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Intense femtosecond x-ray pulses produced by an x-ray free-electron laser can trigger irreversible structural transitions in crystalline solids. For instance, irradiation of diamond can lead to graphitization and, at higher deposited doses, to amorphization. Our Monte Carlo simulations of irradiated diamond under realistic experimental conditions demonstrate that triggering graphitization or other phase transitions with hard x-ray photons can be challenging due to the ballistic escape of photoelectrons out of the beam focus. Decisive parameter here is the photoelectron range in proportion to the focal beam size. For future experiments on x-ray-induced transitions, such dedicated simulations of ballistic transport preceding the beamtime will be necessary. They can predict experimental conditions under which the desired distribution of the absorbed x-ray dose in the irradiated solid can be achieved., Comment: 15 pages, 2 figures, 1 table. Submitted to Phys. Rev. B

Using X-ray free electron laser (XFEL) radiation to conduct an X-ray pump X-ray probe experiment, we studied strongly ionized water as part of our ongoing work on radiation damage. After irradiance with a pump pulse with a nominal fluence of ~$5 \times 10^5$ J/cm$^2$, we observed for pump-probe delays of 75 fs and longer an unexpected structural rearrangement, exhibiting a characteristic length scale of ~9 \r{A}. Simulations suggest that the experiment probes a superposition of ionized water in two distinct regimes. In the first, fluences expected at the X-ray focus create nearly completely ionized water, which as a result becomes effectively transparent to the probe. In the second regime, out of focus pump radiation produces O$^{1+}$ and O$^{2+}$ ions, which rearrange due to Coulombic repulsion over 10s of fs. Importantly, structural changes in the low fluence regime have implications for the design of two-pulse X-ray experiments that aim to study unperturbed liquid samples. Our simulations account for two key observations in the experimental data: the decrease in ambient water signal and an increase in low-angle X-ray scattering. They cannot, however, account for the experimentally observed 9 \r{A} feature. A satisfactory account of this feature presents a new challenge for theory., Comment: 24 main text pages, 6 supplement pages (30 total), 4 main text figures, 3 supplemental figures, 2 supplemental tables

X-ray laser-induced structural changes in silicon undergoing femtosecond melting have been investigated by using an x-ray pump-x-ray probe technique. The experimental results for different initial sample temperatures reveal that the onset time and the speed of the atomic disordering are independent of the initial temperature, suggesting that equilibrium atomic motion in the initial state does not play a pivotal role in the x-ray-induced ultrafast melting. By comparing the observed time-dependence of the atomic disordering and the dedicated theoretical simulations, we interpret that the energy transfer from the excited electrons to ions via electron-ion coupling (thermal effect) as well as a strong modification of the interatomic potential due to electron excitations (non-thermal effect) trigger the ultrafast atomic disordering. Our finding of the interplay of thermal and non-thermal effects in the x-ray-induced melting demonstrates that accurate modeling of intense x-ray interactions with matter is essential to ensure a correct interpretation of experiments using intense x-ray laser pulses.

Studies of light-induced demagnetization started with the experiment performed by Beaupaire et al. on nickel. Here, we present theoretical predictions for X-ray induced demagnetization of nickel, with X-ray photon energies tuned to its $M_3$ and $L_3$ absorption edges. We show that the specific feature in the density of states of the d-band of Ni, a sharp peak located just above the Fermi level, strongly influences the change of the predicted magnetic signal, making it stronger than in the previously studied case of cobalt. We believe that this finding will inspire future experiments on magnetic processes in X-ray irradiated nickel., Comment: 6 pages, 5 figures (10 panels), 1 table, 30 references; pdfRevTeX class; double-column formatting

X-ray diffraction of silicon irradiated with tightly focused femtosecond x-ray pulses (photon energy: 11.5 keV, pulse duration: 6 fs) was measured at various x-ray intensities up to $4.6\times10^{19}$ W/cm$^2$. The measurement reveals that the diffraction intensity is highly suppressed when the x-ray intensity reaches of the order of $10^{19}$ W/cm$^2$. With a dedicated simulation, we confirm the observed reduction of the diffraction intensity is attributed to the femtosecond change in individual atomic scattering factors due to the ultrafast creation of highly ionized atoms through photoionization, Auger decay, and subsequent collisional ionization. We anticipate that this ultrafast reduction of atomic scattering factor will be a basis for new x-ray nonlinear techniques, such as pulse shortening and contrast variation x-ray scattering.

