  We calculate the emissivity for the direct URCA process in strongly
magnetized, degenerate matter in neutron stars, under $\beta $-equilibrium. We
show that, if the magnetic field is large enough for protons and electrons to
be confined to the ground Landau levels, the field-free threshold condition on
proton concentration no longer holds, and direct URCA reactions are open for an
arbitrary proton concentration. Direct URCA process leads to an early phase of
fast neutron star cooling. This circumstance allows us to constrain the initial
magnetic field inside observed pulsars.
