Coupled Electromagnetic/Fluid Dynamic Simulation of Fields Through Plasma and Vacuum

Summary form only given. The analysis of coupled electromagnetic and fluid dynamic phenomena is most often attacked by invoking the MHD approximation which, owing to the magnitude of the speed of light, replaces the wave character of electromagnetic propagation by a diffusion process. Although this approximation is highly accurate for many applications there exist problems in which the EM propagation changes from wave-like to diffusion-like during the time of interest. Our interest in the present paper is directed toward this interesting limit. Two representative applications include the opening of a magnetic switch and the thrust production by a pulsed plasma device. In both of these applications, magnetic fields must be propagated through a vacuum via wave propagation and through a plasma via diffusion and convection. In modeling such problems, it is necessary to solve the full hyperbolic wave problem some of the time, while at other times, the simpler MHD equations are acceptable. The approach used is to express the complete Maxwell equations as a set of first-order, hyperbolic equations which are solved numerically by a dual-time marching procedure. The iterative procedure for the outer (pseudo) time remains hyperbolic throughout the computation, independent of whether the inner (physical) time derivative of the E-field is significant or negligible. Divergence contraints are enforced by a hyperbolic, Lagrange multiplier procedure, and the entire procedure is coupled with a similar first-order hyperbolic representation of the Navier-Stokes equations to provide a coupled system of equations. Having all first-order equations simplifies the coupling between the EM and fluid fields. The method is described in detail and representative results are given to show the transition from wave-like propagation of EM fields in media of very low conductivity to diffusive propagation in high conductivity media without fluid motion. Following this, representative solutions of the transition from the wave regime to the diffusion regime in the presence of moving fluid are given.