Hydromagnetic shock waves in a cold weakly collisional plasma

TL;DR

This paper investigates the existence and characteristics of hydromagnetic shock waves in a cold, weakly collisional plasma using the Adlam-Allen model with dissipation, connecting it to the Korteweg-de-Vries Burgers equation and analyzing shock solutions through phase-plane methods.

Contribution

It establishes a link between the Adlam-Allen model with dissipation and the Korteweg-de-Vries Burgers equation, and demonstrates the existence of various shock wave solutions via phase-plane analysis and simulations.

Findings

Identification of shock wave solutions in the model.

Demonstration of different wavefronts depending on dissipation.

Validation of shock solutions through systematic simulations.

Abstract

In this work we revisit the topic of existence of hydrodynamic shock waves in a cold weakly collisional plasma. For this purpose we consider the well established Adlam-Allen model with the addition of a dashpot term associated with the dissipation of the motion of the electrons relative to the ions. We establish the connection between this model and the Korteweg-de-Vries Burgers equation via an asymptotic multiscale analysis. This fact suggests the possibility that this system may support shock wave solutions. Accordingly, by considering a corresponding dynamical system arising through a co-traveling frame reduction, we identify such orbits via a phase-plane analysis. We then leverage such initial conditions within systematic simulations of the original modified Adlam-Allen model, revealing a variety of supported robust wavefronts depending on the magnitude of the dissipation considered.