Transport of Charged Particles Propagating in Turbulent Magnetic Fields as a Red-noise Process

The transport of charged particles in various astrophysical environments permeated by magnetic fields is described in terms of a diffusion process, which relies on diffusion-tensor parameters generally inferred from Monte-Carlo simulations. In this paper, a theoretical derivation of the diffusion coefficient in the case of a purely turbulent magnetic field is presented. The approach is based on a red-noise approximation to model the 2-pt correlation function of the magnetic field experienced by the particles between two successive times. This approach is shown to describe the regime in which the Larmor radius of the particles is in resonance with the wavelength power spectrum of the turbulence (gyro-resonant regime), extending hence previous results applying to the high-rigidity regime in which the Larmor radius is greater than the larger wavelength of the turbulence. The results are shown to be consistent with those obtained with a Monte-Carlo generator. Although not considered in this study, the presence of a mean field on top of the turbulence is discussed.