where is the deviation in electron density from the mean N, and the brackets denote an ensemble average, r and s are a pair of cylindrical coordinates such that is measured along the magnetic field and is perpendicular to the field; is the transverse Gaussian scale size of the irregularities and is the axial ratio. The electron density in each of the randomly distributed irregularities is given as: where is the excess electron density at the center of the irregularity. The density and the correlation scale sizes differ by a factor of as may be noted from Equations (A-l) and (A-2). The simple model of Gaussian irregularities is amenable to analytic treatment. This mathematical convenience seems to be part of the reason for its wide application. There is some evidence that this model is favored observationally in describing the irregularities induced by high power radio wave modification of the ionosphere. The irregularities, while being Gaussian, may nevertheless exist in more than a single scale size. The observations made during the times of radio wave modification of the ionosphere indicate the presence of two dominant scale sizes and to allow for this, the model is extended accordingly. The results given in Section 3 represent a two scale size model. A.3 PHASE FLUCTUATIONS AND THEIR SPATIAL CORRELATION AT THE DIFFRACTING SCREEN Radio wave scintillation observations are most often made at very high frequencies for which the refractive index deviates only slightly from unity. Using the high frequency approximation and a model of Gaussian irregularities, Briggs and Parkin2 have derived an expression for the spatial correlation function of phase in the emerging wavefront for a plane wave incident on the ionosphere. It is given as;
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