A mathematical analysis of the theory of interplanetary scintillation in the weak scattering approximation

We present a simplified analytic technique for modeling the interplanetary scintillation of radio sources of finite angular size with a power law electron density fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weak scattering but extended medium with <10% error over the entire spectrum. We include parameters describing anisotropic electron irregularities as well as anisotropic source structure, and we derive explicitly the dependence of the spectrum normalization upon the scales of the medium. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. We apply this technique to previously published observations