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Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian. [ABSTRACT FROM AUTHOR]

Copper (Cu), with its ability to exist in various oxidation states, notably Cu(I) and Cu(II), plays a crucial role in diverse biological redox reactions. This includes its involvement in pathways associated with oxidative stress in neurodegenerative disorders such as Alzheimer's disease, Parkinson's disease, and Transmissible Spongiform Encephalopathies. This paper offers an overview of X‐ray Absorption Spectroscopy (XAS) studies designed to elucidate the interactions between Cu ions and proteins or peptides associated with these neurodegenerative diseases. The emphasis lies on XAS specificity, revealing the local coordination environment, and on its sensitivity to Cu oxidation states. Furthermore, the paper focuses on XAS applications targeting the characterization of intermediate reaction states and explores the opportunities arising from recent advancements in time‐resolved XAS at ultrabright synchrotron and Free Electron Laser radiation sources. [ABSTRACT FROM AUTHOR]

Models attempting an analytical description of free-electron laser (FEL) devices have been proposed in the past. They provided interesting results, leading either to a deeper understanding of the FEL dynamics and to semi-analytical formulae, useful for the preliminary design of self amplified spontaneous emission and oscillator FELs. Most of these models work well until the level of mild saturation. In this paper, we comment on the so-called logistic model and a more recent analysis describing the FEL evolution in terms of Jacobi elliptic functions. Both models are shown to be suited to describe the evolution from the low signal to the onset of saturation. We attempt therefore an extension of these theoretical formulations using a delayed logistic model, capable of including characteristic features like the post saturation power oscillations. [ABSTRACT FROM AUTHOR]

A novel design methodology based on a current-tunable magnetic focusing system that can flexibly switch between Brillouin and immersive flow focusing modes is presented in this paper. Such a magnetic system, which comprises cascaded solenoid coils and pole pieces, could be used in beam optics systems of vacuum tubes, particle accelerators, and free-electron lasers. Although the profile of this magnetic system is not brand new, the novel way proposed in this paper to establish and manipulate such a system to fit versatile purposes has never been reported in the literature to the best of the authors' knowledge. The specific structure of the magnetic system should be optimized, starting from the immersive flow focusing mode together with the electron gun design, which will be determined on successful optimization. According to our analysis, such systems could be transformed into the Brillouin bunching mode by simply adjusting the coil currents without modifying the hardware. To verify such an approach, single-beam and multi-beam optical systems are demonstrated in this paper. Moreover, the beam radius in such systems could also be conveniently adjusted via a similar technique. [ABSTRACT FROM AUTHOR]

A free-electron laser is a laser that has the same optical properties as a conventional laser, such as emitting beams of coherent electromagnetic radiation, which can reach high powers, but uses some very different principles of operation to form the beams. The chaotic motion of electrons causes a considerable decrease in the gain and efficiency of free-electron lasers. In this paper, the Hamiltonian of the dual-wiggler free-electron laser with and without axial guide magnetic field is constructed. Hamilton's equations of motion were derived exactly for both cases. The steady-state solution is also derived and investigated so that the initial conditions of the system are clear. The Poincaré surface-of-section maps were plotted after solving Hamilton's equations of motion numerically, where the chaotic behavior of the system was obvious when the axial field was included while the motion became regular and the Hamiltonian is integrable in the absence of the axial guide magnetic field. Regular orbits are observed clearly for large values of the axial field. [ABSTRACT FROM AUTHOR]

The ability to study chemical dynamics on ultrafast timescales has greatly advanced with the introduction of X-ray free electron lasers (XFELs) providing short pulses of intense X-rays tailored to probe atomic structure and electronic configuration. Fully exploiting the full potential of XFELs requires specialized experimental endstations along with the development of techniques and methods to successfully carry out experiments. The liquid jet endstation (LJE) at the Linac Coherent Light Source (LCLS) has been developed to study photochemistry and biochemistry in solution systems using a combination of X-ray solution scattering (XSS), X-ray absorption spectroscopy (XAS), and X-ray emission spectroscopy (XES). The pump–probe setup utilizes an optical laser to excite the sample, which is subsequently probed by a hard X-ray pulse to resolve structural and electronic dynamics at their intrinsic femtosecond timescales. The LJE ensures reliable sample delivery to the X-ray interaction point via various liquid jets, enabling rapid replenishment of thin samples with millimolar concentrations and low sample volumes at the 120 Hz repetition rate of the LCLS beam. This paper provides a detailed description of the LJE design and of the techniques it enables, with an emphasis on the diagnostics required for real-time monitoring of the liquid jet and on the spatiotemporal overlap methods used to optimize the signal. Additionally, various scientific examples are discussed, highlighting the versatility of the LJE. [ABSTRACT FROM AUTHOR]

Single particle imaging at atomic resolution is perhaps one of the most desired goals for ultrafast X-ray science with X-ray free-electron lasers. Such a capability would create great opportunity within the biological sciences, as high-resolution structural information of biosamples that may not crystallize is essential for many research areas therein. In this paper, we report on a comprehensive computational study of diffraction image formation during single particle imaging of a macromolecule, containing over one hundred thousand non-hydrogen atoms. For this study, we use a dedicated simulation framework, SIMEX, available at the European XFEL facility. Our results demonstrate the full feasibility of computational single-particle imaging studies for biological samples of realistic size. This finding is important as it shows that the SIMEX platform can be used for simulations to inform relevant single-particle-imaging experiments and help to establish optimal parameters for these experiments. This will enable more focused and more efficient single-particle-imaging experiments at XFEL facilities, making the best use of the resource-intensive XFEL operation. [ABSTRACT FROM AUTHOR]

We investigate the effect of pre-bunched relativistic electron beams on the output power of a free electron laser by two electron beams in a theoretical study. In general, this highly coherent and stable pulse of laser is known as the best investigator of basic importance for present-day science. Free electron lasers are the best candidates for exploring nature at ultrasmall spatial and ultrafast temporal scales. In this paper, we have considered the distribution function of relativistic electron beams as a water-bag, and the configuration of the wiggler pump has assumed a helical magneto-static wiggler. By a set of nonlinear, 1D, coupled differential equations the wave-particle interaction problem has been analyzed. With the aid of MATLAB-based Runge-Kutta algorithm numerical solution has been obtained. Saturation profiles in different cases of pre-bunching phase region of beams have been plotted. Out-coming has shown that the saturation length decreases by about 7.2%. However, the amplitude of the output pulse increased by about 209.3% in comparison to the non-pre-bunched relativistic electron beams. [ABSTRACT FROM AUTHOR]

