  The recent proposal of photon and neutrino pair beam is extensively
investigated. Production rates, both differential and total, of single photon,
two-photon and neutrino-pair emitted from quantum ions in circular motion are
calculated for any velocity of ion. This part is an extension of our previous
results at highest energies to lower energies of circulating ions, and helps
much to identify the new process at a low energy ion ring. We clarify how to
utilize the circulating ion for a new source of coherent neutrino beam despite
of much stronger background photons. Once one verifies that the coherence is
maintained in the initial phases of time evolution after laser irradiation,
large background photon emission rates are not an obstacle against utilizing
the extracted neutrino pair beam.
