Instability and growth rate of magnetosonic waves in quantum plasmas with oblique magnetic field due to coupling of neutrino beam and flavor oscillations

The instability and growth rates of magnetosonic (fast and slow) waves in a dense magnetized plasma due to its coupling with neutrino beam and two-flavor (muon and electron neutrinos) oscillations are studied. The external magnetic field lies in a plane which makes an angle with the direction of wave propagation. The quantum correction effects, i.e., Fermi pressure and Bohm potential of degenerate electron fluid and its inertia, are included in the model. The analytical expression of growth rates of neutrino beam-driven instability due to its coupling with dense plasma through weak interaction and two-flavor oscillations frequencies with fast and slow magnetosonic waves is obtained under double resonance condition of weak neutrino beam and two-flavor oscillations approximation. It is found that instability growth rates of both fast and slow magnetosonic waves are significantly influenced by neutrino beam through weak force interaction and its flavor oscillations and their numerical plots are also shown for illustration using the dense plasma parameters of Type II core-collapse supernova SN1987A existing in the literature in such a magnetized dense plasma. The growth rates of fast and slow magnetosonic waves with neutrino beam interaction and flavor oscillations are also investigated with a normalized parameter defined as ratio of muon neutrino density to total neutrino density at equilibrium. It is found that the maximum growth rates of fast and slow magnetosonic waves occur when the all the muon neutrinos in beam convert into electron neutrinos in the presence of neutrino oscillations in the model. It is also predicted that neutrino oscillations phenomenon included in the model perturbs the slow magnetosonic waves much earlier than fast magnetosonic wave which can be useful for the better understanding of Type II core-collapse supernova.