Longitudinal beam dynamics in the Frascati DAΦNE e^{+}e^{-} collider with a passive third harmonic cavity in the lengthening regime

Abstract

A high-harmonic rf system is going to be installed in both rings of the DAΦNE Φ-Factory collider to improve the Touschek lifetime. The main goal of this paper is to study the impact of the 3rd harmonic cavity on beam dynamics making a special emphasis on the dynamics of a bunch train with a gap. The shift of the coherent synchrotron frequencies of the coupled-bunch modes has been estimated. In the following we investigated the effect of magnification of the synchrotron phase spread and beam spectrum variation due to the gap. Besides we simulated the bunch lengthening for different bunches along the unevenly filled train and evaluated the Touschek lifetime enhancement taking into account the obtained bunch distributions. Finally, the “cavity parking” option is discussed. It can be considered as a reliable backup procedure consisting of tuning the cavity away from the 3rd harmonic frequency and in between two revolution harmonics. It allows recovering, approximately, the same operating conditions as were before the harmonic cavity installation.