From a single ion to a mesoscopic system - crystallization of ions in Paul traps

In the paper experiments dealing with the formation of ordered ion structures in Paul traps are reviewed. The transition from an ion cloud to a crystal-like structure corresponds to a chaos-order transition. Furthermore recent experiments in polarization gradient cooling of ions in a quadrupole ring trap are described. The results show that it should be possible to cool the trapped ions into their vibrational ground state.