Fusion Plasma Physics

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 11.1 Fusion 11.2 Plasma 61.3 Coulomb Collisions 91.4 Electromagnetic Theory 152 Motion of Charged Particles 212.1 GyromotionandDrifts 212.1.1 Gyromotion 212.1.2 E B Drift 242.1.3 Grad-B Drift 252.1.4 PolarizationDrift 272.1.5 CurvatureDrift 282.2 ConstantsoftheMotion 312.2.1 Magnetic Moment 312.2.2 Second Adiabatic Invariant 322.2.3 Canonical Angular Momentum 342.3 Diamagnetism* 363 Magnetic Confinement 413.1 Confinement in Mirror Fields 413.1.1 SimpleMirror 413.1.2 Tandem Mirrors* 463.2 Closed Toroidal Confinement Systems 493.2.1 Confinement 493.2.2 Flux Surfaces 533.2.3 Trapped Particles 553.2.4 TransportLosses 594 Kinetic Theory 654.1 BoltzmannandVlasovEquations 664.2 DriftKineticApproximation 664.3 Fokker–Planck Theory of Collisions 694.4 PlasmaResistivity 764.5 Coulomb Collisional Energy Transfer 784.6 Krook Collision Operators 825 Fluid Theory 855.1 MomentsEquations 855.2 One-Fluid Model 895.3 Magnetohydrodynamic Model 935.4 Anisotropic Pressure Tensor Model* 965.5 Strong Field, Transport Time Scale Ordering 986 Plasma Equilibria 1036.1 General Properties 1036.2 Axisymmetric Toroidal Equilibria 1056.3 Large Aspect Ratio Tokamak Equilibria 1116.4 SafetyFactor 1166.5 Shafranov Shift* 1206.6 Beta 1236.7 Magnetic Field DiffusionandFluxSurfaceEvolution* 1256.8 Anisotropic Pressure Equilibria* 1287 Waves 1317.1 Waves in an Unmagnetized Plasma 1317.1.1 Electromagnetic Waves 1317.1.2 Ion Sound Waves 1337.2 Waves in a Uniformly Magnetized Plasma 1347.2.1 Electromagnetic Waves 1347.2.2 Shear Alfven Wave 1377.3 Langmuir Waves and Landau Damping 1397.4 Vlasov Theory of Plasma Waves* 1427.5 ElectrostaticWaves* 1488 Instabilities 1558.1 Hydromagnetic Instabilities 1588.1.1 MHD Theory 1598.1.2 Chew–Goldberger–Low Theory 1608.1.3 Guiding Center Theory 1628.2 EnergyPrinciple 1658.3 Pinch and Kink Instabilities 1698.4 Interchange (Flute) Instabilities 1738.5 Ballooning Instabilities 1798.6 Drift Wave Instabilities 1838.7 Resistive Tearing Instabilities* 1868.7.1 Slab Model 1868.7.2 MHDRegions 1878.7.3 Resistive Layer 1898.7.4 Magnetic Islands 1908.8 Kinetic Instabilities* 1928.8.1 Electrostatic Instabilities 1928.8.2 Collisionless Drift Waves 1938.8.3 Electron Temperature Gradient Instabilities 1958.8.4 Ion Temperature Gradient Instabilities 1968.8.5 Loss–Cone and Drift–Cone Instabilities 1978.9 Sawtooth Oscillations* 2019 Neoclassical Transport 2059.1 Collisional Transport Mechanisms 2059.1.1 ParticleFluxes 2059.1.2 HeatFluxes 2079.1.3 MomentumFluxes 2089.1.4 FrictionForce 2109.1.5 ThermalForce 2109.2 ClassicalTransport 2129.3 Neoclassical Transport – Toroidal Effects in Fluid Theory 2159.4 MultifluidTransportFormalism* 2219.5 ClosureofFluidTransportEquations* 2249.5.1 Kinetic Equations for Ion–Electron Plasma 2249.5.2 TransportParameters 2289.6 Neoclassical Transport – Trapped Particles 2319.7 Chang–Hinton Ion Thermal Conductivity* 2379.8 Extended Neoclassical Transport – Fluid Theory* 2389.8.1 RadialElectricField 2399.8.2 ToroidalRotation 2409.8.3 TransportFluxes 2409.9 ElectricalCurrents* 2429.9.1 BootstrapCurrent 2429.9.2 TotalCurrent 2439.10OrbitDistortion 2449.10.1 ToroidalElectricField–WarePinch 2449.10.2 PotatoOrbits 2459.10.3 Orbit Squeezing 2469.11TransportinaPartiallyIonizedGas* 24710 Plasma Rotation* 25110.1 