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

Abstract

Abstract. 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.

Phase-space resolved measurement of 2nd harmonic ion cyclotron heating using FIDA tomography at the ASDEX Upgrade tokamak

“…The main limitation of the code package is that the Fokker-Planck part SSFPQL assumes that ions move on flux surfaces (zero orbit width approximation). Within this approximation, an ad-hoc correction for particle trapping effects is included in the quasi-linear RF diffusion operator [35,36].…”

Direct toroidal torque driven by ICRF heating and its dependence on the plasma rotation

“…The nonlinearities of the set of wave and kinetic equations have visible effects on the shape of T ϕ , but they do not boost the contribution of the total torque T ϕ , as reported in the table 1. Since SSFPQL assumes zero-width orbits [32], the additional contributions to the torque analyzed in [2,3] cannot unfortunately be addressed here.…”

“…Where not specified, in the following it is assumed 5% of H in deuterium plasmas. Simulations of these discharges with TORIC-SSFPQL [26,32], done under the assumption that the coupled RF power is completely absorbed by the plasma, show that close to the peak of ICRF absorption (ρ ≈ 0.4 on the LFS for AUG26621, and ρ ≈ 0.1, 0.3 on the HFS for AUG26620 and AUG26622, respectively) the average energy of ICRF-heated protons is about 50, 96 and 76 keV for AUG26621, AUG26620, and AUG26622, respectively. Because of the zero-banana-width assumption in SSFPQL equations, these values are somewhat overestimated.…”