Angular broadening: Effects of nonzero, spatially varying plasma frequencybetween the source and observer

Angular broadening of radiation due to scattering by density irregularities is usually described using geometric optics (GO) or the parabolic wave equ ation (PWE) with the assumptions that the radiation frequency f greatly exc eeds the local plasma frequency f(p0) or that f(p0)/f is constant along the path. These assumptions are inappropriate for many solar system radio phen omena. Here the PWE and GO formalisms are extended to treat angular broaden ing in plasmas with nonzero, spatially varying ratios, f(p0)(z)/f < 1. The new PWE results show that the correlation function, scattered angular spect rum, and other quantities are modified by inclusion of a denominator factor [1 - f(p0)(2)(z')/f(2)] inside the path integral over z', while the mean-s quare scattering angle [theta(2)] depends on both f(p0)(z)/f at the observe r and the foregoing factor inside the path integral. The PWE and GO predict ions for [theta(2)] are identical and involve equivalent assumptions. Previ ous GO and PWE results are recovered in the limits that f(p0)(z')/f is cons tant or zero. The new PWE and GO results will permit more accurate calculat ion of angular broadening for solar system and astrophysical sources. Moreo ver and importantly, due to the PWE and GO results for [theta(2)] being ide ntical, previous GO analyses of [theta(2)] in solar system contexts are ess entially correct, except for the neglect of or minor deficiencies in the tr eatment of nonzero, spatially varying f(p0)/f effects. The identical GO and PWE results for [theta(2)] and the form of the PWE equation for the correl ation function raise questions as to whether diffraction is unimportant for angular broadening (under the usual PWE conditions). Future direct compari sons of the PWE predictions with angular spectra calculated using existing GO ray-tracing codes should answer these questions. Diffraction effects are probably important when the medium and turbulence are not sufficiently hom ogeneous transverse to the central ray path. The implications are also disc ussed for studies of the 2-3.5 kHz radiation observed in the outer heliosph ere.