Magnetization dynamics triggered with ultrashort laser pulses has been attracting significant attention, with strong focus on the dynamics excited by VIS/NIR pulses. Only recently, strong magnetic response in solid materials induced by intense X-ray pulses from free-electron lasers (FELs) has been observed. The exact mechanisms that trigger the X-ray induced demagnetization are not yet fully understood. They are subject of on-going experimental and theoretical investigations. Here, we present a theoretical analysis of electronic processes occurring during demagnetization of Co multilayer system irradiated by X-ray pulses tuned to L$_3$-absorption edge of cobalt. We show that, similarly as in the case of X-ray induced demagnetization at M-edge of Co, electronic processes play a predominant role in the demagnetization until the pulse fluence does not exceed the structural damage threshold. The impact of electronic processes can reasonably well explain the available experimental data, without a need to introduce the mechanism of stimulated elastic forward scattering., Comment: 10 pages, 4 figures (7 panels), 57 references; pdfRevTeX class; double column formatting; two appendices and 18 references added; title changed; author-created version submitted to and accepted/published in Physical Review B journal. The text of the appendices (including detailed description of the model used) is similar to some parts of arXiv:2202.13845

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$\times$10$^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 $\sim$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 modifies 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 \AA 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.

We review the results of our research on damage mechanisms in materials irradiated with femtosecond free-electron-laser (FEL) pulses. They were obtained using our hybrid approach, XTANT (X-ray-induced Thermal And Nonthermal Transitions). Various damage mechanisms are discussed with respect to the pulse fluence and material properties on examples of diamond, amorphous carbon, C60 crystal, and silicon. We indicate conditions: producing thermal melting of targets as a result of electron-ion energy exchange; nonthermal phase transitions due to modification of the interatomic potential; Coulomb explosion due to accumulated net charge in finite-size systems; spallation or ablation at higher fluences due to detachment of sample fragments; and warm dense matter formation. Transient optical coefficients are compared with experimental data whenever available, proving the validity of our modeling approach. Predicted diffraction patterns can be compared with the results of ongoing or future FEL experiments. Limitations of our model and possible future directions of development are outlined., Comment: This brief review is submitted for publication

Diamond bulk irradiated with a free-electron laser pulse of 6100 eV photon energy, 5 fs duration, at the $\sim 19-25$ eV/atom absorbed doses, is studied theoretically on its way to warm dense matter state. Simulations with our hybrid code XTANT show disordering on sub-100 fs timescale, with the diffraction peak (220) vanishing faster than the peak (111). The warm dense matter formation proceeds as a nonthermal damage of diamond with the band gap collapse triggering atomic disordering. Short-living graphite-like state is identified during a few femtoseconds between the disappearance of (220) peak and the disappearance of (111) peak. The results obtained are compared with the data from the recent experiment at SACLA, showing qualitative agreement. Challenges remaining for the accurate modeling of the transition of solids to warm dense matter state and proposals for supplementary measurements are discussed in detail., Comment: Preprint, submitted

In the present work, a theoretical study of electron-phonon (electron-ion) coupling rates in semiconductors driven out of equilibrium is performed. Transient change of optical coefficients reflects the band gap shrinkage in covalently bonded materials, and thus, the heating of atomic lattice. Utilizing this dependence, we test various models of electron-ion coupling. The simulation technique is based on tight-binding molecular dynamics. Our simulations with the dedicated hybrid approach (XTANT) indicate that the widely used Fermi's golden rule can break down describing material excitation on femtosecond time scales. In contrast, dynamical coupling proposed in this work yields a reasonably good agreement of simulation results with available experimental data.

