Deep learning for ultrafast X-ray scattering and imaging with intense X-ray FEL pulses

High field X-ray laser physics

X-ray free electron lasers (XFELs) have emerged as powerful sources of short and intense X-ray pulses. We propose a simple and robust procedure which takes advantage of the inherent stochasticity of self-amplified stimulated emission (SASE) pulses to enhance the time-resolution and signal strength in the recorded data. Notably, the proposed method is able to enhance the average signal without knowledge of the signal strength of individual shots. Simple metrics for the probe pulses are introduced, such as an effective pulse duration applicable to SASE pulses characterised in the time domain using {\it{e.g.}}\ an X-band transverse cavity (XTCAV). The approach is evaluated using simulated and real pulse data in the context of ultrafast electron dynamics in a molecule. Utilising H$_2$ as a model system, we demonstrate the efficacy of the method theoretically, successfully enhancing the predicted nonresonant ultrafast X-ray scattering signal associated with electron dynamics. The method presented is broadly applicable and offers a general strategy for enhancing time-dependent observables at XFELs.

X-ray Free Electron Lasers (XFELs) are a new generation of x-ray sources, offering highly coherent, intense x-ray pulses with pulse lengths down to a few femtoseconds. Applications for intense X-ray pulses from XFELS span a broad spectrum from atomic and molecular physics to chemical, materials and biological sciences [1]. Recently, XFELs proved the ability to produce two intense femtosecond x-ray pulses with controlled time delay and color [1,2]. This opened the possibility of carrying out time-resolved studies of complex x-ray induced phenomena with x-ray pump / x-ray probe schemes [3].

Development of photo-diodes for Pohang-Accelerator-Laboratory X-ray free-electron laser

Atomic or molecular assemblies irradiated with intense hard x-ray pulses, such as those emitted from x-ray free-electron lasers (XFELs), are subject to a strong ionization, which also releases electrons from atomic inner shells. The resulting core-hole states relax via various channels, including fluorescence and Auger decay. The latter is the predominant relaxation channel for light elements and typically occurs on a time scale of 1--10 fs. In dense samples, the core-hole ions may already undergo electron-impact ionizations during this time due to the abundance of highly energetic photoelectrons and Auger electrons. In this study we perform an ab initio calculation of the electron-impact-ionization cross sections of ions with an arbitrary electronic configuration at zero temperature. This allows us to evaluate and compare impact-ionization cross sections for ions in ground and ``exotic'' electronic states (e.g., with a few core holes), which may be formed during their interaction with intense x-ray pulses. We show that the impact-ionization cross sections for ions of the same charge, but with varying electronic configurations, may significantly differ. This finding has to be taken into account in any modeling tool treating the relaxation of atoms after high-energy-impact collision, e.g., simulations dedicated for coherent x-ray diffraction imaging of nanocrystals and single biological macromolecules, or laser-created plasma studies. Our computationally efficient ab initio calculation scheme can be easily incorporated in such simulation schemes.

Intense femtosecond x-ray pulses from free-electron lasers are used to gain unprecedented insight into the structural and transient electronic properties of nanoscale samples.

