Because magnetically confined plasmas are generally not found in a state of thermodynamic equilibrium, they have been studied extensively with methods of applied kinetic theory. In closed magnetic field line confinement devices such as the tokamak, non-Maxwellian distortions usually occur as a result of auxiliary heating and transport. In magnetic mirror configurations even the intended steady state plasma is far from local thermodynamic equilibrium because of losses along open magnetic field lines. In both of these major fusion devices, kinetic models based on the Boltzmann equation with Fokker-Planck collision terms have been successful in representing plasma behavior. The heating of plasmas by energetic neutral beams or microwaves, the production and thermalization of a-particles in thermonuclear reactor plasmas, the study of runaway electrons in tokamaks, and the performance of two-energy compo­ nent fusion reactors are some examples of processes in which the solution of kinetic equations is appropriate and, moreover, generally necessary for an understanding of the plasma dynamics. Ultimately, the problem is to solve a nonlinear partial differential equation for the distribution function of each charged plasma species in terms of six phase space variables and time. The dimensionality of the problem may be reduced through imposing certain symmetry conditions. For example, fewer spatial dimensions are needed if either the magnetic field is taken to be uniform or the magnetic field inhomogeneity enters principally through its variation along the direction of the field.

1 Introduction.- References.- 2 Fokker - Planck Models of Multispecies Plasmas in Uniform Magnetic Fields.- 2.1. Mathematical Model.- 2.1.1. Fokker - Planck Equations.- 2.1.2. Time-Varying Forces.- 2.1.3. Initial Conditions and Boundary Conditions in Velocity Space.- 2.1.4. Source and Loss Terms in Velocity Space.- 2.2. Solution for a Multispecies Plasma in a One-Dimensional Velocity Space.- 2.2.1. Numerical Methods.- 2.2.2. Applications.- 2.3. Solution in a Two-Dimensional Velocity Space Using an Expansion in Pitch-Angle.- 2.3.1. Numerical Methods.- 2.3.2. Applications.- 2.3.3. Modification of the Lowest Normal Mode Code of Section 2.2 to Include Anisotropic Rosenbluth Potentials.- 2.4. Solution Using Finite-Differences in a Two-Dimensional Velocity Space.- 2.4.1. Numerical Methods.- 2.4.2. Applications.- References.- 3 Collisional Kinetic Models of Multispecies Plasmas in Nonuniform Magnetic Fields.- 3.1. Mathematical Model.- 3.1.1. Bounce-Averaged Fokker - Planck Theory.- 3.1.2. Bounce-Averaged Resonant Diffusion.- 3.1.3. Velocity Space Boundary Conditions.- 3.1.4. Particle and Energy Source and Loss Terms.- 3.1.5. Velocity Space Loss Region Models.- 3.2. Numerical Solution of Bounce-Averaged Fokker - Planck Equations.- 3.2.1. Numerical Methods.- 3.2.2. Bounce-Averaging the Fokker - Planck Coefficients.- 3.2.3. Flux Conservation at the Trapped/Passing Boundary.- 3.2.4. Imphcit Time Advancement: Operator Splitting.- 3.3. Applications.- 3.3.1. Neoclassical Corrections to Classical Resistivity.- 3.3.2. Scanning Charge-Exchange Analyzer Diagnostic for Tokamaks.- Appendix 3 A. Coefficients of the Bounce-Averaged Operator.- Appendix 3B. Boundary Layer Diagnostic.- Appendix 3C. Tangent Resonance Phenomena.- Appendix 3D. Wave Models.- 3D.1. Model Icrft.- 3D.2. Model Icrft0.- References.- 4 A Fokker - Planck/Transport Model for Neutral Beam-Driven Tokamaks.- 4.1. Mathematical Model and Numerical Methods.- 4.1.1. Energetic Ions.- 4.1.2. Bulk Plasma Ions and Electrons.- 4.1.3. Neutrals.- 4.1.4. Fusion.- 4.2. Applications.- 4.2.1. Princeton Large Torus.- 4.2.2. Tokamak Fusion Test Reactor.- 4.2.3. Divertor Injection Tokamak Experiment (DITE).- References.