MHD Rankine-Hugoniot jump conditions for shock waves in van der Waals gases

TL;DR

This paper derives non-relativistic MHD shock jump conditions for van der Waals gases, analyzing the effects of magnetic field strength and non-ideal gas parameters on shock properties.

Contribution

It presents new Rankine-Hugoniot relations for MHD shocks in van der Waals gases, including simplified forms for weak and strong shocks under various magnetic conditions.

Findings

Shock strength depends on magnetic field and non-idealness parameter.

Derived relations for pressure, density, and velocity across MHD shocks.

Analyzed effects of magnetic field strength on shock properties.

Abstract

In this article, we have presented non-relativistic boundary conditions across a magnetohydrodynamic (MHD) shock front propagating in van der Waals gases. The expression for the strength of the non-relativistic MHD shock wave has been obtained, and the Rankine-Hugoniot (R-H) shock jump relations, or boundary conditions, for the pressure, the density, and the particle velocity across an MHD shock front have been derived in terms of a shock compression ratio. The simplified forms of shock jump relations have been written simultaneously for the weak and strong MHD shock waves in terms of the magnetic field strength, the non-idealness parameter, and the ratio of specific heats of the gas. Further, the case of weak shocks has been explored under two distinct conditions, viz., (i) when the applied magnetic field is weak and (ii) when the field is strong, respectively. The case of strong shocks has also been investigated under two distinct ways: (i) as in the purely non-magnetic case, when the ratio of densities on either side of the shock nearly equals $(\gamma+1)/(\gamma-1)$ or (ii) when the applied magnetic field is large. This is when the ambient magnetic pressure is large as compared with the ambient gas pressure. Finally, the effects on the shock strength and the pressure across the MHD shock front are studied due to the magnetic field strength and the non-idealness parameter of the gases. This study presents an overview of the influence of the magnetic field strength and the non-idealness parameter on the shock strength, the pressure, the density, and the particle velocity across the MHD shock front in van der Waals gases.