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Neutrino kinetics in a magnetized dense plasma

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.