Evolutionary Conditions in the Dissipative MHD System Revisited

TL;DR

This paper revisits the evolutionary conditions of dissipative MHD shocks, demonstrating that all shock types, including intermediate shocks, are evolutionary and have unique perturbed solutions, with implications for their physical occurrence.

Contribution

The study modifies existing stability analysis methods for dissipative MHD shocks and extends the formalism to resistive systems, confirming the evolutionary nature of all shock types.

Findings

All MHD shock types are evolutionary with unique solutions.

Intermediate shocks can physically occur in resistive MHD systems.

The formalism applies to systems with resistivity without viscosity.

Abstract

The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure and asymptotic wave modes shows that all types of the MHD shocks, including the intermediate shocks, are evolutionary and perturbed solutions are uniquely defined. We also adopt our formalism to the MHD shocks in the system with resistivity without viscosity, which is often used in numerical simulation, and show that all types of shocks that are found in the system satisfy the evolutionary condition and perturbed solutions are uniquely defined. These results suggest that the intermediate shocks may appear in reality.