An approximate Kappa generator for particle simulations

TL;DR

This paper introduces a fast, GPU-compatible random number generator for the Kappa velocity distribution in particle simulations, using an approximation of the cumulative distribution function with the q-exponential.

Contribution

It presents a novel approximate Kappa generator that is efficient on GPUs and accurate for certain parameter ranges, improving simulation performance.

Findings

Provides practically accurate results for k<4

Runs efficiently on GPUs

Includes derivation and numerical validation

Abstract

A random number generator for the Kappa velocity distribution in particle simulations is proposed. Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The proposed method provides practically accurate results, in particular for k<4. It runs fast on graphics processing units (GPUs). The derivation, numerical validation, and relevance to GPU execution models are discussed.