Efficiency of feedbacks for suppression of transverse instabilities of bunched beams

Which gain and phase have to be set for a bunch-by-bunch transverse damper, and at which chromaticity it is better to stay? These questions are considered for three models: the two-particle model with possible quadrupole wake, the author’s Nested Head-Tail Vlasov solver with a broadband impedance, and the same with the LHC impedance model.