Linear stability of an impulsively accelerated density interface in an ideal two-fluid plasma

Abstract

We investigate the linear evolution of the Richtmyer–Meshkov instability (RMI) in the framework of an ideal two-fluid plasma model. The two-fluid plasma equations of motion are separated into a base state and a set of linearized equations governing the evolution of the perturbations. Different coupling regimes between the charged species are distinguished based on a non-dimensional Debye length parameter dD,0. When dD,0 is large, the coupling between ions and electrons is sufficiently small that the induced Lorentz force is very weak and the two species evolve as two separate fluids. When dD,0 is small, the coupling is strong and the induced Lorentz force is strong enough that the difference between state of ions and electrons is rapidly decreased by the force. As a consequence, the ions and electrons are tightly coupled and evolve like one fluid. The temporal dynamics is divided into two phases: an early phase wherein electron precursor waves are prevalent and a post-ion shock-interface interaction phase wherein the RMI manifests itself. We also examine the effect of an initially applied magnetic field in the streamwise direction characterized by the non-dimensional parameter β0. For a short duration after the ion shock-interface interaction, the growth rate is similar for different initial magnetic field strengths. Time progresses the suppression of the instability because the magnetic field is observed. The growth rate shows oscillations with a frequency that is related to the ion or electron cyclotron frequency. The instability is suppressed due to the oscillation of vorticity on the interface caused by the perturbed Lorentz force.