Linear and nonlinear geometric optics. Part 1. Constitutive relations and three-wave interaction

Abstract

In a weakly dissipative and weakly space-time-varying plasma the propagation of electromagnetic waves may be described by geometric optics. The local tensors governing geometric optics possess approximate symmetries, which become exact in the limit of zero dissipation. These symmetries, which are well known from explicit expressions obtained in various plasma models assuming a homogeneous background, have not previously been created satisfactorily, either with respect to their appearance or to their derivation for an inhomogeneous medium. As an example of the implications of these symmetries, the coupled mode equations for the resonant interaction between three geometric-optics modes are derived in a form such that, in the dissipationless limit, the linear part of the equations conserves wave action. When nonlinear interaction terms are included, the waves are shown to exchange wave action in accordance with the Manley—Rowe relations.