Warm Dense Plasma Research Articles

Ionization by XFEL radiation produces distinct structure in liquid water

In the warm dense matter (WDM) regime, where condensed, gas, and plasma phases coexist, matter frequently exhibits unusual properties that cannot be described by contemporary theory. Experiments reporting phenomena in WDM are therefore of interest to advance our physical understanding of this regime, which is found in dwarf stars, giant planets, and fusion ignition experiments. Using 7.1 keV X-ray free electron laser radiation (nominally 5×105 J/cm2), we produced and probed transient WDM in liquid water. Wide-angle X-ray scattering (WAXS) from the probe reveals a new ~9 Å structure that forms within 75 fs. By 100 fs, the WAXS peak corresponding to this new structure is of comparable magnitude to the ambient water peak, which is attenuated. Simulations suggest that the experiment probes a superposition of two regimes. In the first, fluences expected at the focus severely ionize the water, which becomes effectively transparent to the probe. In the second, out-of-focus pump radiation produces O1+ and O2+ ions, which rearrange due to Coulombic repulsion over 10 s of fs. Our simulations account for a decrease in ambient water signal and an increase in low-angle X-ray scattering but not the experimentally observed 9 Å feature, presenting a new challenge for theory.

Exploring relaxation dynamics in warm dense plasmas by tailoring non-thermal electron distributions with a free electron laser

Exploring relaxation dynamics in warm dense plasmas by tailoring non-thermal electron distributions with a free electron laser

The Impact of Warm Dense Plasma Environments on 2p → 1s Transition of Core-Hole Mg7+ Ions

The Impact of Warm Dense Plasma Environments on 2p → 1s Transition of Core-Hole Mg7+ Ions

Photoionization process of the hydrogenlike carbon ion embedded in warm and hot dense plasmas.

Complicated many-body interactions between ions and surrounding particles exist in warm and hot dense plasmas. It will significantly alter the atomic structures and dynamic properties of the embedded ions. Recently, the atomic-state-dependent (ASD) screening model has been proposed and shown to be valid for investigating the screening effect in warm and hot dense plasmas over a wide range of electron densities and temperatures. By employing the ASD model, we investigate the photoionization process for the hydrogenlike carbon ion embedded in warm and hot dense plasmas with corresponding Coulomb coupling parameter ranges of 0.05 ≤ Γ ≤ 1.16, where Γ characterizes the ratio of the average potential to thermal energy. It is found that there are stronger plasma screening effects on the ionization energy and photoionization cross section due to the negative-energy electron distributions considered in the ASD model compared to those considering only free electrons. The present results from the ASD model show reasonable agreement with the classical Debye-Hückel (DH) model in weakly coupled plasmas. However, significant deviations of the ionization energy and cross section between these two models are observed in moderately and strongly coupled plasmas, due to the approximate treatment of the plasma-electron density distribution of the DH model. In the region of low photoelectron energies, the positions of the shape resonance peaks of the cross sections obtained from the ASD model differ significantly from those of the DH model due to the different screening effects.

The Thomas-Kuhn-Reiche sum rule for bound electrons of ions in warm dense plasmas

The Thomas-Kuhn-Reiche oscillator strength sum rule is analyzed for the case of ionized atoms in warm dense plasmas: The statistical summation of the bound-bound and the bound-free oscillator strength is proportional to the average bound electrons. This sum rule is checked for approximated absorption spectra like the detailed line accounting, detailed configurations accounting, the super transition arrays and the average atom using the CRSTA code. We show that the sum rule is properly satisfied for various elements in ranges of temperature-density that have sufficient bound orbitals. On the other hand, for the cases of few bound orbitals, the sum-rule is poorly satisfied, like in the case of high density and low temperature.

