THEORY OF LONGITUDINAL SCHOTTKY SPECTRA OF ORDERED ION-BEAMS IN A STORAGE RING

The longitudinal Schottky spectrum of an ultracold ion beam in a stora ge ring is calculated in the frame of harmonic oscillations of a one-d imensional (1D) Coulomb lattice. It is assumed that the extremely high cooling rate required to bring the beam into a one-dimensional ordere d chain can be provided by electron or laser cooling. The anharmonic t ransversal oscillations with temperature much higher than the longitud inal one are taken into account within the self-consistent phonon appr oximation. The Schottky spectrum measured by the pickup system consist s of bands located near the harmonics of the revolution frequency of t he beam. The total intensity of each band characterizes the temperatur e distribution of the phonons in an ionic chain. The amplitude and the width of the peaks in the spectrum are a function of the strength of relaxation processes (cooling and heating) and the Coulomb correlation s, respectively. It is suggested that a careful analysis of these spec tra could be a signature of the presence of 1D ordering in the beam.