Velocity decorrelation functions of high-energy cosmic rays propagating in magnetic fields

TL;DR

This paper derives diffusion tensor coefficients for cosmic-ray transport by calculating velocity decorrelation functions using Dyson series, providing approximate solutions validated against Monte-Carlo simulations for particles with sufficiently large Larmor radii.

Contribution

It introduces a formal derivation method for velocity decorrelation functions in cosmic-ray transport using Dyson series expansions, enhancing understanding of magnetic field effects.

Findings

Approximate solutions match Monte-Carlo simulations for large Larmor radii.

Velocity decorrelation functions are expressed as Dyson series, improving modeling accuracy.

The method provides insights into cosmic-ray diffusion in turbulent magnetic fields.

Abstract

Diffusion tensor coefficients play a central role in describing cosmic-ray transport in various astrophysical environments permeated with magnetic fields, which are usually modeled as a fluctuating field on top of a mean field. In this article, a formal derivation of these coefficients is presented by means of the calculation of velocity decorrelation functions of particles. It relies mainly on expanding the 2-pt correlation function of the (fluctuating) magnetic field experienced by the particles between two successive times in the form of an infinite Dyson series and retaining a class of terms that converge to a physical solution. Subsequently, the velocity decorrelation functions, themselves expressed as Dyson series, are deduced from an iteration procedure that improves on the partial summation scheme. The results are shown to provide approximate solutions compared to those obtained by Monte-Carlo simulations as long as the Larmor radius of the particles is larger than at least one tenth of the largest scale of the turbulence.