It is now generally accepted that substorm expansive phase activity involves a release of magnetotail energy, part of which is available for the acceleration of highly energetic particles (E>100 keV) that play a role in ring current and radiation belt formation. However, the physical process whereby this acceleration takes place is not yet fully understood. In this paper we consider the physics of the acceleration process based on the tenet that acceleration of particles to E>100 keV occurs as a cumulative process involving a sequence of substorm expansive phases. In our view, nonadiabatic particle dynamics plays a key role in the energization process. We present both a qualitative description and quantitative treatment which starts with a consideration of a single particle and is then extended to track the evolution of the particle distribution function over several substorm expansive phase cycles. We stress two salient features of the evolution of particle distribution function, namely the rapid formation of a non-Maxwellian high-energy tail and the saturation of this tail distribution toward a kappa distribution in the asymptotic limit. ¿ American Geophysical Union 1995