Diffraction by Crowded, Clustered, and Anisotropic Planetary Ring Models
E. A. Marouf (San Jose State University)
Numerical simulations are used to investigate extinction and near-forward diffraction by planetary ring models that include particle crowding, clustering, and spatial anisotropy. The simulations are based on the stochastic geometry model for interaction of coherent radio waves with a randomly blocked diffraction screen. The screen transmittance is determined by the random union of shadow areas cast by individual particles (Marouf, BAAS 26, 1150, 1994). Simulations for the crowded monolayer case yield estimates of the spatial correlation function C(r) that differ significantly from the sparsely populated case, exhibiting clear ``long-range" correlation several particle diameters in scale. Its two-dimensional Fourier transform, the angular spectrum or diffraction pattern, changes significantly as the fractional area occupied increases, surprisingly shifting the direction of its peak value away from the incidence direction. The long-range correlation is gradually ``washed away" as the layer thickness increases to several particle thick, most likely due to randomization of the overlapping shadow areas. Classical (radiative transfer) normal optical depth values appear to fall systematically below values inferred from the average area blocked, but the classical scaling appears to hold over the incidence angle range examined. For sparse distributions of isotropic particle clusters, two distinct spatial scales contribute to C(r), namely, the particle size and the cluster size; the first controls the initial rate of decrease in C(r), and the second determines the overall width of C(r). In the case of crowded clusters, however, the correlation width is significantly altered by a similar long-range correlation behavior. The corresponding angular spectrum exhibits a peak shifted away from the exact forward scattering direction, a narrow component of width controlled by the cluster size, and a relatively broad component of width controlled by the particle size. Significant enhancement in the peak scattered signal intensity relative to the prediction of a ``classical" model of the same optical depth is observed. Anisotropic clusters yield different correlation and scattering behavior in the two principal planes, however, the qualitative dependence of the observed behavior on particle size, cluster size, and packing fraction in each plane is similar to the isotropic case.