Soft x-rays were applied to induce graphitization of diamond through a non-thermal solid-to-solid phase transition. This process was observed within poly-crystalline diamond with a time-resolved experiment using ultrashort soft x-ray pulses of duration 52.5 fs and cross correlated by an optical pulse of duration 32.8 fs. This scheme enabled for the first time the measurement of a phase transition on a timescale of ~150 fs. Excellent agreement between experiment and theoretical predictions was found, using a dedicated code that followed the non-equilibrium evolution of the irradiated diamond including all transient electronic and structural changes. These observations confirm that soft x-rays can induce a non-thermal ultrafast solid-to-solid phase transition on a hundred femtosecond timescale., Comment: 27 pages, 17 figures (includes supplementary materials)

The irradiation of an atomic cluster with a femtosecond x-ray free-electron laser pulse results in a nanoplasma formation. This typically occurs within a few hundreds femtoseconds. By this time the x-ray pulse is over, and the direct photoinduced processes no longer contributing. All created electrons within the nanoplasma are thermalized. The nanoplasma thus formed is a mixture of atoms, electrons and ions of various charges. While expanding, it is undergoing electron impact ionization and three-body recombination. Below we present a hydrodynamic model to describe the dynamics of such multi-component nanoplasma. The model equations are derived by taking the moments of the corresponding Boltzmann kinetic equations. We include the equations obtained, together with the source terms due to electron impact ionization and three-body recombination, in our hydrodynamic solver. Model predictions for a test case: expanding spherical Ar nanoplasma are obtained. With this model we complete the two-step approach to simulate x-ray created nanoplasmas, enabling computationally efficient simulations of their picosecond dynamics. Moreover, the hydrodynamic framework including collisional processes can be easily extended for other source terms and then applied to follow relaxation of any finite non-isothermal multi-component nanoplasma with its components relaxed into local thermodynamic equilibrium., Comment: 12 pages, 4 figures. This article has been accepted by Physics of Plasmas. After it is published, it will be found at http://scitation.aip.org/content/aip/journal/pop

Femtosecond X-ray irradiation of solids excites energetic photoelectrons that thermalize on a timescale of a few hundred femtoseconds. The thermalized electrons exchange energy with the lattice and heat it up. Experiments with X-ray free-electron lasers have unveiled so far the details of the electronic thermalization. In this work we show that the data on transient optical reflectivity measured in GaAs irradiated with femtosecond X-ray pulses can be used to follow electron-lattice relaxation up to a few tens of picoseconds. With a dedicated theoretical framework, we explain the so far unexplained reflectivity overshooting as a result of band-gap shrinking. We also obtain predictions for a timescale of electron-lattice thermalization, initiated by conduction band electrons in the temperature regime of a few eVs. The conduction and valence band carriers were then strongly non-isothermal. The presented scheme is of general applicability and can stimulate further studies of relaxation within X-ray excited narrow band-gap semiconductors., Comment: 15 pages, 2 figures

As it is known from visible light experiments, silicon under femtosecond pulse irradiation can undergo the so-called 'nonthermal melting' if the density of electrons excited from the valence to the conduction band overcomes a certain critical value. Such ultrafast transition is induced by strong changes in the atomic potential energy surface, which trigger atomic relocation. However, heating of a material due to the electron-phonon coupling can also lead to a phase transition, called 'thermal melting'. This thermal melting can occur even if the excited-electron density is much too low to induce non-thermal effects. To study phase transitions, and in particular, the interplay of the thermal and nonthermal effects in silicon under a femtosecond x-ray irradiation, we propose their unified treatment by going beyond the Born-Oppenheimer approximation within our hybrid model based on tight binding molecular dynamics. With our extended model we identify damage thresholds for various phase transitions in irradiated silicon. We show that electron-phonon coupling triggers the phase transition of solid silicon into a low-density liquid phase if the energy deposited into the sample is above $\sim0.65$ eV per atom. For the deposited doses of over $\sim0.9$ eV per atom, solid silicon undergoes a phase transition into high-density liquid phase triggered by an interplay between electron-phonon heating and nonthermal effects. These thresholds are much lower than those predicted with the Born-Oppenheimer approximation ($\sim2.1$ eV/atom), and indicate a significant contribution of electron-phonon coupling to the relaxation of the laser-excited silicon. We expect that these results will stimulate dedicated experimental studies, unveiling in detail various paths of structural relaxation within laser-irradiated silicon.