The undulator is a key luminous component of the Shanghai high repetition rate x-ray free electron laser and extreme light facility, and the motion control system is an important part of the undulator. The main task of the motion control system is to complete the high precision adjustment of the gap and taper between the upper magnetic pole girder and lower magnetic pole girder, so as to adjust the wavelength of the radiation light. According to the development requirements of the motion control system for the U26 undulator, which is a conventional permanent magnet, this paper proposes a new motion control system with double position feedback closed-loop control, including programmable logic controller (PLC) closed-loop control based on position feedback by a linear absolute encoder (LAE) and driver closed-loop control based on position feedback by a rotary absolute encoder (RAE) of a servo motor. Multiple motion tests of the U26 undulator have shown that the repeatability accuracy of the gap is ±50 nm and the gap drive can reach 0.1 µm step size, the error of which is about ±20 nm according to the feedback of the LAE. The conclusion can be drawn that the motion step size and repeatability accuracy of the motion control system for the U26 undulator are improved by one order of magnitude on the basis of meeting all technical requirements. At the same time, motor torque protection, motor temperature protection, and redundant position protection with RAE can further improve the reliability and safety of the motion control system for the U26 undulator. [ABSTRACT FROM AUTHOR]

Large-bandwidth pulses produced by cutting-edge X-ray free-electron lasers (FELs) are of great importance in research fields like material science and biology. In this paper, a new method to generate high-power ultrashort FEL pulses with tunable spectral bandwidth with spectral coherence using a dielectric-lined waveguide without interfering operation of linacs is proposed. By exploiting the passive and dephasingless wakefield at terahertz frequency excited by the beam, stable energy modulation can be achieved in the electron beam and large-bandwidth high-intensity soft X-ray radiation can be generated. Three-dimensional start-to-end simulations have been carried out and the results show that coherent radiation pulses with duration of a few femtoseconds and bandwidths ranging from 1.01% to 2.16% can be achieved by changing the undulator taper profile. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study the efficiency of modification with CeO2 nanoparticles (average particle size — 20–30 nm) in a concentration range from 0.1 to 10 wt.% aimed at improving the optical features and radiation stability of micron-sized ZnO powders. The optimal concentration of CeO2 nanoparticles, 3 wt.%, was determined. The change of the solar absorptance in a range of 0.2 to 2.2 µm after electron irradiation of the modified powder (E = 30 keV, F = 2·1016 cm−2) is 1.41 less compared to the unmodified powder. The paper demonstrates that the increase in radiation stability of zinc oxide powders modified with cerium dioxide nanoparticles is provided by two mechanisms: relaxation of primary defects on nanoparticles and capture of formed free electrons by cations of a rare-earth element. [ABSTRACT FROM AUTHOR]

In contemporary evacuation systems, the evacuation sign typically points fixedly towards the nearest emergency exit, providing guidance to evacuees. However, this static approach may not effectively respond to the dynamic nature of a rapidly evolving fire situation, in particular if the closest emergency exit is compromised by fire. This paper introduces an intelligent evacuation sign control mechanism that leverages smoke and temperature sensors to dynamically adjust the direction of evacuation signs, ensuring evacuees are guided to the quickest and safest emergency exit. The proposed mechanism is outlined through a rigorous mathematical formulation, and an ESP heuristic is devised to determine temperature-safe, smoke-safe, and congestion-aware evacuation paths for each sign. This algorithm then adjusts the direction light on the evacuation sign to align with the identified evacuation path. To validate the effectiveness of this approach, fire simulations using FDS software 6.7.1 were conducted in the Taipei 101 shopping mall. Temperature and smoke data from sensor nodes were utilized by the ESP algorithm, demonstrating superior performance compared to that of the existing FEL algorithm. Specifically, the ESP algorithm exhibited a notable increase in the probability of evacuation success, surpassing the FEL algorithm by up to 34% in methane fire scenarios and 14% in PVC fire scenarios. The significance of this improvement is more pronounced in densely congested evacuation scenarios. [ABSTRACT FROM AUTHOR]

Hybrid pixel detectors have become indispensable at synchrotron and X-ray free-electron laser facilities thanks to their large dynamic range, high frame rate, low noise, and large area. However, at energies below 3 keV, the detector performance is often limited because of the poor quantum efficiency of the sensor and the difficulty in achieving single-photon resolution due to the low signal-to-noise ratio. In this paper, we address the quantum efficiency of silicon sensors by refining the design of the entrance window, mainly by passivating the silicon surface and optimizing the dopant profile of the n+ region. We present the measurement of the quantum efficiency in the soft X-ray energy range for silicon sensors with several process variations in the fabrication of planar sensors with thin entrance windows. The quantum efficiency for 250 eV photons is increased from almost 0.5% for a standard sensor to up to 62% as a consequence of these developments, comparable to the quantum efficiency of backside-illuminated scientific CMOS sensors. Finally, we discuss the influence of the various process parameters on quantum efficiency and present a strategy for further improvement. [ABSTRACT FROM AUTHOR]

The paper considers a slightly modified one-dimensional infinite mass-in-mass chain. In the case of the long-wave approximation, which corresponds to the transition to a continuous medium, we obtained a system of two equations, which is a generalization of the classical mechanics Klein–Gordon–Fock equation and has both optical and acoustic branches of the dispersion relation. Based on this classical mechanics system of equations, we have proposed a system of two relativistic quantum mechanics equations, which is a generalization of the relativistic quantum mechanics Klein–Gordon–Fock equation. Next, based on this system and following the Dirac approach, we have proposed the generalization of the Dirac equation for a free electron with an eight-component wave function in the form of a system of eight linear partial differential equations of the first order. Unlike the Dirac equation with a four-component wave function, which has only an optical branch of the dispersion relation, the generalized Dirac equation has both optical and acoustic branches of the dispersion relation, each of which has two branches with positive and negative energies, respectively. We have calculated phase and group velocities for all cases. For the positive and negative acoustic branches, the phase and group velocities are equal in modulus to the speed of light. For the positive and negative optical branches, the phase and group velocities have a structure like that of de Broglie waves. In the one-dimensional case, eight linearly independent solutions corresponding to eight combinations of two branches of dispersion, two signs of total energy, and two possible directions of spin orientation, each in the form of four plane waves, are obtained. [ABSTRACT FROM AUTHOR]

