Analytical solutions for anisotropic MHD shocks

Abstract

A new method to analytically solve the anisotropic MHD system of equations describing shock transitions is presented. As this system is known to be under-determined (there is more unknown parameters than available equations) free parameters must be chosen. From observational contraints it appears that the magnetic amplitude jump is a good candidate as it is generally available more frequently and more precisely than other jump variables. With this approach we obtain an explicit expression for the density compression ratio for arbitrary upstream parameters and shock geometry. Downstream anisotropy and pressure are also calculated. The results are tested against an other approach and compared with observations from the Earth's bow shock and the solar wind termination shock.