The interaction of a free-electron-laser pulse with a moderate or large size cluster is known to create a quasi-neutral nanoplasma, which then expands on hydrodynamic timescale, i.e., $>1$ ps. To have a better understanding of ion and electron data from experiments derived from laser-irradiated clusters, one needs to simulate cluster dynamics on such long timescales for which the molecular dynamics approach becomes inefficient. We therefore propose a two-step Molecular Dynamics-Hydrodynamic scheme. In the first step we use molecular dynamics code to follow the dynamics of an irradiated cluster until all the photo-excitation and corresponding relaxation processes are finished and a nanoplasma, consisting of ground-state ions and thermalized electrons, is formed. In the second step we perform long-timescale propagation of this nanoplasma with a computationally efficient hydrodynamic approach. In the present paper we examine the feasibility of a hydrodynamic two-fluid approach to follow the expansion of spherically symmetric nanoplasma, without accounting for the impact ionization and three-body recombination processes at this stage. We compare our results with the corresponding molecular dynamics simulations. We show that all relevant information about the nanoplasma propagation can be extracted from hydrodynamic simulations at a significantly lower computational cost when compared to a molecular dynamics approach. Finally, we comment on the accuracy and limitations of our present model and discuss possible future developments of the two-step strategy., Comment: 14 pages, 6 figures

The charged environment within a dense plasma leads to the phenomenon of ionization potential depression (IPD) for ions embedded in the plasma. Accurate predictions of the IPD effect are of crucial importance for modeling atomic processes occurring within dense plasmas. Several theoretical models have been developed to describe the IPD effect, with frequently discrepant predictions. Only recently, first experiments on IPD in Al plasma have been performed with an x-ray free-electron laser (XFEL), where their results were found to be in disagreement with the widely-used IPD model by Stewart and Pyatt. Another experiment on Al, at the Orion laser, showed disagreement with the model by Ecker and Kr\"oll. This controversy shows a strong need for a rigorous and consistent theoretical approach to calculate the IPD effect. Here we propose such an approach: a two-step Hartree-Fock-Slater model. With this parameter-free model we can accurately and efficiently describe the experimental Al data and validate the accuracy of standard IPD models. Our model can be a useful tool for calculating atomic properties within dense plasmas with wide-ranging applications to studies on warm dense matter, shock experiments, planetary science, inertial confinement fusion and studies of non-equilibrium plasmas created with XFELs., Comment: 13 pages, 9 figures, to be published in Phys. Rev. X; added references [46,47]

Coherent diffraction imaging (CDI) of single molecules at atomic resolution is a major goal for the x-ray free electron lasers (XFELs). However, during an imaging pulse, the fast laser-induced ionization may strongly affect the recorded diffraction pattern of the irradiated sample. The radiation tolerance of the imaged molecule should then be investigated 'a priori' with a dedicated simulation tool. The continuum approach is a powerful tool for modeling the evolution of irradiated large systems consisting of more than a few hundred thousand atoms. However, this method follows the evolution of average single-particle densities, and the experimentally recorded intensities reflect the spatial two-particle correlations. The information on these correlations is then inherently not accessible within the continuum approach. In this paper we analyze this limitation of continuum models and discuss the applicability of continuum models for imaging studies. We propose a formula to calculate scattered intensities (including both elastic and inelastic scattering) from the estimates obtained with a single-particle continuum model. We derive this formula for systems under conditions typical for CDI studies with XFELs.

