An Adaptive $\delta f$ Monte Carlo Method

A new adaptive
$\delta f$
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
$\delta f$
methods is that we model the source term, obtained from the
$\delta f$
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
$G({\bf x})$
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.