Calculation of Asymptotic and RMS Kicks Due To Higher Order Modes in the   3.9GHz Cavity
  FLASH plans to use a "third harmonic" (3.9GHz) superconducting cavity to compensate nonlinear distortions of the longitudinal phase space due to the sinusoidal curvature of the the cavity voltage of the TESLA 1.3GHz cavities. Higher order modes (HOMs) in the 3.9GHz have a significant impact on the dynamics of the electron bunches in a long bunch train. Kicks due to dipole modes can be enhanced along the bunch train depending on the frequency and Q-value of the modes. The enhancement factor for a constant beam offset with respect to the cavity has been calculated. A simple Monte Carlo model of these effects, allowing for scatter in HOM frequencies due to manufacturing variances, has also been implemented and results for both FLASH and for an XFEL-like configuration are presented. 
L.Bellantoni, H.Edwards, and R. Wanzenberg