Hyperbolic Algorithm for Coupled Plasma/Electromagnetic Fields Including Real and Displacement Currents

Abstract

A numerical procedure that applies to both the magnetic diffusion and wave propagation regimes of a general plasma/electromagnetic system is presented. The method solves the full Maxwell equations, with or without displacement current, in combination with the Navier–Stokes equations. The combined system is placed in a fully coupled conservation form and embedded in a dual-time formulation that enables classical hyperbolic solution algorithms to be effective across the wave and diffusion limits of the Maxwell equations. The dual-time formulation introducesapseudotimewithanartificialspeedoflightthatincludesdivergenceconstraintsthataredriventozeroby means of a Lagrange multiplier technique. The validity of the algorithm is first established by verifying results obtained with the hyperbolic procedure for the diffusion form of the telegraph equation against analytical solutions. Additional verification for the electromagnetic equations is obtained by comparison with magnetic diffusion simulationsobtainedfromtheMACH2code.Representative numericalcalculationsarepresentedforboththewave and magnetic diffusion limits to illustrate the importance of a solution technique that handles all regimes, from insulators to conductors.