Loading a relativistic kappa distribution in particle simulations

TL;DR

This paper introduces a new method for accurately initializing particle velocities in simulations using the relativistic kappa distribution, achieving high efficiency and reproducing key distribution features.

Contribution

It develops a rejection sampling procedure based on beta prime distributions for loading relativistic kappa distributions in particle simulations, extending previous methods.

Findings

Acceptance rate reaches approximately 95%.

Successfully reproduces the power-law tail of the distribution.

Provides detailed derivation and numerical validation.

Abstract

A procedure for loading particle velocities from a relativistic kappa distribution in particle-in-cell (PIC) and Monte Carlo simulations is presented. It is based on the rejection method and the beta prime distribution. The rejection part extends earlier method for the Maxwell-Juttner distribution, and then the acceptance rate reaches ~95%. Utilizing the generalized beta prime distributions, we successfully reproduce the relativistic kappa distribution, including the power-law tail. The derivation of the procedure, mathematical preparations, comparison with other procedures, and numerical tests are presented.