Interaction between parallel Gaussian electromagnetic beams in the ionosphere

In this paper, the propagation of two initially (z=0) parallel Gaussian electromagnetic beams, propagating in the z-direction in ionosphere, has been investigated. The nonlinearity in the dielectric function, responsible for the interaction between the beams arises from the redistribution of the electron density, caused by the nonuniform distribution of electron temperature determined by the Ohmic heating of the electrons and the energy loss of electrons on account of collisions. The wave frequencies have been assumed to be much larger than the electron collision frequency and gyrofrequency. A self-consistent solution of the electromagnetic wave equation and energy balance equation (considering the solar radiation) has been obtained in the paraxial approximation. Second-order coupled ordinary differential equations have been obtained for the distance between the centers of the beams and the beam widths in the x and y directions as a function of the distance of propagation along the z-axis. Using the available database for the mid-latitude daytime ionosphere, the equations have been solved numerically for a range of parameters and a discussion of the results has been presented. The physical basis for the fact that the beams move towards each other, when the resulting irradiance distribution of the two beams has a maximum in the space between the two beams, has been highlighted.