  We calculate rates of flavor exchange within clouds of neutrinos interacting
with each other through the standard model coupling, assuming a conventional
mass matrix. For cases in which there is an angular dependence in the relation
among intensity, flavor and spectrum, we find instabilities in the evolution
equations and greatly speeded-up flavor exchange. The instabilities are
categorized by examining linear perturbations to simple solutions, and their
effects are exhibited in complete numerical solutions to the system. The
application is to the region just under the neutrino surfaces in the supernova
core.
