Non-destructive diagnostics for the determination of the beam properti
es are crucial for experiments with cooled heavy ion beams in storage
rings. The techniques presently available to measure the longitudinal
momentum spread and the transverse emittances are briefly described. T
he experimental achievements-in the preparation of cooled heavy ions a
re summarized. Intrabeam scattering heating is the main limitation for
attaining highest beam quality as stronger compression in phase space
causes a correspondingly increased heating rate. In the low intensity
regime a suppression of intrabeam scattering was observed as a sudden
reduction of the momentum spread. This effect opens possibilities for
precision experiments with beams of unprecedented quality.