Free-electron Laser Experiments Research Articles

Measurement bias in self-heating x-ray free electron laser experiments from diffraction studies of phase transformation in titanium

X-ray self-heating is a common by-product of X-ray Free Electron Laser (XFEL) techniques that can affect targets, optics, and other irradiated materials. Diagnosis of heating and induced changes in samples may be performed using the x-ray beam itself as a probe. However, the relationship between conditions created by and inferred from x-ray irradiation is unclear and may be highly dependent on the material system under consideration. Here, we report on a simple case study of a titanium foil irradiated, heated, and probed by a MHz XFEL pulse train at 18.1 keV delivered by the European XFEL using measured x-ray diffraction to determine temperature and finite element analysis to interpret the experimental data. We find a complex relationship between apparent temperatures and sample temperature distributions that must be accounted for to adequately interpret the data, including beam averaging effects, multivalued temperatures due to sample phase transitions, and jumps and gaps in the observable temperature near phase transformations. The results have implications for studies employing x-ray probing of systems with large temperature gradients, particularly where these gradients are produced by the beam itself. Finally, this study shows the potential complexity of studying nonlinear sample behavior, such as phase transformations, where biasing effects of temperature gradients can become paramount, precluding clear observation of true transformation conditions.

Acceleration of flow-focused liquid jets in the presence of a strong electric field

This paper investigates the acceleration of flow-focused micro-jets under an applied external electric field. Such thin and fast jets are needed, for example, to deliver protein crystals in X-ray free electron laser experiments. This contribution focuses on analysing the acceleration of liquid jets produced from 50 % vol water and ethanol mixture. Such jets are focused with nitrogen gas and are subjected to 0 - 7 kV electric potential between a submerged electrode and an external electrode downstream of the nozzle. To gain insights into jet geometric properties an automatic image recognition and computer vision algorithm is utilised on already published data. Jet velocities and acceleration calculated for two jetting regimes show that application of external electric field accelerates the jets up to four orders of magnitude larger than the conventional micro-jets.

Deep residual networks for crystallography trained on synthetic data.

The use of artificial intelligence to process diffraction images is challenged by the need to assemble large and precisely designed training data sets. To address this, a codebase called Resonet was developed for synthesizing diffraction data and training residual neural networks on these data. Here, two per-pattern capabilities of Resonet are demonstrated: (i) interpretation of crystal resolution and (ii) identification of overlapping lattices. Resonet was tested across a compilation of diffraction images from synchrotron experiments and X-ray free-electron laser experiments. Crucially, these models readily execute on graphics processing units and can thus significantly outperform conventional algorithms. While Resonet is currently utilized to provide real-time feedback for macromolecular crystallography users at the Stanford Synchrotron Radiation Lightsource, its simple Python-based interface makes it easy to embed in other processing frameworks. This work highlights the utility of physics-based simulation for training deep neural networks and lays the groundwork for the development of additional models to enhance diffraction collection and analysis.

Development of spinning-disk solid sample delivery system for high-repetition rate x-ray free electron laser experiments.

X-ray free-electron lasers (XFELs) deliver intense x-ray pulses that destroy the sample in a single shot by a Coulomb explosion. Experiments using XFEL pulse trains or the new generation of high-repetition rate XFELs require rapid sample replacement beyond those provided by the systems now used at low repletion-rate XFELs. We describe the development and characterization of a system based on a spinning disk to continuously deliver a solid sample into an XFEL interaction point at very high speeds. We tested our system at the Linac Coherent Light Source and European XFEL hard x-ray nano-focus instruments, employing it to deliver a 25 μm copper foil sample, which can be used as a gain medium for stimulated x-ray emission for the proposed x-ray laser oscillator.

Electron population dynamics in resonant non-linear x-ray absorption in nickel at a free-electron laser.