Serial crystallography has emerged as an important tool for structural studies of integral membrane proteins. The ability to collect data from micrometre-sized weakly diffracting crystals at room temperature with minimal radiation damage has opened many new opportunities in time-resolved studies and drug discovery. However, the production of integral membrane protein microcrystals in lipidic cubic phase at the desired crystal density and quantity is challenging. This paper introduces VIALS (versatile approach to high-density microcrystals in lipidic cubic phase for serial crystallography), a simple, fast and efficient method for preparing hundreds of microlitres of high-density microcrystals suitable for serial X-ray diffraction experiments at both synchrotron and free-electron laser sources. The method is also of great benefit for rational structure-based drug design as it facilitates in situ crystal soaking and rapid determination of many cocrystal structures. Using the VIALS approach, room-temperature structures are reported of (i) the archaerhodopsin-3 protein in its dark-adapted state and 110 ns photocycle intermediate, determined to 2.2 and 1.7 Å, respectively, and (ii) the human A2A adenosine receptor in complex with two different ligands determined to a resolution of 3.5 Å. [ABSTRACT FROM AUTHOR]

Ultralow-temperature sintering plays a vital role in the development of flexible printed electronics, which improves flexibility and reduces energy consumption. This study investigates the ultralow-temperature sintering of large-sized silver nanoparticles (Ag NPs) by laser modification of the substrate surface. Ag NPs in conductive ink were sintered at only 60 °C. Designing the appropriate size of modified regions, the sintered Ag layer exhibits a sheet resistance of only 0.274 Ω and withstands 10 000 folding cycles. Energy-dispersive x-ray spectroscopy showed that TiO2 formed by laser ablation promotes the sintering of Ag NPs and joining with the substrate. A paper-based flexible integrated circuit board was also prepared. [ABSTRACT FROM AUTHOR]

Combining experimental set up and ab initio molecular dynamics simulations, we were able to follow the time evolution of the X-ray absorption near edge spectrum (XANES) of a dense copper plasma. This provides a deep insight into femtosecond laser interaction with a metallic copper target. This paper presents a review of the experimental developments we made to reduce the X-ray probe duration, from approximately 10 ps to fs duration with table-top laser systems. Moreover, we present microscopic scale simulations, performed with Density Functional Theory, as well as macroscopic simulations considering the Two-Temperature Model. These tools allow us to get a complete picture of the evolution of the target at a microscopic level, from the heating process to the melting and expansion stages, with a clear view of the physics involved during these processes. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'. [ABSTRACT FROM AUTHOR]

The wavefront preservation of coherent X-ray free-electron laser beams is pushing the requirement on the quality and performance of X-ray optics to an unprecedented level. The Strehl ratio can be used to quantify this requirement. In this paper, the criteria for thermal deformation of the X-ray optics are formulated, especially for crystal monochromators. To preserve the X-ray wavefront, the standard deviation of the height error should be sub-nm for mirrors and less than 25 pm for crystal monochromators. Cryocooled silicon crystals combined with two techniques can be used to achieve this level of performance for monochromator crystals: (1) using a focusing element to compensate the second-order component of the thermal deformation; (2) introducing a cooling pad between the cooling block and silicon crystal and optimizing the effective cooling temperature. Each of these techniques allows the thermal deformation in standard deviation of the height error to be reduced by an order of magnitude. As an example, for the LCLS-II-HE Dynamic X-ray Scattering instrument, the criteria on thermal deformation of a high-heat-load monochromator crystal can be achieved for a 100 W SASE FEL beam. Wavefront propagation simulations confirm that the reflected beam intensity profile is satisfactory on both the peak power density and focused beam size. [ABSTRACT FROM AUTHOR]

Innovations in small‐angle X‐ray and neutron scattering (SAXS and SANS) at major X‐ray and neutron facilities offer new characterization tools for researching materials phenomena relevant to advanced applications. For SAXS, the new generation of diffraction‐limited storage rings, incorporating multi‐bend achromat concepts, dramatically decrease electron beam emittance and significantly increase X‐ray brilliance over previous third‐generation sources. This results in intense X‐ray incident beams that are more compact in the horizontal plane, allowing significantly improved spatial resolution, better time resolution, and a new era for coherent‐beam SAXS methods such as X‐ray photon correlation spectroscopy. Elsewhere, X‐ray free‐electron laser sources provide extremely bright, fully coherent, X‐ray pulses of <100 fs and can support SAXS studies of material processes where entire SAXS data sets are collected in a single pulse train. Meanwhile, SANS at both steady‐state reactor and pulsed spallation neutron sources has significantly evolved. Developments in neutron optics and multiple detector carriages now enable data collection in a few minutes for materials characterization over nanometre‐to‐micrometre scale ranges, opening up real‐time studies of multi‐scale materials phenomena. SANS at pulsed neutron sources is becoming more integrated with neutron diffraction methods for simultaneous structure characterization of complex materials. In this paper, selected developments are highlighted and some recent state‐of‐the‐art studies discussed, relevant to hard matter applications in advanced manufacturing, energy and climate change. [ABSTRACT FROM AUTHOR]

The optical scheme and technical characteristics of terahertz planar Michelson interferometer based on surface plasmons are presented. A technique for determination of the complex index of refraction of surface plasmons () from interferograms is described. The paper presents the results of test measurements on flat surfaces with gold sputtering coated by ZnS layers 0 to 3 μm thick with application of the high-power coherent radiation from the Novosibirsk free electron laser at the wavelength λ0 = 141 μm. From the measurement results, the value of the effective permittivity of the sputtered gold surface was found, which turned out to be an order of magnitude lower than that of crystalline gold. Analysis of the energy losses in the plasmonic interferometer made it possible to estimate its dynamic range (106–108 in terms of radiation power) required for measurements on samples with different . Ways to increase the signal-to-noise ratio via optimization of the elements of the optical scheme and detector have also been proposed. [ABSTRACT FROM AUTHOR]

