Non Gaussian and non local transport in the Earth's distant magnetotail

We study the ion dynamics in a magnetic field reversal with a constant elec tric field and with a model of three dimensional magnetic turbulence. By co mputing the mean square displacements in the plane of the current sheet we find superdiffusive and superballistic transport regimes. Since velocity in creases with the length of the free path, we have accelerated Levy flights. The possibility to generate power law velocity distribution functions is p ointed out, as well as the long memory effects and non local properties of ion transport.