<sec>In 2005, the FLASH soft X-ray free-electron laser (FEL) in Hamburg, Germany, achieved its first lasing, which began an intensive phase of global FEL construction. Subsequently, the United States, Japan, South Korea, China, Italy, and Switzerland all began building such photon facilities. Recently, the new generation of FEL has started to utilize superconducting acceleration technology to achieve high-repetition-rate pulse output, thereby improving experimental efficiency. Currently completed facility is the European XFEL, ongoing constructions are the LCLS-II in the United States and the SHINE facility in Shanghai, and the facility in preparation is the Shenzhen superconducting soft X-ray free-electron laser (S<sup>3</sup>FEL).</sec><sec>These FEL facilities generate coherent and tunable ultrashort pulses ranging from the extreme ultraviolet to hard X-ray spectrum, which advances the FEL-based scattering techniques such as ultrafast X-ray scattering, spectroscopy, and X-ray nonlinear optics, thereby transforming the way we study correlated quantum materials on an ultrafast timescale.</sec><sec>The self-amplified spontaneous emission (SASE) process in FEL leads to timing jitter between FEL pulses and the synchronized pump laser, influencing the accuracy of ultrafast time-resolved measurements. To address this issue, timing tools have been developed to measure these jitters and reindexed each pump-probe signal after measurement. This success enables ultrafast X-ray diffraction (UXRD) to be first realized, and a systematic study of Peierls distorted materials is demonstrated. In addition, the high flux of FEL pulses enables Fourier transform inelastic X-ray scattering (FT-IXS) method, which can extract the phonon dispersion curve of the entire Brillouin zone by performing the Fourier transform on the measured momentum dependent coherent phonon scattering signals, even when the system is in a non-equilibrium state.</sec><sec>The UXRD is typically used to study ultrafast lattice dynamics, which requires hard X-ray wavelengths. In contrast, time resolved resonant elastic X-ray scattering (tr-REXS) in the soft X-ray regime has become a standard method of investigating nano-sized charge and spin orders in correlated quantum materials on an ultrafast time scale.</sec><sec>In correlated quantum materials, the interplay between electron dynamics and lattice dynamics represents another important research direction. In addition to Zhi-Xun Shen's successful demonstration of the combined tr-ARPES and UXRD method at SLAC, this paper also reports the attempts to integrate UXRD with resonant X-ray emission spectroscopy (RXES) for the simultaneous measurement of electronic and lattice dynamics.</sec><sec>Resonant inelastic X-ray scattering (RIXS) is a powerful tool for studying elementary and collective excitations in correlated quantum materials. However, in FEL-based soft X-ray spectroscopy, the wavefront tilt introduced by the widely used grating monochromators inevitably stretches the FEL pulses, which degrades the time resolution. Therefore, the new design at FEL beamlines adopts low line density gratings with long exit arms to reduce pulse stretch and achieve relatively high energy resolution. For example, the Heisenberg-RIXS instrument at the European XFEL achieves an energy resolution of 92 meV at the Cu <i>L</i><sub>3</sub> edge and approximately 150 fs time resolution.</sec><sec>In recent years, scientists at SwissFEL’s Furka station have drawn inspiration from femtosecond optical covariance spectroscopy to propose a new method of generating two-dimensional time-resolved resonant inelastic X-ray scattering (2D tr-RIXS) spectra. This method involves real-time detection of single-shot FEL incident and scattered spectra, followed by deconvolution calculation to avoid photon waste and wavefront tilt caused by monochromator slits. The SQS experimental station at European XFEL, built in 2023, features a 1D-XUV spectrometer that utilizes subtle variations in photon energy absorption across the sample to induce spatial energy dispersion. Using Wolter mirrors, it directly images spatially resolved fluorescence emission from the sample onto the detector to generate 2D tr-RIXS spectra without the need for deconvolution. However, this design is limited to specific samples. Currently, the S<sup>3</sup>FEL under designing has a novel 2D tr-RIXS instrument that uses an upstream low line density grating monochromator to generate spatial dispersion of the beam spot, allowing the full bandwidth of SASE to project spatially dispersed photon energy onto the sample. Subsequently, an optical design similar to the 1D-XUV spectrometer will be employed to achieve 2D tr-RIXS spectra, thereby expanding the applicability beyond specific liquid samples. These new instruments are designed to minimize pulse elongation by fully utilizing SASE’s full bandwidth, approaching Fourier-transform-limited RIXS spectra in both time and energy resolution.</sec><sec>Nonlinear X-ray optical techniques, such as sum-frequency generation (SFG) and second-harmonic generation, are adapting to X-ray wavelengths and opening up new avenues for detecting elementary excitations. The X-ray transient grating spectroscopy extends its capabilities to studying charge transport and spin dynamics on an ultrafast timescale. The future development of these scattering methods provides unique opportunities for detecting dynamical events in various systems, including surface and interface processes, chirality, nanoscale transport, and so-called multidimensional core-level spectroscopy.</sec>

X-ray free-electron lasers (FELs) produce femtosecond x-ray pulses with unprecedented intensities that are uniquely suited for studying many phenomena in atomic, molecular, and optical (AMO) physics. A compilation of the current developments at the Linac Coherent Light Source (LCLS) and future plans for the LCLS-II and Next Generation Light Source (NGLS) are outlined. The AMO instrumentation at LCLS and its performance parameters are summarized. A few selected experiments representing the rapidly developing field of ultra-fast and peak intensity x-ray AMO sciences are discussed. These examples include fundamental aspects of intense x-ray interaction with atoms, nonlinear atomic physics in the x-ray regime, double core-hole spectroscopy, quantum control experiments with FELs and ultra-fast x-ray induced dynamics in clusters. These experiments illustrate the fundamental aspects of the interaction of intense short pulses of x-rays with atoms, molecules and clusters that are probed by electron and ion spectroscopies as well as ultra-fast x-ray scattering.

