Loading Loss‐Cone Distributions in Particle Simulations

Abstract

AbstractNumerical 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.