Analysis of the feedback system used to damp longitudinal quadrupole-mode bunch oscillations

Longitudinal quadrupole-mode oscillations of the electron bunches sometimes limit the beam quality in storage-ring FEL's or in other storage rings. Such oscillations can be damped by using a feedback system. In this paper, we analyze how the feedback system damps the longitudinal quadrupole oscillations. We also present a result of the feedback test experiment, which was carried out at the KEK Photon Factory