Field-line transport in stochastic magnetic fields: Percolation, Lévy flights, and non-Gaussian dynamics

The transport of magnetic field lines is studied numerically in the case where strong three-dimensional magnetic fluctuations are superimposed to a uniform average magnetic field. The magnetic percolation of field lines between magnetic islands is found, as well as a non-Gaussian regime where the field lines exhibit L\'evy random walks, changing from L\'evy flights to trapped motion. Anomalous diffusion laws 〈{Δ}xᵢ²〉{∝}s^α with {α}>1 and {α}1 are found for low fluctuation levels, while normal diffusion and Gaussian random walks are recovered for sufficiently high fluctuation levels.