**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.