Assessment of the WKB method error by the Gratton kinematic model for the Earth’s magnetic boundary layer task

Abstract

The work touches the flat model of the magnetic boundary layer corresponding to the meridional section of the magnetosphere. It solves the single-component equation of the magnetic induction, which matches so-called Zhigulevs’s first order the magnetic boundary layer, in which field of speed is given by the modified Gratton's kinematic model for the compressible solar wind. The work also describes the obtained exact numerical solution to the above mentioned equation and approximate analysis solution by the Wentzel-Kramers-Brillouin (WKB) method. The boundary conditions correspond to the area containing critical points at the dayside and night side of the magnetosphere, i.e. in the plasmasphere. It defines the error ( of the WKB method and the linear size of the use area(1-0,6) of this method. It assesses the compressibility effect of the solar wind, which must be influencing on the topological image of the magnetic field distribution in the magnetopause and the area alongside the plasmapause.