A Fast 2d Fokker-Planck Solver With Synergetic Effects

Solution of the 2D relativistic quasilinear Fokker-Planck equation is highly desirable in problems of numerical simulation of RF current drive in tokamak plasmas, especially in codes coupling ray-tracing and transport. For practicality, a fast Fokker-Planck solver is needed. We present in this work a fast 2D Fokker-Planck solver which can be applied for time dependent current drive problems. The code is 2D relativistic, and includes the complete first Legendre harmonic term for electron-electron collisions. (The inclusion of this term, part of which is usually neglected in the solution of the quasilinear Fokker-Planck equation, can lead to important differences in the values of the calculated current.) The accurate relativistic collision operator derived in [B. Braams and C.F. Karney, Phys. Fluids B 1 (1989) 1355] is used in the present version of the code. The 2D equation is discretized in momentum space using an implicit 5-point stencil and solved using the NAG library routine D03UAF. Convergence for a steady state solution can be reached in about 30 iterations. Results obtained for the runaway problem and the LH current drive problem are presented, together with results on the synergetic effects of fast waves with lower-hybrid waves.