Fast Laser Cooling of Long Lived Ion Beams

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.