Self-Consistent Simulation of High Power Electromagnetic Wave Heating in Three Dimensional Tokamak Geometry

In tokamak plasmas, high power electromagnetic wave heating in the ion cyclotron range of frequencies (ICRF) often gives rise to supra-thermal ion populations or ``ion tails.'' Previous self-consistent simulations [1] of these tails have included only a single toroidal harmonic in the wave solution, and are thus limited to two spatial dimensions. In this work, these calculations are extended to three spatial dimensions by including a full spectrum of toroidal harmonics for specific antenna geometries. By summing the quasi-linear diffusion coefficients over all toroidal harmonics and iterating between wave and Fokker-Planck solutions, a self-consistent three dimensional solution is obtained for the wave electric field and ion distribution function. This is possible because the quasi-linear diffusion coefficients are flux-surface-averaged quantities, and thus can be summed directly over toroidal harmonics using Parseval's theorem. [1] E. F. Jaeger, L. A. Berry, S. D. Ahern, \textit{et al.,} Phys. Plasmas \textbf{13}, 056101-1 (2006).