An Adaptive $\delta f$ Monte Carlo Method

A new adaptive δf Monte Carlo method is presented with an application to radio frequency heating and transport in fusion plasmas. The method is suitable when an initial zeroth-order approximation of the distribution function is known. The difference between our method and earlier δf methods is that we model the source term, obtained from the δf ansatz, by adding particles. The rate of particles is defined by the inhomogeneous term in the Fokker-Planck equation. We develop an adaptive scheme for modifying the unperturbed part G(x) such that the number of particles used in the simulation for a fixed weight is minimized. This implicitly reduces the variance and improves computational efficiency. The method is tested on a one-dimensional Fokker-Planck model for RF-heating and compared against the analytical stationary solution.