Stability of an ion beam in synchrotrons with digital filters in the feedback loop of a transverse damper

The stability of an ion beam in synchrotrons with digital filters in the feedback loop of a transverse damper is treated. A transverse feedback system (TFS) is required in synchrotrons to stabilize the high-intensity ion beams against transverse instabilities and to damp the beam injection errors. The TFS damper kicker (DK) corrects the transverse momentum of a bunch in proportion to its displacement from the closed orbit at the location of the beam position monitor (BPM). The digital signal processing unit in the feedback loop between BPM and DK ensures a condition to achieve optimal damping. Damping rates of the feedback systems with digital filters are analyzed in comparison with those in an ideal feedback system