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Harmonic lasing provides an opportunity to extend the photon energy range of existing and planned x-ray free electron laser (FEL) user facilities. Contrary to nonlinear harmonic generation, harmonic lasing can generate a much more intense, stable, and narrow-band FEL beam. Another interesting application is harmonic lasing self-seeding that allows to improve the longitudinal coherence and spectral power of a self-amplified spontaneous emission FEL. This concept was tested at the soft x-ray FEL user facility FLASH in the range of 4.5–15 nm and at Pohang accelerator laboratory X-ray Free Electron Laser (XFEL) at 1 nm. In this paper we present recent results from the European XFEL where we successfully demonstrated harmonic lasing at 5.9 Angstrom and 2.8 Angstrom. In the latter case we obtained both third and fifth harmonic lasing and, for the first time, operated a harmonic lasing cascade (fifth-third-first harmonics of the undulator). These results pave the way for reaching very high photon energies, up to 100 keV.

We study the dependence of the peak power of a 1.5 Å Terawatt (TW), tapered x-ray free-electron laser (FEL) on the transverse electron density distribution. Multidimensional optimization schemes for TW hard x-ray free-electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to a Gaussian distribution. The optimizations are performed for a 200 m undulator and a resonant wavelength of λ_{r}=1.5 Å using the fully three-dimensional FEL particle code genesis. The study shows that the flatter transverse electron distributions enhance optical guiding in the tapered section of the undulator and increase the maximum radiation power from a maximum of 1.56 TW for a transversely Gaussian beam to 2.26 TW for the parabolic case and 2.63 TW for the uniform case. Spectral data also shows a 30%–70% reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian. An analysis of the transverse coherence of the radiation shows the coherence area to be much larger than the beam spotsize for all three distributions, making coherent diffraction imaging experiments possible.

The generation of attosecond, highbrightness x-ray pulses is a matter of great interest given their applications in the study of ultra-fast processes. In recent years, the production of x-ray pulses of high brightness, both in the soft and in the hard x-ray range, has been enabled by x-ray free-electron lasers (XFELs). In contrast to conventional quantum lasers, XFELs are based on the use of an ultra-relativistic electron beam as gain medium. They often work in the self-amplified spontaneous emission (SASE) regime, which provides pulses of duration down to a few femtoseconds, composed of several longitudinal modes. In order to further decrease the duration of these pulses, special methods need to be implemented. In this paper we review available methods, with particular focus on the x-ray laser-enhanced attosecond pulse generation, which is one of the most promising techniques. We illustrate the method using the SASE3 soft x-ray undulator of the European XFEL facility as a case study, emphasizing the importance of high-repetition rate attosecond x-ray pulses. The expected attosecond-level radiation output is used for simulations of sequential ionization processes in atoms in the case of ionization in the soft x-ray regime, demonstrating the importance of this opportunity for the user community. [ABSTRACT FROM AUTHOR]

Understanding the interaction of intense, femtosecond X-ray pulses with heavy atoms is crucial for gaining insights into the structure and dynamics of matter. One key aspect of nonlinear light-matter interaction was, so far, not studied systematically at free-electron lasers-its dependence on the photon energy. Here, we use resonant ion spectroscopy to map out the transient electronic structures occurring during the complex charge-up pathways of xenon. Massively hollow atoms featuring up to six simultaneous core holes determine the spectra at specific photon energies and charge states. We also illustrate how different X-ray pulse parameters, which are usually intertwined, can be partially disentangled. The extraction of resonance spectra is facilitated by the possibility of working with a constant number of photons per X-ray pulse at all photon energies and the fact that the ion yields become independent of the peak fluence beyond a saturation point. Our study lays the groundwork for spectroscopic investigations of transient atomic species in exotic, multiple-core-hole states that have not been explored previously., (© 2023. Springer Nature Limited.)

