Abstract
Recent studies have shown a novel coherent head-tail instability induced by beam-beam interaction with a large Piwinski angle. The instability has become an important issue during the designs of CEPC and FCC-ee. Simulations have further revealed that the longitudinal impedance has a strong impact on the beam stability, squeezing the horizontal stable tune area seriously. The cross-wake force has been introduced to represent beam-beam interaction. A mode coupling theory based on the localized wake (impedance) force has been developed to explain the instability. However, the theory did not consider the effects of longitudinal impedance. In this paper, we develop a new transverse mode coupling analysis method that could be used to study the beam-beam instability with and without longitudinal impedance. The result shows that the distortion of longitudinal phase space trajectory and the incoherent synchrotron tune shift induced by longitudinal impedance would reduce the stable tune area.
Highlights
Beam-beam interaction with a crossing angle has been studied for many years
The result shows that the distortion of longitudinal phase space trajectory and the incoherent synchrotron tune shift induced by longitudinal impedance would reduce the stable tune area
The crab waist collision scheme was proposed to suppress the resonance by placing sextupoles before and after interaction point (IP) with proper phase advances, which helps increase the beam-beam parameter [3]
Summary
Beam-beam interaction with a crossing angle has been studied for many years. It has been noticed that increasing the Piwinski angle The crab waist collision scheme was proposed to suppress the resonance by placing sextupoles before and after interaction point (IP) with proper phase advances, which helps increase the beam-beam parameter [3] This crab waist scheme has been successfully tested to achieve a high luminosity [4]. The transverse impedance, a perturbation source, represents the averaged wake force around the circumference of the ring If one employs this ordinary approach to study beam-beam interaction, the localized property of cross-wake force would not be taken into account, which would not exhibit instability [8]. We will develop a new transverse mode coupling analysis method where the effects of longitudinal phase space trajectory distortion and incoherent synchrotron tune shift induced by longitudinal impedance could be considered.
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