Loading non-Maxwellian Velocity Distributions in Particle Simulations

Numerical procedures for generating non-Maxwellian velocity distributions in particle simulations are presented. First, Monte Carlo methods for an $(r,q)$ distribution that generalizes flattop and kappa distributions are discussed. Then, two rejection methods for the regularized kappa distribution are presented, followed by a comparison in the $\kappa$ space. A simple recipe is proposed for the subtracted kappa distribution. Properties and numerical recipes for the ring and shell distributions with a finite Gaussian width are discussed. The ring and shell Maxwellians are further introduced as alternatives to the ring and shell distributions. Finally, methods for the super-Gaussian and the filled-shell distributions are presented.