Ballooning-Mirror Instability and Internally Driven Pc 4-5 Wave Events

A kinetic-MHD field-aligned eigenmode stability analysis of low frequency ballooning-mirror instabilities has been performed for anisotropic pressure plasmas in the magnetosphere. The ballooning mode is mainly a 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 (P⊥/PP‖ > 1) is large. In the limit that the wave frequency is smaller than the energetic trapped particle magnetic drift frequency, which is usually much smaller than the energetic trapped particle bounce frequency, the energetic trapped particles experience the bounce-averaged wave structure due to their rapid bounce motion. For modes with north-south symmetric field-aligned structure of parallel perturbed magnetic field the energetic trapped particle kinetic pressure response is finite and cancels with their fluid pressure response so that the symmetric mode is stable. Physically the energetic trapped particles precess very rapidly across the B field, and their motion becomes very rigid with respect to low frequency symmetric MHD perturbations. For antisymmetric modes the energetic trapped particle kinetic pressure response from the northern hemisphere cancels with that from the southern hemisphere in a bounce period, and the instability j6 threshold of the antisymmetric mode is determined by the energetic particle fluid free energy. Pressure anisotropy with P⊥/P‖ > 1 reduces the βP‖threshold. The antisymmetric mode changes from a ballooning mode with dominant transverse magnetic field components at P⊥/PP‖ = 1 to a hybrid ballooning-mirror type mode with comparable transverse and compressional magnetic field components near the equator as PP⊥/PP‖ increases. With large equatorial plasma beta (βP‖ ≥O(1)) and pressure anisotropy (PP⊥/PP‖ >1) the field-aligned wave structure of antisymmetric ballooning-mirror mode resembles the multisatellite observations of a long lasting compressional Pc 5 wave event during November 14-15, 1979 (Takahashi et al., 1987). From the AMPTE/CCE particle and magnetic field data observed during Pc 4-5 wave events we compute the ballooning-mirror instability parameters and perform a correlation study with the theoretical instability threshold.We find that compressional Pc 5 waves approximately satisfy the ballooning-mirror instability condition, and transverse Pc 4-5 waves are probably related to resonant ballooning instabilities with small pressure anisotropy.