Free-electron lasers provide bright, ultrashort, and monochromatic x-ray pulses, enabling novel spectroscopic measurements not only with femtosecond temporal resolution: The high fluence of their x-ray pulses can also easily enter the regime of the non-linear x-ray-matter interaction. Entering this regime necessitates a rigorous analysis and reliable prediction of the relevant non-linear processes for future experiment designs. Here, we show non-linear changes in the -edge absorption of metallic nickel thin films, measured with fluences up to 60 J/cm2. We present a simple but predictive rate model that quantitatively describes spectral changes based on the evolution of electronic populations within the pulse duration. Despite its simplicity, the model reaches good agreement with experimental results over more than three orders of magnitude in fluence, while providing a straightforward understanding of the interplay of physical processes driving the non-linear changes. Our findings provide important insights for the design and evaluation of future high-fluence free-electron laser experiments and contribute to the understanding of non-linear electron dynamics in x-ray absorption processes in solids at the femtosecond timescale.

Relaxation of Ne1+ 1s02s22p6 np produced by resonant excitation of an ultraintense ultrafast x-ray pulse

The creation and relaxation of double K-hole states 1s02s22p6 np (n ≥ 3) of Ne1+ in the interaction with ultraintense ultrafast x-ray pulses are theoretically investigated. The x-ray photon energies are selected so that x-rays first photoionize 1s22s22p6 of a neon atom to create a single K-hole state of 1s2s2p6 of Ne1+, which is further excited resonantly to double K-hole states of 1s02s22p6 np (n ≥ 3). A time-dependent rate equation is used to investigate the creation and relaxation processes of 1s02s22p6 np, where the primary microscopic atomic processes including photoexcitation, spontaneous radiation, photoionization and Auger decay are considered. The calculated Auger electron energy spectra are compared with recent experimental results, which shows good agreement. The relative intensity of Auger electrons is very sensitive to the photon energy and bandwidth of x-ray pulses, which could be used as a diagnostic tool for x-ray free electron laser and atom experiments.

Photodissociation of water molecule at short photon wavelengths: Dynamical studies

In our last study [J. Phys. B At. Mol. Opt. Phys. 54, 125,102 (2021).], we reported the ab initio calculation of the full-dimensional potential energy surfaces of water molecule including 9 A’ and 9 A” states in Cs symmetry. In this study, we performed additional non-adiabatic semi-classical studies based on the potential energy surfaces. Our simulation successfully repeated the near picosecond lifetime of the F∼1A′ state measured by time resolved photo-electron spectra experiment [Chinese J. Chem. Phys. 32, 53 (2019)]. We also determined the dissociation branching ratio including H + OH(X, A), H + H + O and H2+O channels. In addition, the reaction path corresponding to H2+O (1S) channel is clearly marked out, which is found in recent free-electron laser experiment [Nat. Commun. 12, 6,303 (2021)].

Multiparticle Cumulant Mapping for Coulomb Explosion Imaging.

We extend covariance velocity map ion imaging to four particles, establishing cumulant mapping and allowing for measurements that provide insights usually associated with coincidence detection, but at much higher count rates. Without correction, a fourfold covariance analysis is contaminated by the pairwise correlations of uncorrelated events, but we have addressed this with the calculation of a full cumulant, which subtracts pairwise correlations. We demonstrate the approach on the four-body breakup of formaldehyde following strong field multiple ionization in few-cycle laser pulses. We compare Coulomb explosion imaging for two different pulse durations (30 and 6fs), highlighting the dynamics that can take place on ultrafast timescales. These results have important implications for Coulomb explosion imaging as a tool for studying ultrafast structural changes in molecules, a capability that is especially desirable for high-count-rate x-ray free-electron laser experiments.

Design of the nanopositioning and mechanical system for cavity-based X-ray free electron laser

With forming of an X-ray cavity with a set of narrow bandwidth diamond Bragg crystals and by storing and recirculating the output of an amplifier in an X- ray cavity so that the X-ray pulse can interact with following fresh electron bunches over many passes thus enabling the development of full temporal coherence, we will be able to build cavity-based X-ray FELs (CBXFELs) such as the X-ray free-electron laser oscillator (XFELO) and the X-ray regenerative amplifier free-electron laser (XRAFEL) [1, 2]. One of the key challenges to forming the X-ray cavity is the nanopositioning design and construction of the cavity mechanical system. In this paper, we present the design of the nanopositioning and mechanical system that is currently under construction for use in a proof-of-principle cavity-based X-ray free electron laser experiment at the LCLS-II at SLAC.

