Longitudinal instability due to the randomness of higher mode frequencies of RF cavity

Abstract

The resonance frequencies, shunt impedances and Q-values for the higher order modes in our designed cavity are calculated by the computer codes URMEL and MAFIA. The longitudinal instabilities for the higher order modes are calculated by the eigenmode analysis of Sacherer's (1977) integral equation. The growth rates and the tune shifts in the electron storage ring are calculated by considering the randomness of the higher mode frequencies of a cavity due to the construction errors. The results with the construction errors are compared to those of without error cases for the dipole mode and quadrupole mode.