Measuring stopping power in warm dense matter plasmas at OMEGA

A platform has been developed for accurately measuring the stopping power of high energy protons through warm dense matter (WDM) plasmas characterized by x-ray Thomson scattering. In this work stopping power measurements were successfully made through both WDM Beryllium and Boron plasmas. In the Boron experiments, an increase in stopping was observed over their cold target counter-parts. This increase in stopping was shown to agree well with models that account for the partial ionization of the plasma.

Averaging over atom snapshots in linear-response TDDFT of disordered systems: A case study of warm dense hydrogen.

Linear-response time-dependent density functional theory (LR-TDDFT) simulations of disordered extended systems require averaging over different snapshots of ion configurations to minimize finite size effects due to the snapshot-dependence of the electronic density response function and related properties. We present a consistent scheme for the computation of the macroscopic Kohn-Sham (KS) density response function connecting an average over snapshot values of charge density perturbations to the averaged values of KS potential variations. This allows us to formulate the LR-TDDFT within the adiabatic (static) approximation for the exchange-correlation (XC) kernel for disordered systems, where the static XC kernel is computed using the direct perturbation method [Moldabekov et al., J. Chem. Theory Comput. 19, 1286 (2023)]. The presented approach allows one to compute the macroscopic dynamic density response function as well as the dielectric function with a static XC kernel generated for any available XC functional. The application of the developed workflow is demonstrated for the example of warm dense hydrogen. The presented approach is applicable for various types of extended disordered systems, such as warm dense matter, liquid metals, and dense plasmas.

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'.

Modeling density effects on electronic configurations in warm dense plasmas

We present a method to calculate the shift of the K edge in warm dense aluminum. We use the average-atom model and show how to build the energy of an electronic configuration with integer subshell populations and by taking into account the interaction of the bound electrons with the free electrons. We successfully compare our calculation of the spectral opacity with the Henke table for aluminum at solid density and 300 K. We found a redshift of the K edge along the principal Hugoniot consistent with experimental data. We also compute the 2s and 2p edges. We obtain L edge redshifts similar to the K edge redshift.

Multi-Configuration Calculation of Ionization Potential Depression

The modelling of ionization potential depression in warm and hot dense plasmas constitutes a real theoretical challenge due to ionic coupling and electron degeneracy effects. In this work, we present a quantum statistical model based on a multi-configuration description of the electronic structure in the framework of Density Functional Theory. We discuss different conceptual issues inherent to the definition of ionization potential depression and compare our results with the famous and widely-used Ecker-Kröll and Stewart-Pyatt models.

Plane-wave-based stochastic-deterministic density functional theory for extended systems

Traditional finite-temperature Kohn-Sham density functional theory (KSDFT) has an unfavorable scaling with respect to the electron number or at high temperatures. The evaluation of the ground-state density in KSDFT can be replaced by the Chebyshev trace (CT) method. In addition, the use of stochastic orbitals within the CT method leads to the stochastic density functional theory [Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed stochastic-deterministic density functional theory [Phys. Rev. Lett. 125, 055002 (2020)] (MDFT). We have implemented the above four methods within the first-principles package ABACUS. All of the four methods are based on the plane-wave basis set with the use of norm-conserving pseudopotentials and the periodic boundary conditions with the use of $k$-point sampling in the Brillouin zone. By using the KSDFT calculation results as benchmarks, we systematically evaluate the accuracy and efficiency of the CT, SDFT, and MDFT methods via examining a series of physical properties, which include the electron density, the free energy, the atomic forces, stress, and density of states for a few condensed phase systems. The results suggest that our implementations of CT, SDFT, and MDFT not only reproduce the KSDFT results with a high accuracy, but also exhibit several advantages over the tradition KSDFT method. We expect these methods can be of great help in studying high-temperature and large-size extended systems such as warm dense matter and dense plasma.

