Instabilities driven by higher-order modes in a radio frequency system with a passive higher-harmonic cavity

The effect of a higher-order mode upon longitudinal beam stability in an electron storage ring is modeled analytically and with simulations. Narrow band parasitic modes and broadband impedance are considered for the Aladdin and MAX-II electron storage rings. The simulations confirm that a passive harmonic cavity strongly suppresses parasitic coupled-bunch instabilities, in agreement with the analytic model. In the long-bunch regime where the bunch length exceeds the vacuum pipe radius, analytic modeling and simulations indicate that a harmonic cavity also suppresses the microwave instability. In the short-bunch regime where the bunch length is smaller than the vacuum pipe radius, analytic modeling and simulations indicate that tuning in a harmonic cavity may worsen the microwave instability.