Fluctuations in the amplitude of a wave upon mutual diffusion of rays in a medium with random inhomogeneities

Fluctuations in the plane-wave amplitude and positions of two rays that propagate in a medium with random inhomogeneities of dielectric permittivity are considered. The solution to the problem is based on the ray-diffusion method. The Einstein-Fokker equation is obtained for the density of probabilities of the distance between the rays and relative amplitude in the case where the initial distance between the rays is much smaller than the correlation radius of dielectric permittivity. A conditional probability density for the relative amplitude is obtained provided that the distribution of distances between the rays is described by a logarithmic normal law, which does not take amplitude fluctuations into account. Numerical analysis of the analytical solution is carried out for the propagation of short radio waves in the troposphere and ionosphere.