During the substorm growth phase, thinning of the plasma sheet can energize the unmagnetized ions trapped within it via a Fermi acceleration process. We show here that the energy growth rate, affecting mostly the unmagnetized ions, is exponential in time. The Fermi acceleration will give rise to a large enhancement in the cross-tail ion current density and would be most prominent during the late growth phase. This prediction is quite consistent with previously reported satellite observations which show that the cross-tail current density intensifies rapidly during the final stage of the growth phase just prior to current disruption. ¿ American Geophysical Union 1995