Closed orbit change induced by nonzero dispersion rf cavities

The particle motion in storage rings is coupled between the longitudinal and the transverse planes in the presence of nonzero dispersion rf cavities. We found that the particle motion can be modeled separately with a redefined closed orbit. The closed orbit can be described by a Green’s function, which was confirmed in the simulation and in the experiment. The pathlength is calculated from the redefined closed orbit, and we found that the longitudinal phase slip is related not only to the momentum, but also to the rf phase of the particle. The effect on the longitudinal motion becomes significant if the phase slip caused by the rf cavities is large or if the momentum compaction factor is small, such as in the lower alpha-c lattice which is intended to produce shorter bunches.