Studies of coupled-bunch modes in the Fermilab Booster

Modeling the coupled-bunch motion and calculating the instability growth rates using the measured longitudinal impedance are described. Also described are the dipole and higher-order form factors, which give the beam response as a function of frequency, and, as such, scale the effective electromagnetic force on the beam due to a given impedance. The results show a good correspondence with the data and will potentially impact feedback system and mode damper design.<
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