Monte Carlo Modelling of Boltzmann Equation in Space Plasma With Kappa Velocity Distribution Function

Abstract

This paper presents a Monte Carlo simulation framework for analysing ion dynamics in space plasmas governed by non-Maxwellian Kappa velocity distributions, where we use the Monte Carlo method to solve the Boltzmann equation under the influence of gravitational, electric, and magnetic fields, while accounting for Coulomb collisions, wave-particle interactions, or both together. A central innovation lies in the derivation of the main algorithm formulas, that generate the ion velocities for both drifting and non-drifting Kappa velocity distributions. The algorithm rigorously incorporates interaction effects through friction and diffusion coefficients, adapting the Fokker-Planck formalism for Coulomb collisions and the diffusion equation for wave-particle interactions—each explicitly tailored for Kappa-distributed plasmas. Through this approach, the model demonstrates its capability to produce essential plasma characteristics, including density, drift velocity, parallel and perpendicular temperatures, and parallel and perpendicular heat fluxes, by linking non-thermal particle behavior with macroscopic plasma properties.