  Starting from planetary systems with three giant planets and an outer disk of
planetesimals, we use dynamical simulations to show how dynamical instabilities
can transform planetesimal disks into 100-1000 AU-scale isotropic clouds. The
instabilities involve a phase of planet-planet scattering that concludes with
the ejection of one or more planets and the inward-scattering of the surviving
gas giant(s) to remove them from direct dynamical contact with the
planetesimals. "Mini-Oort clouds" are thus formed from scattered planetesimals
whose orbits are frozen by the abrupt disappearance of the perturbing giant
planet. Although the planetesimal orbits are virtually isotropic, the surviving
giant planets tend to have modest inclinations (typically ~10 degrees) with
respect to the initial orbital plane. The collisional lifetimes of mini-Oort
clouds are long (10 Myr to >10 Gyr) and there is a window of ~100 Myr or longer
during which they produce spherical clouds of potentially observable dust at 70
microns. If the formation channel for hot Jupiters commonly involves planetary
close encounters, we predict a correlation between this subset of extrasolar
planetary systems and mini-Oort clouds.
