Theory of the two fluid resistive-drift-ballooning instability in the near-Earth plasma sheet: local and global magnetospheric mathematical modeling

In light of its auroral appearances, explosive magneto-tail behavior has long been known. Several magnetospheric processes have been interpreted and understood using global magnetohydrodynamic (MHD) models. The global MHD modelling was unable to access the temporal and spatial scales of certain magnetic structure, creating a breach between observational and theoretical studies of these electromagnetic activities. Here, we have presented a significant step towards bridging this breach by preserving both global and local dynamics under a single theoretical work frame using an extended MHD model. We found the self-consistent development and instability in the region of localized magnetic field minimal of the growth phase of a synthetic sub-storm in the near-Earth magneto-tail from the generalized dispersion relation that we obtained from the extended MHD model. The development of the magneto-tail is established by the 2-D static magnetic field equilibrium formation. The coupling of local resistive drift (LRD) and global ballooning instability (GBI) mode is demonstrated. For given equilibrium configuration, the LRD and the GBI are found to be unstable at the equatorial plane. The plasma beta beta dependency on instability occurs due to the stabilizing effect of the plasma compression involved in the high-beta magneto-tail displacement of ballooning flux tube. At moderate plasma beta similar to 0.5 and Lundquist number S similar to 10(10), the decoupling of the mode and various limiting cases have been interpreted.