The High energy Engineering X-ray (HEX) diffraction beamline at the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Lab (BNL) is the first high-energy beamline capable of reaching 200 keV for a monochromatic beam. With the 3 GeV electron beam energy for the NSLS-II ring, only the superconducting wiggler (SCW) producing greater than 4 T peak field can cover these ranges with a sufficient number of photons. The 1.2 m-long HEX-SCW has a period length of 70 mm and a field strength on-axis of 4.3 T. It utilizes no liquid helium, and the vertical aperture size of the electron beam vacuum chamber is 8 mm. Unlike regular undulators/wigglers, there is no standard configuration for the magnetic measurement system for superconducting insertion devices. The NSLS-II Insertion Devices group has developed, in collaboration with the vacuum group, a novel in-vacuum Hall mapper with a 1.75 m in-vacuum linear motor and an in-vacuum flip coil system utilizing many commercial-off-the-shelf products. The measurements were conducted at the BNL, and the device was installed in the ring and commissioned. This paper provides a description of the SCW and its magnetic measurement systems, as well as a brief account of the installation and commissioning efforts. [ABSTRACT FROM AUTHOR]

The uniformity and consistency of X-ray mirror film materials prepared by experimental methods are difficult to guarantee completely. These factors directly affect the service life of free electron laser devices in addition to its own optical properties. Therefore, the quality of the film material, especially the density, has a critical effect on its application. Boron carbide film and monocrystalline silicon substrate were suitable examples to explore their influence of density on the damage threshold based on Monte Carlo and heat-conduction methods. Through simulation results, it was found that the change in film density could affect the energy deposition depth and damage threshold. When the film density was 2.48 g/cm3, it had relatively high damage threshold in all energy ranges. And then the specific incident parameter for practical application was investigated. It was found that the damage mechanism of the B4C/Si was the melting of the interface. And the damage threshold was also higher with the film density of 2.48 g/cm3. Therefore, it was recommended to maintain the density at this value as far as possible when preparing the film, and to ensure the uniformity and consistency of the film material. [ABSTRACT FROM AUTHOR]

The remarkable success of x-ray free-electron lasers and their ability to image biological macromolecules while outrunning secondary radiation damage due to photoelectrons, by using femtosecond pulses, raise the question of whether this can be done using pulsed high-energy electron beams. In this paper, we use excited state molecular dynamics simulations, with tabulated potentials, for rare gas solids to investigate the effect of radiation damage due to inelastic scattering (by plasmons, excitons, and heat) on the pair distribution function. We use electron energy loss spectra to characterize the electronic excitations responsible for radiation damage. [ABSTRACT FROM AUTHOR]

The generation of hollow atoms will reduce the probability of light absorption and provide a high-quality diffraction image in the experiment. In this paper, we calculated the ionization rate of the Kr atom under x-ray free-electron laser (XFEL) using Hartree–Fock–Slater model and simulated the ionization model of Kr atom using Monte–Carlo method to determine the response of the hollow atom of Kr atom to the XFEL photon energy. Calculating the correlation between the total photoionization cross-section of the ground state of Kr atom and the photon energy, we determined three particular photon energies of 1.75 keV, 1.90 keV, and 14.30 keV. The dynamics simulation under the experimental condition's 17.50 keV photon energy was achieved by implementing the Monte–Carlo method and calibrating the photon flux modeling parameters. Consequently, our calculated data are more consistent with experimental phenomena than previous theoretical studies. The saturable absorption of Kr at 1.75 keV, 1.90 keV, 14.30 keV, and 17.50 keV energies was further investigated by using the optimized photon flux model theory. We compared the statistics on main ionization paths under those four specific photon energies and calculated the population changes of various Kr hollow atoms with different configurations. The results demonstrate that the population of hollow atoms produced at the critical ionization photon energy is high. Furthermore, the change of population with respect to position is smooth, which shows a significant difference between the generation mode of ions with low and high photon energies. The result is important for the study of medium- and high- Z element hollow atoms, which has substantial implications for the study of hollow atoms with medium and high charge states, as well as for the scaling of photon energy of free electron lasers. [ABSTRACT FROM AUTHOR]

At present, there is no non-perturbative theory of scattering of nonclassical electromagnetic waves by free electrons that describes the scattering process completely with the help of quantum physics. In this paper, such a theory is presented, which takes into account the statistics and the number of scattered photons. This theory is completely analytical for an arbitrary number of electrons in the system and, in a particular case, is equivalent to the previous theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons. [ABSTRACT FROM AUTHOR]

The Extremely Brilliant Source (EBS) is the experimental implementation of the novel Hybrid Multi Bend Achromat (HMBA) storage ring magnetic lattice concept, which has been realised at European Synchrotron Radiation Facility. We present its successful commissioning and first operation. We highlight the strengths of the HMBA design and compare them to the previous designs, on which most operational synchrotron X-ray sources are based. We report on the EBS storage ring's significantly improved horizontal electron beam emittance and other key beam parameters. EBS extends the reach of synchrotron X-ray science confirming the HMBA concept for future facility upgrades and new constructions. X-ray science at modern Synchrotrons and X-ray Free Electron Laser facilities are enabling the study of subtle structural changes of matter from the single atom to the macroscopic scale. This paper reviews new concepts in synchrotron storage rings design and reports on the successful commissioning and operation of the new X-ray storage ring of the European Synchrotron Radiation Facility (ESRF) in Grenoble. [ABSTRACT FROM AUTHOR]

