Threshold studies of coherent synchrotron radiation induced microwave instability beyond adiabatic approximation - J. H. Bian; X. J. Deng; W. H. Huang; C. X. Tang (Physical Review Accelerators and Beams)
In typical studies of collective effects in a storage ring, an important assumption is that the longitudinal bunch length remains constant over one turn, which is referred to as the adiabatic approximation. This approximation is reasonable for conventional storage rings. However, for extremely short bunch length storage rings, such as steady-state microbunching storage ring, the global phase slippage is very small, and the local or partial phase slippage can significantly influence the longitudinal dynamics of the bunch. Consequently, the bunch length can vary greatly around the ring, and the adiabatic approximation no longer holds. In this work, we investigate the microwave instability caused by the coherent synchrotron radiation, which represents one of the dominant collective effects in short bunch storage rings, beyond the adiabatic approximation. We present a general formula for the instability threshold considering the variation of longitudinal optics around the ring and offer valuable guidance for the design of extremely short bunch storage rings. Our results show that depending on the distribution of the partial phase slippage, the instability threshold of a real lattice can be increased by a factor of 2 or even more compared to the classical prediction.