Numerical scheme for treatment of Uehling-Uhlenbeck equation for two-particle interactions in relativistic plasma

TL;DR

This paper introduces an efficient numerical method for computing the Uehling-Uhlenbeck collision integral in relativistic plasma, significantly reducing computation time while ensuring energy and particle number conservation.

Contribution

The paper presents a novel, faster numerical scheme for the Uehling-Uhlenbeck equation that accurately models two-particle interactions in relativistic plasma, including multiple QED processes.

Findings

Significant reduction in computation time compared to existing methods.

Exact conservation of energy and particle number in simulations.

Numerical reaction rates agree with analytical expressions where available.

Abstract

We present a new efficient method to compute Uehling-Uhlenbeck collision integral for all two-particle interactions in relativistic plasma with drastic improvement in computation time with respect to existing methods. Plasma is assumed isotropic in momentum space. The set of reactions consists of: Moeller and Bhabha scattering, Compton scattering, two-photon pair annihilation, and two-photon pair production, which are described by QED matrix elements. In our method exact energy and particle number conservation laws are satisfied. Reaction rates are compared, where possible, with the corresponding analytical expressions and convergence of numerical rates is demonstrated.