Modelling of lower hybrid current drive in the presence of spatial radial diffusion

A code to solve the full three dimensional Fokker-Planck kinetic equation in the presence of lower hybrid current drive (LHCD) is applied to study numerically the problem of modelling LHCD, including the combined effects of spatial radial diffusion and an electric field The code uses the Beliaev-Budker relativistic collision operator, and applies a method of fractional steps to the numerical solution of the time evolution equation for the three dimensional Fokker-Planck equation. The importance of the numerical approach associated with an exact relativistic treatment for the solution is emphasized in order to study accurately all the physics associated with this problem, especially the shape of the distribution function and the physics associated with its hot tail as, for instance, the fast electron transport and lower hybrid absorbed power profiles. The aim of the simulation is to match hard X ray imaging profiles and current density profiles. An accurate relativistic treatment of the hot tail helps make the study of these problems less phenomenological and more physical. Some preliminary results from the Tokamak de Varennes (TdeV) are analysed in order to illustrate the power of the method.