Curing coupled-bunch instabilities with uneven fills

A new, unified theoretical description of coupled-bunch instabilities in un evenly filled storage rings is presented. Uneven-fill longitudinal dynamics are explained in terms of two physical phenomena: fill-induced tune-spread damping and modulation coupling of strong even-fill eigenmodes. The latter is also present in the transverse plane. The analysis yields simple criter ia for optimizing fill shapes to reduce the growth rates of the most unstab le modes. Experimental results from the ALS and PEP-II are shown to be in g ood agreement with the theory.