Landau Damping for TMCI: with vs. without Transverse Damper

The Landau damping of the Transverse Mode-Coupling Instability (TMCI) is discussed both without and with a resistive transverse damper. In these two cases, a more involved treatment than the usual “stability diagram approach” is needed, as the modes cannot be considered independently. Considering the case of the “short-bunch” regime, where the mode-coupling takes place between modes 0 and -1 (such as in the CERN LHC) with zero chromaticity, it is shown that below the TMCI intensity threshold, the transverse damper is detrimental, whereas above the TMCI intensity threshold it is beneficial.