The distributed energy system (DES) is a promising technology that could enable decarbonization in the building sector. Comprehensive DES system assessment from a holistic perspective is crucial for system design, operation strategy selection, and performance optimization. This paper proposes a techno-economic-environmental integrated assessment model for comprehensive system evaluation. The DES configuration mainly includes a photovoltaic panel, ground source heat pump, gas turbine, absorption heat pump, and thermal storage tank. The system is simulated under three operation strategies with MATLAB/Simulink, which are following thermal load (FTL), following electric load (FEL), and following electric load with thermal storage (FELTS). Entropy-TOPSIS method is used to evaluate the DES's techno-economic-environmental performance under various operation strategies. The results indicate that the DES' primary energy efficiency ratio under the three operation strategies of FTL, FEL and FELTS are 51.49%, 86.78%, and 125.69%, respectively. The dynamic annual values are 1.05 × 10 6 CNY, 7.23 × 10 5 CNY, and 5.94 × 10 5 CNY, respectively. The total greenhouse gas emissions are 36.2 kgCO2eq/( m 2 ∙ a) , 22.8 kgCO2eq/( m 2 ∙ a) , and 16.4 kgCO2eq/( m 2 ∙ a) , respectively. The entropy-TOPSIS analysis results showed that under FELTS operation strategy, DES performs the best; it has the best indicators for technical and environmental evaluation. [ABSTRACT FROM AUTHOR]

Atmosphere is a complex mixture system including various gaseous molecules and particulate matters as well as free radicals. The cases of atmospheric pollution often occur in urban or suburban areas during the evolution of industry, and have adverse influences on the human health and daily life. The origins of atmospheric pollution are complicated, which often comprise a series of chemical reactions involving abundant volatile organic compounds (VOCs), free radicals and aerosol particles. How to analyze these species operando is a hot, significant and challenging topic of atmospheric chemistry. In the past decades, benefiting from the rapid development of analytical techniques used in the atmospheric chemistry, abundant reaction mechanisms for the formation of pollutants have been proposed and revealed. However, due to the complexity of atmospheric chemistry, presently the formation mechanisms of atmospheric pollution are still very limited or coarse and deserve to be comprehensively investigated. As a widely used analytical technique, vacuum ultraviolet photoionization mass spectrometry (VUV-PIMS) can provide mass information of molecular ions benefiting from its “soft” ionization at the threshold ionization energy of molecules. Therefore, the obtained VUV photoionization mass spectra have the characters of no or less fragment ions and are easier to be assigned. Then the key chemical components involved in the atmospheric chemical reactions can be identified efficiently, which are very helpful to reveal the complex mechanisms of atmospheric chemical reactions. In this paper, the recent development of VUV-PIMS and its wide applications in atmospheric chemistry were summarized. Several kinds of VUV light sources, including VUV laser, synchrotron radiation, free electron laser and VUV discharge lamp, were presented. In combination with these advanced light sources, several kinds of VUV-PIMS setups were introduced and their advantages were discussed. In addition, the applications of VUV-PIMS to analyze atmospheric VOCs, free radicals and their reactions, and the chemical compositions of aerosol particles were reviewed. Concretely, in the aspect to detect VOCs in laboratory or on site, several strategies to improve the sensitivity of detection, in particular the improvement of the photoionization source, were presented here in detail. The analysis of several elusive free radicals and their atmospheric oxidation reactions studied by VUV-PIMS were described. Then, the utilization of VUV-PIMS to measure the chemical compositions of aerosols was introduced. Moreover, the perspectives of VUV-PIMS and its further applications in atmospheric chemistry were also discussed. [ABSTRACT FROM AUTHOR]

High-energy particles, including photons (x-ray, γ-ray, bremsstrahlung), electrons, and protons, possess the capability to penetrate materials and deposit energy within them. The degree of absorption depends on both the energy and type of particles, as well as the properties of the materials with which they interact. This energy deposition can manifest either at the material's surface or throughout its volume, potentially resulting in various failure modes. The primary aim of this paper is to establish a structured analysis methodology for evaluating the structural integrity of beam-intercepting devices when subjected to high-energy particles. The paper also reviews some of the underlying physics, pertinent to the scope of the thermomechanical analysis, potential failure modes, and introduces verification and validation methodologies. Engineers and researchers can utilize the guidelines presented in this paper to effectively plan the development of beam intercepting devices, thereby ensuring their reliability and performance in the presence of high-energy particle exposure. • The structural integrity of beam intercepting devices subjected to high-energy free electron lasers is investigated. • The underlying physics, and potential failure modes of beam intercepting devices are reviewed. • FEA verification and validation methodologies are presented. [ABSTRACT FROM AUTHOR]

Stanford Synchrotron Radiation Lightsource serves a wide scientific community with its variety of X‐ray capabilities. Recently, a wiggler X‐ray source located at beamline 10‐2 has been employed to perform high‐resolution rocking curve imaging (RCI) of diamond and silicon crystals. X‐ray RCI is invaluable for the development of upcoming cavity‐based X‐ray sources at SLAC, including the cavity‐based X‐ray free‐electron laser and X‐ray laser oscillator. In this paper, the RCI apparatus is described and experimental results are provided to validate its design. Future improvements of the setup are also discussed. [ABSTRACT FROM AUTHOR]

The wide-ranging requirements for the photon properties from multiple beamlines in superconducting based free-electron lasers (FELs) demand more challenging beam manipulation techniques. Shot-by-shot control of electron beam bunch length and peak current at high repetition rate up to megahertz is highly desired. In this paper, we present a comprehensive study of a method based on a 2-m-long normal conducting radio-frequency cavity to achieve fast and flexible control of beam compression and realize the full potential of the facility, including theoretical analysis, beam dynamics simulations, and conceptual cavity design for the Linac Coherent Light Source II and its high-energy upgrade. We illustrate the physical mechanism of the chirping cavity on the control of the final beam compression and propose methods to lower the requirements for the cavity parameters. The application of this method will allow tailored photon properties of individual beamlines to optimize their performance and drastically improve the multiplexing capabilities of a high-repetition rate FEL facility. [ABSTRACT FROM AUTHOR]

Plasma and beam physics are usually considered as classical physics disciplines with quantum effects featuring only rarely. In particular, free electron lasers (FELs) even in the Angstrom regime (developed recently and being upgraded towards even shorter wavelengths) are well described by classical mechanics and electrodynamics. There is, however, a quantum effect that can influence the operation of these devices and limit the shortest achievable wavelength, namely energy diffusion in an electron beam due to quantum fluctuations in undulator radiation. Although this effect has been calculated theoretically, it has never been measured. In this paper we present measurements of quantum diffusion effect at the European X-Ray Free-Electron Laser. The method uses a recently installed wakefield structure, which enables measurements of the longitudinal phase space after the hard X-ray undulator. The effect of quantum diffusion in the undulator is measured for the first time, and the results are in good agreement with theoretical predictions. [ABSTRACT FROM AUTHOR]

