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TY - CONF AU - Xu, J.Y. AU - Xu, H.S. ED - Liu, Lin ED - Byrd, John M. ED - Neuenschwander, Regis T. ED - Picoreti, Renan ED - Schaa, Volker R. W. TI - Longitudinal Dynamics with Harmonic Cavities under the Over-stretching Conditions J2 - Proc. of IPAC2021, Campinas, SP, Brazil, 24-28 May 2021 CY - Campinas, SP, Brazil T2 - International Particle Accelerator Conference T3 - 12 LA - english AB - Higher harmonic cavities (HHCs) are often used to lengthen the bunches, mainly for increasing the Touschek lifetime or for suppressing the coupled-bunch instabilities in electron storage rings. There have been quite many studies on the beam dynamics with the consideration of HHCs. We revisited the basic longitudinal dynamics with HHCs. The derivation of the longitudinal equations of motion with HHCs will be presented in this paper. The difference in the number of fixed points at different HHC settings (mainly under the over-stretching conditions) is also discussed. PB - JACoW Publishing CP - Geneva, Switzerland SP - 1939 EP - 1941 KW - cavity KW - detector KW - beam-loading KW - longitudinal-dynamics KW - bunching DA - 2021/08 PY - 2021 SN - 2673-5490 SN - 978-3-95450-214-1 DO - doi:10.18429/JACoW-IPAC2021-TUPAB220 UR - https://jacow.org/ipac2021/papers/tupab220.pdf ER -