A new model describing the magnetic field in the Earth's magnetosheath duri
ng an interaction of a supersonic flow of magnetized solar-wind plasma with
the geomagnetic field is proposed. The MHD equations for the magnetosheath
, where electrically conducting solar-wind plasma passes around the Earth's
magnetosphere, are considered as a singularly perturbed system with two in
dependent small parameters inversely proportional to the Mach-Alfven and ma
gnetic Reynolds numbers. Models are developed for the plasma how and magnet
ic field structure in the dayside magnetosheath for the specified shapes of
the Earth's magnetopause and bow shock. The compressibility of the solar-w
ind plasma results in an additional enhancement of the magnetic field in th
e magnetosheath. A rise in the magnetic-field component tangential to the b
ow shock is proportional to the plasma density jump on the shock wave. The
magnetic field in the magnetosheath proves to be stronger than in the case
when the incompressible plasma flows around the magnetosphere, which was co
nsidered in our previous papers. In this case, the components of the interp
lanetary magnetic field parallel and perpendicular to the solar-wind flow a
re enhanced in different ways. The first component increases as the plasma
compression; the second component, as the square root of this value.