Comparison of the coupled-bunch mode theory to experimental observations in the Fermilab Booster

The well-known longitudinal coupled-bunch mode theory is reviewed and evaluated including finite bunch length effects and Landau damping for the parameters of the Fermilab Booster. Predictions of mode growth rates are found to be in general good agreement with experimental observations, both temporally and in frequency space. The inclusion of Landau damping in the stability analysis is required to achieve overall agreement with the observed unstable mode spectrum. Particle simulation using the ESME code are carried out to describe observations of large amplitude oscillations and saturation effects near the end of the acceleration cycle. Finally, a model of the emittance growth, which is valid for growth rates slow with respect to mode frequencies, is explored