Coupled-bunch instability study of multi-cell deflecting mode cavities for the Advanced Photon Source

The short-pulse X-ray project at the Advanced Photon Source (APS) uses four room-temperature, three-cell, 2.815-GHz, deflecting-mode cavities in two consecutive straight sections. Undamped, these cavities´ higher-order and lower-order resonator modes will cause multi-bunch instabilities in longitudinal and transverse planes for any bunch pattern of a 100-mA store. Damping of these modes must be part of the design of the cavities. We report calculations of instability growth rates that were essential in specifying and checking the rf design of the damping structures. We used various operating bunch patterns and scanned levels of damping of the cavities. Because one of the operating bunch patterns is not symmetric, we used a normal mode analysis implemented in the APS code clinchor. Our calculation included random sampling of resonator frequencies in a reasonable range.