Dynamics of thin current sheets and their disruption by ballooning instabilities: A mechanism for magnetospheric substorms

Multipoint satellite observations indicate the development of thin current sheets and an impulsive intensification of the cross-tail current density in the growth phase at near-earth distances during a short interval (<1 min) just before onset, after a period of sluggish growth (∼0.5-1.5 h). These multiple time scales are accounted for by analysis and two-dimensional magnetohydrodynamic simulation of the magnetotail in the high-Lundquist number regime, including the earth's dipole field. In the slow growth phase, a thin current sheet develops spanning Y points that stretch from the midtail region (∼30R_E) to the near-earth region (∼10R_E). This is followed by an impulsive enhancement in the current sheet amplitude due to flux pileup, consistent with observations. The stretched magnetotail with an embedded thin current sheet is found to be unstable to an ideal compressible ballooning instability with rapid spatial variation in the dawn-dusk direction. The linear instability is demonstrated by numerical solutions of the ideal ballooning eigenmode equation for a sequence of two-dimensional magnetotail configurations containing a thin current sheet, realized during the impulsive growth phase. Line-tied boundary conditions are imposed at the ionosphere, and shown to have a strong influence on the linear stability of ballooning modes at near-earth distances. It is suggested that the ideal ballooning instability provides a possible mechanism for disrupting the cross-tail current at substorm onset.