Higher order mode absorption in TTF modules in the frequency range of the 3rd dipole band

One of the sources of transverse emittance dilution in the superconducting e$^+$e$^−$ linear collider TESLA are transverse wakefields of higher frequency modes (HOM) excited in the accelerating cavities by long trains of intense bunches. Traditionally HOM couplers (HOMC) have been designed to damp modes from the 1$^{st}$ and 2$^{nd}$ dipole bands, however measurements have shown that modes with unexpectedly high Q-factors and R/Q values occur in the 3$^{rd}$ dipole band. The present work quantitatively analyses the fields and their damping in the frequency range of the 3$^{rd}$ dipole band (~2580 MHz). In our investigation we use an S-parameter concept. For the calculations the TESLA Test Facility (TTF) accelerating module is split into several components, such as the nine-cell cavity, different types of HOM and fundamental mode couplers, cylindrical and coaxial bellows, cold windows etc., for which the S-parameters are independently calculated using the MAFIA and Microwave Studio (MWS) codes. Using the scattering matrixes of all these components, we have the ability to calculate the scattering matrix of complex sub- systems or of complete modules. The frequency dependence of the S-parameters permits us to find resonant frequencies and Q-factors of complex devices and to study the field distribution in cavities and along waveguides for a given excitation. An understanding of the damping mechanisms in the 3$^{rd}$ dipole band was obtained and an improved design of the HOM couplers is proposed in order to suppress those 3$^{rd}$ dipole band modes with high values of R/Q

Resonance frequencies and Q-factors of multi-resonance complex electromagnetic systems

We present the calculation results for a lossless TTF cavity-coupler unit, for combination cavity-coupler units and for an 8-cavity accelerating module, at the frequency band corresponding to third dipole band of the 9-cell TTF cavity. Experimental investigations of the copper TESLA Test Facility cavity, equipped with two higher order mode couplers, are also presented, for the original and the modified (“mirrored”) downstream higher order mode couplers.Here we developed the procedure for the determination of resonant frequencies and Q-factors using the dependence of the complex transmission coefficient S$_{m,n}$(f) or the complex reflection coefficient S$_{m,m}$(f) on frequency in the frequency band under investigation. These dependencies were obtained from the numerical calculation of S- parameters of lossless TESLA Test Facility (TTF) modules in the third dipole mode frequency band and from the experimental investigation of the copper TESLA Test Facility cavity equipped with two higher order mode couplers in the first, second and third dipole mode frequency bands, second quadrupole and second monopole mode frequency band. The procedure permits us to determine resonant frequencies and Q- factors (Q$_o$, Q$_{Load}$ and Q$_{ext}$) using a large enough frequency step (∆f) with only few frequency points located on the resonance curve corresponding to the high Q-factor resonance

Higher Order Mode Absorption in TTF Modules in the Frequency Range of the Third Dipole Band

Measurements in the TESLA Test Facility (TTF) have shown that modes with unexpectedly high Q-factors and R/Q values occur in the third dipole band. The present work quantitatively analyses the fields and their damping in the frequency range of the third dipole band (~2.5 GHz). In our investigation we use a scattering (S)-parameter concept. For the calculations the TTF accelerating module is split into several components, forwhich the S-parameters are independently calculated. Using the S-matrices of all these components, we have the ability to calculate the S-matrix of complex systems or of complete modules. The frequency dependence of the Sparameters permits us to find resonant frequencies and Qfactors of complex devices. An understanding of the damping mechanisms in the third dipole band was obtained and an improved design of the higher order mode (HOM) couplers was proposed in order to suppress those third dipole band modes with high values of R/Q