Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation

TL;DR

This paper develops a Monte Carlo method for solving the guiding-center Fokker-Planck kinetic equation, accounting for magnetic field nonuniformity, and demonstrates its consistency with standard Coulomb operators in uniform fields.

Contribution

It introduces a Monte Carlo approach for the guiding-center Fokker-Planck equation that includes magnetic field nonuniformity effects, extending previous methods.

Findings

The method reduces to standard Coulomb operators in uniform magnetic fields.

Coefficients for the Monte Carlo implementation are explicitly provided.

The approach enables more accurate modeling of plasma collisions in nonuniform magnetic fields.

Abstract

A Monte Carlo method for the collisional guiding-center Fokker-Planck kinetic equation is derived to include the effects of background magnetic-field nonuniformity. It is shown that, in the limit of a homogeneous magnetic field, the guiding-center Monte Carlo collision operators reduce to the standard Coulomb operators. The coefficients required for the implementation of the method are also given.