Fast Flavor Conversions at the Edge of Instability in a Two-Beam Model

A dense neutrino gas exhibiting angular crossings in the electron lepton number is unstable and develops fast flavor conversions. Instead of assuming an unstable configuration from the onset, we imagine that the system is externally driven toward instability. We use the simplest model of two neutrino beams initially of different flavor that either suddenly appear or one or both slowly build up. Flavor conversions commence well before the putative unstable state is fully attained, and the final outcome depends on how the system is driven. The system generally sticks to the closest state that is linearly stable, a conclusion that we prove for the first time using quasilinear theory. Our results suggest that in an astrophysical setting, one should focus less on flavor instabilities in the neutrino radiation field and more on the external dynamics that leads to the formation of the unstable state.