Path integral analysis of high-frequency wave propagation in a random ionosphere

High-frequency waves propagating through or reflected by the ionosphere represent an important tool in long-distance radio communication and in ionospheric probing. The complexity of the propagation medium provides various effects not observed, for example, in a turbulent atmosphere. The regularly layered background, deterministic and random inhomogeneities of arbitrary spatial scales, dispersion and anisotropy, and the nonlinear and nonlocal character of the wave-medium interaction, make the ionosphere a natural laboratory for the investigation of wave processes. We restrict our attention to a limited number of simplified models to demonstrate the efficiency of a generalized path integral approach to the analysis of wave propagation in complicated environments. As is known, the path integral is formulated in a more natural manner for the parabolic type equations. Therefore, the main intermediate step is the transfer from the initial elliptic equation to some approximate or exact parabolic one. We consider the following two propagation models. The first one is related to HF narrow beam propagation in a reflection channel, and the second deals with wave scattering by random anisotropic inhomogeneities in the ionosphere, and with the resulting stochastic localization of radiation along quasilayered structures