Application of Boltzmann kinetic equations to model X-ray-created warm dense matter and plasma.

In this review, we describe the application of Boltzmann kinetic equations for modelling warm dense matter and plasma formed after irradiation of solid materials with intense femtosecond X-ray pulses. Classical Boltzmann kinetic equations are derived from the reduced N-particle Liouville equations. They include only single-particle densities of ions and free electrons present in the sample. The first version of the Boltzmann kinetic equation solver was completed in 2006. It could model non-equilibrium evolution of X-ray-irradiated finite-size atomic systems. In 2016, the code was adapted to study plasma created from X-ray-irradiated materials. Additional extension of the code was then also performed, enabling simulations in the hard X-ray irradiation regime. In order to avoid treatment of a very high number of active atomic configurations involved in the excitation and relaxation of X-ray-irradiated materials, an approach called 'predominant excitation and relaxation path' (PERP) was introduced. It limited the number of active atomic configurations by following the sample evolution only along most PERPs. The performance of the Boltzmann code is illustrated in the examples of X-ray-heated solid carbon and gold. Actual model limitations and further model developments are discussed. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Quantifying electron cascade size in various irradiated materials for free-electron laser applications.

Studying electron- and X-ray-induced electron cascades in solids is essential for various research areas at free-electron laser facilities, such as X-ray imaging, crystallography, pulse diagnostics or X-ray-induced damage. To better understand the fundamental factors that define the duration and spatial size of such cascades, this work investigates the electron propagation in ten solids relevant for the applications of X-ray lasers: Au, B4C, diamond, Ni, polystyrene, Ru, Si, SiC, Si3N4 and W. Using classical Monte Carlo simulation in the atomic approximation, we study the dependence of the cascade size on the incident electron or photon energy and on the target parameters. The results show that an electron-induced cascade is systematically larger than a photon-induced cascade. Moreover, in contrast with the common assumption, the maximal cascade size does not necessarily coincide with the electron range. It was found that the cascade size can be controlled by careful selection of the photon energy for a particular material. Photon energy, just above an ionization potential, can essentially split the absorbed energy between two electrons (photo- and Auger), reducing their initial energy and thus shrinking the cascade size. This analysis suggests a way of tailoring the electron cascades for applications requiring either small cascades with a high density of excited electrons or large-spread cascades with lower electron densities.

Delayed Onset and Directionality of X-Ray-Induced Atomic Displacements Observed on Subatomic Length Scales.

Transient structural changes of Al_{2}O_{3} on subatomic length scales following irradiation with an intense x-ray laser pulse (photon energy: 8.70 keV; pulse duration: 6 fs; fluence: 8×10^{2} J/cm^{2}) have been investigated by using an x-ray pump x-ray probe technique. The measurement reveals that aluminum and oxygen atoms remain in their original positions by ∼20 fs after the intensity maximum of the pump pulse, followed by directional atomic displacements at the fixed unit cell parameters. By comparing the experimental results and theoretical simulations, we interpret that electron excitation and relaxation triggered by the pump pulse modify the potential energy surface and drives the directional atomic displacements. Our results indicate that high-resolution x-ray structural analysis with the accuracy of 0.01 Å is feasible even with intense x-ray pulses by making the pulse duration shorter than the timescale needed to complete electron excitation and relaxation processes, which usually take up to a few tens of femtoseconds.

Self-Learning Method for Construction of Analytical Interatomic Potentials to Describe Laser-Excited Materials.

Large-scale simulations using interatomic potentials provide deep insight into the processes occurring in solids subject to external perturbations. The atomistic description of laser-induced ultrafast nonthermal phenomena, however, constitutes a particularly difficult case and has so far not been possible on experimentally accessible length scales and timescales because of two main reasons: (i) ab initio simulations are restricted to a very small number of atoms and ultrashort times and (ii) simulations relying on electronic temperature- (T_{e}) dependent interatomic potentials do not reach the necessary ab initio accuracy. Here we develop a self-learning method for constructing T_{e}-dependent interatomic potentials which permit ultralarge-scale atomistic simulations of systems suddenly brought to extreme nonthermal states with density-functional theory (DFT) accuracy. The method always finds the global minimum in the parameter space. We derive a highly accurate analytical T_{e}-dependent interatomic potential Φ(T_{e}) for silicon that yields a remarkably good description of laser-excited and -unexcited Si bulk and Si films. Using Φ(T_{e}) we simulate the laser excitation of Si nanoparticles and find strong damping of their breathing modes due to nonthermal melting.

