Stability of cooled beams

Because of their high density together with extremely small spreads in betatron frequency and momentum, cooled beams are very vulnerable to incoherent and coherent space-charge effects and instabilities. Moreover, the cooling system itself, i.e. the electron beam in the case of e-cooling, presents large linear and non-linear 'impedances' to the circulating ion beam, in addition to the usual beam-environment coupling impedances of the storage ring. Beam blow-up and losses, attributed to such effects, have been observed in virtually all the existing electron cooling rings. The adverse effects seem to be more pronounced in those rings, like CELSIUS, that are equipped with a cooler capable of reaching the presently highest energy (100 to 300 keV electrons corresponding to 180 to 560 MeV protons). The stability conditions will be revisited with emphasis on the experience gained at LEAR. It will be argued that for all present coolers, three conditions are necessary (although probably not sufficient) for the stability of intense cold beams: (i) operation below transition energy, (ii) active damping to counteract coherent instability, and (iii) careful control of the e-beam neutralisation. An extrapolation to the future 'medium energy coolers', planned to work for (anti)protons of several GeV, will also be attempted.