Field line random walk in magnetic turbulence

Abstract

The stochastic behavior of magnetic field lines in turbulence is explored analytically and numerically. This problem is a fundamental aspect of turbulence research but also highly relevant in the theory of energetic particles. In the current paper, previous approaches are reviewed and some simple heuristic arguments are provided helping the reader to understand the reason for the form of analytical results. The importance of the so-called Kubo number in field line random walk theory is also discussed. Furthermore, analytical results for a position-dependent field line diffusion coefficient are provided. For more realistic turbulence configurations, the field line diffusion coefficients are computed numerically. This includes quasi-slab, quasi-2D, two-component, and three-dimensional turbulence. Specific aspects of the field line random walk in each model are also discussed. Results based on a diffusion approximation are compared with numerical results obtained without employing this approximation with the aim to explore its validity and accuracy. Numerical results based on simulations for incompressible and compressible turbulence are also discussed.