Abstract
Abstract. 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. Key words. Magnetospheric physics (magnetotail; plasma sheet; magnetospheric configuration and dynamics)
Highlights
The major purpose of the present study is to develop an exact two-dimensional mathematical description of the stationary current sheet configurations and their quasi-stationary evolution under varying geomagnetic conditions
The region of transition from dipolar to stretched magnetic field lines is considered, which the topology determines the choice of the boundary conditions for the problem
Manankova: 2-D current-carrying plasma sheet monotonously declining down the tail nor oscillating solution can be applied to describe the formation in the near tail of such structures as thin, intense current sheets, formation of a “neck”, steep gradients of plasma and magnetic field distributions, etc
Summary
The major purpose of the present study is to develop an exact two-dimensional mathematical description of the stationary current sheet configurations and their quasi-stationary evolution under varying geomagnetic conditions. Manankova: 2-D current-carrying plasma sheet monotonously declining down the tail nor oscillating solution can be applied to describe the formation in the near tail of such structures as thin, intense current sheets, formation of a “neck” (a region with minimum current density and negative Bz values), steep gradients of plasma and magnetic field distributions, etc. This makes an attempt reasonable to build a more general class of solutions of the Grad– Shafranov equation which could be used to reproduce the structure of the near-Earth geomagnetic tail region in the quiet and disturbed conditions (Manankova and Pudovkin, 2002). A quasi-stationary evolution is modeled only as a series of stationary solutions at any fixed value of time
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