Instability in crab crossing caused by interaction between beam loading on crab cavities and beam-beam force on colliding beams

Abstract

This study investigated an unknown instability in the crab-crossing scheme, which is caused by the interaction between beam loading on crab cavities and the coherent beam-beam force at the interaction point (IP). We developed an analysis method by formulating the transfer functions of the beam loading on the crab cavities and the related rf control loops, considering the beam-beam force on the colliding beams. The analysis was first applied to simple cases with no control loops to demonstrate the intrinsic stability of crab cavities under the beam loading and the beam-beam force, which corresponds to the Robinson stability for accelerating cavities. Furthermore, analysis with the control loops was applied to analyze unexpected oscillation phenomena observed in the crab-crossing operation in KEKB. The results obtained from the analysis were consistent with the observed phenomena at the following points: First, a time-domain simulation based on this analysis reproduced the observed coherent oscillation. Second, the relative orbit displacement between the colliding beams estimated in the analysis of the measured oscillation amplitude was consistent with the saturation effect of the beam-beam force at the IP. Third, rf-related parameter dependencies of stability obtained in the analysis were consistent with those in the measurements. The mechanism investigated in this study explained its essential function in the instability observed during the KEKB crab-crossing operation.