Broad-band impedance of LHC shielded bellows

To compensate for thermal expansion, the LHC ring has to accommodate about 2500 bellows which, together with beam position monitors, are the main contributors to the LHC broad-band impedance budget. In order to reduce this impedance to an acceptable value the bellows have to be shielded. In this paper we compare different designs proposed for the bellows and calculate their transverse and longitudinal wake fields and impedances. Owing to the 3D geometry of the bellows, the code MAFIA was used for the wake field calculations. The results presented in this paper indicate that the latest bellows design, in which shielding is provided by sprung fingers which can slide along the beam screen, has impedances smaller than those previously estimated according to a rather conservative scaling of SSC calculations and LEP measurements. Several failure modes, such as missing fingers and imperfect RF contact, have also been studied.