  In environments with high dense neutrino gases, such as in core-collapse
supernovae, the neutrinos can experience collective neutrino oscillation due to
their self-interactions. In particular, fast flavor conversion driven by the
crossings in the neutrino angular distribution can affect explosion mechanism,
nucleosynthesis, and neutrino observation. We perform the numerical computation
of nonlinear flavor evolution on the neutrino angular distribution with tiny
crossings expected to be generated in the preshock region. We demonstrate that
the fast instability is triggered and a cascade develops under a realistic
three-flavor model considering muon production and weak magnetism in the SN
dynamics. The tiny crossing excites specific spatial modes, and then the flavor
instability propagates into other modes which otherwise remain stable due to
the nonlinear effects. Our results indicate that fast flavor conversion can
rise in the preshock region and have a sufficient impact on the flavor
contents.
