We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios $l_{\Vert }{/l}_{\perp }.$ We find, in addition to the fact that a higher fluctuation level $\delta {B/B}_0$ makes the system more stochastic, that by increasing the ratio $l_{\Vert }{/l}_{\perp }$ at fixed $\delta {B/B}_0,$ the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number $R=\left(\delta {B/B}_0{\left)\right(l}_{\Vert }{/l}_{\perp }\right).\mathrm{}$ The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When $R\ll 1$ weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When $R\approx 1$ the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient $D_{\perp }\sim (\delta {B/B}_0{)}^2$ is recovered. Finally, for $R\gg 1$ the percolation scaling of the diffusion coefficient $D_{\perp }\sim (\delta {B/B}_0{)}^{0.7}$ is obtained.

The transport of energetic particles in a mean magnetic field and in the presence of anisotropic magnetic turbulence is studied numerically, for parameter values relevant to astrophysical plasmas. A numerical realization of magnetic turbulence is set up, in which the degree of anisotropy is varied by changing the correlation lengths $l_x$ , $l_y$ , and $l_z$ . The ratio $\rho ∕\lambda$ of the particle Larmor radius $\rho$ over the turbulence correlation length $\lambda$ is also varied. It is found that for $l_x$ ,$l_y⪢l_z$ , and for $\rho ∕\lambda \lesssim {10}^{-2}$ transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. In addition, the spatial distribution of particles is clearly non-Gaussian. Such regimes are characterized by a Levy statistics, with diverging second-order moments. Decreasing the ratio $l_x∕l_z$ , nearly Gaussian (normal) diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Changing the particle Larmor radius, normal diffusion is found for ${10}^{-2}\lesssim \rho ∕\lambda \lesssim 1$ because of increased pitch angle diffusion. New anomalous superdiffusive regimes appear when $\rho ∕\lambda \gtrsim 1$ showing that the interaction between particles and turbulence decreases in these cases. A new regime, called generalized double diffusion, is proposed for the cases when particles are able to trace back field lines. A summary of the physical conditions which lead to non-Gaussian transport is given.