Fusion Plasma Physics

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.

Professor Stacey received his PhD in Nuclear Engineering from the Massachusetts Institute of Technology in 1966. He then worked in naval reactor design at Knolls Atomic Power Laboratory and led the fast reactor theory and computations and the fusion research programs at Argonne National Laboratory. In 1977, he became Callaway Professor of Nuclear Engineering at the Georgia Institute of Technology, where he has been teaching and performing research in reactor physics and plasma physics. He is the author of six books and about 250 research papers. He led the international INTOR Workshop which defined the design features and R&D needs for the first fusion experimental reactor, for which he received the US Dept. of Energy Distinguished Associate Award. Professor Stacey is a Fellow of the American Nuclear Society and of the American Physical Society and is the recipient of, among other awards, the Seaborg Award for Nuclear Research and the Wigner Reactor Physics Award from the American Nuclear Society.

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 FokkerPlanck 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 ChewGoldbergerLow 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 LossCone and DriftCone 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 IonElectron Plasma 224

9.5.2 TransportParameters 228

9.6 Neoclassical Transport Trapped Particles 231

9.7 ChangHinton 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 ToroidalElectricFieldWarePinch 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

11.4WaveWaveInteractions* 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 PlasmaMaterial 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 LH Transition 374

15.3 Thermal Instabilities 376

15.3.1 TemperaturePerturbationsinthePlasmaEdge 376

15.3.2 Coupled Two-Dimensional DensityVelocityTemperature Perturbations 379

15.3.3 Spontaneous Edge Transport Barrier Formation 384

15.3.4 Consistency with Observed LH 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 DP 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 NavierStokes 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 TemperatureDensity 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