FULLY IMPLICIT KINETIC SOLUTION OF COLLISIONAL PLASMAS

In this paper we describe a numerical technique, matrix-free Newton-Kr ylov, for solving a single species, stationary, one spatial dimension, one velocity dimension, Vlasov-Fokker-Planck equation. This method is both deterministic and fully implicit and may not have been a viable option before recent developments in numerical methods. It is demonstr ated that efficient steady-state solutions to the nonlinear integro-di fferential equation, can be achieved, obtaining quadratic convergence, but not incurring the large memory requirements of an integral operat or. We present a model problem which simulates ion transport in the ed ge plasma of a tokamak fusion reactor and use this model problem to de monstrate the performance of the new solution method. We demonstrate t hat the solution algorithm is compatible with a higher-order, monotone , convective differencing scheme. (C) 1997 Academic Press.