  Some peculiarities of fast laser cooling of long-lived ion beams in storage
rings are discussed. Selective interaction of ions and broadband laser beam
with sharp frequency and geometric edges is used while laser and ion beams are
partially overlapped. The rates of change of the ion beam density in different
regions of the phase space and at different moments of time in this scheme of
cooling differ. That is why the generalized Robinson theorem valid for the
infinitesimal phase space regions of non exponential cooling in turn is used to
interpret the results.
