Linear coupling of the modes of coherent beam oscillations in a storage ring

Abstract In this paper we consider the coherent stability of a charged particle beam interacting with a matched line at a shift of the frequencies of particular modes of coherent beam oscillation of the order of the synchrotron frequency. The analysis has been made for a short bunch in the limiting cases of small and large chromaticity. It has been shown that in the case of a small and even zero chromaticity when the frequency shift of coherent dipole mode oscillations becomes of the order of a half of the synchrotron frequency, the instability of the lowest synchrobetatron modes occurs.