Loading of Relativistic Maxwellian-type Distributions Revisited

TL;DR

This paper introduces a simple numerical method based on inverse transform sampling for efficiently generating relativistic Maxwellian-type distributions, providing an alternative to the Maxwell-Jüttner distribution with successful numerical validation.

Contribution

The paper proposes a novel, straightforward numerical approach for loading relativistic Maxwellian-type distributions using inverse transform sampling, improving upon existing methods.

Findings

Successfully reproduces relativistic Maxwellian energy distribution

Demonstrates the method's accuracy through numerical tests

Provides an efficient alternative to Maxwell-Jüttner distribution

Abstract

A simple numerical method for loading of a relativistic Maxwellian-type distribution is proposed based on inverse transform sampling. The relativistic Maxwellian energy distribution is introduced as an alternative to the Maxwell-J\"{u}ttner distribution. The cumulative distribution of the shifted-Maxwellian energy distribution is approximated by an invertible function. Random variates of energy is transformed from uniformly distributed random variables. Then, the energy variates are converted to momentum vector variates. Numerical tests are presented to show that the present method successfully reproduce the relativistic Maxwellian energy distribution.