The coupling of the accelerating cavities to dummy cavities was recently found to reduce beam breakup growth. This paper analyzes a more sophisticated model, proposed by George Caporaso, that includes the time delay between coupled cavities and covers the possibilities of wave cutoff and resonance in the coupling path. A dispersion relation is obtained. We show that the peak spatial exponentiation rate of the dominant BBU mode is reduced by as much as a factor of two, and this reduction is insensitive to the coupling path length. Other modes are destabilized, however, but they have lower growth rates, in general.
Denis G. Colombant,
Yue Ying Lau,
"Model of cavity coupling for beam breakup control", Proc. SPIE 1629, Intense Microwave and Particle Beams III, (1 April 1992); doi: 10.1117/12.137155; https://doi.org/10.1117/12.137155