Time reversal duality of magnetohydrodynamic shocks

Abstract

The shock conditions in magnetohydrodynamics ͑MHD͒ are reduced to their most concise, three-parameter, distilled form by consistent use of the scale independence of the MHD equations and of the de Hoffmann-Teller transformation. They then exhibit a distinct time reversal duality between entropy-allowed shocks and entropy-forbidden jumps. This yields a new classification of MHD shocks by means of the monotonicity properties with respect to upstream and downstream Alfvén Mach numbers, it exhibits the central role of intermediate discontinuities, and permits straightforward construction of all relevant dimensionless quantities of the shocks. An exhaustive overview is presented of solutions in the different parameter regimes.

Shock structures of astrospheres

“…Other types of shocks are possible, for instance, intermediate shocks and switch-on or switch-off shocks. For an in-depth view see Goedbloed (2008) and Goedbloed et al (2010), and for an application to the heliosphere see . Large-scale MHD models for the heliosphere can be found, for example, in Pogorelov et al (2013) and Opher et al (2012) and references therein.…”

Distilled shock conditions for ideal magneto-acoustic shock waves in an optically thick medium

“…The correct procedure is to integrate the conservation equations (4.1)-(4.4) across the shock and to keep the leading order contributions arising from the gradients normal to the shock front only, since these gradients become infinitely large (Goedbloed and Poedts 2004). The ideal model breaks down inside a layer of infinitesimal thickness δ, but it holds on either side of the layer.…”

“…Following the work of Goedbloed (2008), exploiting relations (5.1) and (5.2) to form dimensionless variables, and transforming to the de Hoffmann-Teller frame (de Hoffmann and Teller 1950), the following jump conditions (similar to the case of ideal gas only) are obtained: where the dimensionless variables are defined as:…”

“…Goedbloed (2008) has analyzed ideal MHD distilled shock conditions and, among others, discussed the classification of MHD discontinuities. Following (and comparing with) the work of Goedbloed (2008), the shock conditions are derived in Sec. In this paper the effects of thermal (black-body) radiation on non-relativistic shock waves in an ideal radiation MHD model for an optically thick case are discussed.…”

Magnetized plasma flows and magnetoplasmadynamic thrusters

“…As shown in Refs. 10 and 11 this equation can present three points of transition, each with a corresponding class of shock discontinuities, 12 which depend on the Alfvén Mach number. The nonlinear dependence of the coefficients of this PDE on the flux functions and the change in its differential nature at the transition points complicates its explicit solution.…”