Substorm trigger conditions

Critical conditions for the onset of fast interchange dynamics in the stressed geotail during the growth phase of the substorm are derived. We compare the ideal MHD interchange stability condition [Hurricane, 1997] with that for kinetically modified interchange-ballooning motions. It is shown that fast interchange growth is possible only in the near-Earth boundary of the plasma sheet where the local plasma pressure-to-magnetic pressure ratio (beta) is near unity since compressibility stabilizes the high-beta geotail. The growth rate is proportional to the local current density and exceeds the ion bounce frequency in the local region of beta less than or similar to 1. Only after sufficient thinning of the current sheet will the kinetic theory growth rate exceed the bounce frequency of the ions, which is the effective condition for the substorm MHD-space-timescale unloading of the plasma energy stored in the geotail.