We apply Boltzmann equations for modelling the radiation damage in samples irradiated by photons from free electron laser (FEL). We test this method in a study case of a spherically symmetric xenon cluster irradiated with VUV FEL photons. The results obtained demonstrate the potential of the Boltzmann method for describing the complex and non-equilibrium dynamics of samples exposed to FEL radiation., Comment: 31 pages, 11 figures

Secondary electron cascades are responsible for significant ionizations in macroscopic samples during irradiation with X-rays. A quantitative analysis of these cascades is needed, e.g. for assessing damage in optical components at X-ray free-electron lasers, and for understanding damage in samples exposed to the beam. Here we present results from Monte Carlo simulations, showing the space-time evolution of secondary electron cascades in diamond. These cascades follow the impact of a single primary electron at energies between 0.5-12 keV, representing the usual range for photoelectrons. The calculations describe the secondary ionizations caused by these electrons, the three-dimensional evolution of the electron cloud, and monitor the equivalent instantaneous temperature of the free-electron gas as the system cools during expansion. The dissipation of the impact energy proceeds predominantly through the production of secondary electrons whose energies are comparable to the binding energies of the valence (40-50 eV) and the core electrons (300 eV) in accordance with experiments and the models of interactions. The electron cloud generated by a 12 keV electron is strongly anisotropic in the early phases of the cascade (t <= 1 fs). At later times, the sample is dominated by low energy electrons, and these are scattered more isotropically by atoms in the sample. The results show that the emission of secondary electrons approaches saturation within about 100 fs, following the primary impact. At an impact energy of 12 keV, the total number of electrons liberated in the sample is <= 400 at 1000 fs. The results provide an understanding of ionizations by photoelectrons, and extend earlier models on low-energy electron cascades (E=0.25 keV, [ziaja,ziaja2]) to the higher energy regime of the photoelectrons., Comment: 17 pages, latex, 10 figures

Predictions for g_1(x,Q^2) at low Q^2 are obtained in the framework of the GVMD model. Contributions from both light and heavy vector mesons are evaluated. The DHGHY sum rule is employed to fix the magnitude of the light vector meson contribution to g_1, using the recent measurements in the region of baryonic resonances. The DHGHY moment function is calculated. Predictions are compared to the data., Comment: 5 pages, including 3 postscript figures; presented by B. Bade{\l}ek at 10th International Workshop on Deep Inelastic Scattering (DIS2002), Cracow, 30 April - 4 May 2002

Theoretical predictions show that at low values of Bjorken $x$ the spin structure function, $g_1$ is influenced by large logarithmic corrections, $ln^2(1/x)$, which may be predominant in this region. These corrections are also partially contained in the NLO part of the standard DGLAP evolution. Here we calculate the non-singlet component of the nucleon structure function, $g_1^{NS}=g_1^p-g_1^n$, and its first moment, using a unified evolution equation. This equation incorporates the terms describing the NLO DGLAP evolution and the terms contributing to the $ln^2(1/x)$ resummation. In order to avoid double counting in the overlapping regions of the phase-space, a unique way of including the NLO terms into the unified evolution equation is proposed. The scheme-independent results obtained from this unified evolution are compared to the NLO fit to experimental data, GRSV'2000. Analysis of the first moments of $g_1^{NS}$ shows that the unified evolution including the $ln^2(1/x)$ resummation goes beyond the NLO DGLAP analysis. Corrections generated by double logarithms at low $x$ influence the $Q^2$-dependence of the first moments strongly., Comment: 13 pages, latex, 2 figures; Appendix added

