyclotron Resonance Heating 308
12.4.4 Lower Hybrid Resonance Heating 309
12.4.5 Electron Cyclotron Resonance Heating 310
12.4.6 CurrentDrive 311
13 Plasma-Material Interaction 315
13.1 Sheath 315
13.2Recycling 318
13.3 Atomic and Molecular Processes 319
13.4Sputtering 324
13.5ImpurityRadiation 326
14 Divertors 331
14.1 Configuration, Nomenclature and Physical Processes 331
14.2 Simple Divertor Model 334
14.2.1 StripGeometry 334
14.2.2 RadialTransportandWidths 334
14.2.3 ParallelTransport 336
14.2.4 SolutionofPlasmaEquations 337
14.2.5 Two-Point Model 338
14.3DivertorOperatingRegimes 340
14.3.1 Sheath-Limited Regime 340
14.3.2 Detached Regime 341
14.3.3 HighRecyclingRegime 341
14.3.4 ParameterScaling 342
14.3.5 Experimental Results 343
14.4ImpurityRetention 343
14.5 Thermal Instability* 346
14.62DFluidPlasmaCalculation* 349
14.7Drifts* 351
14.7.1 BasicDriftsintheSOLandDivertor 351
14.7.2 Poloidal and Radial E B Drifts 352
14.8ThermoelectricCurrents* 354
14.8.1 Simple Current Model 354
14.8.2 RelaxationofSimplifyingAssumptions 356
14.9 Detachment 358
15 Plasma Edge 361
15.1H-ModeEdgeTransportBarrier 361
15.1.1 RelationofEdgeTransportandGradients 362
15.1.2 MHD Stability Constraints on Pedestal Gradients 364
15.1.3 RepresentationofMHDPressureGradientConstraint 368
15.1.4 Pedestal Widths 369
15.2 E B Shear Stabilization of Turbulence 371
15.2.1 E B Shear Stabilization Physics 372
15.2.2 Comparison with Experiment 374
15.2.3 Possible "Trigger" Mechanism for the L-H Transition 374
15.3 Thermal Instabilities 376
15.3.1 TemperaturePerturbationsinthePlasmaEdge 376
15.3.2 Coupled Two-Dimensional Density-Velocity-Temperature Perturbations 379
15.3.3 Spontaneous Edge Transport Barrier Formation 384
15.3.4 Consistency with Observed L-H Phenomena 389
15.4MARFEs 392
15.5RadiativeMantle 397
15.6 Edge Operation Boundaries 398
15.7 Ion Particle Transport in the Edge* 398
15.7.1 Generalized "Pinch-Diffusion" Particle Flux Relations 399
15.7.2 Density Gradient Scale Length 402
15.7.3 Edge Density, Temperature, Electric Field and Rotation Profiles 403
16 Neutral Particle Transport* 413
16.1 Fundamentals 413
16.1.1 1DBoltzmannTransportEquation 413
16.1.2 Legendre Polynomials 414
16.1.3 Charge Exchange Model 415
16.1.4 Elastic Scattering Model 416
16.1.5 Recombination Model 419
16.1.6 First Collision Source 419
16.2 P N Transport and Diffusion Theory 421
16.2.1 P N Equations 421
16.2.2 Extended Diffusion Theories 424
16.3 Multidimensional Neutral Transport 428
16.3.1 FormulationofTransportEquation 428
16.3.2 Boundary Conditions 430
16.3.3 Scalar Flux and Current 430
16.3.4 PartialCurrents 432
16.4 Integral Transport Theory 432
16.4.1 Isotropic Point Source 433
16.4.2 Isotropic Plane Source 434
16.4.3 Anisotropic Plane Source 435
16.4.4 Transmission and Probabilities 437
16.4.5 Escape Probability 437
16.4.6 Inclusion of Isotropic Scattering and Charge Exchange 438
16.4.7 Distributed Volumetric Sources in Arbitrary Geometry 439
16.4.8 Flux from a Line Isotropic Source 439
16.4.9 Bickley Functions 440
16.4.10 Probability of Traveling a Distance t from a Line, Isotropic Source without a Collision 441
16.5 Collision Probability Methods 442
16.5.1 Reciprocity among Transmission and Collision Probabilities 442
16.5.2 Collision Probabilities for Slab Geometry 443
16.5.3 Collision Probabilities in Two-Dimensional Geometry 443
16.6 Interface Current Balance Methods 445
16.6.1 Formulation 445
16.6.2 Transmission and Escape Probabilities 445
16.6.3 2D Transmission/Escape Probabilities (TEP) Method 447
16.6.4 1DSlabMethod 452
16.7 Discrete Ordinates Methods 453
16.7.1 P L and D-P L Ordinates 454
16.8 Monte Carlo Methods 456
16.8.1 Probability Distribution Functions 456
16.8.2 AnalogSimulationofNeutralParticleTransport 457
16.8.3 StatisticalEstimation 459
16.9 Navier-Stokes Fluid Model 460
17 Power Balance 463
17.1 Energy Confinement Time 463
17.1.1 Definition 463
17.1.2 Experimental Energy Confinement Times 464
17.1.3 EmpiricalCorrelations 465
17.2Radiation 468
17.2.1 RadiationFields 468
17.2.2 Bremsstrahlung 470
17.2.3 CyclotronRadiation 471
17.3 Impurities 473
17.4 Burning Plasma Dynamics 475
18 Operational Limits 479
18.1Disruptions 479
18.1.1 PhysicsofDisruptions 479
18.1.2 CausesofDisruptions 481
18.2DisruptionDensityLimit 481
18.2.1 Radial Temperature Instabilities 483
18.2.2 SpatialAveraging 485
18.2.3 Coupled Radial Temperature-Density Instabilities 487
18.3 Nondisruptive Density Limits 490
18.3.1 MARFEs 490
18.3.2 Confinement Degradation 491
18.3.3 ThermalCollapseofDivertorPlasma 494
18.4EmpiricalDensityLimit 495
18.5 MHD Instability Limits 495
18.5.1 -Limits 495
18.5.2 Kink Mode Limits on q.a/=q.0/ 498
19 Fusion Reactors and Neutron Sources 501
19.1 Plasma Physics and Engineering Constraints 501
19.1.1 Confinement 501
19.1.2 DensityLimit 502
19.1.3 Beta Limit 503
19.1.4 Kink Stability Limit 504
19.1.5 Start-Up Inductive Volt-Seconds 504
19.1.6 Noninductive Current Drive 505
19.1.7 BootstrapCurrent 506
19.1.8 Toroidal Field Magnets 506
19.1.9 BlanketandShield 507
19.1.10 Plasma Facing Component Heat Fluxes 507
19.1.11 Radiation Damage to Plasma Facing Components 510
19.2 International Tokamak Program 511
19.2.1 Advanced Tokamak 514
19.3 Neutron Sources 515
Appendices
A Frequently Used Physical Constants 521
B DimensionsandUnits 523
c VectorCalculus 527
d Curvilinear Coordinates 529
E PlasmaFormulas 537
F Further Reading 539
G Attributions 543
Subject Index 549
by "Nielsen BookData"
