Transverse MHD shock waves in a partly ionized plasma. Part 1. Structure equations and topology

The structure of transverse MHD shock waves in an initially partly ionized plasma is studied using a three-fluid model with collisional transport coefficients. This model includes the effects of non-equilibrium ionization and of ion velocity slip. A closed set of structure equations is obtained and it is shown that they have a saddle-point - saddle-point topology which prohibits direct integration. In distinction from previous MHD shock structure studies, it is not possible to reduce the number of variables in a realistic manner to allow direct integration, nor is it possible to use the method of matched asymptotic expansions. An iterative solution method is presented in this paper, based on a detailed analysis of the integral curve topology.