Cooling in this sense means that an actual reduction of phase space volume is acheived. In other words, phase space density increased. This can only be done by VIOLATING Liouville's theorem.
Number of cooling methods reducing phase space density have been devised. Of interest for Crystalline Beams are:
Pictorial representation of the most interesting, laser, cooling mechanism. The net effect of photon absorption and emissions is change in velocity of the ion! (Click on the picture for larger version).