Effects of non-zero dispersion at crab cavities on the beam dynamics

摘要

The idea of crab crossing, which has been proposed to allow a non-zero crossing angle without a loss of luminosity, is based on avoiding the excitation of synchro-betatron resonances in a storage ring collider. The validity of the crab crossing scheme relies on the cancellation of kick effects at a crab cavity by those at another crab cavity located on the other side of the interaction point (IP). For the effects to be cancelled exactly, the energy change due to the beam-beam interaction must also be cancelled by these two cavities. We can show, however, that the effect of the energy change is not cancelled exactly if the dispersion, (eta), and its derivative with respect to s, (eta)(prime), are non-zero at the crab cavities. Consequently, the crab crossing scheme may induce synchro-betatron resonances with, and even without, the beam-beam effect. We show an example of stopbands due to synchro-betatron resonances when only crab kicks are taken into account. We also present a stability criterion that can be used to determine tolerable values of (eta) and (eta)(prime), or the crossing the angle, when beam-beam effects are included. 7 refs., 2 figs., 1 tab.