Total, state-selective, and angular-differential cross sections for electron capture in He2++H collisions in warm dense plasmas

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

Hybrid Kohn-Sham+Thomas-Fermi scheme for high-temperature density functional theory

Density functional theory has revolutionised our understanding of dense, strongly coupled systems in the condensed-matter limit. At elevated temperatures, such as those found in warm dense matter and dense plasma, the computational cost of calculating enough states to accurately describe a thermal ensemble of electrons is a major obstacle to practical Kohn-Sham calculations. This problem has recently been tackled from a number of approaches, including a plane-wave approximation for electrons at high energy. In this work, we demonstrate how the Thomas-Fermi density of states, equivalent to a local plane-wave approximation, can yield improved results for thermodynamic quantities, electron density profiles, and interatomic forces while requiring fewer states than existing methods.

Proton stopping measurements at low velocity in warm dense carbon

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Traversing of fast electrons in dense plasmas with dynamical screening

The traversing of fast electrons in dense D and T plasmas is discussed by different models with dynamical screening by means of dielectric functions. The traversing process is caused by a series of binary collision. It is found that the screening model with a classical dielectric function and Debye screening model only work in hot plasmas. Even for warm dense plasmas, the screening model with quantum dielectric function is reliable, which is well reproduced by the model with quantum static dielectric function. The related reasons are explored thoroughly. This work is helpful to study the transport of electrons in fully ionized dense plasmas.

Kinetic studies of exchange-correlation effect on the collective excitations of warm dense plasmas.

The exchange-correlation of electrons, as a fundamental effect in quantum mechanics, plays an important role in the collective motions of electrons in warm dense matter. We derive the quantum kinetic equationsbased on the time-dependent Kohn-Sham equation. By using a temperature-dependent functional for the exchange correlation, the excitations of electrostatic waves are analyzed under the adiabatic local density approximation (ALDA). We find that the influences of the exchange-correlation effect on the group velocity of electrostatic waves can be as high as 10% when both the density and temperature are low. Moreover, we also compare the results obtained by using ALDA-based kinetic theory, exchange kinetic theory, and quantum hydrodynamics, and discuss the differences among them.

Accuracy analysis of opacity models from transmission measurements in laser-produced plasmas

The accuracy of opacity models, for warm-dense plasmas, is discussed by a comparison to nine transmission experiments in Al, Fe, FeNaF, Mo, Ho, and Au. The transmission measurements were performed in the NOVA, ASTERIX IV, and Shenguang-II laser facilities during the last three decades, where the achieved temperatures and densities were in the regime of 20–85 eV and 6–30 mg/cc, and the measured energy regimes were relevant to estimate the Rosseland and Planck opacities. A detailed error analysis of the measurements and accuracy analysis of the CRSTA and other models are presented.

Atomic-state-dependent screening model for hot and warm dense plasmas

An ion embedded in warm/hot dense plasmas will greatly alter its microscopic structure and dynamics, as well as the macroscopic radiation transport properties of the plasmas, due to complicated many-body interactions with surrounding particles. Accurate theoretically modeling of such kind of quantum many-body interactions is essential but very challenging. In this work, we propose an atomic-state-dependent screening model for treating the plasmas with a wide range of temperatures and densities, in which the contributions of three-body recombination processes are included. We show that the electron distributions around an ion are strongly correlated with the ionic state studied due to the contributions of three-body recombination processes. The feasibility and validation of the proposed model are demonstrated by reproducing the experimental result of the line-shift of hot-dense plasmas as well as the classical molecular dynamic simulations of moderately coupled ultra-cold neutral plasmas. Our work opens a promising way to treat the screening effect of hot and warm dense plasma, which is a bottleneck of those extensive studies in high-energy-density physics, such as atomic processes in plasma, plasma spectra and radiation transport properties, among others.

Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons.

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas.

We present a free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin-Kohn-Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo-Greenwood optic data with a single atom in simulation cell calculations to close the photon energy gap between the L and K edges and extend the K-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo-Greenwood calculations with AIMD snapshots. Kubo-Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the L edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-Z materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomenon of redshift-to-blueshift in K-L (1s→2p) and K-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of 1s→2p to the K-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.