Loading Relativistic Maxwell Distributions in Particle Simulations

TL;DR

This paper introduces efficient algorithms for accurately loading relativistic Maxwell distributions in particle simulations, improving upon existing methods with higher acceptance rates and flexibility.

Contribution

It presents two novel rejection algorithms for boosting particles to relativistic shifted-Maxwellian distributions, enhancing efficiency and compatibility with various base algorithms.

Findings

Acceptance efficiency of approximately 50% for generic cases.

Acceptance efficiency of 100% for symmetric distributions.

Algorithms are compatible with arbitrary base methods.

Abstract

Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ${\approx}50\%$ for generic cases and $100\%$ for symmetric distributions. They can be combined with arbitrary base algorithms.