Experimental validation of collective effects modeling at injector section of x-ray free-electron laser

We consider the collective beam dynamics at the injector section of the European XFEL. The results of the measurements for the longitudinal phase space (LPS) of the electron beam are compared with those obtained from numerical modeling. A new approach is proposed for the analysis of the self-field effects in the LPS measurements. It allows to determine accurately the synchronous RF phase in an accelerating module and to subtract properly the RF curvature imprinted in the LPS. A further incorporation with the simulation made it possible to separate the collective effects originating from different sources and thus to quantify, individually, the impact of these effects on the beam dynamics. This includes the space-charge dominated beam dynamics in the RF gun as well as the collective effects dominated by the wake fields after the gun up to the end of the injector section. A new analytical model is also proposed for the short-range wake function of a finite chain of RF cavities and verified by both numerical analysis and experimental results. It is shown that the physical models used in the simulation of the beam dynamics after the gun allow to reduce the absolute error in the modeling of the correlated energy chirp by order of magnitude in comparison with the case when the collective effects after the gun are neglected.