Heuristic construction of field line random walk diffusion coefficients

Abstract

To understand the statistics of magnetic field lines in turbulence is complicated. Previous descriptions have been based on either pure numerical treatments, often called simulations, or analytical theory. In the latter case one operates with nonlinear integral or differential equations which are difficult to solve. In order to achieve a complete analytical description, one needs to employ a set of approximations which are often difficult to justify. Although, previously developed numerical and analytical treatments of field line random walk agree with each other, they do not provide simple arguments for the analytical form of field line diffusion coefficients. It is the purpose of the current article to derive field line random walk coefficients entirely based on simple heuristic arguments. Special cases such as slab, two-dimensional, three-dimensional, and two-component turbulence are considered. Heuristically constructed diffusion parameters are compared with previously obtained analytical results. It is shown that the heuristic arguments provide the same scaling behavior as the formulas derived by employing systematic analytical theories.