A problem concerning stationary configurations of an inhomogeneous, current-carrying, two-dimensional plasma sheet as the solution of the Grad–Shafranov equation with boundary conditions given on cross-sheet profiles at the foot of the sheet and at infinity is considered, with the aim of using its solution for the description of the interaction of two current systems: the current system of the geomagnetic field, and the tail currents. The obtained solution is an exact analytical solution which contains 5 independent parameters characterizing the intensity of the current sheet. As the solution is exact, it may be applied to describe the most interesting transitional magnetospheric region: that of a strong interaction between the magnetic fields of the geodipole and of the current sheet, i.e. the region where characteristic scales of the change of all variables along and across the sheet are of the same order. This makes it possible to model the structure of the transitional region and its dynamics under quasi-stationary variation of the input parameters. The obtained solution describes the principal processes developing at various phases of magnetospheric disturbances, such as (1) formation of a very intense thin current sheet localized within the transition region, (2) changing from the quasi-dipolar magnetic field to the configuration when a "neck" is formed in this region. An important feature of the obtained solution is the existence of a critical value of one of the parameters of the problem, which leads to the change in the geomagnetic field configuration described above. The solution can be used as an initial condition in simulating dynamical processes in the magnetotail current sheet, as well as in testing the current sheet stability. In the summary a series of limitations in the model problem under consideration is discussed. Magnetospheric physics (magnetotail; plasma sheet; magnetospheric configuration and dynamics)
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