Abstract
AbstractIn this paper the focusing/defocusing of (i) a single Gaussian electromagnetic beam and (ii) a number of coaxial Gaussian electromagnetic beams, propagating in the extraordinary mode along the Earth's magnetic field in the ionosphere has been investigated in the paraxial approximation. The growth of a sinusoidal instability on account of self-focusing has also been studied. The nonlinearity in the dielectric function, responsible for the focusing/defocusing arises from the redistribution of the electron density, caused by the non-uniform distribution of the electron temperature. The electron temperature is determined by the energy balance for electrons/ions taking into account the Ohmic heating, the collisions and the radiation from the sun. The wave frequency has been assumed to be greater than the plasma frequency. The electron cyclotron frequency due to the Earth's magnetic field in the ionosphere is much larger than the electron collision frequency. This is specifically true for a height of 150 km. Numerical results have been presented for a range of parameters and a discussion of the same has been presented.
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