Theoretical predictions for polarized nucleon structure function $g_1(x,Q^2)$ at low $Q^2$ are obtained in the framework of the Generalized Vector Meson Dominance model. Contributions from both light and heavy vector mesons are evaluated. In the photoproduction limit the first moment of $g_1$ is related to the static properties of nucleon via the Drell-Hearn-Gerasimov-Hosoda-Yamamoto sum rule. This property is employed to fix the magnitude of the light vector meson contribution to $g_1$, using the recent measurements in the region of baryonic resonances. Results are compared to the data on $g_1(x,Q^2)$. Finally, the DHGHY moment function $I(Q^2)$ is calculated, and our theoretical predictions are confronted with the recent preliminary data obtained at the Jefferson Laboratory., Comment: 12 pages including 6 postscript figures, corrected ref.22, caption to fig.4 and a few typos

Here we describe model calculations to follow the spatio-temporal evolution of secondary electron cascades in diamond. The band structure of the insulator has been explicitly incorporated into the calculations as it affects ionizations from the valence band. A Monte-Carlo model was constructed to describe the path of electrons following the impact of a single electron of energy E 250 eV. The results show the evolution of the secondary electron cascades in terms of the number of electrons liberated, the spatial distribution of these electrons, and the energy distribution among the electrons as a function of time. The predicted ionization rates (5-13 electrons in 100 fs) lie within the limits given by experiments and phenomenological models. Calculation of the local electron density and the corresponding Debye length shows that the latter is systematically larger than the radius of the electron cloud. This means that the electron gas generated does not represent a plasma in a single impact cascade triggered by an electron of E 250 eV energy. This is important as it justifies the independent-electron approximation used in the model. At 1 fs, the (average) spatial distribution of secondary electrons is anisotropic with the electron cloud elongated in the direction of the primary impact. The maximal radius of the cascade is about 50 A at this time. As the system cools, energy is distributed more equally, and the spatial distribution of the electron cloud becomes isotropic. At 90 fs maximal radius is about 150 A. The Monte-Carlo model described here could be adopted for the investigation of radiation damage in other insulators and has implications for planned experiments with intense femtosecond X-ray sources., Comment: 26 pages, latex, 13 figures

Photoionisation of an atom by X-rays usually removes an inner-shell electron from the atom, leaving behind a perturbed "hollow ion" whose relaxation may take different routes. In light elements, emission of an Auger electron is common. However, the energy and the total number of electrons released from the atom may be modulated by shake-up and shake-off effects. When the inner-shell electron leaves, the outer-shell electrons may find themselves in a state that is not an eigen-state of the atom in its surroundings. The resulting collective excitation is called shake-up. If this process also involves the release of low energy electrons from the outer shell, then the process is called shake-off. It is not clear how significant shake-up and shake-off contributions are to the overall ionisation of biological materials like proteins. In particular, the interaction between the out-going electron and the remaining system depends on the chemical environment of the atom, which can be studied by quantum chemical methods. Here we present calculations on model compounds to represent the most common chemical environments in proteins. The results show that the shake-up and shake-off processes affect about 20% of all emissions from nitrogen, 30% from carbon, 40% from oxygen, and 23% from sulphur. Triple and higher ionisations are rare for carbon, nitrogen and oxygen, but are frequent for sulphur. The findings are relevant to the design of biological experiments at emerging X-ray free-electron lasers., Comment: 14 pages, latex, 1 figure

We have analyzed the cascade of secondary electrons in diamond and amorphous carbon generated by the thermalisation of a single Auger electron. The elastic electron mean free path was calculated as a function of impact energy in the muffin-tin potential approximation. The inelastic scattering cross section and the energy loss of the electron (expressed in terms of differential inverse mean free path) were estimated from two "optical" models, that utilise the measured dielectric constants of the materials. Using these data, a Monte-Carlo model describing the time evolution of the cascade was constructed. The results show that at most around 20-40 secondary cascade electrons are released by a single Auger electron in a macroscopic sample of diamond or amorphous carbon. Consideration of the real band structure of diamond reduces this number further. The release of the cascade electrons happens within the first 100 femtoseconds after the emission of the primary Auger electron. The results have implications to planned experiments with femtosecond X-ray sources., Comment: 18 pages, latex, 9 figures