INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 36 (2003) 6119–6127 PII: S0305-4470(03)55116-2 Structural changes in bunched crystalline ion beams M Bussmann, U Schramm, T Sch¨ atz 1 and D Habs Sektion Physik, Ludwig Maximilians Universit¨ at M¨ unchen, Germany E-mail: ulrich.schramm@physik.uni-muenchen.de Received 22 October 2002, in final form 9 December 2002 Published 22 May 2003 Online at stacks.iop.org/JPhysA/36/6119 Abstract Measurements of the spatial distribution of bunched crystalline ion beams in the radio frequency quadrupole storage ring PALLAS are presented for different ratios of the longitudinal and the transverse confinement strengths. The length of highly elongated crystalline ion bunches and its dependence on the bunching voltage is compared to predictions for a one-dimensional ion string and three-dimensional space-charge-dominated beams. The length is found to be considerably shorter than that predicted by the models. Furthermore, the scaling of the length with the bunching voltage is shown to differ from the expected inverse cube root scaling. These differences can partially be attributed to the formation of a mixed crystalline structure. Additionally, a concise mapping of the structural transition from a string to a zig-zag configuration as a function of the ratio of the confinement strengths is presented, which in a similar way deviates from the predictions. PACS numbers: 29.20.Dh, 41.75.−I, 52.27.Gr, 05.70.Fh 1. Introduction In the PALLAS (PAuL Laser cooling Acceleration System) rf quadrupole storage ring [1], crystalline ion beams [2–4] have recently been experimentally realized at a beam energy of around 1 eV [1, 5–7]. Generally, the phase transition to the Coulomb-ordered ‘crystalline’ state, the state of ultimate brilliance, can occur when the mutual Coulomb energy of stored ions overcomes their mean kinetic energy by about two orders of magnitude. As typical inter-ion distances amount to the order of 10 µm, beam temperatures in the mK range are required to fulfil this condition. Therefore, Doppler laser cooling is applied for the efficient reduction of the longitudinal velocity spread of the ion beam. Providing sufficient confinement, the transverse ion motion is coupled to the longitudinal motion and cooling of all degrees of freedom is achieved. 1 Present address: NIST, Boulder, CO, USA. 0305-4470/03/226119+09$30.00 © 2003 IOP Publishing Ltd Printed in the UK 6119