A simple procedure for generating a Kappa distribution in PIC simulation

TL;DR

The paper addresses the challenge of generating a Kappa velocity distribution for PIC simulations with a portable, uniform-variates-only method. It introduces a rejection-sampling scheme using a Pareto envelope to sample from the beta-prime form of the Kappa distribution and presents a practical, stepwise algorithm. The authors analyze acceptance efficiency and propose two candidate settings for the envelope parameter, recommending a choice that achieves about 0.73–0.8 efficiency. The approach reduces reliance on gamma or normal variate generators, potentially lowering computational cost and improving portability for kinetic plasma simulations.

Abstract

For kinetic modeling of plasma processes in space, a rejection-sampling procedure for generating a Kappa distribution in particle-in-cell (PIC) simulation is proposed. A Pareto distribution is employed as an envelope distribution. The procedure only requires uniform variates, and its acceptance efficiency is $\approx 0.73$--$0.8$.

Figures (1)

• Figure 1: (a) Velocity distribution of the Kappa distribution with $\kappa=2$. The black line and the blue histogram show the theoretical curve and numerical results. (b) Acceptance efficiency in the $(\kappa,n)$ space (Eq. \ref{['eq:eff']}). The thin red line, the red dashed line, and the blue dashed line indicate the optimum line, the near-optimum approximation ($n= {2\kappa}/{3} - {1}/{5}$), and my recommendation ($n = \kappa/2$), respectively.