A Hybrid Monte Carlo Method for Coulomb Collisions

This presentation describes a hybrid computational method for Coulomb collisions in a plasma that combines a Monte Carlo particle simulation and a fluid dynamic solver in a single uniform method throughout phase space. The new method is based on a hybrid representation of the velocity distribution function $f(v)$, as a combination of a Maxwellian equilibrium $M(v)$ and a collection of discrete particles $g(v)$. The Maxwellian $M$ evolves in space and time through fluid-like equations, and the particles in $g$ convect and collide through Nanbu's Monte Carlo particle method (PRE 1997). Interactions between $M$ and $g$ are represented by a thermalization process that removes particles from g and includes them in $M$ and a dethermalization process that samples particles from $M$ and inserts them into $g$. As test cases for the hybrid method, we have used relaxation of an anisotropic Maxwellian and evolution of a bump-on-tail.