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Fusion Plasma Physics (2nd Ed.)

Langue : Anglais

Auteur :

Couverture de l’ouvrage Fusion Plasma Physics
This revised and enlarged second edition of the popular textbook and reference contains comprehensive treatments of both the established foundations of magnetic fusion plasma physics and of the newly developing areas of active research. It concludes with a look ahead to fusion power reactors of the future. The well-established topics of fusion plasma physics -- basic plasma phenomena, Coulomb scattering, drifts of charged particles in magnetic and electric fields, plasma confinement by magnetic fields, kinetic and fluid collective plasma theories, plasma equilibria and flux surface geometry, plasma waves and instabilities, classical and neoclassical transport, plasma-materials interactions, radiation, etc. -- are fully developed from first principles through to the computational models employed in modern plasma physics.
The new and emerging topics of fusion plasma physics research -- fluctuation-driven plasma transport and gyrokinetic/gyrofluid computational methodology, the physics of the divertor, neutral atom recycling and transport, impurity ion transport, the physics of the plasma edge (diffusive and non-diffusive transport, MARFEs, ELMs, the L-H transition, thermal-radiative instabilities, shear suppression of transport, velocity spin-up), etc. -- are comprehensively developed and related to the experimental evidence. Operational limits on the performance of future fusion reactors are developed from plasma physics and engineering constraints, and conceptual designs of future fusion power reactors are discussed.

