  Superconducting current instability in thin rings, irradiated by a coherent
microwave electromagnetic field, is studied. On the regular circular motion of
the Cooper pairs in the supercurrent states the field imposes coherent
oscillations of the condensate as a whole. The oscillating condensate should
emit photons with the energies determined mainly by the discrete values of the
superconducting ring energy. For the first time the probability of the
supercurrent decay accompanied by the two- photon emission, is derived. The
ring thickness is less than both the field skin-depth and the London
penetration depth. Numerical results for the energy-angular distributions of
the photons, as well as the waiting time of the stimulated two-photon
transition depending on both the ring sizes and fluxoid number in the initial
current state, are presented.
