Damping of coherent betatron oscillations of charged particles in synchrotrons

The problems of increasing intensity and decreasing phase space density of stored and accelerated beams are currently important issues in modern charged-particle circular accelerator physics and technology. Among the key problems to be solved is the fast damping of coherent oscillations resulting from injection errors and the appropriate reaction to coherent (collective) beam instability. Here the major workload has to be carried by beam feedback systems in which the correcting action on the bunch is proportional to the coherent displacement of this bunch at preceding times. Current researches on beam dynamics in synchrotrons with digital wideband transverse feedback systems are reviewed. Particular attention is given to quantitative and qualitative regularities in frequency shifts and decrements of coherent betatron oscillation damping. Theoretical predictions are compared with the experimental data obtained at the Large Hadron Collider (CERN, Geneva).