Field line random walk, field line separation, and particle transport in turbulence with weak transverse complexity

We study the random walk of magnetic field lines as well as field line separation in a magnetized plasma such as the solar wind or the interstellar medium. By doing so we focus on turbulence with small Kubo numbers. For field line random walk this allows us to employ an approach based on a Taylor expansion which is essentially an expansion in the Kubo number. Compared to previous non-linear descriptions, no assumption concerning the field line distribution or diffusivity has to be made. Based on this approach, we compute corrections to the quasi-linear formula allowing us also to test assumptions usually made in non-linear theories of field line random walk. We show that up to the considered order, the assumption of Gaussian statistics does not alter the diffusion coefficient whereas the diffusion approximation provides a correction term which is a factor two too large. We also discuss the separation of two magnetic field lines. We develop a quasi-linear theory for field line separation and introduce a fundamental scale of turbulence describing its transverse structure. Furthermore, we discuss applications of our results in the theory of energetic particle transport. Besides quasi-linear diffusion we also discuss compound sub-diffusion as well as the recovery of diffusion due to transverse complexity. Furthermore, we derive a formula for the perpendicular diffusion coefficient of energetic particles similar compared to the famous Rechester & Rosenbluth result. Applications in astrophysics are also discussed. (C) 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.