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 general form of the drift kinetic equation is reduced to a stochastic mapping equation which is valid in the weak collisions regime. This equation describes the evolution of the distribution function on Poincaré cuts of phase space. The proposed Monte Carlo algorithm applied to the stochastic mapping equation turns out to solve the drift kinetic equation much faster than a direct integration of stochastic orbits. It can be applied to study quasilinear effects of radio frequency heating and transport in systems with complex magnetic field geometries such as stellarators, tokamaks with toroidal magnetic field ripples, or ergodic divertors. For systems with axial space symmetry the stochastic mapping equation is shown to reduce to the well-known canonical (bounce) averaged equation. For nonaxisymmetric magnetic fields the bounce averaged equation for trapped particles is recovered.