Neoclassical Viscosity 25110.1.1 Rate-of-StrainTensorinToroidalGeometry 25110.1.2 Viscous Stress Tensor 25210.1.3 Toroidal Viscous Force 25310.1.4 Parallel Viscous Force 25710.1.5 Neoclassical Viscosity Coefficients 25810.2RotationCalculations 26010.2.1 PoloidalRotationandDensityAsymmetries 26010.2.2 Radial Electric Field and Toroidal Rotation Velocities 26210.3 Momentum Confinement Times 26410.3.1 Theoretical 26410.3.2 Experimental 26511 Turbulent Transport 26711.1ElectrostaticDriftWaves 26711.1.1 General 26711.1.2 IonTemperatureGradientDriftWaves 27011.1.3 Quasilinear Transport Analysis 27011.1.4 SaturatedFluctuationLevels 27211.2 Magnetic Fluctuations 27311.3 Candidate Microinstabilities 27511.3.1 Drift Waves and ITG Modes 27611.3.2 Trapped Ion Modes 27611.3.3 Electron Temperature Gradient Modes 27711.3.4 Resistive Ballooning Modes 27711.3.5 Chaotic Magnetic Island Overlap 27711.4Wave–WaveInteractions* 27811.4.1 ModeCoupling 27811.4.2 DirectInteractionApproximation 27911.5 Drift Wave Eigenmodes* 28011.6 Gyrokinetic and Gyrofluid Simulations 28212 Heating and Current Drive 28512.1 Inductive 28512.2AdiabaticCompression* 28812.3FastIons 29112.3.1 NeutralBeamInjection 29112.3.2 FastIonEnergyLoss 29312.3.3 FastIonDistribution 29612.3.4 NeutralBeamCurrentDrive 29812.3.5 Toroidal Alfven Instabilities 29912.4 Electromagnetic Waves 30112.4.1 Wave Propagation 30112.4.2 WaveHeatingPhysics 30412.4.3 Ion Cyclotron Resonance Heating 30812.4.4 Lower Hybrid Resonance Heating 30912.4.5 Electron Cyclotron Resonance Heating 31012.4.6 CurrentDrive 31113 Plasma–Material Interaction 31513.1 Sheath 31513.2Recycling 31813.3 Atomic and Molecular Processes 31913.4Sputtering 32413.5ImpurityRadiation 32614 Divertors 33114.1 Configuration, Nomenclature and Physical Processes 33114.2 Simple Divertor Model 33414.2.1 StripGeometry 33414.2.2 RadialTransportandWidths 33414.2.3 ParallelTransport 33614.2.4 SolutionofPlasmaEquations 33714.2.5 Two-Point Model 33814.3DivertorOperatingRegimes 34014.3.1 Sheath-Limited Regime 34014.3.2 Detached Regime 34114.3.3 HighRecyclingRegime 34114.3.4 ParameterScaling 34214.3.5 Experimental Results 34314.4ImpurityRetention 34314.5 Thermal Instability* 34614.62DFluidPlasmaCalculation* 34914.7Drifts* 35114.7.1 BasicDriftsintheSOLandDivertor 35114.7.2 Poloidal and Radial E B Drifts 35214.8ThermoelectricCurrents* 35414.8.1 Simple Current Model 35414.8.2 RelaxationofSimplifyingAssumptions 35614.9 Detachment 35815 Plasma Edge 36115.1H-ModeEdgeTransportBarrier 36115.1.1 RelationofEdgeTransportandGradients 36215.1.2 MHD Stability Constraints on Pedestal Gradients 36415.1.3 RepresentationofMHDPressureGradientConstraint 36815.1.4 Pedestal Widths 36915.2 E B Shear Stabilization of Turbulence 37115.2.1 E B Shear Stabilization Physics 37215.2.2 Comparison with Experiment 37415.2.3 Possible “Trigger” Mechanism for the L–H Transition 37415.3 Thermal Instabilities 37615.3.1 TemperaturePerturbationsinthePlasmaEdge 37615.3.2 Coupled Two-Dimensional Density–Velocity–Temperature Perturbations 37915.3.3 Spontaneous Edge Transport Barrier Formation 38415.3.4 Consistency with Observed L–H Phenomena 38915.4MARFEs 39215.5RadiativeMantle 39715.6 Edge Operation Boundaries 39815.7 Ion Particle Transport in the Edge* 39815.7.1 Generalized “Pinch-Diffusion” Particle Flux Relations 39915.7.2 Density Gradient Scale Length 