SOLUTION OF THE DRIFT KINETIC-EQUATION IN THE REGIME OF WEAK COLLISIONS BY STOCHASTIC MAPPING TECHNIQUES

A new method for solving the drift kinetic equation applicable for non -integrable particle motion is presented. To obtain this goal, the gen eral form of the drift kinetic equation is reduced to a stochastic map ping equation which is valid in the weak collisions regime. This equat ion describes the evolution of the distribution function on Poincare c uts of phase spare. The proposed Monte Carlo algorithm applied to the stochastic mapping equation turns out to solve the drift kinetic equat ion much faster than a direct integration of stochastic orbits. It can be applied to study quasilinear effects of radio frequency heating an d transport in systems with complex magnetic field geometries such as stellarators, tokamaks with toroidal magnetic held ripples, or ergodic diverters. For systems with axial space symmetry the stochastic mappi ng equation is shown to reduce to the well-known canonical (bounce) av eraged equation. For nonaxisymmetric magnetic fields the bounce averag ed equation for trapped particles is recovered. (C) 1997 American Inst itute of Physics.