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FLASH and the European XFEL are SASE-FEL user facilities, at whichsuperconducting TESLA cavities are operated in a pulsed mode to accelerate longbunch-trains. Several cavities are powered by one klystron. While the low-levelrf system is able to stabilize the vector sum of the accelerating gradient ofone rf station sufficiently, the rf parameters of individual cavities varywithin the bunch-train. In correlation with misalignments, intrabunch-traintrajectory variations are induced. An efficient model is developed to describethe effect at low beam energy, using numerically adjusted transfer matrices anddiscrete coupler kick coefficients, respectively. Comparison with start-to-endtracking and dedicated experiments at the FLASH injector will be shown. Theshort computation time of the derived model allows for comprehensive numericalstudies on the impact of misalignments and variable rf parameters on thetransverse intra-bunch-train beam stability at the injector module. Resultsfrom both, statistical multibunch performance studies and the deduction ofmisalignments from multibunch experiments are presented.

Efficient model for low-energy transverse beam dynamics in a nine-cell 1.3 GHz cavity