Geometric optics in space− and time−varying plasmas

The formal theory of geometric optics in a space− and time−varying plasma is developed assuming that there propagates a small amplitude wave, that there is a linear, causal, but, in general, nonlocal relation between current density and electric field, and that the background plasma does not change much in a locally defined wavelength or period. The description reduces to a system of ordinary differential equations along rays everywhere tangent to the group velocity, one such system of rays for each mode. These equations are formally Hamiltonian in character. They permit the introduction of an energy density such that negative energy waves will be unstable in a lossy medium, as seen by an observer moving with the group velocity, providing that the divergence of the bundles of rays is not too great.