In the dense-neutrino region at 50–400 km above the neutrino sphere in a supernova , neutrino-neutrino interactions cause large flavor transformations .
We study when the multi-angle nature of the neutrino trajectories leads to flavor decoherence between different angular modes .
We consider a two-flavor mixing scenario between \nu _ { e } and another flavor \nu _ { x } and assume the usual hierarchy F _ { \nu _ { e } } > F _ { \bar { \nu } _ { e } } > F _ { \nu _ { x } } = F _ { \bar { \nu } _ { x } } for the number fluxes .
We define \epsilon = ( F _ { \nu _ { e } } - F _ { \bar { \nu } _ { e } } ) / ( F _ { \bar { \nu } _ { e } } - F _ { \bar { \nu } _ { x } } ) as a measure for the deleptonization flux which is the one crucial parameter .
The transition between the quasi single-angle behavior and multi-angle decoherence is abrupt as a function of \epsilon .
For typical choices of other parameters , multi-angle decoherence is suppressed for \epsilon \gtrsim 0.3 , but a much smaller asymmetry suffices if the neutrino mass hierarchy is normal and the mixing angle small .
The critical \epsilon depends logarithmically on the neutrino luminosity .
In a realistic supernova scenario , the deleptonization flux is probably enough to suppress multi-angle decoherence .