An analysis of BNS damping techniques in storage rings and colliders

Transverse instabilities in linacs can be controlled by BNS damping, in which the transverse oscillation frequency is chirped from the head to the tail of the bunch. It has been suggested that this technique could be applied to quasi-isochronous rings, such as are proposed for a muon collider. We adopt a reduced phase space model, taking averages over transverse coordinates and with proscribed longitudinal synchrotron motion, to study the growth of transverse displacements of a bunch in the presence of synchrotron oscillations.