The past six years have led to a wealth of experimental and theoretical data revealing the nature of the interaction between gas-phase molecules and short and intense x-ray pulses, from the Linac coherent light source free electron laser (FEL). We present here a few highlights that describe some of the first photoabsorption measurements of gas-phase molecules. In particular, we report on a three decades long prediction of single-site double core holes (ss-DCH) and two-site double core holes (ts-DCH) in diatomic and triatomic molecules. We also describe recent measurements that validate a simple theory regarding femtosecond intense x-ray induced fragmentation dynamics of C60 as well as photoabsorption measurements of encapsulated fullerenes, Ho3N@C80. The latter investigation opens the way for even more complex molecular studies with FELs. In all of the described highlights, working in close collaboration with theorists enabled the interpretation of, or predicted our measurements, and in some cases our experiments guided the modeling. We conclude this article by describing the potential of new instrumentation for chemical and biological sciences especially in light of new or improved FELs.

We study theoretically the quantum dynamics of nitrogen molecules (N2) exposed to intense and ultrafast x-rays at a wavelength of ( photon energy) from the Linac Coherent Light Source (LCLS) free electron laser. Molecular rate equations are derived to describe the intertwined photoionization, decay, and dissociation processes occurring for N2. This model complements our earlier phenomenological approaches, the single-atom, symmetric-sharing, and fragmentation-matrix models of 2012 (J. Chem. Phys. 136 214310). Our rate-equations are used to obtain the effective pulse energy at the sample and the time scale for the dissociation of the metastable dication . This leads to a very good agreement between the theoretically and experimentally determined ion yields and, consequently, the average charge states. The effective pulse energy is found to decrease with shortening pulse duration. This variation together with a change in the molecular fragmentation pattern and frustrated absorption—an effect that reduces absorption of x-rays due to (double) core hole formation—are the causes for the drop of the average charge state with shortening LCLS pulse duration discovered previously.

Structural studies of biological macromolecules are severely limited by radiation damage. Traditional crystallography curbs the effects of damage by spreading damage over many copies of the molecule of interest in the crystal. X-ray lasers offer an additional opportunity for limiting damage by out-running damage processes with ultrashort and very intense X-ray pulses. Such pulses may allow the imaging of single molecules, clusters, or nanoparticles. Coherent flash imaging will also open up new avenues for structural studies on nano- and microcrystalline substances. This paper addresses the theoretical potentials and limitations of nanocrystallography with extremely intense coherent X-ray pulses. We use urea nanocrystals as a model for generic biological substances and simulate the primary and secondary ionization dynamics in the crystalline sample. The results establish conditions for ultrafast single-shot nanocrystallography diffraction experiments as a function of X-ray fluence, pulse duration, and the size of nanocrystals. Nanocrystallography using ultrafast X-ray pulses has the potential to open up a new route in protein crystallography to solve atomic structures of many systems that remain inaccessible using conventional X-ray sources.

The Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) operates hard X-ray and soft X-ray beamlines for conducting scientific experiments providing intense ultrashort X-ray pulses based on the self-amplified spontaneous emission (SASE) process. The X-ray free-electron laser is characterized by strong pulse-to-pulse fluctuations resulting from the SASE process. Therefore, online photon diagnostics are very important for rigorous measurements. The concept of photo-absorption and emission using solid materials is seldom considered in soft X-ray beamline diagnostics. Instead, gas monitoring detectors, which utilize the photo-ionization of noble gas, are employed for monitoring the beam intensity. To track the beam position at the soft X-ray beamline in addition to those intensity monitors, an X-ray ionization beam position monitor (XIBPM) has been developed and characterized at the soft X-ray beamline of PAL-XFEL. The XIBPM utilizes ionization of either the residual gas in an ultra-high-vacuum environment or injected krypton gas, along with a microchannel plate with phosphor. The XIBPM was tested separately for monitoring horizontal and vertical beam positions, confirming the feasibility of tracking relative changes in beam position both on average and down to single-shot measurements. This paper presents the basic structure and test results of the newly developed non-invasive XIBPM.

