Loading loss-cone distributions in particle simulations

TL;DR

This paper introduces new numerical algorithms for generating loss-cone velocity distributions in particle simulations, including simple summation and transformation methods for various distribution types.

Contribution

The paper presents novel algorithms for efficiently generating loss-cone and kappa loss-cone distributions, extending previous methods and enabling better simulation of anisotropic plasma behaviors.

Findings

Developed a summation algorithm for Ashour-Abdalla--Kennel-type loss-cone distribution.

Created a gamma variate-based method for Dory-type loss-cone distribution.

Proposed transformation algorithms to generate loss-cone distributions from isotropic distributions.

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 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 kappa loss-cone distributions from the Maxwell and kappa distributions.