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Neutrino cloud instabilities just above the neutrino sphere of a supernova

The usual treatments of the neutrino flavor-evolution, beyond a surface above the last scattering, assume identical angular distributions at this distance for the different initial (unmixed) flavors, and for particles and antiparticles. Taking into account differences in these distributions that must be present, as a result of the species-dependent scattering cross-sections lower down in the star, leads to a new set of non-linear equations. These equations are unstable, even at the initial surface, with respect to perturbations that have both tiny mixing from neutrino oscillations and that break all-over spherical-symmetry. There could be important consequences for: 1) the dynamics of the explosion, 2) R-process-nucleosynthesis, and 3) some future observable neutrino pulse.