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.
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