The ultrafast, high brightness x-ray free electron laser (XFEL) sources of the future have the potential to revolutionize the study of time dependent phenomena in the natural sciences. These linear accelerator (linac) sources will generate femtosecond (fs) x-ray pulses with peak flux comparable to conventional lasers, and far exceeding all other x-ray sources. The Stanford Linear Accelerator Center (SLAC) has pioneered the development of linac science and technology for decades, and since 2000 SLAC and the Stanford Synchrotron Radiation Laboratory (SSRL) have focused on the development of linac based ultrafast electron and x-ray sources. This development effort has led to the creation of a new x-ray source, called the Sub-Picosecond Pulse Source (SPPS), which became operational in 2003 [1]. The SPPS represents the first step toward the world's first hard x-ray free electron laser (XFEL), the Linac Coherent Light Source (LCLS), due to begin operation at SLAC in 2009. The SPPS relies on the same linac-based acceleration and electron bunch compression schemes that will be used at the LCLS to generate ultrashort, ultrahigh peak brightness electron bunches [2]. This involves creating an energy chirp on the electron bunch during acceleration and subsequent compression of the bunch in a series ofmore » energy-dispersive magnetic chicanes to create 80 fs electron pulses. The SPPS has provided an excellent opportunity to demonstrate the viability of these electron bunch compression schemes and to pursue goals relevant to the utilization and validation of XFEL light sources.« less

This article reviews recent developments in research on coherence properties of femtosecond XUV and x-ray lasers. Coherence is one of the most conspicuous features of laser sources. It describes how an electromagnetic wave field is correlated at different times and at different points in space. Coherence is a property that enables stationary interferences and thereby enables holographic and diffractive or lens less imaging. While a large number of different laser systems radiating in the infrared, visible and UV spectral range have been developed in the past five decades since the invention of the laser, the generation of intense and coherent XUV and x-ray radiation is still a formidable goal of basic research. Developed first in the mid and far infrared spectral region free electron lasers (FEL) provide a new means to generate widely tunable coherent radiation [Madey, 1971; Deacon et al., 1977; Oepts et al., 1995]. In the XUV and soft x-ray spectral region the present lack of appropriate mirrors prevent the construction of optical resonators, essential for a laser with well-defined mode properties. Therefore in this spectral region free-electron lasers have to rely on the principle of self-amplified spontaneous emission (SASE), where in a single path enough gain is accumulated to evolve a pulse from shot noise. These machines then provide pulsed XUV and x-ray radiation which shows only partial coherence (Kondratenko & Saldin, 1980; Bonifacio et al., 1984; Murphy & Pellegrini, 1985). A characterisation of the coherence properties of SASE FEL radiation is not only important for the understanding and improvement of the SASE process. With the concomitant development of coherent diffraction imaging it is also of great practical importance in a broad field of fundamental scientific applications, like holographic imaging of artificial magnetic structures or single pulse imaging of large biomolecules. The theoretical description of the coherence properties of SASE FEL has made tremendous progress in the recent years. In this chapter we will briefly review measurement methods and description of partially coherent optical fields. The considerations will be applied to characterize the spatial and temporal coherence of pulses from the SASE free electron laser in Hamburg (FLASH) and of high harmonic radiation.

The most recent light sources, extreme ultraviolet (EUV) and X-ray free electron lasers (FELs), have extended tabletop laser experiments to shorter wavelengths, adding element and chemical state specificity by exciting and probing electronic transitions from core levels. Through their unique properties, combining femtosecond X-ray pulses with coherence and enormous peak brightness, the FELs have enabled studies of a broad class of dynamic phenomena in matter that crosses many scientific disciplines and have led to major breakthroughs in the last few years. In this article, we review how the advances in the performance of the FELs, with respect to coherence, polarization and multi-color pulse production, have pushed the development of original experimental strategies to study non-equilibrium behavior of matter at the femtosecond–nanometer time–length scales. In this review, the emphasis is placed on the contribution of the EUV and soft X-ray FELs on three important subjects: (i) the new regime of X-ray matter interactions with ultrashort very intense X-ray pulses, (ii) the new potential of coherent imaging and scattering for answering questions about nano dynamics in complex materials and (iii) the unique possibility to stimulate and probe nonlinear phenomena that are at the heart of conversion of light into other forms of energy, relevant to photovoltaics, femtosecond magnetism and phase transitions in correlated materials.