Anomalous and Gaussian transport regimes in anisotropic three-dimensional magnetic turbulence

The effects of the anisotropy of magnetic turbulence on the transport of magnetic field lines are investigated numerically. The three-dimensional magnetic turbulence is represented by a Fourier expansion with a power law band spectrum, and anisotropy is introduced by considering different correlation lengths $l_{\mathrm{cx}}$ and $l_{\mathrm{cy}}$ in the plane perpendicular to the average magnetic field ${\mathbf{B}}_0{=B}_0{e}_z.$ Transport in this plane is analyzed for different fluctuation levels $\delta {B/B}_0$ and for various degrees of anisotropy $l_{\mathrm{cx}}{/l}_{\mathrm{cy}}.$ The results of the simulation show that there are anomalous (subdiffusive and superdiffusive) transport regimes at low fluctuation levels, while Gaussian diffusive regimes are attained in the presence of high fluctuation levels, like in the isotropic case; as anisotropy is increased the Gaussian regime is reached for higher fluctuation levels; for significant degrees of anisotropy $l_{\mathrm{cx}}{/l}_{\mathrm{cy}},$ a percolative regime is found at a low fluctuation level, with superdiffusion in the direction where the correlation length is shorter; conversely, in the diffusive regime transport is faster in the direction of the longer correlation length, and the obtained ratio of diffusion coefficients $D_x{/D}_y$ is close to the ratio of anisotropy $l_{\mathrm{cx}}{/l}_{\mathrm{cy}}.$ The application of these results to energetic particle propagation in the solar wind is discussed.