Stationary self‐focusing of Gaussian electromagnetic beams in the ionosphere

Abstract

[1] 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 w = 5 Â 10 7 s À1 and duration less than the electron concentration relaxation time, during which the electron density remains almost unaffected by the enhanced electron temperature.Citation: Sodha, M. S., and A. Sharma (2006), Stationary self-focusing of Gaussian electromagnetic beams in the ionosphere,

Combined radar observations of equatorial electrojet irregularities at Jicamarca

“…The problem of the electrostatic potential surrounding uniform, elliptical irregularities in an E-region plasma in two dimensions has been solved analytically by Hysell and Drexler (2006), extending an analysis by St.-Maurice and Hamza (2001). The results offer further insights into the up-down and east-west asymmetries.…”

Self-focusing instability in ionospheric plasma with thermal conduction

“…Initially these gradients push the electrons and ions from regions of higher irradiance and thus temperature ͑and hence pressure͒ to regions of lower irradiance; this transport of electrons and ions continues until a steady state is reached; i.e., when these gradients are balanced by the space charge field. With this reasoning in mind and following earlier workers, 27 one can write…”

Focusing of electromagnetic beams in ionosphere with finite thermal conduction

“…Thus, referring to , where ∈ j 0 and ∈ j 2 are functions of z and axial irradiance. Following earlier workers [ Sodha et al , 1976; Akhmanov et al , 1968; Sodha et al , 1974, 2006; Sodha and Sharma , 2006a, 2006b], the solution (corresponding to a Gaussian beam) of the wave equation in the paraxial approximation, consistent with the radial dependence of the dielectric function, expressed by is where and the beam width parameter f j ( ξ j ) is given by ρ j 0 = r j 0 ω j / c is the initial dimensionless beam width; and ξ j = ( c / ω j r j 0 2 ) z is the dimensionless distance.…”

“…In this communication the authors have used the formalism of Sodha and Sharma [2006a], the database of Gurevich [1978] for midlatitude ionosphere and the exposition by Akhmanov et al [1968], as developed by Sodha et al [1976] to investigate the self‐focusing of a Gaussian electromagnetic beam in the ionosphere in the paraxial approximation; the technique of Sodha et al [2006] to obtain the axial electron temperature and its radial distribution (in the case, when both collisions and thermal conduction contribute significantly to the energy loss by the electrons) has also been made use of.…”