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 simultaneous measurement of growth rates and (feedback induced) damping rates of all unstable beam modes via a time-domain transient technique. The damping rates of naturally stable modes are measured via a related external transient technique. The measured rates are compared to projections based on the estimated cavity impedance. Measurements were made using a high-speed digital signal processing system at the Lawrence Berkeley National Laboratory Advanced Light Source.