Mechanism of single-shot damage of Ru thin films irradiated by femtosecond extreme UV free-electron laser.

Ruthenium is a perspective material to be used for XUV mirrors at free-electron laser facilities. Yet, it is still poorly studied in the context of ultrafast laser-matter interaction. In this work, we present single-shot damage studies of thin Ru films irradiated by femtosecond XUV free-electron laser pulses at FLASH. Ex-situ analysis of the damaged spots, performed by different types of microscopy, shows that the weakest detected damage is surface roughening. For higher fluences we observe ablation of Ru. Combined simulations using Monte-Carlo code XCASCADE(3D) and the two-temperature model reveal that the damage mechanism is photomechanical spallation, similar to the case of irradiating the target with optical lasers. The analogy with the optical damage studies enables us to explain the observed damage morphologies.

Picosecond to microsecond dynamics of X-ray irradiated materials at MHz pulse repetition rate.

Modern X-ray free-electron lasers (XFELs) produce intense femtosecond X-ray pulses able to cause significant damage to irradiated targets. Energetic photoelectrons created upon X-ray absorption, and Auger electrons emitted after relaxation of core-hole states trigger secondary electron cascades, which contribute to the increasing transient free electron density on femtosecond timescales. Further evolution may involve energy and particle diffusion, creation of point defects, and lattice heating. This long-timescale (up to a microsecond) X-ray-induced dynamics is discussed on the example of silicon in two-dimensional geometry. For modeling, we apply an extended Two-Temperature model with electron density dynamics, nTTM, which describes relaxation of an irradiated sample between two successive X-ray pulses, emitted from XFEL at MHz pulse repetition rate. It takes into account ambipolar carrier diffusion, electronic and atomic heat conduction, as well as electron-ion coupling. To solve the nTTM system of equations in two dimensions, we developed a dedicated finite-difference integration algorithm based on Alternating Direction Implicit method with an additional predictor-corrector scheme. We show first results obtained with the model and discuss its possible applications for XFEL optics, detectors, and for diagnostics tools. In particular, the model can estimate the timescale of material relaxation relevant for beam diagnostic applications during MHz operation of contemporary and future XFELs.

Non-thermal structural transformation of diamond driven by x-rays.

Intense x-ray pulses can cause the non-thermal structural transformation of diamond. At the SACLA XFEL facility, pump x-ray pulses triggered this phase transition, and probe x-ray pulses produced diffraction patterns. Time delays were observed from 0 to 250 fs, and the x-ray dose varied from 0.9 to 8.0 eV/atom. The intensity of the (111), (220), and (311) diffraction peaks decreased with time, indicating a disordering of the crystal lattice. From a Debye-Waller analysis, the rms atomic displacements perpendicular to the (111) planes were observed to be significantly larger than those perpendicular to the (220) or (311) planes. At a long time delay of 33 ms, graphite (002) diffraction indicates that graphitization did occur above a threshold dose of 1.2 eV/atom. These experimental results are in qualitative agreement with XTANT+ simulations using a hybrid model based on density-functional tight-binding molecular dynamics.

Density functional tight binding approach utilized to study X-ray-induced transitions in solid materials.

Intense X-ray pulses from free-electron lasers can trigger ultrafast electronic, structural and magnetic transitions in solid materials, within a material volume which can be precisely shaped through adjustment of X-ray beam parameters. This opens unique prospects for material processing with X rays. However, any fundamental and applicational studies are in need of computational tools, able to predict material response to X-ray radiation. Here we present a dedicated computational approach developed to study X-ray induced transitions in a broad range of solid materials, including those of high chemical complexity. The latter becomes possible due to the implementation of the versatile density functional tight binding code DFTB+ to follow band structure evolution in irradiated materials. The outstanding performance of the implementation is demonstrated with a comparative study of XUV induced graphitization in diamond.

