Methods for deriving the transverse narrow-band impedance model from coupled-bunch instabilities in circular accelerators

Abstract Transverse coupled-bunch instabilities, driven by narrow-band impedances, can degrade beam quality in multi-bunch, high-intensity circular accelerators. To mitigate this effect, strict constraints on transverse narrow-band impedance are typically imposed during the accelerator design phase. However, slight deviations in component structures during the construction of accelerators and modifications during subsequent operations may result in impedance deviations from the design value. Therefore, determining the impedance parameters of circular accelerators through experimental beam measurements during operation is of greater practical significance. In this study, by analyzing the mode distribution of coupled-bunch instabilities and growth rates, we proposed two methods to obtain the transverse narrow-band impedance model, which is represented by an RLC resonator. The analysis is limited to the case of short bunches in a storage ring with narrow-band impedance, which is characteristic of the BEPCII accelerator. The corresponding approximation of considering only the lowest mode l = 0 for the growth rate of coupled-bunch mode was applied. Finally, we provided numerical calculation examples with predefined RLC resonators to demonstrate the implementation process of the two methods.