1 Basic Physics 1

1.1 Fusion 1

1.2 Plasma 7

1.3 Coulomb Collisions 10

1.4 Electromagnetic Theory 17

2 Motion of Charged Particles 23

2.1 Gyromotion and Drifts 23

2.1.1 Gyromotion 23

2.1.2 E B Drift 26

2.1.3 Grad-B Drift 27

2.1.4 Polarization Drift 29

2.1.5 Curvature Drift 30

2.2 Constants of the Motion 33

2.2.1 Magnetic Moment 33

2.2.2 Second Adiabatic Invariant* 34

2.2.3 Canonical Angular Momentum 36

2.3 Diamagnetism* 38

3 Magnetic Confinement 43

3.1 Confinement in Mirror Fields 43

3.1.1 Simple Mirror 43

3.1.2 Tandem Mirrors* 48

3.2 Closed Toroidal Confinement Systems 51

3.2.1 Confinement 51

3.2.2 Flux Surfaces 55

3.2.3 Trapped Particles 57

3.2.4 Transport Losses 61

4 Kinetic Theory 67

4.1 Boltzmann and Vlasov Equations 68

4.2 Drift Kinetic Approximation 68

4.3 Fokker–Planck Theory of Collisions 71

4.4 Plasma Resistivity 78

4.5 Coulomb Collisional Energy Transfer 80

4.6 Krook Collision Operators* 84

5 Fluid Theory 87

5.1 Moments Equations 87

5.2 One-Fluid Model 91

5.3 Magneto hydrodynamic Model 95

5.4 Anisotropic Pressure Tensor Model* 98

5.5 Strong Field, Transport Time Scale Ordering 100

6 Plasma Equilibria 105

6.1 General Properties 105

6.2 Axisymmetric Toroidal Equilibria 107

6.3 Large Aspect Ratio Tokamak Equilibria 113

6.4 Safety Factor 119

6.5 Shafranov Shift* 122

6.6 Beta* 125

6.7 Magnetic Field Diffusion and Flux Surface Evolution* 127

6.8 Anisotropic Pressure Equilibria* 130

6.9 Elongated Equilibria* 132

6.9.1 Geometry 132

6.9.2 Flux surface average 134

6.9.3 Equivalent toroidal models 134

6.9.4 Interpretation of thermal diffusivities from measured temperature gradients 136

6.9.5 Prediction of poloidal distribution of conductive heat flux 137

6.9.6 Mapping radial gradients to different poloidal locations 138

7 Waves 141

7.1 Waves in an Unmagnetized Plasma 141

7.1.1 Electromagnetic Waves 141

7.1.2 Ion Sound Waves 143

7.2 Waves in a Uniformly Magnetized Plasma 144

7.2.1 Electromagnetic Waves 144

7.2.2 Shear Alfven Wave 147

7.3 Langmuir Waves and Landau Damping 149

7.4 Vlasov Theory of Plasma Waves* 152

7.5 Electrostatic Waves* 158

8 Instabilities 165

8.1 Hydromagnetic Instabilities 168

8.1.1 MHD Theory 169

8.1.2 Chew–Goldberger–Low Theory 170

8.1.3 Guiding Center Theory 172

8.2 Energy Principle 175

8.3 Pinch and Kink Instabilities 179

8.4 Interchange (Flute) Instabilities 183

8.5 Ballooning Instabilities 189

8.6 Drift Wave Instabilities 193

8.7 Resistive Tearing Instabilities* 196

8.7.1 Slab Model 196

8.7.2 MHD Regions 197

8.7.3 Resistive Layer 199

8.7.4 Magnetic Islands 200

8.8 Kinetic Instabilities* 202

8.8.1 Electrostatic Instabilities 202

8.8.2 Collisionless Drift Waves 203

8.8.3 Electron Temperature Gradient Instabilities 205

8.8.4 Ion Temperature Gradient Instabilities 206

8.8.5 Loss–Cone and Drift–Cone Instabilities 207

8.9 Sawtooth Oscillations* 211

9 Neoclassical Transport 215

9.1 Collisional Transport Mechanisms 215

9.1.1 Particle Fluxes 215

9.1.2 Heat Fluxes 217

9.1.3 Momentum Fluxes 218

9.1.4 Friction Force 220

9.1.5 Thermal Force 220

9.2 Classical Transport 222

9.3 Neoclassical Transport – Toroidal Effects in Fluid Theory 225

9.4 Multifluid Transport Formalism* 231

9.5 Closure of Fluid Transport Equations* 234

9.5.1 Kinetic Equations for Ion–Electron Plasma 234

9.5.2 Transport Parameters 238

9.6 Neoclassical Transport–Trapped Particles 241

9.7 Extended Neoclassical Transport–Fluid Theory* 247

9.7.1 Radial Electric Field 248

9.7.2 Toroidal Rotation 249

9.7.3 Transport Fluxes 249

9.8 Electrical Currents 251

9.8.1 Bootstrap Current 251

9.8.2 Total Current 252

9.9 Orbit Distortion* 253

9.9.1 Toroidal Electric Field–Ware Pinch 253

9.9.2 Potato Orbits 254

9.9.3 Orbit Squeezing 255

9.10 Neoclassical Ion Thermal Diffusivity 256

9.11 Paleo classical Electron Thermal Diffusivity 258

9.12 Transport in a Partially Ionized Gas* 259

10 Plasma Rotation* 263

10.1 Neoclassical Viscosity 263

10.1.1 Rate-of-Strain Tensor in Toroidal Geometry 263

10.1.2 Viscous Stress Tensor 264

10.1.3 Toroidal Viscous Force 265

10.1.4 Parallel Viscous Force 269

10.1.5 Neoclassical Viscosity Coefficients 270

10.2 Rotation Calculations 272

10.2.1 Poloidal Rotation and Density Asymmetries 272

