Loading a relativistic Kappa distribution in particle simulations

A procedure for loading particle velocities from a relativistic kappa distribution in particle-in-cell 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-Jüttner 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.