Observations have shown that electrons and protons are energized up to at least 1 MeV in the magnetotail during substorms. This magnitude cannot be explained by the cross-tail electrostatic field, which typically has a modest potential difference of only 50 kV. A rotational electric field induced by a time-dependent magnetic field does not have such a limitation. In order to evaluate its capabilities a simple model of a localized, growing disturbance in the neutral sheet current was used to calculate perturbation magnetic and electric fields; the model includes the formation of X and O type neutral lines. Plasma sheet test particles were followed in these time-dependent fields by using the full relativistic equation of motion. The most efficient energizing mechanism is a two-step process, with an initial linear acceleration along a neutral line up to moderate energies, followed by betatron acceleration. The former imparts a large magnetic moment &mgr;=W⊥/B to the particle as it begins to gyrate and drift in the magnetic field, W⊥ being the transverse kinetic energy. During this drift into regions of stronger magnetic field there is a large increase in W⊥, the relativistic invariant &ggr;&mgr; remaining constant. Because of the rotational property of the induced electric field it is possible for a particle to gain energy even when the drift motion by itself would cause a loss. The model also includes acceleration along magnetic field lines in the plasma sheet, with moderate energy gain. A cyclic pattern of electron and proton precipitation is predicted, such as is observed during auroral breakup.