Analytic formulas for the D -mode Robinson instability

The passive superconducting harmonic cavity (PSHC) scheme is adopted by several existing and future synchrotron light source storage rings, as it has a relatively smaller R / Q and a relatively larger quality factor ( Q ), which can effectively reduce the beam-loading effect and suppress the mode-on...

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Bibliographic Details
Published in:Physical review. Accelerators and beams 2024-06, Vol.27 (6), Article 064402
Main Authors: He, Tianlong, Li, Weiwei, Bai, Zhenghe, Li, Weimin
Format: Article
Language:English
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Summary:The passive superconducting harmonic cavity (PSHC) scheme is adopted by several existing and future synchrotron light source storage rings, as it has a relatively smaller R / Q and a relatively larger quality factor ( Q ), which can effectively reduce the beam-loading effect and suppress the mode-one instability. By using a minimum search algorithm to solve the mode-zero Robinson instability equation of uniformly filled rigid bunches, we have revealed that the fundamental mode of PSHC with a large loaded Q possibly triggers the D -mode Robinson instability [T. He , Mode-zero Robinson instability in the presence of passive superconducting harmonic cavities, ]. This instability is a mode-zero coupled bunch instability, with an oscillation frequency close to the PSHC detuning ( D -mode). Uniquely, it is anti-damped by the radiation damping effect. In this paper, we derive analytical formulas for the frequency and growth rate of the D -mode Robinson instability by taking several appropriate approximations. These formulas provide crucial insights for analyzing and understanding the D -mode Robinson instability.
ISSN:2469-9888
2469-9888
DOI:10.1103/PhysRevAccelBeams.27.064402