Analytic modeling of instabilities driven by higher-order modes in the HLS Ⅱ RF system with a higher-harmonic cavity

The utility of a passive fourth-harmonic cavity plays a key role in suppressing longitudinal beam instabilities in the electron storage ring and lengthens the bunch by a factor of 2.6 for the phase Ⅱ project of the Hefei Light Source (HLS Ⅱ ). Meanwhile, instabilities driven by higher-order modes (HOM) may limit the performance of the higher-harmonic cavity. In this paper, the parasitic coupled-bunch instability, which is driven by narrow band parasitic modes, and the microwave instability, which is driven by broadband HOM, are both modeled analytically. The analytic modeling results are in good agreement with those of our previous simulation study and indicate that the passive fourth-harmonic cavity suppresses parasitic coupled-bunch instabilities and microwave instability. The modeling suggests that a fourth-harmonic cavity may be successfully used at the HLS Ⅱ .