Hall magnetohydrodynamic ballooning instability in the magnetotail

Abstract

The ballooning stability of the magnetotail is considered within the framework of Hall magnetohydrodynamics (MHD). In particular, the extent to which Hall MHD effects modify ideal MHD ballooning modes is explored extensively. It is shown that Hall MHD effects primarily enter the stability analysis through changes introduced in the plasma compressibility. Hence, the incompressible ideal MHD modes are not affected, while the compressible ideal MHD modes are altered both quantitatively and qualitatively. In addition to modifying the growth rate of the compressible ideal MHD mode, Hall effects also introduce a new instability, called the entropy interchange instability, which is a variant of the ion temperature gradient instability, when the gradient ratio η≡d ln Ti/d ln ρ of the configuration becomes greater than 2/3, where Ti is the ion temperature and ρ is the plasma density. The theory is applied to two types of magnetotail configurations—analytic equilibria developed by Voigt [in Solar Wind-Magnetosphere Coupling, edited by Y. Kamide and J. A. Slavin (Terra Scientific, Tokyo, 1986), pp. 233–273], and more realistic magnetotail configurations containing thin current sheets obtained from Hall MHD simulations of substorm dynamics by Ma and Bhattacharjee [Geophys. Res. Lett. 25, 3277 (1998)].