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 k y ), the modes have two groups depending on the relations of the three equilibrium parameters: plasma , pressure gradient k p , and magnetic curvature k c (magnetic gradient k B is no more than a tenth of k c and thus neglected in magnetotail plasma). If the constraint is relaxed (a finite k y ), the dispersion relation includes the following: (1) the fast compressional Alfvén branch; (2) two groups of ballooning instabilities: Group 1 appears when k p is independent of , and Group 2 emerges when k c is independent of ; and (3) in Group 1, a critical exists above which the wave mode becomes unstable, while the perpendicular wave number (k ⟂ ) affects the instability by modulating the critical values; by contrast, in Group 2, there is no critical , and the wave keeps its original stable or unstable mode, while k ⟂ has a critical value above which the wave mode becomes unstable.

Effect of heat flux on Alfvén ballooning modes in isotropic Hall‐MHD plasmas

“…Concerning these important issues discussed above, Ma and Hirose [2014; paper 1] reformulated Hirose et al's [2004] Hall-MHD study on fusion plasmas within the context of an ideal MHD magnetosphere. By referring to previous work done by, e.g., Ohtani et al [1989], Tamao [1993], andLiu [1997], paper 1 elucidated the relationship among different dispersion relations of the ballooning modes introduced by different authors.…”