Transmission measurements of the soft X-ray beamline to the Small Quantum Systems (SQS) scientific instrument at the SASE3 undulator of European XFEL are presented. Measurements are reported for a wide range of photon energies (650 eV to 2400 eV), using X-ray gas monitors as well as a bolometric radiometer. The results are in good agreement with simulations for the beam transport and show a transmission of up to 80% over the whole photon energy range. The contribution of second- and third-harmonic radiation of the soft X-ray undulator is determined at selected photon energies by performing transmission measurements using a gas absorber to provide variable attenuation of the incoming photon flux. A comparison of the results with semi-analytic calculations for the generation of free-electron laser pulses in the SASE3 undulator reveals an influence of apertures along the beam transport on the exact harmonic content to be accounted for at the experiment. The second-harmonic content is measured to be in the range of 0.1% to 0.3%, while the third-harmonic contributed a few percent to the SASE3 emission. For experiments at the SQS instrument, these numbers can be reduced through specific selections of the mirror reflection angles., (open access.)

A scheme to generate wide-bandwidth radiation using a step-wise tapered undulator with a segmented structure is proposed. This magnetic field configuration allows to broaden the undulator harmonic spectrum by two orders of magnitude, providing 1 keV bandwidth with spectral flux density exceeding 10 16  photons s -1 mm -2 (0.1% bandwidth) -1 at 5 keV on the sample. Such a magnetic setup is applicable to superconducting devices where magnetic tapering cannot be arranged mechanically. The resulting radiation with broadband spectrum and flat-top shape may be exploited at a multipurpose beamline for scanning over the spectrum at time scales of 10-100 ms. The radiation from a segmented undulator is described analytically and derivations with numerical simulations are verified. In addition, a start-to-end simulation of an optical beamline is performed and issues related to the longitudinally distributed radiation source and its image upon focusing on the sample are addressed., (open access.)

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., (open access.)

Addressing the ultrafast coherent evolution of electronic wave functions has long been a goal of nonlinear x-ray physics. A first step toward this goal is the investigation of stimulated x-ray Raman scattering (SXRS) using intense pulses from an x-ray free-electron laser. Earlier SXRS experiments relied on signal amplification during pulse propagation through dense resonant media. By contrast, our method reveals the fundamental process in which photons from the primary radiation source directly interact with a single atom. We introduce an experimental protocol in which scattered neutral atoms rather than scattered photons are detected. We present SXRS measurements at the neon K edge and a quantitative theoretical analysis. The method should become a powerful tool in the exploration of nonlinear x-ray physics., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

The (spectral) brightness for partially transverse coherent sources such as synchrotron radiation and free-electron laser sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single-electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy spread, currently build on the simplified brightness expression derived under the assumption of Gaussian beams. The influence of energy spread on undulator radiation properties is becoming important in view of diffraction-limited rings with ultralow emittance coming on-line. Here the effects of energy spread on the brightness of undulator radiation at resonance are discussed, as well as relevant relations with coherence properties.

A hard X-ray Split-and-Delay Line (SDL) under construction for the Materials Imaging and Dynamics station at the European X-Ray Free-Electron Laser (XFEL) is presented. This device aims at providing pairs of X-ray pulses with a variable time delay ranging from -10 ps to 800 ps in a photon energy range from 5 to 10 keV for photon correlation and X-ray pump-probe experiments. A custom designed mechanical motion system including active feedback control ensures that the high demands for stability and accuracy can be met and the design goals achieved. Using special radiation configurations of the European XFEL's SASE-2 undulator (SASE: Self-Amplified Spontaneous Emission), two-color hard x-ray pump-probe schemes with varying photon energy separations have been proposed. Simulations indicate that more than 10 9 photons on the sample per pulse-pair and up to about 10% photon energy separation can be achieved in the hard X-ray region using the SDL.

