Linear mode conversion and singularities of geometric optics approximation in plasmas

The general, unreduced, one-dimensional, linear wave propagation problem in weakly inhomogeneous plasmas is considered. Conventional geometric optics perturbation expansion reduces this high-order, multimode problem to the solution of a first-order ordinary differential equation for the wave amplitude along the rays given by epsilon/sub i/ = 0, where epsilon/sub i/ is one of the eigenvalues of the generalized tensor E characterizing the problem. In some plasma regions, however, this perturbation expansion, based on following only one mode at a time, fails, predicting fast variation of the zero-order amplitude and local wave vector k of the wave, or leading to large first-order corrections to the amplitude. Typically, in this region either (a) an additional eigenvalue of E becomes small and couples a new mode into the problem, or (b) all the eigenvalues except epsilon/sub i/ remain large; however, partialepsilon/sub i//partialk/sub x/→0, x being the direction of the inhomogeneity. Following an earlier work on case (a), a renormalization technique is employed in formulating a consistent, nonsingular, eikonal type perturbation expansion in case (b). The method yields a single, second-order, ordinary differential equation for amplitude of the wave, in contrast to case (a), more naturally described by a system of two first-order equations for the amplitudes of the coupled modes. Both theories thus comprise a complete general description of pairwise, linear mode conversion in the aforementioned singular regions. The approach is illustrated by the example of wave interaction in a cold magnetized plasma with plane parallel stratification