40215.7.3 Edge Density, Temperature, Electric Field and Rotation Profiles 40316 Neutral Particle Transport* 41316.1 Fundamentals 41316.1.1 1DBoltzmannTransportEquation 41316.1.2 Legendre Polynomials 41416.1.3 Charge Exchange Model 41516.1.4 Elastic Scattering Model 41616.1.5 Recombination Model 41916.1.6 First Collision Source 41916.2 P N Transport and Diffusion Theory 42116.2.1 P N Equations 42116.2.2 Extended Diffusion Theories 42416.3 Multidimensional Neutral Transport 42816.3.1 FormulationofTransportEquation 42816.3.2 Boundary Conditions 43016.3.3 Scalar Flux and Current 43016.3.4 PartialCurrents 43216.4 Integral Transport Theory 43216.4.1 Isotropic Point Source 43316.4.2 Isotropic Plane Source 43416.4.3 Anisotropic Plane Source 43516.4.4 Transmission and Probabilities 43716.4.5 Escape Probability 43716.4.6 Inclusion of Isotropic Scattering and Charge Exchange 43816.4.7 Distributed Volumetric Sources in Arbitrary Geometry 43916.4.8 Flux from a Line Isotropic Source 43916.4.9 Bickley Functions 44016.4.10 Probability of Traveling a Distance t from a Line, Isotropic Source without a Collision 44116.5 Collision Probability Methods 44216.5.1 Reciprocity among Transmission and Collision Probabilities 44216.5.2 Collision Probabilities for Slab Geometry 44316.5.3 Collision Probabilities in Two-Dimensional Geometry 44316.6 Interface Current Balance Methods 44516.6.1 Formulation 44516.6.2 Transmission and Escape Probabilities 44516.6.3 2D Transmission/Escape Probabilities (TEP) Method 44716.6.4 1DSlabMethod 45216.7 Discrete Ordinates Methods 45316.7.1 P L and D–P L Ordinates 45416.8 Monte Carlo Methods 45616.8.1 Probability Distribution Functions 45616.8.2 AnalogSimulationofNeutralParticleTransport 45716.8.3 StatisticalEstimation 45916.9 Navier–Stokes Fluid Model 46017 Power Balance 46317.1 Energy Confinement Time 46317.1.1 Definition 46317.1.2 Experimental Energy Confinement Times 46417.1.3 EmpiricalCorrelations 46517.2Radiation 46817.2.1 RadiationFields 46817.2.2 Bremsstrahlung 47017.2.3 CyclotronRadiation 47117.3 Impurities 47317.4 Burning Plasma Dynamics 47518 Operational Limits 47918.1Disruptions 47918.1.1 PhysicsofDisruptions 47918.1.2 CausesofDisruptions 48118.2DisruptionDensityLimit 48118.2.1 Radial Temperature Instabilities 48318.2.2 SpatialAveraging 48518.2.3 Coupled Radial Temperature–Density Instabilities 48718.3 Nondisruptive Density Limits 49018.3.1 MARFEs 49018.3.2 Confinement Degradation 49118.3.3 ThermalCollapseofDivertorPlasma 49418.4EmpiricalDensityLimit 49518.5 MHD Instability Limits 49518.5.1 ˇ-Limits 49518.5.2 Kink Mode Limits on q.a/=q.0/ 49819 Fusion Reactors and Neutron Sources 50119.1 Plasma Physics and Engineering Constraints 50119.1.1 Confinement 50119.1.2 DensityLimit 50219.1.3 Beta Limit 50319.1.4 Kink Stability Limit 50419.1.5 Start-Up Inductive Volt-Seconds 50419.1.6 Noninductive Current Drive 50519.1.7 BootstrapCurrent 50619.1.8 Toroidal Field Magnets 50619.1.9 BlanketandShield 50719.1.10 Plasma Facing Component Heat Fluxes 50719.1.11 Radiation Damage to Plasma Facing Components 51019.2 International Tokamak Program 51119.2.1 Advanced Tokamak 51419.3 Neutron Sources 515AppendicesA Frequently Used Physical Constants 521B DimensionsandUnits 523c VectorCalculus 527d Curvilinear Coordinates 529E PlasmaFormulas 537F Further Reading 539G Attributions 543Subject Index 549