The stability of the near-Earth magnetotail against the ballooning instability

In an extension to a previous study, conditions for the ballooning instability in the magnetohydrodynamic approximation are derived. It is necessary for exciting the ballooning instability that the plasma pressure is higher where plasma is convected outward. However, the expansion of plasma, which results from the divergence of outward flows in the curved geometry of field lines, may overcompensate for the convective change in the plasma pressure. Conditions for the instability are derived from the equation describing the linear coupling between the Alfven and slow magnetosonic waves. The result indicates that excessive curvature stabilizes, rather than destabilizes, perturbations, as well as the field aligned current and the field aligned flow. That is the field line curvature should be smaller than the pressure gradient for exciting the ballooning instability. It is inferred that this condition is not satisfied during quiet times in the near Earth tail. The plasma sheet becomes more stable to the instability in accordance with the thinning of the plasma sheets during the growth phase of substorms, while in the region nearer to the Earth (the inner edge of the plasma sheet or the ring current region) the plasma pressure gradient, which is possibly localized during the growth phase, may drive the instability.