A Linear Theory of MHD Stability in the Geomagnetotail

A stability analysis in the geomagentotail is presented within MHD limit with a modified form ideal Ohm's law. Using the high ky approximation (ballooning limit), we derive the basic eigenmode equations which can be reduced to the ideal MHD limit. The incompressible limit is numerically solved for a number of model equilibria of tail by Kan [1973], and we have found no unstable Kan equilibrium. Also, an analytic theory is carried out for the case where Bkc is assumed to be constant along the field line, following the idea by Lee and Min [1996]. In that case, it is suggested that the tail stability to the incompressible antisymmetric mode is determined by the ideal MHD.