Two-dimensional current-carrying plasma sheet in the near-Earth geomagnetic tail region:a quasi-stationary evolution

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 quasistationary 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.

Generalized magnetotail equilibria: Effects of the dipole field, thin current sheets, and magnetic flux accumulation

“…However, none of those solutions presented a generalization of the original class of equilibria described by Schindler [1972] (hereafter the 1972 class), which assumed in particular a broad spectrum of profiles of the normal magnetic field B z (x) along the tail. Such a generalization proved to be evasive as initial attempts did not yield nontrivial solutions [Wang and Bhattacharjee, 1999;Manankova, 2003]. Here we show that the dipole field effect can be included in the original 1972 class solution by the corresponding modification of the boundary conditions.…”

“…Thus, in principle, the dipole field effect could be taken into account by choosing the appropriate generating function. An example of such a solution was developed by Manankova []. However, our goal is to seek solutions where the dipole field effect would be a correction to the general class of approximate 2‐D tail equilibria first described by Schindler [] in the approximation | ∂ / ∂ x |≪| ∂ / ∂ z | and usually defined by the vector potential …”

“…One of the key effects in the magnetotail still missing from the majority of equilibrium models is the impact of the Earth's dipole field. It was modeled earlier in the form of the specific exact solutions of 2-D Grad-Shafranov equation [Kan, 1973;Manankova, 2003;Yoon and Lui, 2005;Schindler, 2007], 3-D axisymmetric solutions with a point dipole, and the finite plasma pressure [Tur et al, 1998;Krasheninnikov et al, 2000] or numerical solutions [Pritchett and Coroniti, 1995;Zaharia et al, 2004]. However, none of those solutions presented a generalization of the original class of equilibria described by Schindler [1972] (hereafter the 1972 class), which assumed in particular a broad spectrum of profiles of the normal magnetic field B z (x) along the tail.…”

On the nature of precursor flows upstream of advancing dipolarization fronts

“…The revised equilibrium current sheet model used herein can be found in work by Pritchett and Büchner [1995]. It is an analytical solution of the two‐dimensional Vlasov‐Maxwell equations [ Schindler , 1972; Lembége and Pellat , 1982; Manankova , 2003]. Its key element is a generalization of the traditional Harris [1962] model: assuming that particle distributions are functions of two invariants of motion (the particle energy W and the canonical momentum P y ), the Vlasov equation is automatically satisfied, and the substitution of the particle distribution moments in the Maxwell equations suggests solutions of the equilibrium current sheet.…”

Comparison of multi-point measurements of current sheet structure and analytical models

“…In general the condition B z =0 requires two-dimensionality (∂ ∂x =0, ∂ ∂z =0). This problem was solved by Schindler (1972), Kan (1973), Lembege and Pellat (1982) and Manankova (2003), who presented 2-D kinetic current sheet models. 2-D fluid models have been built as a solution of Grad-Shafranov equation Schindler, 1983, 2002).…”