RELAXATION OF ENERGY FROM THE TRANSVERSE TO THE LONGITUDINAL DIRECTION OF A COLD-ION STRING IN A STORAGE RING

With the help of molecular dynamics we study the properties of a string of ions that is confined by an external harmonic potential and that initially is cold in the beam direction but warm in the transverse one. Under the influence of the mutual Coulomb repulsion, intrabeam scattering leads to a flow of energy from the transverse to the longitudinal direction. Depending on the density and the initial transverse temperature T(perpendicular-to 0), three regimes can be distinguished: a fast transient increase of the longitudinal temperature T(parallel-to) in a fraction of a betatron period, a slow linear increase in some ten betatron periods, and a fast exponential increase followed by complete thermal equilibration. If T(perpendicular-to 0) is large, linear order is lost and thermal equilibrium is postponed to large times. Fourier analyses show that the energy flows into the long-wavelength modes of the collective string excitations. A comparison of calculated heating rates with achievable cooling rates reveals that maintaining linear order in a storage ring is marginal.