Destabilising effect of resistive transverse dampers

A resistive transverse damper is needed for multi-bunch operation in a machine like the CERN LHC and it is very efficient as it considerably reduces the necessary amount of nonlinearities (from octupoles) needed to reach beam stability through Landau damping. However, a resistive transverse damper also destabilizes the single-bunch motion below the transverse mode coupling instability (TMCI) intensity threshold (for zero chromaticity), introducing a new kind of instability, which has been called “ISR instability” (for Imaginary tune Split and Repulsion). The purpose of this contribution is to explain in detail this new instability mechanism and its mitigation.