Abstract
The European x-ray free-electron laser (XFEL) provides x-ray self-amplified spontaneous emission (SASE) FEL radiation in the wavelength range from 0.1 to 3 nm using three undulator systems. The SASE mode of operation at the European XFEL defines specific behavior of longitudinal and transverse coherence properties. In this paper, we describe the evolution of the temporal and transverse correlation functions along the undulator length, and we extract the corresponding evolution of coherence time and degree of transverse coherence as typical figures of merit. Generation of coherent radiation inside the FEL undulators is followed by beam transport to the experiments. During transport, the total number of coherent modes is preserved, but the wavefront can be disturbed, and we analyze the conditions under which this occurs. It is emphasized that the development of experimental observables for the degree of coherence and wavefront properties will be important for experiments using coherent x-ray radiation.
Highlights
The European x-ray free-electron laser (XFEL) provides x-ray self-amplified spontaneous emission (SASE) FEL radiation in the wavelength range from 0.1 to 3 nm using three undulator systems
We show the effects of a single grazing incidence mirror on the propagation of coherent radiation for the cases of the SASE 1 and SASE 3 beam transport systems of the European XFEL [6]
As many experiments at the European XFEL [6] require focusing of the x-ray beam to sub-μm spots, we have modeled focusing of the beam after reflection by mirror surfaces B and C using a perfect ellipsoidal mirror
Summary
The amplification bandwidth of the high-gain FEL amplifier is restricted by the resonance properties of the undulator. The spectral distribution contains hundreds of spikes, corresponding to poor longitudinal coherence This can be seen, which presents temporal and spectral distributions of single-pulse FEL radiation for the case of 0.1 nm radiation at the SASE 1 beamline. We will consider the radiation process quasi-stationary, meaning that the averaged intensity of the radiation pulse is a slowly varying function of time with respect to the width of the correlation function g1. This assumption is a good approximation in our case, as can be seen by inspection of figure 1. This behavior is illustrated in figure 2 for different undulators of the European XFEL
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