Damping rate limitations for transverse dampers in large hadron colliders

The paper focuses on two issues important for the de-sign and operation of bunch-by-bunch transverse damper in a very large hadron collider, where fast damping is required to suppress beam instabilities and noise induced emittance growth. The first issue is associated with kick variation along a bunch which affects the damping of head-tail modes. The second issue is associated with ef-fect of damper noise on the instability threshold. The paper accounts for developments motivated by the discus-sions at this conference and carried out after it.