A Statistical Ray Analysis of The Scattering of Radio Waves by the Solar Corona

The scattering of radio waves by an anisotropically turbulent solar corona exhibiting large-scale refraction (due to a radial gradient in average electron density) is discussed in terms of a statistical ray analysis similar to that of Chandrasekhar. The corona is assumed to be spherically symmetric throughout. The ray equations of geometrical optics are written in terms of the spherical coordinate system natural to the solar corona, and discussed for the case of an anisotropically turbulent corona for which the electron density may be known in only a statistical sense. A linear perturbation analysis is employed to obtain explicit solutions for the statistical fluctuations in the ray position, signal phase, and pulse propagation times. The general expressions thus obtained are discussed in particular for the special case of nearly linear rays. It is shown that at appropriate frequencies even very slight ray bending can have a significant effect on the fluctuations in the times of propagation of pulse signals across the corona. Throughout the work we seek to provide a proper analytical framework in which to interpret observed fluctuations in the apparent source position (or angular sixe), the arrival times of pulse signals, and variations in the signal bandwidth. Our attention is drawn specifically to deducing, as functions of distance from the sun, the mean-square fluctuations in electron density, the statistical correlation lengths, and the degree of anisotropy. We point out that the scattering data available at present is consistent, beyond some ten solar radii, with a coronal density behaving as , a degree of anisotropy nearly constant with distance from the sun, and a statistical correlation length which during solar minimum does not vary with (r), but which tends to increase linearly with (r) near solar maximum indicating that the interplanetary plasma develops a radial filamentary structure as solar maximum is approached. In the region three to six solar radii, we find a2/ ', where a is the correlation length in the radial direction and b the correlation length in the transverse direction. This behavior can result if both the anisotropy ratio a/b and the transverse correlation length vary linearly with r in that region.