OBSERVATION AND MODAL-ANALYSIS OF COUPLED-BUNCH LONGITUDINAL INSTABILITIES VIA A DIGITAL FEEDBACK-CONTROL SYSTEM

A modal decomposition is used to study the coupled longitudinal motion of electron bunches in a storage ring. The decomposition allows the s imultaneous measurement of growth rates and (feedback induced) damping rates of all unstable beam modes via a time-domain transient techniqu e. The damping rates of naturally stable modes are measured via a rela ted external transient technique. The measured rates are compared to p rojections based on the estimated cavity impedance. Measurements were made using a high-speed digital signal processing system at the Lawren ce Berkeley National Laboratory Advanced Light Source.