The relativistic kinetic equations (RKE) for lepton plasma in the presence of
a strong external magnetic field are derived in Vlasov approximation. The new
RKE for the electron spin distribution function includes the weak interaction
with neutrinos originated by the axial vector current ($\sim c_A$) and provided
by the parity nonconservation. In a polarized electron gas Bloch equation
describing the evolution of the magnetization density perturbation is derived
from the electron spin RKE being modified in the presence of neutrino fluxes.
Such modified hydrodynamical equation allows to obtain the new dispersion
equation in a magnetized plasma from which the neutrino driven instability of
spin waves can be found. It is shown that this instability is more efficient
e.g. in a magnetized supernova than the analogous one for Langmuir waves
enhanced in an isotropic plasma.Comment: 20 pages, no figures, added subsection 2.3 about the lepton current
conservation, to be published in Astroparticle Physic