Effect of Auger recombination on transient optical properties in XUV and soft X-ray irradiated silicon nitride.

Spatially encoded measurements of transient optical transmissivity became a standard tool for temporal diagnostics of free-electron-laser (FEL) pulses, as well as for the arrival time measurements in X-ray pump and optical probe experiments. The modern experimental techniques can measure changes in optical coefficients with a temporal resolution better than 10 fs. This, in an ideal case, would imply a similar resolution for the temporal pulse properties and the arrival time jitter between the FEL and optical laser pulses. However, carrier transport within the material and out of its surface, as well as carrier recombination may, in addition, significantly decrease the number of carriers. This would strongly affect the transient optical properties, making the diagnostic measurement inaccurate. Below we analyze in detail the effects of those processes on the optical properties of XUV and soft X-ray irradiated Si[Formula: see text]N[Formula: see text], on sub-picosecond timescales. Si[Formula: see text]N[Formula: see text] is a wide-gap insulating material widely used for FEL pulse diagnostics. Theoretical predictions are compared with the published results of two experiments at FERMI and LCLS facilities, and with our own recent measurement. The comparison indicates that three body Auger recombination strongly affects the optical response of Si[Formula: see text]N[Formula: see text] after its collisional ionization stops. By deconvolving the contribution of Auger recombination, in future applications one could regain a high temporal resolution for the reconstruction of the FEL pulse properties measured with a Si[Formula: see text]N[Formula: see text]-based diagnostics tool.

Femtosecond laser produced periodic plasma in a colloidal crystal probed by XFEL radiation.

With the rapid development of short-pulse intense laser sources, studies of matter under extreme irradiation conditions enter further unexplored regimes. In addition, an application of X-ray Free-Electron Lasers (XFELs) delivering intense femtosecond X-ray pulses, allows to investigate sample evolution in IR pump - X-ray probe experiments with an unprecedented time resolution. Here we present a detailed study of the periodic plasma created from the colloidal crystal. Both experimental data and theory modeling show that the periodicity in the sample survives to a large extent the extreme excitation and shock wave propagation inside the colloidal crystal. This feature enables probing the excited crystal, using the powerful Bragg peak analysis, in contrast to the conventional studies of dense plasma created from bulk samples for which probing with Bragg diffraction technique is not possible. X-ray diffraction measurements of excited colloidal crystals may then lead towards a better understanding of matter phase transitions under extreme irradiation conditions.

X-ray induced damage of B4C-coated bilayer materials under various irradiation conditions.

In this report, we analyse X-ray induced damage of B4C-coated bilayer materials under various irradiation geometries, following the conditions of our experiment performed at the free-electron-laser facility SACLA. We start with the discussion of structural damage in solids and damage threshold doses for the experimental system components: B4C, SiC, Mo and Si. Later, we analyze the irradiation of the experimentally tested coated bilayer systems under two different incidence conditions of a linearly polarized X-ray pulse: (i) grazing incidence, and (ii) normal incidence, in order to compare quantitatively the effect of the pulse incidence on the radiation tolerance of both systems. For that purpose, we propose a simple theoretical model utilizing properties of hard X-ray propagation and absorption in irradiated materials and of the following electron transport. With this model, we overcome the bottleneck problem of large spatial scales, inaccessible for any existing first-principle-based simulation tools due to their computational limitations for large systems. Predictions for damage thresholds obtained with the model agree well with the available experimental data. In particular, they confirm that two coatings tested: 15 nm B4C/20 nm Mo on silicon wafer and 15 nm B4C/50 nm SiC on silicon wafer can sustain X-ray irradiation at the fluences up to ~10 µJ/µm2, when exposed to linearly polarized 10 keV X-ray pulse at a grazing incidence angle of 3 mrad. Below we present the corresponding theoretical analysis. Potential applications of our approach for design and radiation tolerance tests of multilayer components within X-ray free-electron-laser optics are indicated.