Wave Coupling across a Shock Wave in a Viscous Plasma

Abstract

This paper presents a theory of the coupling between electron-acoustic, ion-acoustic, and electromagnetic plane waves at an idealized shock front in a two-fluid, fully ionized viscous plasma. The viscous-fluid equations and Maxwell's equations are used to derive the dispersion equation relating the frequency and propagation constant of possible modes of propagation in a viscous plasma. Boundary conditions which must hold at the shock front in the presence of an incoming perturbation are then derived, and the amplitudes and energies of predicted wave modes generated at the boundary are calculated. In the limit of small viscosity, the energy-coupling ratios reduce to the values found previously in the inviscid problem, and for all values of viscosity we find enhanced wave transmission as previously found in the inviscid problem. Additionally, maxima in the energy-coupling ratios are found to exist, depending upon the viscosity of the medium.