Modifications to Swisdak (2013)'s rejection sampling algorithm for a Maxwell-J\"{u}ttner distribution in particle simulations

TL;DR

This paper presents improved modifications to Swisdak's rejection sampling algorithm for efficiently generating Maxwell-J"{u}ttner distributed particles in simulations, with new approximations for key parameters.

Contribution

It introduces self-contained, more efficient modifications to the existing rejection sampling algorithm for Maxwell-J"{u}ttner distributions.

Findings

Enhanced efficiency of the sampling algorithm.

Proposed approximations simplify parameter calculations.

Algorithm is now self-contained and more practical.

Abstract

Modifications to Swisdak [Phys. Plasmas 20, 062110 (2013)]'s rejection sampling algorithm for drawing a Maxwell-J\"{u}ttner distribution in particle simulations are presented. Handy approximations for $e$-folding points and a linear slope in the envelope function are proposed, to make the algorithm self-contained and more efficient.