On storm weakening during substorm expansion phase

Abstract. Iyemori and Rao recently presented evidence that the strength of a magnetic storm, as measured by -Dst, weakens, or its rate of growth slows, during the substorm expansion phase. Yet the expansion phase is known to inject energetic particles into the ring current, which should strengthen the storm. We propose to reconcile these apparently contradictory results by combining the virial theorem and a principle of energy partitioning between energy storage elements in a system with dissipation. As applied to the unloading description of the substorm expansion phase, the virial theorem states that -Dst is proportional to the sum of the total magnetic energy and twice the total kinetic energy in the magnetosphere including the tail. Thus if expansion phase involves converting magnetic energy stored in the tail into kinetic energy stored in the ring current, a drop in -Dst during expansion phase requires that less than half the drop in magnetic energy goes into the ring current, the rest going into the ionosphere. Indeed Weiss et al., have estimated that the energy dissipated in the ionosphere during expansion phase is twice that injected into the ring current. This conclusion is also consistent with the mentioned energy partitioning principle, which requires that more energy be dissipated than transferred between storage elements. While Iyemori and Rao's observations seem to contradict the hypothesis that storms consist at least in part of a sum of substorms, this mode of description might nonetheless be preserved by including the substorm's growth-phase contribution. Then the change in storm strength measured from before the growth phase to after the expansion phase is positive, even though the expansion phase alone makes a negative contribution.