A promising accelerator light source mechanism called steady-state microbunching (SSMB) is being actively studied. With the combination of strong coherent radiation from microbunching and high repetition rate of a storage ring, high-average-power narrow-band radiation can be anticipated from an SSMB storage ring, with wavelengths ranging from THz to soft X-ray. Such a novel light source could provide new opportunities for accelerator photon science like high-resolution angle-resolved photoemission spectroscopy and industrial applications like extreme ultraviolet (EUV) lithography. In this paper, a theoretical and numerical study of the average and statistical properties of coherent radiation from SSMB are presented. The results show that 1 kW average-power quasi-continuous-wave EUV radiation can be obtained from an SSMB ring provided that an average current of 1 A and a microbunch train with bunch length of 3 nm can be formed at the radiator which is assumed to be an undulator. Together with the narrow-band feature, the EUV photon flux can reach 6 × 1015 photons s-1 within a 0.1 meV energy bandwidth, which is three orders of magnitude higher than that in a conventional synchrotron source and is appealing for fundamental condensed matter physics and other research. In this theoretical investigation, we have generalized the definition and derivation of the transverse form factor of an electron beam which can quantify the impact of its transverse size on coherent radiation. In particular, it has been shown that the narrow-band feature of SSMB radiation is strongly correlated with the finite transverse electron beam size. Considering the pointlike nature of electrons and quantum nature of radiation, the coherent radiation fluctuates from microbunch to microbunch, or for a single microbunch from turn to turn. Some important results concerning the statistical properties of SSMB radiation are presented, with a brief discussion on its potential applications, for example the beam diagnostics. The presented work is of value for the development of SSMB to better serve potential synchrotron radiation users. In addition, this also sheds light on understanding the radiation characteristics of free-electron lasers, coherent harmonic generation, etc. [ABSTRACT FROM AUTHOR]

The development of high-brightness X-ray free electron lasers (XFELs), such as hard X-ray self-seeding free electron lasers and XFEL oscillators (XFELOs), brings a severe challenge to the crystal monochromator due to a strong non-uniform thermal load. The distortion caused by spatial temperature gradients can severely affect the optical performance of crystals. Therefore, this paper presents a model to estimate the performance of non-uniform thermally distorted crystals. The model not only takes into account thermal strain, slope error and incident angle deviation, but also considers temperature-dependent factors such as the Debye--Waller factor and electric susceptibility. Our investigation indicates that the Debye--Waller factor reduces the height and bandwidth of rocking curves, and the impact of the electric susceptibility is tiny. The proposed model can describe the distortion of the reflectivity and transmissivity curves of non-uniform thermally loaded crystals and can be applied in the design of crystal monochromators, crystal splitters, crystal compressors and XFELOs. [ABSTRACT FROM AUTHOR]

Attosecond soft X-ray pulses are of great importance for the study of ultrafast electronic phenomena. In this paper, a feasible method is proposed to generate isolated fully coherent attosecond soft X-ray free electron laser via optical frequency beating. Two optical lasers with the opposite frequency chirps are used to induce a gradient frequency energy modulation, which helps to generate a gradually varied spacing electron pulse train. Subsequently, the undulator sections with electron beam delay lines are used to amplify the target ultra-short radiation. Numerical start-to-end simulations have been performed and the results demonstrate that an isolated soft X-ray pulse with the peak power of 330 GW and pulse duration of 620 as can be achieved by the proposed technique. [ABSTRACT FROM AUTHOR]

This paper mainly studies the influence of multilayer hyperbolic metamaterials (HMMs) with different structural parameters on the intensity of spontaneous radiation of quantum wells, thereby improving the coupling efficiency of incident electromagnetic waves and free electrons on metal nano-surfaces. In this paper, numerical simulations of visible light bands of 450–700 nm of Ag, Au, and Cu thin films are performed. The local field enhancements of multilayer HMMs with different shapes are compared, and it is found that circle Ag/Si multilayer HMMs have stronger field enhancement effects than other structures. At the same time, Purcell analysis was performed by changing various parameters of multilayer HMMs. It is found that the thickness of the metal/dielectric layer, the distance between the dipole and the HMMs, and the length of the multilayer HMMs change the intensity of the plasmon resonance radiation and have a great impact on the position of the resonance wavelength. [ABSTRACT FROM AUTHOR]

The scope of this paper is to outline the main marks and performances of the MagneDyn beamline, which was designed and built to perform ultrafast magnetodynamic studies in solids. Open to users since 2019, MagneDyn operates with variable circular and linear polarized femtosecond pulses delivered by the externally laser-seeded FERMI free-electron laser (FEL). The very high degree of polarization, the high pulse-to-pulse stability, and the photon energy tunability in the 50–300 eV range allow performing advanced time-resolved magnetic dichroic experiments at the K-edge of light elements, e.g., carbon and at the M- and N-edge of the 3d-transition-metals and rare earth elements, respectively. To this end, two experimental end-stations are available. The first is equipped with an in situ dedicated electromagnet, a cryostat, and an extreme ultraviolet Wollaston-like polarimeter. The second, designed for carry-in user instruments, hosts also a spectrometer for pump-probe resonant x-ray emission and inelastic spectroscopy experiments with a sub-eV energy resolution. A Kirkpatrick-Baez active optics system provides a minimum focus of ∼ 20 × 20 μ m2 FWHM at the sample. A pump laser setup, synchronized with the FEL-laser seeding system, delivers sub-picosecond pulses with photon energies ranging from the mid-IR to near-UV for optical pump-FEL probe experiments with a minimal pump-probe jitter of few femtoseconds. The overall combination of these features renders MagneDyn a unique state-of-the-art tool for studying ultrafast magnetic and resonant emission phenomena in solids. [ABSTRACT FROM AUTHOR]

This paper describes how to efficiently solve time‐dependent X‐ray dynamic diffraction problems in distorted crystals with a fast Fourier transform based beam propagation method. Examples are given of using the technique to simulate the propagation of X‐ray beams in deformed crystals in space and time domains relevant to the cavity‐based X‐ray free‐electron lasers and X‐ray free‐electron laser self‐seeding systems. [ABSTRACT FROM AUTHOR]

