Loading of Relativistic Maxwellian-type Distributions Revisited

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-Jüttner 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.