Moment-preserving Monte-Carlo Coulomb collision method for particle codes

TL;DR

This paper extends Monte-Carlo Coulomb collision methods in particle-in-cell simulations to weighted particles, ensuring accurate scattering physics on average and exact conservation of momentum and energy through a new velocity adjustment technique.

Contribution

It introduces a novel extension for weighted particles and a velocity correction method to preserve physical laws exactly in Monte-Carlo Coulomb collision simulations.

Findings

Method accurately models Coulomb collisions with weighted particles.

Velocity adjustment restores exact conservation of momentum and energy.

Test problems demonstrate the method's effectiveness.

Abstract

Binary-pairing Monte-Carlo methods are widely used in particle-in-cell codes to capture effects of small angle Coulomb collisions. These methods preserve momentum and energy exactly when the simulation particles have equal weights. However, when the interacting particles are of varying weight, these physical conservation laws are only preserved on average. Here, we 1) extend these methods to weighted particles such that the scattering physics is correct on average, and 2) describe a new method for adjusting the particle velocities post scatter to restore exact conservation of momentum and energy. The efficacy of the model is illustrated with various test problems.