Magnetostatically equilibrated plasma sheet with developed medium-scale turbulence: Structure and implications for substorm dynamics

A simple theory of the magnetostatic equilibrium of the magnetospheric plasma sheet is proposed. It takes into consideration the effects of the large-scale dawn-to-dusk electric field and developed medium-scale turbulence. This makes it possible to describe the main features of the plasma sheet dynamics. The suggested model assumes that the magnetic field lines are not equipotential and that the regular velocity of a plasma parcel is much lower than the chaotic velocity. Hence the plasma is intensely mixed. One of the main consequences of such mixing is the experimentally observed temperature equalization across the plasma sheet. The obtained dependence of plasma pressure on the magnetic vector potential permits one to solve the Grad-Shafranov equation and reconstruct, in the tail approximation, the magnetic field line configuration for the case of inhomogeneous distribution of the dawn-to-dusk electric field along the tail. The thickness of the plasma sheet in the model is determined by the magnitudes of the regular and stochastic electric fields, their scales, and plasma temperature. A quasi three-dimensional model of the plasma sheet is developed. The substorm dynamics of the plasma sheet is analyzed. The model can explain the thinning of the plasma sheet without variations in the plasma pressure at the tail axis (thinning without compression) during the substorm growth phase. The plasma sheet expansion during substorm expansion phase is related to the growth of turbulent fluctuations.