10.2.2 Shaing-Sigmar-Stacey Parallel Viscosity Model 275

10.2.3 Stacey-Sigmar Poloidal Rotation Model 276

10.2.4 Radial Electric Field and Toroidal Rotation Velocities 280

10.3 Momentum Confinement Times 281

10.3.1 Theoretical 281

10.3.2 Experimental 282

10.4 Rotation and Transport in Elongated Geometry 283

10.4.1 Flux surface coordinate system 283

10.4.2 Flux surface average 285

10.4.3 Differential Operators in Generalized Geometry 285

10.4.4 Fluid Equations in Miller Elongated Flux Surface Coordinates 286

11 Turbulent Transport 293

11.1 Electrostatic Drift Waves 293

11.1.1 General 293

11.1.2 Ion Temperature Gradient Drift Waves 296

11.1.3 Quasilinear Transport Analysis 296

11.1.4 Saturated Fluctuation Levels 298

11.2 Magnetic Fluctuations 299

11.3 Wave–Wave Interactions* 301

11.3.1 Mode Coupling 301

11.3.2 Direct Interaction Approximation 302

11.4 Drift Wave Eigen modes* 304

11.5 Micro instability thermal diffusivity models* 306

11.5.1 Ion transport 307

11.5.2 Electron transport 312

11.6 Gyrokinetic and Gyrofluid Theory* 315

11.6.1 Gyrokinetic Theory of Turbulent Transport 316

11.6.2 Gyrofluid Theory of Turbulent Transport 318

11.7 Zonal Flows* 321

12 Heating and Current Drive 323

12.1 Inductive 323

12.2 Adiabatic Compression* 326

12.3 Fast Ions 329

12.3.1 Neutral Beam Injection 329

12.3.2 Fast Ion Energy Loss 331

12.3.3 Fast Ion Distribution* 334

12.3.4 Neutral Beam Current Drive 336

12.3.5 Toroidal Alfven Instabilities 337

12.4 Electromagnetic Waves 339

12.4.1 Wave Propagation 339

12.4.2 Wave Heating Physics 342

12.4.3 Ion Cyclotron Resonance Heating 346

12.4.4 Lower Hybrid Resonance Heating 347

12.4.5 Electron Cyclotron Resonance Heating 348

12.4.6 Current Drive 349

13 Plasma–Material Interaction 355

13.1 Sheath 355

13.2 Recycling 358

13.3 Atomic and Molecular Processes 359

13.4 Penetration of Recycling Neutrals 364

13.5 Sputtering 365

13.6 Impurity Radiation 367

14 Divertors 373

14.1 Configuration, Nomenclature and Physical Processes 373

14.2 Simple Divertor Model 376

14.2.1 Strip Geometry 376

14.2.2 Radial Transport and Widths 376

14.2.3 Parallel Transport 378

14.2.4 Solution of Plasma Equations 379

14.2.5 Two-Point Model 380

14.3 Divertor Operating Regimes* 382

14.3.1 Sheath-Limited Regime 382

14.3.2 Detached Regime 383

14.3.3 High Recycling Regime 383

14.3.4 Parameter Scaling 384

14.3.5 Experimental Results 385

14.4 Impurity Retention 385

14.5 Thermal Instability* 388

14.6 2DFluidPlasmaCalculation* 391

14.7 Drifts 393

14.7.1 Basic Drifts in the SOL and Divertor 393

14.7.2 Poloidal and Radial E B Drifts 394

14.8 Thermoelectric Currents 396

14.8.1 Simple Current Model 396

14.8.2 Relaxation of Simplifying Assumptions 398

14.9 Detachment 400

14.10 Effect of Drifts on Divertor and SOL Plasma Properties* 402

14.10.1 Geometric Model 402

14.10.2 Radial Transport 403

14.10.3 Temperature, Density and Velocity Distributions 404

14.10.4 Electrostatic Potential 406

14.10.5 Parallel Current 407

14.10.6 Grad-B and Curvature Drifts 408

14.10.7 Solution for Currents and Potentials at Divertor Plates 410

14.10.8 E B Drifts 411

14.10.9 Total Parallel Ion Flux 413

14.10.10 Impurities 413

14.10.11GeometricInvariance 415

14.10.12 Model Problem Calculation: Effect of B Direction on SOL-Divertor Parameters 416

14.11 Blob Transport* 422

15 Plasma Edge 425

15.1 H-Mode Edge Plasma 425

15.2 Transport in the Plasma Edge 426

15.2.1 Fluid Theory 426

15.2.2 Multi-Fluid Theory* 430

15.2.3 Torque Representation* 431

15.2.4 Kinetic Corrections for Non-Diffusive Ion Transport 433

15.3 Differences Between L-Mode and H-Mode Plasma Edges 439

15.4 Effect of Recycling Neutrals 443

15.5 E B Shear Stabilization of Turbulence 444

15.5.1 E B Shear Stabilization Physics 445

15.5.2 Comparison with Experiment 447

15.5.3 Possible “Trigger” Mechanism for the L–H Transition 448

15.6 Thermal Instabilities 449

15.6.1 Temperature Perturbations in the Plasma Edge 449

15.6.2 Coupled Two-Dimensional Density–Velocity–Temperature Perturbations* 453

15.6.3 Spontaneous Edge Pressure Pedestal Formation 458

15.7 Poloidal Velocity Spin-Up* 461

15.7.1 Neoclassical Spin-Up 463

15.7.2 Fluid Momentum Balance Calculation of Poloidal Velocity Spin-Up 463

15.7.3 Poloidal Velocity Spin-Up Due to Poloidal Asymmetries 464