X-ray free-electron lasers (XFELs) provide extremely bright and highly spatially coherent x-ray radiation with femtosecond pulse duration. Currently, they are widely used in biology and material science. Knowledge of the XFEL statistical properties during an experiment may be vitally important for the accurate interpretation of the results. Here, for the first time, we demonstrate Hanbury Brown and Twiss (HBT) interferometry performed in diffraction mode at an XFEL source. It allowed us to determine the XFEL statistical properties directly from the Bragg peaks originating from colloidal crystals. This approach is different from the traditional one when HBT interferometry is performed in the direct beam without a sample. Our analysis has demonstrated nearly full (80%) global spatial coherence of the XFEL pulses and an average pulse duration on the order of ten femtoseconds for the monochromatized beam, which is significantly shorter than expected from the electron bunch measurements.

Inelastic X-ray scattering (IXS) is an important tool for studies of equilibrium dynamics in condensed matter. A new spectrometer recently proposed for ultra-high-resolution IXS (UHRIX) has achieved 0.6 meV and 0.25 nm(-1) spectral and momentum-transfer resolutions, respectively. However, further improvements down to 0.1 meV and 0.02 nm(-1) are required to close the gap in energy-momentum space between high- and low-frequency probes. It is shown that this goal can be achieved by further optimizing the X-ray optics and by increasing the spectral flux of the incident X-ray pulses. UHRIX performs best at energies from 5 to 10 keV, where a combination of self-seeding and undulator tapering at the SASE-2 beamline of the European XFEL promises up to a 100-fold increase in average spectral flux compared with nominal SASE pulses at saturation, or three orders of magnitude more than what is possible with storage-ring-based radiation sources. Wave-optics calculations show that about 7 × 10(12) photons s(-1) in a 90 µeV bandwidth can be achieved on the sample. This will provide unique new possibilities for dynamics studies by IXS.

The Single Particles, Clusters and Biomolecules & Serial Femtosecond Crystallography (SPB/SFX) instrument at the European XFEL is located behind the SASE1 undulator and aims to support imaging and structure determination of biological specimen between about 0.1 μm and 1 μm size. The instrument is designed to work at photon energies from 3 keV up to 16 keV. Here, we propose a cost-effective proof-of-principle experiment, aiming to demonstrate the actual feasibility of a single molecule diffraction experiment at the European XFEL. To this end, we assume self-seeding capabilities at SASE1 and we suggest to make use of the baseline European XFEL accelerator complex-with the addition of a slotted-foil setup-and of the SPB/SFX instrument. As a first step towards the realization of an actual experiment, we developed a complete package of computational tools for start-to-end simulations predicting its performance. Single biomolecule imaging capabilities at the European XFEL can be reached by exploiting special modes of operation of the accelerator complex and of the SASE1 undulator. The output peak power can be increased up to more than 1.5 TW, which allows to relax the requirements on the focusing efficiency of the optics and to reach the required fluence without changing the present design of the SPB/SFX instrument. Explicit simulations are presented using the 15-nm size RNA Polymerase II molecule as a case study. Noisy diffraction patterns were generated and they were processed to generate the 3D intensity distribution. We discuss requirements to the signal-to-background ratio needed to obtain a correct pattern orientation. When these are fulfilled, our results indicate that one can achieve diffraction without destruction with about 0.1 photons per Shannon pixel per shot at 4 Å resolution with 10(13) photons in a 4 fs pulse at 4 keV photon energy and in a 0.3 μm focus, corresponding to a fluence of 10(14) photons/μm(2). We assume negligible structured background. At this signal level, one needs only about 30 000 diffraction patterns to recover full 3D information. At the highest repetition rate manageable by detectors at European XFEL, one will be able to accumulate these data within a fraction of an hour, even assuming a relatively low hit probability of about a percent.

The Linac Coherent Light Source has added a self-seeding capability to the soft x-ray range using a grating monochromator system. We report the demonstration of soft x-ray self-seeding with a measured resolving power of 2000-5000, wavelength stability of 10(-4), and an increase in peak brightness by a factor of 2-5 across the photon energy range of 500-1000 eV. By avoiding the need for a monochromator at the experimental station, the self-seeded beam can deliver as much as 50-fold higher brightness to users.