# General expression for the group refractive index of the ionosphere

01 Apr 1961-Journal of Atmospheric and Solar-Terrestrial Physics (Pergamon)-Vol. 21, Iss: 1, pp 65-69

Abstract: A general expression for the group refractive index of the ionosphere has been deduced. Considering the relevant quadrants for the phase-difference between the normal and the abnormal components of the magnetic vector of the radio wave, the general expression gives the values of the group refractive index for the ordinary and the extraordinary modes for different frequencies and for different electron-densities and electron-collisional frequencies of the ionospheric medium and also under different conditions of the earth's magnetic field.

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Abstract: A formula is derived from which the group index for normal incidence, including collision effects, can be easily computed as a function of μ and χ for frequencies below one megacycle. A set of curves can then be prepared from which the group height to be expected from a given electron density profile can be quickly determined by graphical methods.

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Abstract: The phase difference between the normal and the abnormal components of the magnetic vector of the radio wave (i.e., the components in and at right angles to the plane containing the wave normal and the direction of the earth's magnetic field) and the limits of the tilt angle of the major axis of the polarization ellipse (traced out by the electric vector) measured anticlockwise with respect to the direction of the magnetic north for the ordinary and the extraordinary modes of propagation have been obtained on the ray theory of propagation through the ionosphere. The values are given in a table for the ordinary and the extraordinary modes in both the hemispheres for regions below and above the level of ionospheric reflection.
Scott's treatment of the same problem on the ray theory and the results given by Roy and Verma on the basis of the coupled wave equations of Saha and others are reviewed. It is shown that the discrepancies in the results of the polarization parameters obtained by different workers on ray theory are only apparent and arise out of the differences in the forms and notations used in the different formulas. It is also shown that the discrepancies in the limits of the major axis of the polarization ellipse obtained from the ray theory and the wave theory are due to the interchange in the expressions for the amplitude ratio of the normal to the abnormal components for the ordinary and the extraordinary waves given by Saha and others. The experimental results of Roy and Verma are shown to confirm our theoretical conclusions about the limits of the tilt angle of the polarization ellipse.

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Abstract: A general expression is obtained for the group refractive index for low-frequency radio wave propagation in the ionosphere. It is shown that, in the limiting case when electron collisional frequency is small, this expression for the group refractive index is identical with the approximate expression obtained by Gibbons and Rao .

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