MHD THEORY OF EARTHS MAGNETOSHEATH FOR AN AXISYMMETRICAL MODEL

An analysis is made of the Earth's magnetosheath along the Sun-Earth l ine under conditions that the IMF (Interplanetary Magnetic Field) is n early parallel or anti-parallel to the solar wind flow. MHD conservati on equations in temporally-averaged steady-state form for the mass, mo mentum and energy density are combined with the magnetic divergence an d induction equations, a hard conducting-sphere model for the magnetop ause, and an adiabatic equation of state in the magnetosheath. The equ ations are integrated from the nose of the bow shock to the magnetopau se and reduced to a set of nonlinear-coupled equations for the magneto sheath thickness and average magnetosheath parameters, which are then used to obtain a new equation for the thickness of the magnetosheath. This is the first analytical equation for the magnetosheath thickness that has been derived, and it exhibits an interesting functional depen dence on Alfven and sonic Mach number M(A) and M(s), the angle theta(o ) between the bow shock normal and the IMF, the Chapman-Ferraro consta nt k(o) at the magnetopause, the polytropic index gamma, and the therm al conductivity Q(r) at the bow shock. The thickness is found to decre ase for decreasing M(s), but increase with decreasing M(A). It exhibit s the qualitative feature found in both gasdynamic and theta(o) greate r than or equal to 45 degrees MHD simulations of an approximate linear variation of the magnetosheath thickness with the density jump ratio X across the bow shock, but it also exhibits a unique negative slope a nd an offset that is a function both of M(A) and of k(o).