In order to develop a portable flash x-ray source, a compact explosive pulsed power source based on an explosive-driven ferroelectric generator (EDFEG) is investigated numerically and experimentally in this paper. The EDFEG is used as a primary power supply to charge a pulse capacitor, and then the capacitor outputs high current through an inductor and an electrical exploding opening switch (EEOS). Finally, a high voltage fast pulse is generated on a diode, which generates x rays. A circuit model was built to analyze the performance of this compact pulsed power source. A portable flash x-ray generator prototype was constructed in our laboratory. The typical experimental results illustrated that after metal wires of the EEOS exploded, a high-voltage fast pulse with a peak value of 180 kV, a rise time of 2.8 ns, and a pulse width of 30 ns was generated on the x-ray diode. Meanwhile, an x-ray pulse with a pulse width of 19 ns, a focus of about 1 mm, and a dose of 100 mR at 15 cm was obtained. [ABSTRACT FROM AUTHOR]

The Paul Scherrer Institute is a unique Swiss research institute that operates five large-scale research facilities in which different types of particles, such as electrons, protons, neutrons, pions and muons, are accelerated or produced. Depending on the facility and location, the operational radiation protection has to deal with challenging measurements of mixed radiation fields, which can be in addition pulsed and of high-energy. In this article, we provide insight into the associated demands and challenges using two examples with different requirements for the monitoring technology. Using the example of the high-intensity proton accelerator (HIPA), the measurement technology around high-energy accelerators is examined in more detail. On the other hand, the problems of measuring technology for pulsed radiation and its dynamic range are discussed using the example of the Swiss X-ray free electron laser SwissFEL. The aim of this paper is to highlight the different requirements and technical challenges in radiation measurements for such complex facilities and, thus, to raise awareness and provide a stimulus for further developments in measurement technology. • Operational radiation protection must deal with various complex radiation fields. • Ensure the correct radiation protection measurement technology is used. • Not all rem counters are adequate for use around existing high-energy accelerators. • At pulsed radiation fields the actual dose can be underestimated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Advanced synchrotron radiation sources are major facilities for analyzing the formation and evolution of material structure in multidisciplinary research, owing to their high luminosity, low emittance, wide energy bandwidth and other characteristics. In China, several advanced synchrotron radiation sources are under construction, including the HEPS (High Energy Photon Source) and SHINE (Shanghai high repetition rate X-ray Free Electron Laser and extreme light facility). These facilities are poised to become major multidisciplinary research platforms in China. To meet the requirements of pixel detectors in these facilities, dedicated pixel readout chips are being developed, including HEPS-BPIX and HYLITE. This paper presents a high-speed serializer circuit developed in a commercial 130-nm CMOS technology for the full-scale (128 × 128) pixel readout chip of HYLITE, which requires a data rate of 4 Gbps currently. The serializer consists of a 16-to-1 binary-tree multiplexer, a ring-oscillating-based phase-locked loop (RO-PLL) and a current-mode logic driving stage with a multi-stage pre-amplifier. Test results demonstrate its expected functionality within a wide operating range from 0.52 Gbps to 5.5 Gbps. At 5.12 Gbps, the measured jitter values are about 2 ps for random jitter, 20 ps for deterministic jitter, and 47 ps for total jitter with a 10−12 bit error rate. Additionally, the horizontal and vertical eye openings are 0.84 UI and 72%, respectively. These positive results indicate that the serializer meets the requirements of HYLITE. [ABSTRACT FROM AUTHOR]

A 6 MeV hybrid RF e-gun is currently driving a THz FEL in Ariel University. Ultra-fast electron diffraction (UED) experimental plans are currently in progress in the center, and therefore, a secondary parallel beam line is required. The addition of a secondary beamline using a single e-gun can be achieved using a dogleg section. However, the high-quality beam parameters such as emittance and electron bunch duration are significantly distorted after passing a dispersive section, such as a dogleg section, making the e-beam quality insufficient for UED experiments. In this paper, we suggest an optimization method, for the reconstruction of the beam quality after the dogleg using realistic quad-fields and sextupoles. Full 3D general particle tracer simulations of this secondary beamline were used in the optimization procedure using realistic field-maps and fringe fields of the quadrupoles, which were designed in-house, and their 3D field-maps were exported using computer simulation technology. Significantly improved beam parameters were obtained using the real quadrupoles field profile combined with an optimization procedure using a large number of electron optical optimization variables. [ABSTRACT FROM AUTHOR]

Single‐particle imaging with X‐ray free‐electron lasers depends crucially on algorithms that merge large numbers of weak diffraction patterns despite missing measurements of parameters such as particle orientations. The expand–maximize–compress (EMC) algorithm is highly effective at merging single‐particle diffraction patterns with missing orientation values, but most implementations exhaustively sample the space of missing parameters and may become computationally prohibitive as the number of degrees of freedom extends beyond orientation angles. This paper describes how the EMC algorithm can be modified to employ Metropolis Monte Carlo sampling rather than grid sampling, which may be favorable for reconstruction problems with more than three missing parameters. Using simulated data, this variant is compared with the standard EMC algorithm. [ABSTRACT FROM AUTHOR]

Microwave undulators (MUs) have great potential to be an alternative solution to permanent magnet undulators in a free electron laser (FEL) when shorter undulator periods are required. In this paper, the factors that affect the choice of the high-power drive sources were studied via a Ka-band cavity-type MU with a corrugated waveguide proposed for the CompactLight X-ray FEL. They include the technology of the high-power vacuum electronic devices, the quality factor of the MU cavity that was demonstrated by prototyping a short section of the MU structure, and the beam dynamic study of the electrons' trajectories inside the MU. It showed that at high beam energy, a high-power oscillator is feasible to be used as the drive source. At low beam energy, the maximum transverse drift distance becomes larger therefore an amplifier has to be used to minimize the drift distance of the electrons by controlling the injection phase. [ABSTRACT FROM AUTHOR]

