Phase fluctuations of radio waves experiencing total reflection from a randomly inhomogeneous plasma layer

We examine the problem of small-angle scattering of radio waves experiencing total reflection from a randomly inhomogeneous layer of plasma. We consider the waves to be normally incident on the layer. To take into account the scattering peculiarities in the neighborhood of the reflection point, we introduce an analytical transformation for the eikonal equation solution derived by the perturbation method. This transformation permits calculations of radio-wave phase fluctuations for any monotonous profile of the regular dielectric permittivity of the plasma in the layer. Using this approach, we have derived analytical formulas for the variance and two-dimensional spatial spectrum of phase fluctuations, depending on the three-dimensional power spectrum of plasma fluctuations. We have also estimated a contribution of reflection point fluctuations to the phase fluctuations and determined the limits of applicability of the derived formulas. The presented analytical transformation of the eikonal equation solution can be used to calculate other statistical moments of the radio wave phase in many problems of solar–terrestrial physics where scattering and reflection of radio waves by plasma formations are important.