Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of geodesics to be computed.

The motion of an ion in a lower hybrid wave in a tokamak type plasma is studied. For ions with ν_⊥≳ω/k_⊥ the motion is stochastic for fields satisfying E/B₀≳ (1/4)(Ω_i/ω)^1/3(ω/k_⊥). Provided that the perpendicular phase velocity, ω/k_⊥, can be slowed down to a few times the ion thermal speed, this stochastic ion motion may be an important mechanism by which injected rf power near the lower hybrid frequency can directly heat the ions.

By injecting radio-frequency traveling waves into a tokamak, continuous toroidal electron currents may be generated. This process is studied by numerically solving the two-dimensional Fokker–Planck equation with an added quasi-linear term. The results are compared with the one-dimensional analytic treatment of Fisch, which predicted a reduced plasma resistivity when high-phase-velocity waves are employed. It is shown that two-dimensional velocity space effects, while retaining the predicted scaling, further reduce the ratio of power dissipated to current generated by about 40%. These effects enhance the attractiveness of steady-state tokamak reactors utilizing this method of current generation.

The motion of an ion in a coherent lower hybrid wave (characterized by ‖k∥‖<<‖k⊥‖ and ω≳≳Ωi) in a tokamak plasma is studied. For ions satisfying v⊥≳ω/k⊥, the Lorentz force law for the ions is reduced to a set of difference equations which give the Larmor radius and phase of an ion on one cyclotron orbit in terms of these quantities a cyclotron period earlier. These equations exhibit stochastic behavior when the wave amplitude exceeds a threshold. The stochasticity threshold is given a simple physical interpretation. In addition, the difference equations are used to derive a diffusion equation governing the heating of the ions above the stochasticity threshold. Far above the stochasticity threshold, ion Landau damping is recovered. By including the effects of collisions, the heating rate for the bulk ions is obtained.