The paper deals with X-ray free-electron lasers (FEL) with the variable deflection parameter of undulators with the electron buncher and harmonic amplifier. The analysis is given to the power evolution in the harmonic lasing self-seeded free electron laser (HLSS FEL), which is compared with the self-amplified spontaneous emission (SASE). Exact analytic expressions are used for Bessel coefficients in real beams and undulators as well as the analytic description of the FEL power evolution. The latest FELs with the variable deflection parameter are considered herein, namely: FLASH-II, European XFEL, SACLA and SwissFEL. A comparative analysis is presented for the FEL operation in the HLSS and SASE modes. The results of the analytical simulation of the FEL spectral parameters are in good agreement with the experimental data. It is shown that the HLSS FEL power grows more rapidly than during the self-amplified spontaneous emission at the same wavelength. The obtained results are compared with the experimental data on the FLASH-II FEL. It is found that the electron beam in the SACLA X-Ray FEL, which has a large energy spread, does not allow to use harmonic cascade amplification. As for the SwissFEL, the small spread in energy and the beam emittance provide an effective electron bunching on the second-harmonic wavelength. This allows reaching the HLSS FEL saturation power 10 m earlier than in the SASE, the radiation power and wavelength being constant. The calculations show that the effective harmonic amplification is also possible in the European XFEL. [ABSTRACT FROM AUTHOR]

Penetrating, high‐energy synchrotron X‐rays are in strong demand, particularly for high‐pressure research in physics, chemistry and geosciences, and for materials engineering research under less extreme conditions. A new high‐energy wiggler beamline P61 has been constructed to meet this need at PETRA III in Hamburg, Germany. The first part of the paper offers an overview of the beamline front‐end components and beam characteristics. The second part describes the performance of the instrumentation and the latest developments at the P61B endstation. Particular attention is given to the unprecedented high‐energy photon flux delivered by the ten wigglers of the PETRA III storage ring and the challenges faced in harnessing this amount of flux and heat load in the beam. Furthermore, the distinctiveness of the world's first six‐ram Hall‐type large‐volume press, Aster‐15, at a synchrotron facility is described for research with synchrotron X‐rays. Additionally, detection schemes, experimental strategies and preliminary data acquired using energy‐dispersive X‐ray diffraction and radiography techniques are presented. [ABSTRACT FROM AUTHOR]

A wiggler is a high‐power insertion device that was used in the past to produce a smooth wide‐band X‐ray spectrum. It is widely believed that on low‐emittance synchrotrons this X‐ray source loses its spatial and spectral homogeneity and therefore becomes less ideal than a scanning undulator. In this paper, we report on experimental and computational studies of an in‐vacuum wiggler installed on the first fourth‐generation synchrotron MAX IV. We investigate how several physical parameters affect the wiggler spectrum and propose a combination of a few of them that results in significant spectral smoothing. We also examine EXAFS spectra for possible distortions originating from the source imperfection. For this purpose, we scrutinize samples of various homogeneity. We conclude that wigglers are still an appropriate class of insertion devices, also on low‐emittance synchrotrons. [ABSTRACT FROM AUTHOR]

Extremely short X-ray pulses in the attosecond (as) range are important tools for ultrafast dynamics, high resolution microscopy, and nuclear dynamics study. In this paper, we numerically examine the generation of gigawatt (GW) mode-locked (ML) multichromatic X-rays using the parameters of the Pohang Accelerator Laboratory (PAL)-X-ray free electron laser (XFEL), the Korean XFEL. In this vein, we analyze the ML-FEL [Thompson and McNeil, Phys. Rev. Lett. 100, 203901 (2008)] and mode-locked afterburner (MLAB) FEL [Dunning et al., Phys. Rev. Lett. 110, 104801 (2013)] schemes on the hard X-ray beamline of the PAL-XFEL. Using the ML scheme, we numerically demonstrate a train of radiation pulses in the hard X-ray (photon energy ~12.4 keV) with 3.5GW power and 16 as full-width half maximum (FWHM) pulse duration. On the other hand, using the MLAB scheme, a train of radiation pulses with 3GW power and 1 as FWHM (900 zs in RMS) pulse duration has been obtained at 12.4 keV photon energy. Both schemes generate broadband, discrete, and coherent spectrum compared to the XFEL's narrowband spectrum. Furthermore, the effect of slotted foil is also studied first time on the MLAB-FEL output. Numerical comparisons show that the temporal structure of the MLAB-FEL output can be improved significantly by the use of the slotted foil. Such short X-ray pulses at XFEL facilities will allow the studies of electron-nuclear and nuclear dynamics in atoms or molecules, and the broadband radiation will substantially improve the efficiency of the experimental techniques such as Xray crystallography and spectroscopy, paving the way for outstanding progress in biology and material science. [ABSTRACT FROM AUTHOR]

In this paper, an analytical theory for the diffraction of a Bessel beam of arbitrary order Jl(κr) on a 2D amplitude grating is presented. The diffraction pattern behind the grating turned out to be more complicated in comparison with the classical Talbot effect observed under illumination by a plane wave. In particular, the patterns in the main and fractional Talbot planes under certain conditions that are found in the article, are lattices of ring microbeams, the diameters of which depend on the period of the grating, the diameter of the illuminating beam, the number of the Talbot plane, and the topological charge l. For the rings near the optical axis, the latter reproduces l of the illuminating beam. The diffraction patterns observed in experiments on the Novosibirsk free electron laser behind gratings with periods of 1 to 6 mm, illuminated by zero- to second-order Bessel beams at a radiation wavelength λ = 141 µm, are in good agreement with both theoretical predictions and numerical calculations. We emphasize that an analytical theory based on the scalar theory of diffraction perfectly describes resulting diffraction patterns with hole diameters down to 0.25 mm, which are less than 2λ, when, formally speaking, the scalar theory becomes incorrect. Since the Laguerre–Gaussian beams can be represented as a superposition of Bessel beams, results of this paper can be applied to analysis of the Talbot effect with the Laguerre–Gaussian beams. A regular lattice of ring-like vortex microbeams, which can be formed in the Talbot planes, can be applied, for example, to creation of a lattice of optical traps, transmission of orbital angular momentum to elements of micromechanical devices, and to launching surface plasmon polaritons on an array of metal wires by 'the end-fire coupling technique'. [ABSTRACT FROM AUTHOR]