### Modeling of the frequency spectrum of magnetogradient waves in the equatorial magnetopause in the case of variable electric conductivity of the solar wind plasma

#### Abstract

** **It is known that after a bow shock in front of the day-side of the magnetosphere, i.e. in the magnetosheath, the solar wind flow decelerates. Therefore, the solar wind an anomalous resistance develops, which causes an increase in the magnetic viscosity of the plasma. This effect is especially felt in the focal area of the magnetosheath (the stagnation zone before the magnetosphere) where, according to our discussion, unlike in the peripheral areas of the magnetosheath, the approximation of single-fluid magnetic hydrodynamics (MHD) is not correct. This is especially characteristic of the base of the stagnation zone, which is the central area of the Earth’s magnetic boundary layer (the magnetopause). Thus, it will be correct to describe the large scale motion of the solar wind plasma, having finite electric conductivity, with an equation system of double-fluid magnetic hydrodynamics. Generally, working out self-consistent analytical solutions to the magnetic and velocity fields, except in extremely simple cases, is impossible due to mathematical complications. However, there is a solution to this problem in the case of the flow around of the magnetosphere as due to violent deceleration of the solar wind. In the focal area of the magnetosheath it is possible to determine the flow topology in the kinematic approximation. Such a solution enables to solve the equation of the magnetic induction, constituent of the MHD equations system and corresponding to the magnetopause, by analytical approximation methods. Among different kinematic models, which include the solar wind deceleration effect near the critical point of the magnetosphere, Parker’s plane (two dimensional) kinematic model for incompressible medium is especially simple [1]. This model and its spatial modification were effectively used in different tasks [2]. Namely, it appeared convenient for obtaining the magnetosphere parameters in quasi-stationary approximation by means of different models of variations in time of the magnetic viscosity of the solar wind [3,4].

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