Relaxation Dynamics in a Long-Range System with Mixed Hamiltonian and Non-Hamiltonian Interactions

Sometimes the dynamics of a physical system is described by non-Hamiltonian equations of motion, and additionally, the system is characterized by long-range interactions. A concrete example is that of particles interacting with light as encountered in free-electron laser and cold-atom experiments. In this work, we study the relaxation dynamics to non-Hamiltonian systems, more precisely, to systems with interactions of both Hamiltonian and non-Hamiltonian origin. Our model consists of $N$ globally-coupled particles moving on a circle of unit radius; the model is one-dimensional. We show that in the infinite-size limit, the dynamics, similarly to the Hamiltonian case, is described by the Vlasov equation. In the Hamiltonian case, the system eventually reaches an equilibrium state, even though one has to wait for a long time diverging with $N$ for this to happen. By contrast, in the non-Hamiltonian case, there is no equilibrium state that the system is expected to reach eventually. We characterize this state with its average magnetization. We find that the relaxation dynamics depends strongly on the relative weight of the Hamiltonian and non-Hamiltonian contributions to the interaction. When the non-Hamiltonian part is predominant, the magnetization attains a vanishing value, suggesting that the system does not sustain states with constant magnetization, either stationary or rotating. On the other hand, when the Hamiltonian part is predominant, the magnetization presents long-lived strong oscillations, for which we provide a heuristic explanation. Furthermore, we find that the finite-size corrections are much more pronounced than those in the Hamiltonian case; we justify this by showing that the Lenard-Balescu equation, which gives leading-order corrections to the Vlasov equation, does not vanish, contrary to what occurs in one-dimensional Hamiltonian long-range systems.

A machine learning photon detection algorithm for coherent x-ray ultrafast fluctuation analysis.

X-ray free electron laser experiments have brought unique capabilities and opened new directions in research, such as creating new states of matter or directly measuring atomic motion. One such area is the ability to use finely spaced sets of coherent x-ray pulses to be compared after scattering from a dynamic system at different times. This enables the study of fluctuations in many-body quantum systems at the level of the ultrafast pulse durations, but this method has been limited to a select number of examples and required complex and advanced analytical tools. By applying a new methodology to this problem, we have made qualitative advances in three separate areas that will likely also find application to new fields. As compared to the “droplet-type” models, which typically are used to estimate the photon distributions on pixelated detectors to obtain the coherent x-ray speckle patterns, our algorithm achieves an order of magnitude speedup on CPU hardware and two orders of magnitude improvement on GPU hardware. We also find that it retains accuracy in low-contrast conditions, which is the typical regime for many experiments in structural dynamics. Finally, it can predict photon distributions in high average-intensity applications, a regime which up until now has not been accessible. Our artificial intelligence-assisted algorithm will enable a wider adoption of x-ray coherence spectroscopies, by both automating previously challenging analyses and enabling new experiments that were not otherwise feasible without the developments described in this work.

Development of slurry targets for high repetition-rate x-ray free electron laser experiments

Combining an x-ray free electron laser with a high-power laser driver enables the study of equations-of-state, high strain-rate deformation processes, structural phase transitions, and transformation pathways as a function of pressure to hundreds of GPa along different thermodynamic compression paths. Future high repetition-rate laser operation will enable data to be accumulated at >1 Hz, which poses a number of experimental challenges, including the need to rapidly replenish the target. Here, we present a combined shock compression and an x-ray diffraction study on epoxy (50% vol.)-crystalline grains (50% vol.) slurry targets, which can be fashioned into extruded ribbons for high repetition-rate operation. For shock-loaded NaCl-slurry samples, we observe pressure, density, and temperature states within the embedded NaCl grains consistent with observations from shock-compressed single-crystal NaCl.

Intersubunit Coupling Enables Fast CO2-Fixation by Reductive Carboxylases.

Enoyl-CoA carboxylases/reductases (ECRs) are some of the most efficient CO2-fixing enzymes described to date. However, the molecular mechanisms underlying the extraordinary catalytic activity of ECRs on the level of the protein assembly remain elusive. Here we used a combination of ambient-temperature X-ray free electron laser (XFEL) and cryogenic synchrotron experiments to study the structural organization of the ECR from Kitasatospora setae. The K. setae ECR is a homotetramer that differentiates into a pair of dimers of open- and closed-form subunits in the catalytically active state. Using molecular dynamics simulations and structure-based mutagenesis, we show that catalysis is synchronized in the K. setae ECR across the pair of dimers. This conformational coupling of catalytic domains is conferred by individual amino acids to achieve high CO2-fixation rates. Our results provide unprecedented insights into the dynamic organization and synchronized inter- and intrasubunit communications of this remarkably efficient CO2-fixing enzyme during catalysis.

