Advances in numerical simulations of ion cyclotron heating of non-Maxwellian plasmas

Abstract

Abstract. Coupling the full-wave solver TORIC (Plasma Phys. Contr. Fusion 41, 1, (1999)) and the bounce-averaged quasilinear Fokker-Planck solver SSFPQL (Nucl. Fusion 34, 1121, (1994) allows to determine the suprathermal ion populations produced by ion cyclotron heating of tokamak plasmas, while taking into account their effects on wave propagation and absorption. By using new numerical methods for the evaluation of the coefficients of the wave equations in non-Maxwellian plasmas and the transmission of data between TORIC and SSFPQL, the interface between the two codes has been made very efficient and accurate. As an example, we have re-analysed a minority heating scenario in the ASDEX Upgrade tokamak. The results illustrate the differences between the quasilinear evolution of fundamental and first harmonic ion cyclotron heating due to the fact that the latter is a finite Larmor radius effect. They also suggest that the main missing element for fully satisfactory self-consistent simulations of ion cyclotron experiments in toroidal devices is the absence of a detailed model for the losses of suprathermal ions due, for example, to interactions with low frequency turbulence or magnetohydrodynamic instabilities.

Simulations of NBI-ICRF synergy with the full-wave TORIC package

“…The first two terms are respectively the linearized collision operator and the RF quasilinear operator, and S i ∆T is the source term required to maintain in steady-state charged species at different temperatures. All these terms are discussed in [2]. Here, new are the particle source S i nbi , representing NBI, and the particle loss term L i nbi , necessary to compensate the corresponding particle input.…”

“…In the presence of ICRF heating the number of LPs necessary to obtain a convergent solution increases greatly when the distortion of the distribution functions from Maxwellians are relatively large for nearly parallel velocities, µ ∼ ±1. This follows from the convergence property of the series used to separate the µ and v dependence in the argument of the Bessel functions in the QLO [2]. A special effort, therefore, had to be devoted to reduce the round-off errors which limit the number of LPs which can be included in the numerical solution.…”

“…As already noted in [2], the main limitation of the SSFPQL model is the absence of a term describing losses of very energetic ions. The first comparisons of the numerical and experimental neutron rates in the presence of simultaneous NBI and harmonic IC heating have further evidentiated the need of such a term.…”

“…Numerical simulations of IC heating, therefore, require a self-consistency loop between a wave solver and a solver of the kinetic Fokker-Planck (FP) equation. In view of this, the full wave code TORIC has been recently modified to evaluate the coefficients of the wave equations with the ion distribution functions (DFs) calculated by FP solver SSFPQL, which, in turn, takes into account the quasilinear power source due to the radio-frequency (RF) waves [2]. At IC harmonics (ω = n Ω ci with n ≥ 2) ion heating is a finite Larmor radius (FLR) effect, and, therefore, preferentially accelerates ions with large Larmor radius, ρ k ⊥ > ∼ 1 with k ⊥ the perpendicular wave number, and ρ = v ⊥ /Ω ci .…”

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

“…The package TORIC-SSFPQL [1] for numerical simulations of Ion Cyclotron (IC) Heating in Tokamaks is particularly fast. This is due in part to the fact that in SSFPQL the solution of the surface-averaged quasilinear kinetic equation is obtained as a velocity dependent superposition of Legendre polynomials in the velocity pitch-angle.…”