Time-domain electromagnetic plane waves in static and dynamic conducting media. I

Solutions are derived for the time-domain Maxwell equations for static (J=σE) and dynamic (τ∂/∂t+J= σ₀ E) conducting media where the field is assumed to vary with respect to only one spatial direction, i.e., plane-wave propagation. The plane wave is introduced into the media via the imposition of an electric field boundary condition at the plane boundary of a half-space and it is assumed that the fields inside the half-space are initially zero. Solutions are derived directly from the first-order system of partial differential equations and it is shown that once the electric field at the plane boundary is imposed, the magnetic field is automatically determined for causal solutions. It is shown that the form of the Maxwell equations, without a magnetic conductivity term added, is sufficient to allow well and uniquely defined solutions of this problem