A new method for solving the MHD equations in the magnetosheath

摘要

We present a new analytical method to derive steady-state magnetohydrodynamic (MHD) solutions ofthe magnetosheath in different levels of approximation. With this method, wecalculate the magnetosheath's density, velocity, and magnetic fielddistribution as well as its geometry. Thereby, the solution depends on thegeomagnetic dipole moment and solar wind conditions only. To simplify therepresentation, we restrict our model to northward IMF with the solar windflow along the stagnation streamline. The sheath's geometry, with itsboundaries, bow shock and magnetopause, is determined self-consistently. Ourmodel is stationary and time relaxation has not to be considered as in globalMHD simulations. Our method uses series expansion to transfer the MHDequations into a new set of ordinary differential equations. The number ofequations is related to the level of approximation considered includingdifferent physical processes. These equations can be solved numerically;however, an analytical approach for the lowest-order approximation is alsopresented. This yields explicit expressions, not only for the flow and fieldvariations but also for the magnetosheath thickness, depending on the solarwind parameters. Results are compared to THEMIS data and offer a detailedexplanation of, e.g., the pile-up process and the corresponding plasmadepletion layer, the bow shock and magnetopause geometry, the magnetosheaththickness, and the flow deceleration.