New Analytic Results for the Spectrum of Intensity Fluctuations in Strong Scatter

Abstract:

In a recent work, Carrano and Rino (Proc. of the Ionospheric Effects Symposium, 2015) extended the phase screen power law theory of ionospheric scintillation to account for the case where the refractive index irregularities follow a two-component power law spectrum. A specific normalization was invoked to exploit the self-similar properties of the problem and achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. Using this model, numerical quadrature was employed to obtain essentially exact solutions of the 4th moment equation governing the intensity fluctuations resulting from propagation through two-dimensional field-aligned ionospheric irregularities. In this paper, we present a series of new asymptotic solutions for the case of a one-component spectrum for all integer and half-integer values of the phase spectral index, p, between 1 and 5. In addition, we present an asymptotic solution to the high frequency portion of the intensity spectrum for the case of a general two-component spectrum with 1<p₁<3 and 3<p₂<5, where p₁ and p₂ are the low frequency and high frequency spectral indices, respectively. We show these analytic results, which are strictly valid for asymptotically large values of the universal strength of scatter parameter (U>>1), agree rather well with the exact numerical results even as U approaches unity from above. This suggests the asymptotic results are more widely applicable than perhaps previously appreciated and may prove useful in the interpretation of scintillation data collected under a wide range of scattering conditions.