A 2-D Fokker-Planck solver for the current drive problem

Solution of the 2-D relativistic quasilinear Fokker-Planck equation is of major importance in problems of RF current drive in tokamak plasmas. In many codes coupling ray-tracing and transport, the solution of the Fokker-Planck equation is short-circuited in order to accelerate the calculations, by reducing the 2-D equation to a simpler 1-D equation, or by using some simple formulae relating the current density to the absorbed power in order to calculate the current density. This leads to a value of the current density which is not in very good agreement with the solution of the full 2-D Fokker-Planck equation. We present in this work a fast 2-D Fokker-Planck solver which we hope can be applied for time-dependent current drive problems. The code is 2-D, relativistic, and includes the first Legendre harmonic reaction term. (The inclusion of this term can lead to important differences in the values of the calculated current.) The 2-D equation is discretized using a fully implicit 5-point stencil and solved using the NAG routine D03UAF. Convergence to the steady state can be reached in about 20 to 30 iterations. (author) 3 refs., 1 fig., 2 tabs