Neutrino emissivity in direct URCA processes in superdense strongly magnetized quark medium is calculated. In calculations, we use the covariant method of density matrixes for charge fermions in uniform constant magnetic field. One-gluon exchanges between quarks are also take into account. In evaluations, the strength of magnetic field corresponds to the case, where the quarks of medium occupy a lot of Landau levels, while the electrons are in ground Landau level. The analytical dependence of neutrino emissivity on chemical potentials of quarks and electrons, temperature and magnetic field strength is obtained and briefly discussed. The result could be important in application to a massive strongly magnetized neutron star with quark core.
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