Feedback Control of Coupled - Bunch Instabilities *

May 1993 (4 Feedback Control of Coupled-Bunch Instabilities* J. D. Fox, N. Eisen, H. Hindi, I. Linscott, G. Oxoby, and L. Sapozhnikov Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 USA and M. Serio, INFN Laboratori Nazionali, Frascati, Italy The next generation of synchrotron light sources and .particle accelerators will require active feedback systems to control multi-bunch instabilities [1,2,3]. Stabilizing hundreds or thousands of potentially unstable modes in these accelerator designs presents many technical challenges. Feedback systems to stabilize coupled-bunch instabilities may be understood in the frequency domain (modebaaed feedback) or in the time domain (bunch-by-bunch feedback). In both approaches an external amplifier sys tern is used to create damping fields that prevent coupledbunch oscillations from growing without bound. The system requirements for transverse (betatron) and longitudinal (@nchrotronj feedback are presented, and possible implementation options developed. Feedback system designs based on digital signal-processing techniques are described. Experieental results are shown from a synchrotron oscilla. ,. < tion damper in the SSRL/SLAC storage ring SPEAR that uses digital signal-processing techniques. I. A CLASSICAL ANALOGY The dynamics of coupled-bunch motion can be illustrated by the mechanical analog of coupled pendulums. In Figure 1 this analogy is applied to the charged particle bunches in a storage ring, with each pendulum representing the oscillatory motion (synchrotron or betatron) of a bunch. The coupling springs represent the impedances of the accelerating cavities and vacuum structures. Bunchi+ and subsequent bunches are driven from the excitations of bunchi, much as pendulumi drives pendulumsi+k through the coupling springs [4].