The stability diagram for longitudinal coupled instabilities of the ALBA upgrade

The design of the ALBA upgrade forsees the use of an active harmonic cavity system for bunch lengthening. The resulting RF-potential will be a combination of a harmonic and a quartic potential. The corresponding stability diagram will be computed and compared to the stability diagram based on a pure quartic RF-potential. It will be checked if an already existing HOM in the DAMPY cavities and a parasitic mode found in the bellows can be damped with this mechanism. Since the radiation damping of the ALBA upgrade is rather weak the Landau damping is an asset for the stability of the upgrade.