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.
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 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 FokkerPlanck 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 ChewGoldbergerLow 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 LossCone and DriftCone 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 IonElectron Plasma 234
9.5.2 Transport Parameters 238
9.6 Neoclassical TransportTrapped Particles 241
9.7 Extended Neoclassical TransportFluid 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 FieldWare 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 WaveWave 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 PlasmaMaterial 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 LH Transition 448
15.6 Thermal Instabilities 449
15.6.1 Temperature Perturbations in the Plasma Edge 449
15.6.2 Coupled Two-Dimensional DensityVelocityTemperature 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 DP 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 NavierStokes 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 TemperatureDensity 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 -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