Molecular Principles of Redox-Coupled Protonation Dynamics in Photosystem II.

Photosystem II (PSII) catalyzes light-driven water oxidization, releasing O2 into the atmosphere and transferring the electrons for the synthesis of biomass. However, despite decades of structural and functional studies, the water oxidation mechanism of PSII has remained puzzling and a major challenge for modern chemical research. Here, we show that PSII catalyzes redox-triggered proton transfer between its oxygen-evolving Mn4O5Ca cluster and a nearby cluster of conserved buried ion-pairs, which are connected to the bulk solvent via a proton pathway. By using multi-scale quantum and classical simulations, we find that oxidation of a redox-active Tyrz (Tyr161) lowers the reaction barrier for the water-mediated proton transfer from a Ca2+-bound water molecule (W3) to Asp61 via conformational changes in a nearby ion-pair (Asp61/Lys317). Deprotonation of this W3 substrate water triggers its migration toward Mn1 to a position identified in recent X-ray free-electron laser (XFEL) experiments [Ibrahim et al. Proc. Natl. Acad. Sci. USA 2020, 117, 12,624–12,635]. Further oxidation of the Mn4O5Ca cluster lowers the proton transfer barrier through the water ligand sphere of the Mn4O5Ca cluster to Asp61 via a similar ion-pair dissociation process, while the resulting Mn-bound oxo/oxyl species leads to O2 formation by a radical coupling mechanism. The proposed redox-coupled protonation mechanism shows a striking resemblance to functional motifs in other enzymes involved in biological energy conversion, with an interplay between hydration changes, ion-pair dynamics, and electric fields that modulate the catalytic barriers.

X-ray free-electron laser heating of water at picosecond time scale

Split-pulse x-ray photon correlation spectroscopy using x-ray free-electron laser is a promising tool to probe atomic dynamics in liquid and soft-matter in picosecond time scale, which has been accessible only by spectroscopy. However, sample heating by x-ray beam is a major obstacle for this technique. Using molecular dynamics and the two-temperature model we examine the atomic level response of water to x-ray laser pulse at picosecond time scale and compare with observations from recent x-ray free-electron laser experiments. We investigate the effects of the heating due to x-ray laser pulses of different energies and the effects of the heat dissipation on the structure and dynamics of water through the atomic density correlation and the dynamic structure factor. Our results indicate, in agreement with experiment that in addition to the beam energy the time delay between the two pulses is a critical factor for obtaining reliable information on the atomic level dynamics of water.

Theoretical Analysis of the Radiation Properties of Some Major X‐Ray Free Electron Lasers

AbstractA theoretical analysis of the radiation in X‐ray free electron lasers (FELs) LCLS, PAL‐XFEL, SwissFEL, as well as SACLA, FLASH 2, and European XFEL is presented. Major losses in FELs are analytically accounted for and analyzed, using exact expressions for the Bessel factors in terms of the generalized Bessel functions. This allows distinguishing the contributions of key parameters and accounting for the losses individually for each harmonic, considering higher sensitivity of the electron‐photon interaction at higher harmonic wavelengths. The harmonic power evolution along FELs and the spectral width of the radiation lines is studied. The theoretical results are analyzed and are compared with the available experimental data for the FEL experiments. The harmonic generation and amplification in the FELs are modeled and studied with the harmonic lasing self‐seed (HLSS) with separate buncher and radiator, and the results are compared with those for SASE. The spectral properties of the radiation are analytically calculated and compared with the measured spectral characteristics. The advantages of HLSS versus SASE FEL are elucidated in the examples of FLASH2, European XFEL, and SwissFEL. The prospected radiation properties of LCLS‐II FEL are analyzed and the possibilities of using harmonics in this FEL are proposed.