15.7.4 Bifurcation of the Poloidal Velocity Spin-Up 466

15.8 ELM Stability Limits on Edge Pressure Gradients 467

15.8.1 MHD Instability Theory of Peeling Modes* 468

15.8.2 MHD Instability Theory of Coupled Ballooning-Peeling Modes* 470

15.8.3 MHD Instability Analysis of ELMs 472

15.9 MARFEs 476

15.10 Radiative Mantle 480

15.11 Edge Operation Boundaries 482

16 Neutral Particle Transport 485

16.1 Fundamentals* 485

16.1.1 1DBoltzmannTransportEquation 485

16.1.2 Legendre Polynomials 486

16.1.3 Charge Exchange Model 487

16.1.4 Elastic Scattering Model 488

16.1.5 Recombination Model 491

16.1.6 First Collision Source 491

16.2 P N Transport and Diffusion Theory* 493

16.2.1 P N Equations 493

16.2.2 Extended Diffusion Theories 496

16.3 Multidimensional Neutral Transport* 500

16.3.1 Formulation of Transport Equation 500

16.3.2 Boundary Conditions 502

16.3.3 Scalar Flux and Current 502

16.3.4 Partial Currents 504

16.4 Integral Transport Theory* 504

16.4.1 Isotropic Point Source 505

16.4.2 Isotropic Plane Source 506

16.4.3 Anisotropic Plane Source 507

16.4.4 Transmission Probabilities 509

16.4.5 Escape Probabilities 509

16.4.6 Inclusion of Isotropic Scattering and Charge Exchange 510

16.4.7 Distributed Volumetric Sources in Arbitrary Geometry 511

16.4.8 Flux from a Line Isotropic Source 511

16.4.9 Bickley Functions 512

16.4.10 Probability of Traveling a Distance t from a Line, Isotropic Source without a Collision 513

16.5 Collision Probability Methods* 514

16.5.1 Reciprocity among Transmission and Collision Probabilities 514

16.5.2 Collision Probabilities for Slab Geometry 515

16.5.3 Collision Probabilities in Two-Dimensional Geometry 515

16.6 Interface Current Balance Methods 517

16.6.1 Formulation 517

16.6.2 Transmission and Escape Probabilities 517

16.6.3 2D Transmission/Escape Probabilities (TEP) Method 519

16.6.4 1DSlabMethod 524

16.7 Extended Transmission-Escape Probabilities Method* 525

16.7.1 Basic TEP Method 525

16.7.2 Anisotropic Angular Fluxes 526

16.7.3 Extended Directional Escape Probabilities 528

16.7.4 Average Neutral Energy Approximation 531

16.8 Discrete Ordinates Methods* 533

16.8.1 P L and D–P L Ordinates 534

16.9 Monte Carlo Methods* 536

16.9.1 Probability Distribution Functions 537

16.9.2 Analog Simulation of Neutral Particle Transport 537

16.9.3 Statistical Estimation 539

16.10 Navier–Stokes Fluid Model* 541

16.11 Tokamak Plasma Refueling by Neutral Atom Recycling 542

17 Power Balance 549

17.1 Energy Confinement Time 549

17.1.1 Definition 549

17.1.2 Experimental Energy Confinement Times 550

17.1.3 Empirical Correlations 551

17.2 Radiation 554

17.2.1 Radiation Fields 554

17.2.2 Bremsstrahlung 556

17.2.3 Cyclotron Radiation 557

17.3 Impurities 559

17.4 Burning Plasma Dynamics 561

18 Operational Limits 565

18.1 Disruptions 565

18.1.1 Physics of Disruptions 565

18.1.2 Causes of Disruptions 567

18.2 Disruption Density Limit 567

18.2.1 Radial Temperature Instabilities 569

18.2.2 Spatial Averaging* 571

18.2.3 Coupled Radial Temperature–Density Instabilities* 573

18.3 Nondisruptive Density Limits 576

18.3.1 MARFEs 576

18.3.2 Confinement Degradation 577

18.3.3 Thermal Collapse of Divertor Plasma 580

18.4 Empirical Density Limit 581

18.5 MHD Instability Limits 581

18.5.1 ˇ-Limits 581

18.5.2 Kink Mode Limits on q(a)/q(0) 584

19 Fusion Reactors and Neutron Sources 587

19.1 Plasma Physics and Engineering Constraints 587

19.1.1 Confinement 587

19.1.2 Density Limit 588

19.1.3 Beta Limit 589

19.1.4 Kink Stability Limit 590

19.1.5 Start-Up Inductive Volt-Seconds 590

19.1.6 Noninductive Current Drive 591

19.1.7 Bootstrap Current 592

19.1.8 Toroidal Field Magnets 592

19.1.9 Blanket and Shield 593

19.1.10 Plasma Facing Component Heat Fluxes 593

19.1.11 Radiation Damage to Plasma Facing Components 596

19.2 International Tokamak Program 597

19.3 Fusion Beyond ITER 600

19.4 Fusion-Fission Hybrids? 603

Appendices

A Frequently Used Physical Constants 611

B Dimensions and Units 613

C Vector Calculus 617

D Curvilinear Coordinates 619

E Plasma Formulas 627

F Further Reading 629

G Attributions 633

Subject Index 641

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.

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