Resonant X-ray excitation of the nuclear clock isomer 45Sc.

Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices1. The search for more stable and convenient reference oscillators is continuing2-6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations7-9. One of the most promising cases is an ultra-narrow nuclear resonance transition in 45Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. 10). The scientific potential of 45Sc was realized long ago, but applications require 45Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources11 that have become available only recently. Here we report on resonant X-ray excitation of the 45Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as [Formula: see text] with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications.

Harmonic radiation contribution and X-ray transmission at the Small Quantum Systems instrument of European XFEL.

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.

Shot-to-shot two-dimensional photon intensity diagnostics within megahertz pulse-trains at the European XFEL.

Characterizing the properties of X-ray free-electron laser (XFEL) sources is a critical step for optimization of performance and experiment planning. The recent availability of MHz XFELs has opened up a range of new opportunities for novel experiments but also highlighted the need for systematic measurements of the source properties. Here, MHz-enabled beam imaging diagnostics developed for the SPB/SFX instrument at the European XFEL are exploited to measure the shot-to-shot intensity statistics of X-ray pulses. The ability to record pulse-integrated two-dimensional transverse intensity measurements at multiple planes along an XFEL beamline at MHz rates yields an improved understanding of the shot-to-shot photon beam intensity variations. These variations can play a critical role, for example, in determining the outcome of single-particle imaging experiments and other experiments that are sensitive to the transverse profile of the incident beam. It is observed that shot-to-shot variations in the statistical properties of a recorded ensemble of radiant intensity distributions are sensitive to changes in electron beam current density. These changes typically occur during pulse-distribution to the instrument and are currently not accounted for by the existing suite of imaging diagnostics. Modulations of the electron beam orbit in the accelerator are observed to induce a time-dependence in the statistics of individual pulses - this is demonstrated by applying radio-frequency trajectory tilts to electron bunch-trains delivered to the instrument. We discuss how these modifications of the beam trajectory might be used to modify the statistical properties of the source and potential future applications.

Spatial-frequency features of radiation produced by a step-wise tapered undulator.

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 1016 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.

Wigner distribution of self-amplified spontaneous emission free-electron laser pulses and extracting its autocorrelation.

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.

Photon diagnostics at the FLASH THz beamline.

The THz beamline at FLASH, DESY, provides both tunable (1-300 THz) narrow-bandwidth (∼10%) and broad-bandwidth intense (up to 150 uJ) THz pulses delivered in 1 MHz bursts and naturally synchronized with free-electron laser X-ray pulses. Combination of these pulses, along with the auxiliary NIR and VIS ultrashort lasers, supports a plethora of dynamic investigations in physics, material science and biology. The unique features of the FLASH THz pulses and the accelerator source, however, bring along a set of challenges in the diagnostics of their key parameters: pulse energy, spectral, temporal and spatial profiles. Here, these challenges are discussed and the pulse diagnostic tools developed at FLASH are presented. In particular, a radiometric power measurement is presented that enables the derivation of the average pulse energy within a pulse burst across the spectral range, jitter-corrected electro-optical sampling for the full spectro-temporal pulse characterization, spatial beam profiling along the beam transport line and at the sample, and a lamellar grating based Fourier transform infrared spectrometer for the on-line assessment of the average THz pulse spectra. Corresponding measurement results provide a comprehensive insight into the THz beamline capabilities.

Dynamical effects on superradiant THz emission from an undulator.

Superradiant emission occurs when ultra-relativistic electron bunches are compressed to a duration shorter than the wavelength of the light emitted by them. In this case the different electron contributions to the emitted field sum up in phase and the output intensity scales as the square of the number of electrons in the bunch. In this work the particular case of superradiant emission from an undulator in the THz frequency range is considered. An electron bunch at the entrance of a THz undulator setup has typically an energy chirp because of the necessity to compress it in magnetic chicanes. Then, the chirped electron bunch evolves passing through a highly dispersive THz undulator with a large magnetic field amplitude, and the shape of its longitudinal phase space changes. Here the impact of this evolution on the emission of superradiant THz radiation is studied, both by means of an analytical model and by simulations.

Interferometry and coherence of nonstationary light.

We consider temporally integrating interferometric measurements and their relation to the coherence properties of nonstationary light. We find that performing such experiments as a function of time delay is equivalent to spectrally resolving the interference patterns, and time-domain coherence information can be obtained from field autocorrelation only if the source is of the Schell-model type. In an analogy to autocorrelation, we introduce field cross-correlation, which can be used to determine the complete complex field of unknown signal pulses if suitable probe pulses are available. We demonstrate our findings with simulated supercontinuum and free-electron laser ensembles, and discuss the prospect of carrying out experiments.

Effects of energy spread on brightness and coherence of undulator sources.

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.

Ultra-high-resolution inelastic X-ray scattering at high-repetition-rate self-seeded X-ray free-electron lasers.

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.

Brightness of synchrotron radiation from undulators and bending magnets.

The maximum of the Wigner distribution (WD) of synchrotron radiation (SR) fields is considered as a possible definition of SR source brightness. Such a figure of merit was originally introduced in the SR community by Kim [(1986), Nucl. Instrum. Methods Phys. Res. A, 246, 71-76]. The brightness defined in this way is always positive and, in the geometrical optics limit, can be interpreted as the maximum density of photon flux in phase space. For undulator and bending magnet radiation from a single electron, the WD function can be explicitly calculated. In the case of an electron beam with a finite emittance the brightness is given by the maximum of the convolution of a single electron WD function and the probability distribution of the electrons in phase space. In the particular case when both electron beam size and electron beam divergence dominate over the diffraction size and the diffraction angle, one can use a geometrical optics approach. However, there are intermediate regimes when only the electron beam size or the electron beam divergence dominate. In these asymptotic cases the geometrical optics approach is still applicable, and the brightness definition used here yields back once more to the maximum photon flux density in phase space. In these intermediate regimes a significant numerical disagreement is found between exact calculations and the approximation for undulator brightness currently used in the literature. The WD formalism is extended to a satisfactory theory for the brightness of a bending magnet. It is found that in the intermediate regimes the usually accepted approximation for bending magnet brightness turns out to be inconsistent even parametrically.

Perspectives for imaging single protein molecules with the present design of the European XFEL.

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.

Coherent synchrotron radiation transient effects in the energy-dependent region.

Coherent synchrotron radiation (CSR) is a well known phenomenon that originates from coherent superposition of electromagnetic waves by ultrarelativistic electrons. CSR longitudinal effects during the passage of a Gaussian beam from a straight to a circular path have often been studied in a regime in which they are energy independent. Nevertheless, the approximations used in such a regime may fail in several practical situations, as in the case of low-energy injectors or for small-wavelength structures within the bunch distribution in CSR-related instability problems. These situations demand a deeper investigation of longitudinal transient effects in the region where the approximations above are no longer valid: a strong gamma dependence is found, and described in this paper, in the rate of energy change induced by CSR during the transient of a Gaussian bunch between a straight and a circular path, which was studied with the help of the authors' previous work. Results show that the overall CSR longitudinal effects, in this case, are reduced. One of the outcomes of previous work by Saldin et al. was extended to this situation and very good agreement between the two studies was found.