Cherenkov emissions of Langmuir plasmons and light neutrinos by the flux of neutrinos

We consider the system of neutrino-antineutrino (nu <(<nu>)over bar>) - plasma taking into account their weak Fermi interaction, when the density of neutrinos <(<nu>)over bar> and the plasma particles are rather high and their collective interaction plays a vital role. New fluid instabilities driven by strong neutrino flux in a plasma are observed. It is shown that a bunch of neutrinos, drifting with a constant velocity across a homogeneous plasma, can also induce emission of lower energy neutrinos due to scattering, i.e. the decay of a heavy neutrino nu (H) into a heavy and a light neutrino nu (L) (nu (H)--> nu (H)nu (L)) in a plasma. Furthermore we find that the neutrino production in stars does not lead in general to energy losses from the neutron stars.