Wave propagation in one-dimensional inhomogeneous random media with an application to lower hybrid waves in fusion plasmas

Abstract

Wave propagation in a one-dimensional stratified medium, whose physical parameters are subject to random fluctuations, is considered. The complex-valued reflection coefficient obeys, as a function of the slab width L, a stochastic Riccati differential equation, associated with an initial-value problem. Using this fact, solving first the boundary-value problem satisfied by the field on [0,L] is avoided. The reflection coefficient can be computed numerically by a Monte-Carlo-type procedure by the generation of suitable sequences of random numbers aimed at constructing realizations of the stochastic processes that enter the refractive index. An application is made to the propagation of ‘‘lower hybrid waves’’ in thermonuclear (fusion) plasmas for realistic models of the deterministic density profile using available experimental data for the statistics of the random fluctuations. Several functional forms of the density profile are considered, and the relevant physical approximations are discussed. This work generalizes a previous analysis that did not include the inhomogeneous background density profile. Results show that the reflected power is a sensitive function of the form of the density profile.