Coupled-bunch instability for arbitrary multibunch configurations

The coupled-bunch instability for arbitrary multibunch configurations is investigated in its generality. The theoretical framework adopted is based on the general eigenvalue analysis based on the known formulas of the complex frequency shifts for the uniform multibunch configuration case. Closed formulas are derived for special cases. For the configuration consisting of a uniform filling pattern with a gap of missing bunches, the theoretical results are found to be in good agreement with measurements of the transverse coupled-bunch instability driven by the resistive wall impedance performed at the NSLS-II storage ring.