A numerical tool based on FEM and wavelets to account for spatial dispersion in ICRH simulations

Modeling of Ion Cyclotron Resonance Heating (ICRH) is difficult because of spatial dispersion. Numerical methods based on finite element or finite difference have difficulties in handling spatial dispersive effects, because the response is non-local. Fourier spectral methods can handle spatial dispersion, however, these methods have difficulties in handling the complex geometries outside the plasma domain and tend to produce dense matrices that are time consuming to invert. In this study, we investigate the potential of a new numerical method for solving the spatially dispersive wave equation based on FEM and wavelets. The spatially dispersive terms in the wave equation are evaluated using wavelets, and its contribution is represented as an induced current density in the wave equation. The wave equation is then solved using a finite element scheme, where the induced current density is represented as an inhomogeneous term and added using a fixed point iteration scheme. The method is applied to a case of one dimensional fast wave minority heating, including the up- and downshift in the parallel wave number, where we show that convergence can be obtained in a few iterations.