Revisit of Alfvén ballooning modes in isotropic, ideal MHD plasmas: Effect of diamagnetic condition

Abstract

Alfvén ballooning modes provide an important mechanism to explain explosive phenomena in regions where field lines transit from dipole‐like to taillike shapes. However, commonly used analytical results were unable to recover Alfvén modes in uniform plasmas and basic ballooning mode in inhomogeneous plasmas. We rigidly revisited previous work on isotropic, ideal magnetospheric plasmas and found where the problems occurred. This paper shows accurate expressions of the ballooning modes. Under the dimagnetic condition (an infinite ky), the modes have two groups depending on the relations of the three equilibrium parameters: plasma β, pressure gradient kp, and magnetic curvature kc (magnetic gradient kB is no more than a tenth of kc and thus neglected in magnetotail plasma). If the constraint is relaxed (a finite ky), the dispersion relation includes the following: (1) the fast compressional Alfvén branch; (2) two groups of ballooning instabilities: Group 1 appears when kp is independent of β, and Group 2 emerges when kc is independent of β; and (3) in Group 1, a critical β exists above which the wave mode becomes unstable, while the perpendicular wave number (k⊥) affects the instability by modulating the critical β values; by contrast, in Group 2, there is no critical β, and the wave keeps its original stable or unstable mode, while k⊥ has a critical value above which the wave mode becomes unstable.