Theory of ballooning-mirror instabilities for anisotropic pressure plasmas in the magnetosphere

Abstract

This paper deals with a kinetic-MHD eigenmode stability analysis of low frequency ballooning-mirror instabilities for anisotropic pressure plasmas in the magnetosphere. The ballooning mode is a dominant transverse wave driven unstable by pressure gradient in the bad curvature region. The mirror mode with a dominant compressional magnetic field perturbation is excited when the product of plasma beta and pressure anisotropy is large. The field-aligned eigenmode equations take into account the coupling of the transverse and compressional components of the perturbed magnetic field and describe the coupled ballooning-mirror mode. Because the energetic trapped ions precess very rapidly across the {rvec B} field, their motion becomes very rigid with respect to low frequency MHD perturbations with symmetric structure of parallel perturbed magnetic field {delta}B{sub {parallel}} and electrostatic potential {Phi} along the north-south ambient magnetic field, and the symmetric ballooning-mirror mode is shown to be stable. On the other hand, the ballooning-mirror mode with antisymmetric {delta}B{sub {parallel}}, and {Phi} structure along the north-south ambient magnetic field is only weakly influenced by energetic trapped particle kinetic effects due to rapid trapped particle bounce motion and has the lowest instability threshold determined by MHD theory. With large plasma beta ({beta}{sub {parallel}} {ge} O(1)) and pressure anisotropy (P{sub {perpendicular}}/P{sub {parallel}} > 1) at equator the antisymmetric ballooning-mirror mode structures resemble the field-aligned wave structures of the multisatellite observations of a long lasting compressional Pc 5 wave event during November 14--15, 1979 [Takahashi et al.]. The study provides the theoretical basis for identifying the internal excitation mechanism of ULF (Pc 4-5) waves by comparing the plasma stability parameters computed from the satellite particle data with the theoretical values.