Longitudinal Dynamics of Laser-cooled Fast Ion Beams: Square-well Buckets, Space-charge Eeects, and Anomalous Beam Behaviour I Introduction Ii Laser Cooling at the Tsr a Longitudinal Laser Cooling

We present recent results of our experiments on laser cooling of fast stored ion beams at the Heidelberg Test Storage Ring. The longitudinal motion of the ions is directly cooled by the light pressure force, whereas eecient transverse cooling is obtained indirectly by longitudinal-transverse coupling mechanisms. Laser cooling in novel bunch forms consisting of square-well buckets leads to longitudinally space-charge dominated beams. The observed longitudinal ion density distributions can be well described by a self-consistent mean-eld model based on a thermodynamic Debye-H uckel approach. When applying laser cooling in square-well buckets over long time intervals, hard Coulomb collisions suddenly disappear and the longitudinal temperature drops by about a factor of three. The observed longitudinal behaviour of the beam shows strong resemblance with the transition to an Coulomb-ordered ion string. Laser cooling is the method-of-choice for the crystallization of ion clouds connned at rest in ion traps 1{4]. The resonant light pressure acting on the ions provides an extremely strong damping force resulting in very low temperatures. At these low temperatures, the plasma parameter ?, deened as the ratio of the Coulomb potential energy between nearest neighbor ions to the thermal kinetic energy per ion, becomes larger than one already at moderate densities. For a one-component plasma with ? > 1, a phase transition into a Coulomb ordered state takes place. At ? ' 1, a one-dimensional Coulomb string of ions can be formed, whereas for two-and three-dimensional system, the phase transition to the crystalline state occurs at ? 1. Although storage rings connning ions with large speed share many common features with ion traps (except their size, of course), there is, at present, no unambiguous proof for ion beam crystallization 5,6]. One may wonder why laser cooling of fast ion beams in storage rings, as introduced about ten years ago 7{10], did not immediately lead to the observation of beam crystallization. Two main reasons have so far prevented the attainment of crystalline ion beams by laser cooling: the forces exerted on the ions by the ring lattice in cooperation with the huge beam energy lead to extreme heating rates 11], and direct transverse laser cooling of a fast ion beam is practically impossible. In addition, destructive eeects by the ring lattice, such as shear in the bending sections of the ring, will break any kind of Coulomb-ordered structure except the linear string and possibly zigzag bands a. In the course …