Stability analysis of the plasma sheet using Hall magnetohydrodynamics

Linear stability analysis of the plasma sheet configuration is performed using Hall magnetohydro dynamics, which is more appropriate than the strict ideal MHD for the stressed current sheet during the substorm growth phase. By adding the Hall term in Ohm's law we study the impact of the error involved in assuming perfect conductivity on the stability. The ballooning-like mode with large perpendicular wavenumber is considered, and its basic eigenmode equations are derived. The ballooning instability is currently one of the strong candidates for causing the substorm onset. Numerical computations of the eigenmode equations are carried out for some model equilibria. It is found that the Hall-MHD effect is not so significant in determining the ballooning stability, as the result is not much different from that of ideal MHD: (1) The ballooning instability is rather easily triggered in the model where the field lines are not too much stretched but the plasma beta still exceeds some critical value, which depends on the situation; (2) The ballooning mode, however, seems to be stabilized in the very stretched field models and is not destabilized by adding the Hall-MHD effect in such models. The result implies that the ballooning stability in the plasma sheet seems to be much more dependent on equilibrium properties such as the field shape than on the physical formulation. It is further suggested that extensive field modeling and subsequent tests for the ballooning mode are a high priority in future in order to establish a firm connection between ballooning instability and the substorm onset.