On the ability of different diffusion theories to account for directly simulated diffusion coefficients

We present direct numerical simulations of charged-particle transport in a turbulent magnetic field. The magnetic field model used in the simulations consists of a composite of statistically homogeneous slab and two-dimensional turbulence representative of solar wind conditions at Earth. This turbulent magnetic field is then added to a uniform background magnetic field. We find that the parallel and perpendicular mean free paths are well described by power laws as a function of rigidity at different turbulence levels. At a low level of turbulence we find that quasi-linear theory and the field line random walk theory for the parallel and perpendicular mean free paths, respectively, provide predictions that are in good agreement with the simulated mean free paths. At intermediate turbulence levels the simulated parallel and perpendicular mean free paths are best accounted for by recently proposed nonlinear theories, while quasi-linear theory and the field line random walk theory overestimate the simulated mean free paths. At high turbulence levels neither quasi-linear theory and the field line random walk theory nor the nonlinear theories provide predictions that are in good agreement with the simulated parallel and perpendicular mean free paths.