On the structure of resistive MHD intermediate shocks

Abstract

An overview is presented of the resistive steady state structure of intermediate MHD shocks, i.e., shocks that effect a transition from super‐alfvénic to sub‐alfvénic flow. The results are presented in terms of magnetic hodograms in which the two components of the magnetic field tangential to the shock surface are plotted against each other. By performing fixed‐point analysis in this plane, at the possible upstream and downstream states of these shocks, and by solving the one‐dimensional, steady state, resistive, nonviscous MHD equations numerically, it is found that three basic types of hodogram topology exist, describing the resistive intermediate shock structure. These topologies are characterized by the normal flow speed (in the shock frame) relative to the fast‐wave speed and the sound speed at the upstream and downstream states. Fast‐mode and slow‐mode shocks are contained within these hodograms as well. In brief summary, it is found that all intermediate shocks that have an upstream normal flow speed, νx1, less than the local small‐amplitude fast‐mode wave speed, cf1, and a downstream normal flow speed, νx2, greater than the local small‐amplitude slow‐mode wave speed, cs2, have a unique magnetic structure consisting mainly of a rotation of the tangential magnetic field, accompanied by a more or less pronounced change in field magnitude. This type of shock is called a subfast (νx1<cf1) weak (νx2>cs2) intermediate shock. A subfast strong intermediate shock has νx1<cf1 and νx2<cs2 instead. Its magnetic structure is found to be nonunique and the shock thickness depends on this structure. When the upstream normal flow speed exceeds cf1, the shock is said to be superfast (νx1>cf1). The structures of both weak (νx2>cs2) and strong (νx2<cs2) superfast intermediate shocks are found to be nonunique. When the intermediate shock involves a transition from supersonic (νx1>c1) to subsonic (νx2<c2) conditions, the resistive intermediate shock structure usually contains a discontinuous substructure consisting of a gas dynamic shock in which dissipation processes other than resistivity, namely, viscosity and/or heat conductivity, are dominant. However, in certain cases a continuous, purely resistive transition from supersonic to subsonic flow is possible.