Monte-Carlo simulations of intensity profiles for energetic particle propagation

TL;DR

This paper uses Monte-Carlo simulations to analyze energetic particle propagation, emphasizing the importance of time-dependent diffusion coefficients and perpendicular distribution components for accurate modeling.

Contribution

It extends simulation tools to generate intensity and anisotropy profiles, highlighting the necessity of time-dependent diffusion and perpendicular components for diffusion equation applicability.

Findings

Intensity profiles match diffusion solutions when using time-dependent diffusion coefficients.

Perpendicular distribution components are crucial for accurate flux modeling.

Initial ballistic phase affects the applicability of classical diffusion models.

Abstract

Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used to critically judge the applicability of diffusion to the stochastic transport of energetic particles in magnetized turbulence. Methods. A Monte-Carlo simulation code is extended to allow for the generation of intensity profiles as well as anisotropy-time profiles. Due to the relatively low number density of computational particles, a kernel function has to be used to describe the spatial extent of each particle. Results. The obtained intensity profiles are interpreted as solutions of the diffusion equation by inserting the diffusion coefficients that have been directly determined from the mean-square displacements. The comparison shows that the time dependence of the diffusion coefficients needs to be considered, in particular the initial ballistic phase and the often sub-diffusive perpendicular coefficient. Conclusions. It is argued that the perpendicular component of the distribution function is essential if agreement between the diffusion solution and the simulated flux is to be obtained. In addition, time-dependent diffusion can provide a better description than the classic diffusion equation only after the initial ballistic phase.