Effect of plasma compression on plasma sheet stability

Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast-MHD, and the Kruskal-Oberman formulation. It is shown that the major difference among them lies in the plasma compression expression. Explicit computations using the corresponding ballooning equations were performed for two different types of model field lines. For very high beta field lines that are excessively stretched where the stochastic description is most appropriate, the ballooning mode is found to be stable or at best weakly unstable. For field lines that are not too much stretched but even rather round, the ballooning instability can be triggered, within both ideal MHD and the stochastic theory, when beta(e) > beta(e)(c): Here the threshold value of the equatorial beta, beta(e)(c), is roughly less than unity and practically set by the ideal MHD limit. Also in contrast to a recent suggestion, the fast-MHD description where the time scale of interest is too short to allow plasma parallel motion is shown to be more stable than ideal MHD. It indicates no instability in all the equilibria that were tested. The Kruskal-Oberman description is even more stable than fast-MHD.