Toroidal trapping effects in the surface-averaged Fokker-Planck SSFPQL solver

The kinetic equation solved by SSFPQL was obtained by surface-averaging the Fokker-Planck (FP) equation, thus neglecting both the finite width of the ion orbits and the poloidal modulation of their velocity. Owing to the latter effect and depending on the position of the resonance layer, a fraction of trapped particles do not even reach the ion-cyclotron resonance. In addition, since the resonant ions gain perpendicular energy, they tend to accumulate on trapped orbits barely intercepting the resonance. Still neglecting the effects due to the finite width of the orbits, here we discuss the form of the FP equation when the velocity modulation is taken into account. In particular, we examine the implementation of this effect in the quasilinear operator of SSFPQL, and present a few numerical results.