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

Abstract

A kinetic‐MHD eigenmode analysis of ballooning‐mirror instabilities is performed for anisotropic pressure plasmas in the magnetosphere. The energetic particle kinetic effects and the coupling between the ballooning and mirror modes are taken into account. Without energetic trapped particle kinetic effects the ballooning‐mirror modes with symmetric field‐aligned structure of parallel perturbed magnetic field δB∥ and electrostatic potential Φ have lower β instability threshold than the antisymmetric modes. Pressure anisotropy with (P⊥/P∥ > 1) reduces the β threshold for ballooning‐mirror instabilities. In the limit that the wave frequency is smaller than the energetic trapped particle magnetic drift frequency, the symmetric ballooning‐mirror mode is completely stabilized by the energetic trapped particle kinetic effects. However, the antisymmetric ballooning‐mirror mode is only weakly influenced by the energetic trapped particle kinetic effects and has the lowest β threshold. For symmetric modes the energetic trapped particles experience a bounce‐averaged wave structure due to their rapid bounce motion, and their nonadiabatic kinetic pressure response cancels with their fluid pressure response so that they do not contribute to the mode stability. Physically, the energetic trapped particles precess very rapidly across the 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 thus the instability β thresholds is mainly determined by the energetic particle fluid free energy. The field‐aligned perturbed magnetic field structure of the antisymmetric mode changes from a ballooning mode with dominant transverse magnetic field components at P⊥/P∥ = 1 to a mixed ballooning‐mirror mode with comparable transverse and compressional components near the equator as P⊥/P∥ increase. With large equatorial plasma β (β∥ ≥ O(1)) and pressure anisotropy (P⊥/P∥ > 1) the field‐aligned wave structure of antisymmetric ballooning‐mirror mode resembles the multisatellite observation of a long lasting compressional Pc 5 wave event during November 14‐15, 1979 [Takahashi et al., 1987].