Monte Carlo simulations of intensity profiles for energetic particle propagation

¹ Zentrum für Astronomie und Astrophysik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
e-mail: robert.c.tautz@gmail.com
² Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
e-mail: andreasm4@yahoo.com

Received: 26 August 2015
Accepted: 24 November 2015

Abstract

Aims. Numerical test-particle simulations are a reliable and frequently used tool for testing analytical transport theories and predicting 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 and anisotropy-time profiles. Because of 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 subdiffusive 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.