Finite k_y ballooning instability in the near-Earth magnetotail

Two-dimensional initial value MHD simulations of the linear ideal MHD ballooning instability in the near-Earth magnetotail are presented. The configuration of the magnetotail is modeled by the analytic two-dimensional static equilibrium developed by Voigt. For an intermediate range of plasma β values (∼1-100) at the equatorial plane, the Voigt configuration of the near-Earth magnetotail is shown to be unstable to ballooning modes with finite k_y (A similar intermediate range of plasma β was also obtained in the stability analyses of ballooning modes in the infinite k _y limit.) Such a β dependence of the instability arises because of the stabilizing effect of plasma compression involved in the ballooning displacement of flux tubes in the high-β regime of the magnetotail. The growth rate of the finite k_y ballooning instability is found to increase with-the wave number k_y, approaching a saturated value in the very large k_y limit. The thinning of the current sheet is found to enhance the regime of unstable β as well as the growth rate of the linear ballooning instability of the near-Earth magnetotail, suggesting a possible scenario for the substorm trigger.