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

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 two-point 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.