Transverse Multibunch Instabilities for Non-Rigid Bunches

In this paper, we present a method for computing growth rates and frequency shifts of a beam containing multiple non-rigid bunches. With this approach, we calculate non-rigid multibunch effects which can impact phenomena which are traditionally treated as single-bunch effects, such as the transverse mode-coupling instability. This approach is important for high current storage rings such as PEP-II at SLAC (the B-Factory) which have very strong interbunch forces. Typical calculations treat multibunch and single bunch effects separately, and thus eliminate important interactions between the two. To illustrate the technique, we calculate growth rates and frequency shifts using PEP-II as an example.