Instabilities driven by higher-order modes in an RF system with a passive higher harmonic cavity

Abstract

A passive higher-harmonic cavity may be used to suppress parasitic longitudinal coupled-bunch instabilities. Our analytic modeling already predicts whether a parasitic higher-order mode (HOM) will cause longitudinal coupled bunch instability for a worst-case scenario where a synchrotron sideband has the same frequency as the HOM. An analytic prediction of whether a broadband HOM will cause microwave instability has also been added to the modeling. The capability to include a higher-order mode (HOM) has also been added to a simulation code that models Robinson instabilities with a higher harmonic cavity. To speed the computations, the fundamental modes in the RF cavities and the HOM wake fields are represented by in-phase and quadrature components. The analytic modeling and simulations are compared for passive harmonic-cavity operation of Aladdin with the base lattice and low-emittance lattice, for the UVSOR ring, and for MAXlab rings. For the parasitic coupled bunch instability, the analytic predictions are in approximate agreement with simulations. For the microwave instability, the analytic predictions are in rough agreement with simulations. For low-emittance operation of the Aladdin ring, the bunchlength in simulations of the microwave instability is consistent with experimental measurements. This suggests that our estimate of the reduced longitudinal broadband impedance (5.7 Ω) is reasonable. In modeling of MAX-II, a typical parasitic coupled-bunch instability is suppressed by the harmonic cavity in the new 100-MHz/500-MHz RF system and the previously installed 500-MHz/1500-MHz RF system. Both RF systems are expected to show little or no evidence of microwave instability at full ring energy, provided that the reduced longitudinal broadband impedance is less than 4 Ω. The simulations confirm that a passive harmonic cavity may be used to suppress parasitic coupled bunch instabilities, in approximate agreement with the analytic model.