Calculation of Rf Properties of the Third Harmonic Cavity

Recently a third harmonic structure has been proposed for the injector of the TTF-FEL to avoid nonlinear distortions in the longitudinal phase space. This structure consists of four nine cell TESLA-like cavities. For the use of this structure in combination with the TTF-FEL it might be interesting to investigate higher order modes (HOM) in the structure and their effect on the beam dynamics. In the 5th dipole passband one mode with a frequency around 9.05 Ghz was found to be almost trapped in the cavity with very small fields in the end cells and the beam pipes. CST MicrowaveStudio® (MWS) and Coupled S-Parameter Calculation (CSC) have been applied to investigate this frequency range. The CSC method [1] is based on the scattering parameter description of the rf components found with field solving codes or analytically for components of special symmetry. This paper presents the results of the calculation of frequencies and field distributions of dipole modes in the frequency range around 9.05 GHz. INTRODUCTION A 3.9 GHz 3 harmonic superconducting section for the photoinjector of the TTF 2 has been proposed [2] and designed [3] recently. This section consists of four nine cell cavities. Its purpose is to correct for nonlinearities of the longitudinal phase space to produce highly charged bunches. The basic rf parameters for many monopole, dipole and quadrupole modes for one nine cell cavity of the 3 harmonic section have been calculated [4] using MAFIA eigenmode solver [5]. As a result of these calculations a dipole mode in the frequency range around 9.05 GHz was found which has almost no electric field in the beam pipes and even in the cavity end cells. Therefor this mode might be difficult to be damped by the HOMcouplers. This paper presents the first results of CSC calculations of frequencies and field distributions for dipole modes in this frequency range and compares the results with the results of calculations done with CST MicrowaveStudio® [5] for the same frequency range.