Detuning related coupler kick variation of a superconducting nine-cell 1.3 GHz cavity

Superconducting TESLA-type cavities are widely used to accelerate electrons in long bunch trains, such as in high repetition rate free electron lasers. The TESLA cavity is equipped with two higher order mode couplers and a fundamental power coupler (FPC), which break the axial symmetry of the cavity. The passing electrons therefore experience axially asymmetrical coupler kicks, which depend on the transverse beam position at the couplers and the rf phase. The resulting emittance dilution has been studied in detail in the literature. However, the kick induced by the FPC depends explicitly on the ratio of the forward to the backward traveling waves at the coupler, which has received little attention. The intention of this paper is to present the concept of discrete coupler kicks with a novel approach of separating the field disturbances related to the standing wave and a reflection dependent part. Particular attention is directed to the role of the penetration depth of the FPC antenna, which determines the loaded quality factor of the cavity. The developed beam transport model is compared to dedicated experiments at FLASH and European XFEL. Both the observed transverse coupling and detuning related coupler kick variations are in good agreement with the model. Finally, the expected trajectory variations due to coupler kick variations at European XFEL are investigated and results of numerical studies are presented.