Analysis of the spectral properties of free electron lasers in X-RAY and other bands

Analytical formalism for the description of free electron laser (FEL) spectrum is proposed with account for the electron beam size, divergences, beam energy spread, the off-axis deflection and the periodic harmonic and non-periodic constant magnetic field components in undulators. The exact analytical expressions for the spontaneous undulator radiation (UR) are obtained in terms of generalized Bessel and Airy functions, which describe the spectrum line shape and intensities. The obtained analytical formulae distinguish the effects of each installation and beam parameter on the FEL harmonic radiation. The enhanced phenomenological model is employed for the FEL modeling; it describes the harmonic powers evolution along the undulators and gradual saturation around the saturation length with account for the saturated powers oscillations. With this model, we study the generation of FEL harmonics, including even, in several instances of FEL experiments at LCLS, LEUTL and PAL-XFEL. We analytically demonstrate the even harmonics reasons in the LCLS and LEUTL FEL experiments. The spectrum line split due to the beam size is demonstrated analytically and compared with experimentally measured spectral characteristics. The PAL-XFEL experiment is analyzed and compared with the LCLS experiment; the possibility of high harmonic radiation in it is explored. The modeling results fully agree with the measured values in the studied FELs. The analytical formalism shows physical background for each harmonic in every FEL. It allows the analysis of the radiation and beam alignment in projected, built and working FELs and it can help minimizing losses and correcting magnetic fields as well as projecting experiments with FELs.

Photodissociation dynamics of water molecule at short photon wavelengths: full dimensional potential energy surface of Rydberg states

In this work, we have combined the multi-reference double-excitation configuration interaction method, developed by Buenker and Peyerimhoff (1974 Theor. Chim. Acta 35 33), with molecular orbitals optimized with a multi-configurational self-consistent-field approach. Using the example of the water molecule, we show that such a combined technique lowers the computational costs while improving the overall accuracy, especially for highly excited states. With this new approach, we have computed the full-dimensional potential energy surfaces (PESs) of water molecule up to the states. Furthermore, using these PESs we study the photodissociation dynamics of water triggered with short wavelength photons, which have been investigated in recent free electron laser experiments. Our results indicate new and efficient fragmentation pathways. This work paves the way to the study of reaction dynamics of polyatomic molecules in high-lying electronic states.

Numerical study of the second harmonic generation in FELs

A numerical study of the effect of betatron oscillations on the second harmonic generation in free-electron lasers (FELs) is presented. Analytical expressions for the effective coupling strength factors are derived that clearly distinguish all contributions in subharmonics and each polarization of the radiation. A three-dimensional time-dependent numerical FEL code that takes into account the main FEL effects and the individual contribution of each electron to the second harmonic generation is presented. Also, the X- and Y-polarizations of the second harmonic are analyzed. The second harmonic was detected in experiments at the Advanced Photon Source (APS) Low Energy Undulator Test Line (LEUTL) and Linac Coherent Light Source (LCLS) in the soft X-ray regime. The approach presented in the article can be useful for a comprehensive study and diagnostics of XFELs. In the paper, the LCLS and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) experiments are modeled. The simulation results are in a good agreement with the experimental data.

Few-Cycle Infrared Pulse Evolving in FEL Oscillators and Its Application to High-Harmonic Generation for Attosecond Ultraviolet and X-ray Pulses

Generation of few-cycle optical pulses in free-electron laser (FEL) oscillators has been experimentally demonstrated in FEL facilities based on normal-conducting and superconducting linear accelerators. Analytical and numerical studies have revealed that the few-cycle FEL lasing can be explained in the frame of superradiance, cooperative emission from self-bunched systems. In the present paper, we review historical remarks of superradiance FEL experiments in short-pulse FEL oscillators with emphasis on the few-cycle pulse generation and discuss the application of the few-cycle FEL pulses to the scheme of FEL-HHG, utilization of infrared FEL pulses to drive high-harmonic generation (HHG) from gas and solid targets. The FEL-HHG enables one to explore ultrafast science with attosecond ultraviolet and X-ray pulses with a MHz repetition rate, which is difficult with HHG driven by solid-state lasers. A research program has been launched to develop technologies for the FEL-HHG and to conduct a proof-of-concept experiment of FEL-HHG.