The distribution function of ions heated in the ion cyclotron range of frequencies is obtained by solving the Fokker–Planck equation. For non-minority heating scenarios, the full non-linear Coulomb collision operator must be used in this equation. A method of resolution accounting for the complexity of this operator is presented. We consider a plasma immersed in a homogeneous magnetic field. The adopted method of resolution is based on an expansion of the distribution function in a series of Legendre polynomials. Results of the corresponding code non-linear Fokker–Planck in two-dimensional velocity space (NLFP-2D) are discussed for experimentally relevant JET-like parameters. The convergence of the Legendre expansion has been tested and the importance of the non-linear effects has been shown. Three different regimes, characterized by different modes of indirect ion heating and depending on the absorbed RF power density as well as the minority concentration, were identified. The NLFP-2D code has been used to study the validity of the Maxwellian approximation of the self-collision operator. One finds that this model is only correct in a very limited range of parameters, and leads mostly to an overestimation of the indirect ion heating.
Global-wave solutions with self-consistent velocity distributions in ion cyclotron heated plasmas