Neutrino induced vorticity, Alfven waves and the normal modes

We consider plasma consisting of electrons and ions in presence of a background neutrino gas and develop the magneto hydrodynamic equations for the system. We show that electron neutrino interaction can induce vorticity in the plasma even in the absence of any electromagnetic perturbations if the background neutrino density is left-right asymmetric. This induced vorticity support a new kind of mode which will vanish when the background neutrino asymmetry vanishes. The normal mode analysis of the equations is done to show that, in the presence of neutrino back-ground, the normal modes get modified and the corrections are proportional to the neutrino asymmetry parameter.