Stationary self‐focusing of Gaussian electromagnetic beams in the ionosphere

Abstract

The self‐focusing of a Gaussian electromagnetic beam in the ionosphere has been investigated in the paraxial approximation, when the wave frequency is much higher than the electron collision frequency and the electron cyclotron frequency; the radial redistribution of the electron/ion density on account of nonuniform Ohmic heating by the Gaussian beam is taken as the dominant self‐focusing mechanism. Using the energy balance equation (considering the solar radiation) and the available database for the midlatitude daytime ionosphere, the irradiance, corresponding to different values of the electron temperature has been evaluated. A curve fit yields (at a given height) a relatively simple analytical representation of the electron temperature as a function of irradiance. This expression has been used to obtain an analytical equation for the critical curve (the relation between initial beam width versus initial axial irradiance for propagation without change in beam width). It is seen that the critical curve has two humps, which implies that there may be none, one, two, three, or four values of critical axial irradiance, corresponding to a given beam width; such a possibility has not been pointed out before. The beam width–beam power plane may be divided into three regions, corresponding to self‐focusing, oscillatory divergence, and steady divergence of the beam. The dependence of the beam width parameter on the distance of propagation has been obtained for three typical points in the three regions. The numerical results correspond to horizontal propagation at a height of 150 km in the daytime midlatitude ionosphere for the wave frequency ω = 5 × 107 s−1 and duration less than the electron concentration relaxation time, during which the electron density remains almost unaffected by the enhanced electron temperature.