Hydromagnetic shock waves in a cold weakly collisional plasma

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.