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 electric field and with a model of three dimensional magnetic turbulence. By computing the mean square displacements in the plane of the current sheet we find superdiffusive and superballistic transport regimes. Since velocity increases with the length of the free path, we have accelerated Lévyflights. The possibility to generate power law velocity distribution functions is pointed out, as well as the long memory effects and non local properties of ion transport. This revised version was published online in July 2006 with corrections to the Cover Date.