  We modeled the 3-D structure of the Kuiper Belt dust cloud at four different
dust production rates, incorporating both planet-dust interactions and
grain-grain collisions using the collisional grooming algorithm. Simulated
images of a model with a face-on optical depth of ~10^-4 primarily show an
azimuthally-symmetric ring at 40-47 AU in submillimeter and infrared
wavelengths; this ring is associated with the cold classical Kuiper Belt. For
models with lower optical depths (10^-6 and 10^-7), synthetic infrared images
show that the ring widens and a gap opens in the ring at the location of of
Neptune; this feature is caused by trapping of dust grains in Neptune's mean
motion resonances. At low optical depths, a secondary ring also appears
associated with the hole cleared in the center of the disk by Saturn. Our
simulations, which incorporate 25 different grain sizes, illustrate that
grain-grain collisions are important in sculpting today's Kuiper Belt dust, and
probably other aspects of the Solar System dust complex; collisions erase all
signs of azimuthal asymmetry from the submillimeter image of the disk at every
dust level we considered. The model images switch from being dominated by
resonantly-trapped small grains ("transport dominated") to being dominated by
the birth ring ("collision dominated") when the optical depth reaches a
critical value of tau ~ v/c, where v is the local Keplerian speed.
