Numerical solution of the Fokker-Planck equation

A code to solve the Fokker-Planck kinetic equation for electrons and ions is presented. The electrons are treated with a relativistic collision operator. The importance of the numerical approach associated with an exact relativistic treatment for the solution of the electrons dynamic is emphasized in order to study accurately all the physics associated with the electron distribution function, as for instance the physics associated with the hot tail, the fast electron transport and the shape of the distribution function. Accurate relativistic treatment of the hot tail helps make the study of these problems less phenomenological and more physical. The pertinent equations for two different ions species, a majority ion and a minority ion population, are included in the code. The ions are treated with non-relativistic equations. The code also includes the appropriate quasi-linear operator for lower hybrid current drive, electron cyclotron heating and current drive, ion cyclotron heating for each of the ion species. This allows accurate study of synergy effects between the different sources for plasma heating and current drive. The exchange terms between the different species are included. The code includes also the option of a variable grid size for electrons and ions. (authors)