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.