Self-focusing of an electromagnetic pulse in the ionosphere

In this paper, the self-focusing of electromagnetic pulsed beams having Gaussian and sine profiles in the ionosphere have been studied. The self-focusing of an electromagnetic pulse is caused by the nonlinearity in the dielectric function caused by the nonuniform distribution of electron temperature, determined by the Ohmic heating, solar radiation and energy loss in collisions with ions and neutrals. The radial distribution of the electron temperature causes a radial distribution of electron density and thereby that of the refractive index, which causes self-focusing. The wave frequency has been assumed to be much larger than the electron collision frequency, and the temperature of the ions has been assumed to be equal to the temperature of neutrals; this assumption is justified in the ionosphere up to a height of 400 km. In the analysis, the electromagnetic wave equation and the energy balance equation has been solved simultaneously to obtain ordinary differential equations governing the beam width parameter and the electron temperature ( on and away from the axis), respectively, in the paraxial approximation. For computations, the database for the midlatitude daytime ionosphere at the height of 150 km, compiled by Gurevich ( 1978), has been used. The transient behavior of the electron temperature ( on and away from the axis) has been graphically presented for different values of pulse widths. The dependence of the beam width parameter on the distance of propagation for different times of retardation has also been plotted and discussed.