Ionospheric scintillation calculations based on in situ irregularity spectra

TLDR: In this article, the authors presented a closed-form solution for S4 and the characteristic scale as a function of x = 2 k20/k2ƒ, where k0 is the outer scale wave number of the irregularity spectrum and kƒ the Fresnel wave number.

Abstract: Recent results from rocket, satellite, and radar experiments have greatly increased our understanding of equatorial spread-F and its effects upon communication systems. In situ measurements have shown that the typical irregularity spectrum is a power law with a one-dimensional index of −2. Previous applications of scintillation theory to such irregularities have utilized an anisotropic power law, in an effort to model elongation of irregularities along the magnetic field, and have found approximate solutions for the scintillation index S4, the rms phase deviation, and the characteristic scale size of the scintillation spectrum. We present here rigorous closed-form solutions for these quantities which are valid to the extent that weak scattering thin screen theory allows. In addition we introduce a second “hybrid” form for irregularity spectra which is gaussian along the magnetic field and a power law in the perpendicular plane. The index is chosen in such a way that a one-dimensional spectrum obtained on a spacecraft whose velocity V¯s makes a reasonable angle to the magnetic field and varies as k−2. Such a spectrum is introduced since it seems likely that at least at long wavelengths equatorial spread-F is an interchange instability and that the density variation along B¯ is that of the zero-order density variation. One-dimensional spectra for small angles between V¯s and B¯ would hence be steeper than k−2 at intermediate k values, a result consistent with some in situ measurements. If particle precipitation is responsible for high latitude irregularities at long wavelengths, the hybrid spectrum might also be more appropriate for their characterization. At longer k, waves with small but finite kz such as drift waves might be important and hence the anisotropic power law more appropriate. Using both spectral forms, curves are presented for S4 and the characteristic scale as a function of x = 2 k20/k2ƒ, where k0 is the outer scale wave number of the irregularity spectrum and kƒ the Fresnel wave number. The frequency dependence of S4 based on the power law spectrum is also plotted in the regime where the theory is applicable.