Hall MHD and Electron Inertia Effects in Current Sheet Formation at a Magnetic Neutral Line

An exact self-similar solution is used to investigate current sheet formation at a magnetic neutral line in incompressible Hall magnetohydrodynamics. The collapse to a current sheet is modelled as a finite-time singularity in the solution for electric current density at the neutral line. We establish that a finite-time collapse to the current sheet can occur in Hall magnetohydrodynamics, and we find a criterion for the finite-time singularity in terms of the initial conditions. We derive an asymptotic solution for the singularity formation and a formula for the singularity formation time. The analytical results are illustrated by numerical solutions, and we also investigate an alternative similarity reduction. Finally, we generalise our solution to incorporate resistive, viscous and electron inertia terms.

Statistical visualization of the Earth's magnetotail based on Geotail data and the implied substorm model

We investigated the temporal and spatial development of the near-Earth magnetotail during substorms based on multi-dimensional superposed-epoch analysis of Geotail data. The start time of the auroral break-up (t=0) of each substorm was determined from auroral data obtained by the Polar and IMAGE spacecraft. The key parameters derived from the plasma, magnetic-field, and electric-field data from Geotail were sorted by their meridional X(GSM)–Z(proxy) coordinates. The results show that the Poynting flux toward the plasma-sheet center starts at least 10 min before the substorm onset, and is further enhanced at X~−12 RE (Earth radii) around 4 min before the onset. Simultaneously, large-amplitude fluctuations occurred, and earthward flows in the central plasma sheet between X~−11 RE and X~−19 RE and a duskward flow around X=−10 RE were enhanced. The total pressure starts to decrease around X=−16 RE about 4 min before the onset of the substorm. After the substorm onset, a notable dipolarization is observed and tailward flows commence, characterised by southward magnetic fields in the form of a plasmoid. We confirm various observable-parameter variations based on or predicted by the relevant substorm models; however, none of these can explain our results perfectly. Therefore, we propose a catapult (slingshot) current-sheet relaxation model, in which an earthward convective flow produced by catapult current-sheet relaxation and a converted duskward flow near the Earth are enhanced through flow braking around 4 min before the substorm onset. These flows induce a ballooning instability or other instabilities, causing the observed current disruption. The formation of the magnetic neutral line is a natural consequence of the present model, because the relaxation of a highly stretched catapult current-sheet produces a very thin current at its tailward edge being surrounded by intense earthward and tailward magnetic fields which were formerly the off-equatorial lobe magnetic fields. This location is the boundary between a highly stressed catapult current sheet and a Harris-type current sheet characterized by little stress. In addition, the flows induced around the boundary toward the current-sheet center may enhance the formation of the magnetic neutral line and the efficiency of magnetic reconnection. After magnetic reconnection is induced, it plays a significant role in driving the substorm.