Stochastic ion heating by a lower hybrid wave: II

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.