Finite ky 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.