Molecular-dynamics approach for studying the nonequilibrium behavior of x-ray-heated solid-density matter

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'.

Plasma environmental effects in the atomic structure for simulating x-ray free-electron-laser-heated solid-density matter

High energy density (HED) matter exists extensively in the Universe, and it can be created with extreme conditions in laboratory facilities such as x-ray free-electron lasers (XFEL). In HED matter, the electronic structure of individual atomic ions is influenced by a dense plasma environment, and one of the most significant phenomena is the ionization potential depression (IPD). Incorporation of the IPD effects is of great importance in accurate modeling of dense plasmas. All theoretical treatments of IPD so far have been based on the assumption of local thermodynamic equilibrium, but its validity is questionable in ultrafast formation dynamics of dense plasmas, particularly when interacting with intense XFEL pulses. A treatment of transient IPD, based on an electronic-structure calculation of an atom in the presence of a plasma environment described by classical particles, has recently been proposed [Phys. Rev. E 103, 023203 (2021)2470-004510.1103/PhysRevE.103.023203], but its application to and impact on plasma dynamics simulations have not been investigated yet. In this work, we extend XMDYN, a hybrid quantum-classical approach combining Monte Carlo and molecular dynamics, by incorporating the proposed IPD treatment into plasma dynamics simulations. We demonstrate the importance of the IPD effects in theoretical modeling of aluminum dense plasmas by comparing two XMDYN simulations: one with electronic-structure calculations of isolated atoms (without IPD) and the other with those of atoms embedded in a plasma (with IPD). At equilibrium, the mean charge obtained in the plasma simulation with IPD is in good agreement with the full quantum-mechanical average-atom model. The present approach promises to be a reliable tool to simulate the creation and nonequilibrium evolution of dense plasmas induced by ultraintense and ultrashort XFEL pulses.

Transient ionization potential depression in nonthermal dense plasmas at high x-ray intensity

The advent of x-ray free-electron lasers (XFELs), which provide intense ultrashort x-ray pulses, has brought a new way of creating and analyzing hot and warm dense plasmas in the laboratory. Because of the ultrashort pulse duration, the XFEL-produced plasma will be out of equilibrium at the beginning, and even the electronic subsystem may not reach thermal equilibrium while interacting with a femtosecond timescale pulse. In the dense plasma, the ionization potential depression (IPD) induced by the plasma environment plays a crucial role for understanding and modeling microscopic dynamical processes. However, all theoretical approaches for IPD have been based on local thermal equilibrium (LTE), and it has been controversial to use LTE IPD models for the nonthermal situation. In this work, we propose a non-LTE (NLTE) approach to calculate the IPD effect by combining a quantum-mechanical electronic-structure calculation and a classical molecular dynamics simulation. This hybrid approach enables us to investigate the time evolution of ionization potentials and IPDs during and after the interaction with XFEL pulses, without the limitation of the LTE assumption. In our NLTE approach, the transient IPD values are presented as distributions evolving with time, which cannot be captured by conventional LTE-based models. The time-integrated ionization potential values are in good agreement with benchmark experimental data on solid-density aluminum plasma and other theoretical predictions based on LTE. The present work is promising to provide critical insights into nonequilibrium dynamics of dense plasma formation and thermalization induced by XFEL pulses.

Structural dynamics in proteins induced by and probed with X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) enable crystallographic structure determination beyond the limitations imposed upon synchrotron measurements by radiation damage. The need for very short XFEL pulses is relieved through gating of Bragg diffraction by loss of crystalline order as damage progresses, but not if ionization events are spatially non-uniform due to underlying elemental distributions, as in biological samples. Indeed, correlated movements of iron and sulfur ions were observed in XFEL-irradiated ferredoxin microcrystals using unusually long pulses of 80 fs. Here, we report a femtosecond time-resolved X-ray pump/X-ray probe experiment on protein nanocrystals. We observe changes in the protein backbone and aromatic residues as well as disulfide bridges. Simulations show that the latter’s correlated structural dynamics are much slower than expected for the predicted high atomic charge states due to significant impact of ion caging and plasma electron screening. This indicates that dense-environment effects can strongly affect local radiation damage-induced structural dynamics.

The local X-ray-induced dynamics that occur in protein crystals during serial femtosecond crystallography (SFX) measurements at XFELs are not well understood. Here the authors performed a time-resolved X-ray pump X-ray probe SFX experiment, and they observe distinct structural changes in the disulfide bridges and peptide backbone of proteins; complementing theoretical approaches allow them to further characterize the details of the X-ray induced ionization and local structural dynamics.

Towards the theoretical limitations of X-ray nanocrystallography at high intensity: the validity of the effective-form-factor description

X-ray free-electron lasers (XFELs) broaden horizons in X-ray crystallography. Facilitated by the unprecedented high intensity and ultrashort duration of the XFEL pulses, they enable us to investigate the structure and dynamics of macromolecules with nano-sized crystals. A limitation is the extent of radiation damage in the nanocrystal target. A large degree of ionization initiated by the incident high-intensity XFEL pulse alters the scattering properties of the atoms leading to perturbed measured patterns. In this article, the effective-form-factor approximation applied to capture this phenomenon is discussed. Additionally, the importance of temporal configurational fluctuations at high intensities, shaping these quantities besides the average electron loss, is shown. An analysis regarding the applicability of the approach to targets consisting of several atomic species is made, both theoretically and via realistic radiation-damage simulations. It is concluded that, up to intensities relevant for XFEL-based nanocrystallography, the effective-form-factor description is sufficiently accurate. This work justifies treating measured scattering patterns using conventional structure-reconstruction algorithms.