Abstract
The emerging concept of `beam by design' in free-electron laser (FEL) accelerator physics aims for accurate manipulation of the electron beam to tailor spectral and temporal properties of the radiation for specific experimental purposes, such as X-ray pump/X-ray probe and multiple wavelength experiments. `Beam by design' requires fast, efficient, and detailed feedback on the spectral and temporal properties of the generated X-ray radiation. Here a simple and cost-efficient method to extract information on the longitudinal Wigner distribution function of emitted FEL pulses is proposed. The method requires only an ensemble of measured FEL spectra and is rather robust with respect to accelerator fluctuations. The method is applied to both the simulated SASE spectra with known radiation properties as well as to the SASE spectra measured at the European XFEL revealing underlying non-linear chirp of the generated radiation. In the Appendices an intuitive understanding of time-frequency representations of chirped SASE radiation is provided.
Highlights
Various fields of science such as structural biology (Seibert et al, 2011; Chapman et al, 2011), plasma physics (Vinko et al, 2012), atomic physics (Young et al, 2010), ultrafast photochemistry (Liekhus-Schmaltz et al, 2015), and many others have benefited from the development of X-ray and extreme ultraviolet (XUV) free-electron lasers (XFELs) (Saldin et al, 2010; McNeil & Thompson, 2010; Pellegrini et al, 2016)
If the area covered by Wf is much larger than that of Wh, given a proper choice of a window function, the effect of convolution is small, the outlines of the statistically averaged Wigner and the spectrogram are similar and to a certain extent these distributions can be referred to interchangeably
In order to assess the actual performance of our technique, we studied a set of 700 single-shot spontaneous emission (SASE) spectra acquired with the SASE3 beamline spectrometer (Gerasimova, 2018)
Summary
Various fields of science such as structural biology (Seibert et al, 2011; Chapman et al, 2011), plasma physics (Vinko et al, 2012), atomic physics (Young et al, 2010), ultrafast photochemistry (Liekhus-Schmaltz et al, 2015), and many others have benefited from the development of X-ray and extreme ultraviolet (XUV) free-electron lasers (XFELs) (Saldin et al, 2010; McNeil & Thompson, 2010; Pellegrini et al, 2016). Of particular importance is the information on the longitudinal phase space of electrons or on the spectrogram (time–frequency representation) of the radiation They can be obtained by installing a transverse deflecting structure (Behrens et al, 2014) or an optical streaking setup (Grguraset al., 2012; Hartmann et al, 2018), respectively. The resolution, as well as the minimum group duration applicable to the spectrum-based methods, is several coherence lengths of the SASE radiation, i.e. the length of several temporal ‘spikes’ In this contribution we show that by exploiting the full information contained in the correlation function it is possible to analyze the shape of the radiation pulse at each photon energy. We present results of an experimental application of the algorithm at the European XFEL where information about a nonlinear frequency chirp is extracted
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