Influence of vacuum chamber port terminations on beam coupling impedances

Vacuum chambers of particle accelerators are typically equipped with radio-frequency couplers. The couplers are employed to excite modes for particle acceleration, to extract the energy of higher-order modes, or for diagnostic purposes. From a network theory perspective, these couplers represent terminal ports by which means the structure can exchange energy with its exterior. Usually, these ports are terminated with fixed impedances corresponding to the characteristic impedances of the coaxial lines attached to them. In this paper, we investigate the influence of the termination conditions of vacuum chambers on beam coupling impedances. For this purpose, we introduce a novel approach that allows us to determine beam coupling impedances for arbitrary port terminations. A full-wave Maxwell solver is employed to determine a generalized scattering matrix of the vacuum chamber and its couplers terminated with prespecified reference impedances. Often, these impedances are chosen to be the characteristic line impedances of the waveguides so that coupler ports are free of reflection. Using the generalized scattering matrix, the beam coupling impedances can be readily determined by means of a computationally inexpensive postprocessing step that takes into account arbitrary impedance loads at the coupler ports. Thus, the influence of various port terminations on the beam coupling impedances can be conveniently examined. This is relevant to improve older structures that were designed when no sophisticated design tools were available or to improve the operation of existing structures for a purpose they were initially not designed for. Using the proposed approach, we investigate the 33-cell 200 MHz traveling-wave accelerating structures of the SPS at CERN. It is shown that port termination conditions do have an important influence on the beam coupling impedance and, therefore, must be taken into account in beam stability considerations.