Renormalized geometric optics description of mode conversion in weakly inhomogeneous plasmas

Conventional mode conversion theory in inhomogeneous plasmas starts with a local dispersion relation, which serves as a base for constructing a differential equation describing the waves in nearly degenerate plasma regions, where the mode conversion can take place. It will be shown, however, that the usual geometric optics perturbation scheme, which in the zero order leads to the aforementioned dispersion relation, predicts either rapid variations of the local wave vector and amplitude of the wave, or large first-order corrections to the amplitude in nearly degenerate plasma regions. A novel, general, renormalized perturbation scheme will be suggested in order to remove this singular behavior. The new method is formulated in terms of the conventional, general plasma dielectric tensor and yields two coupled, energy-conserving differential equations describing the mode conversion. Simple asymptotic solutions of these equations exist if the mode coupling is localized and weak. The method is applied to the classical problem of transformation of the extraordinary mode propagating in a cold magnetized plasma at small angles to the magnetic field. Generalization of the method to the case of an unreduced, multicomponent wave propagation problem is discussed.