General Geometric Optics Formalism in Plasmas

This paper exploits a general approach to geometric optics in inhomogeneous plasmas based on the properties of the local dielectric tensor ¿. We express ¿ in terms of its eigenvalues ¿j and eigenvectors ¿. Then to zeroth order in the geometric optics approximation the determinant D = ¿1¿2¿3 vanishes and the elements ¿j vanish separately in pairs or simultaneously. It is shown that this branching in the dispersion relation changes the formulation of the geometric optics equations. The ray tracing and the transport of the amplitude of the wave in both degenerate and nondegenerate cases is described. The general procedure for transition through a boundary between degenerate and nondegenerate regions, where the rays split into two parts each following a different branch of the dispersion relation is also presented in this paper. We demonstrate our general method in a case, where radiation from a vacuum region enters an inhomogeneous magnetized plasma layer.