Efficiency of feedbacks for suppression of transverse instabilities of bunched beams

Abstract

Which gain and phase have to be set for a bunch-by-bunch transverse damper, and at which chromaticity is it better to stay? These questions are considered for three models: the two-particle model with possible quadrupole wake, the author's nested head-tail (NHT) model with the broadband impedance, and the NHT with the LHC impedance model. Details of 2D areas of stability in the chromaticity-intensity and chromaticity-gain planes and possibilities to use them are discussed. It is shown that resistive feedbacks may generate asymmetry of the tune shift distribution, which requires positively-shifted stability diagrams.