Formation of thin current sheets in the magnetotail: Effects of propagating boundary deformations

[1] Observations and simulations have demonstrated the important role of thin current sheet formation in the course of substorms. Previously, using two-dimensional magnetohydrostatic equilibrium theory together with magnetic flux, entropy, and topology conservation, we demonstrated that a finite boundary deformation of magnetotail equilibria can lead to a loss of equilibrium; that is, equilibrium configurations that satisfy the constraints cease to exist when the boundary deformation exceeds a critical value. When the critical threshold is approached, locally the current density becomes infinite; that is, a thin current sheet is formed. Using time-dependent MHD simulations, we confirm the basic theoretical results. We further extend this work to study the effects of tailward propagating boundary perturbations, corresponding to the rise and subsequent reduction of a duskward electric field (rise and subsequent northward turning of southward IMF B-z). We demonstrate that these boundary conditions again can lead to thin current sheet formation and the possible loss of equilibrium (catastrophe) or onset of instability. Finite perturbations of magnitudes consistent with those observed can produce a strong local increase of the current density and a local reduction of the magnetic field component B-z in the center of the plasma sheet, so that kinetic instabilities and a dynamic evolution may be triggered. The current sheet formation is influenced not only by the magnitude and the duration of the applied electric field but also by the temporal profile: A sudden decrease of the driving electric field following a more gradual increase is more effective than a gradual decrease following a sudden increase. This may provide a clue for the apparent substorm triggering by sudden northward turning of the IMF.