Loading Loss-Cone Distributions in Particle Simulations

Abstract

Numerical procedures to generate random variates that follow loss-cone velocity distributions in particle simulations are presented. We propose a simple summation algorithm for the Ashour-Abdalla–Kennel-type loss-cone distribution, also known as the subtracted Maxwellian. For the Dory-type loss-cone distribution, we use a random variate for the gamma distribution. Extending earlier algorithms for the kappa and Dory-type distributions, we construct a novel algorithm to generate a popular form of a kappa loss-cone (KLC) distribution. To better express the loss cone, we discuss another family of loss-cone distributions based on the pitch angle. In addition to the acceptance-rejection method, we propose two transformation algorithms that convert an isotropic distribution into a loss-cone distribution. This allows us to generate loss-cone and KLC distributions from the Maxwell and kappa distributions.