Ballooning instability and structure of diamagnetic hydromagnetic waves in a model magnetosphere

Abstract

A linear eigenmode analysis of ballooning instability of an Alfvén wave and a drift‐Alfvén wave is performed for a curved magnetic field line configuration in a finite‐β plasma to examine stability of the tail plasma sheet and to find a generation mechanism of diamagnetic storm time Pc 5 pulsations, which are characterized by a large azimuthal mode number (m>50). A curved magnetic field line is obtained from a self‐consistent model of magnetic field and plasma pressure distributions, which is constructed on the basis of a two‐dimensional equilibrium model of the tail plasma sheet. An eigenmode equation is solved along the field line in order to obtain the eigenfrequency and eigenmode structure of the ballooning instability of the Alfvén and the drift‐Alfvén waves. Only fundamental mode is unstable to the ballooning instability, which is driven by the pressure gradient combined with the unfavorable magnetic field line curvature, while higher harmonic modes are stable. The eigenfunction of the unstable wave (fundamental mode) is evanescent or decaying exponential toward the ionosphere along the field line and strongly confined near the equator with its plasma pressure and magnetic pressure being out of phase. The stable higher harmonic modes, on the other hand, have standing Alfvén mode structures along the field line and have frequencies determined by oscillation periods of the standing Alfvén modes. In the absence of the coupling to the drift wave, the unstable fundamental wave is aperiodic with zero real frequency. When the unstable fundamental wave is coupled to the drift wave, however, the unstable wave (drift‐Alfvén wave) has a real frequency determined by an ion diamagnetic drift speed. The obtained oscillation period of a few hundred seconds for the unstable drift‐Alfvén wave with an azimuthal model number m = 50, its westward propagation, diamagnetic relationship between the perturbed magnetic and plasma pressures, and strong spatial confinement of the unstable wave near the equator suggest to us that the unstable drift‐Alfvén wave destabilized by the ballooning instability is a strong candidate mechanism for explaining the observed storm time Pc 5 pulsations. By changing parameters of the equilibrium plasma sheet configuration it is found that the growth rate of the ballooning instability increases as the pressure gradient in the plasma sheet increases.