  Collective pair conversion $\nu_e\bar\nu_e\leftrightarrow \nu_{x}\bar\nu_{x}$
by forward scattering, where $x=\mu$ or $\tau$, may be generic for supernova
neutrino transport. Depending on the local angular intensity of the electron
lepton number carried by neutrinos, the conversion rate is "fast," i.e., of the
order of $\sqrt{2}G_{\rm{F}}(n_{\nu_e}{-}\,n_{\bar\nu_e})\gg\Delta m^2_{\rm
atm}/2E$. We present a novel approach to understand these phenomena: A
dispersion relation for the frequency and wave number $(\Omega,\bf{K})$ of
disturbances in the mean field of $\nu_e\nu_x$ flavor coherence. Run-away
solutions occur in "dispersion gaps," i.e., in "forbidden" intervals of
$\Omega$ and/or $\bf{K}$ where propagating plane waves do not exist. We stress
that the actual solutions also depend on the initial and/or boundary conditions
which need to be further investigated.
