  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 Alfv\'en wave whose velocity depends on both the external
magnetic field and on the neutrino asymmetry. The normal mode analysis show
that in the presence of neutrino background the Alfv\'en waves can have
different velocities. We also discuss our results in the context of dense
astrophysical plasma such as magnetars and show that the difference in the
Alfv\'en velocities can be used to explain the observed pulsar kick. We discuss
also the relativistic generalization of electron fluid in presence of
asymmetric neutrino background.
