Multi-Bunch Longitudinal Dynamics and Diagnostics via a Digital Feedback System at PEP-II, DAFNE, ALS and SPEAR

A bunch-by-bunch longitudinal feedback system based on a programmable DSP architecture is used to study coupled-bunch motion and its sources. Experimental results are presented from PEP-II, DA{Phi}NE, ALS and SPEAR to highlight the operational experience from 4 installations, plus show novel accelerator diagnostics possible with the digital processing system. Modal growth and damping rates are measured via short (20 ms) transient recordings for unstable and stable coupled-bunch modes. Data from steady-state measurements are used to identify unstable modes and noise-driven beam motion. A novel impedance measurement technique is presented which reveals the longitudinal impedance as a function of frequency. This technique uses the measured synchronous phase and charge of every bucket to calculate the impedance seen by the beam at revolution harmonics