Coulomb strings in heavy ion storage rings: explanation and stability criteria

Systems with low numbers of charged ions cooled to very low temperature by electron cooling in the heavy ion rings ESR and SIS at GSI and in CRYring at Stockholm exhibit anomalously low momentum spreads, thus indicating a breakdown of intrabeam scattering. These data are explained by molecular dynamics calculations as that the ions are ordered in linear chains where they cannot pass each other any more. From the possible excitations of such Coulomb ordered chains, we derive criteria for the longitudinal and transverse temperatures and the maximum transverse amplitudes which guarantee their stability. Also, the anomalous frequency shifts of the precision mass measurements in the FRS are explained as the different isotopes run on slightly different Coulomb ordered circular orbits which lock into a common frequency if their radial orbital displacement is smaller than the maximum thermal excursion.