Energy relaxation in dense, strongly coupled two-temperature plasmas

Unified description of thermal and nonthermal laser-induced ultrafast structural changes in materials

The ultrafast ionic dynamics in solids induced by intense femtosecond laser excitation are controlled by two fundamentally different yet interrelated phenomena. First, the substantial generation of hot electron-hole pairs by the laser pulse modifies the interatomic bonding strength and characteristics, inducing nonthermal ionic motion. Second, incoherent electron-ion collisions facilitate thermal equilibration between electrons and ions, achieving a uniform temperature on a picosecond timescale. This article presents a unified theoretical description that effectively integrates both processes. Our method is adaptable for use in both ab-initio simulations and extensive molecular dynamics simulations, extending the conventional two-temperature model to incorporate molecular dynamics equations of motion. To demonstrate the efficacy of our approach, we apply it to the laser excitation of silicon thin films. Our simulations closely match experimental observations, accurately reproducing the temporal evolution of the Bragg peaks.

Multitemperature atomic ensemble: Nonequilibrium evolution after ultrafast electronic excitation

Ultrafast laser radiation or beams of fast charged particles primarily excite the electronic system of a solid driving the target transiently out of thermal equilibrium. Apart from the nonequilibrium between the electrons and atoms, each subsystem may be far from equilibrium. From first principles, we derive the definition of various atomic temperatures applicable to electronically excited ensembles. It is shown that the definition of the kinetic temperature of atoms in the momentum subspace is unaffected by the excitation of the electronic system. When the electronic temperature differs from the atomic one, an expression for the configurational atomic temperature is proposed, applicable to the electronic-temperature-dependent interatomic potentials (such as ab initio molecular dynamics simulations). We study how the configurational temperature behaves during nonthermal phase transition, triggered by the evolution of the interatomic potential due to the electronic excitation. It is revealed that upon the ultrafast irradiation, the atomic system of a solid exists temporarily in a multitemperature state: separate equilibria in the momentum and configurational subspaces. Complete equilibration between the various atomic temperatures takes place at longer timescales, forming the energy equipartition. Based on these results, we propose a formulation of multitemperature heat transport equations.

Dynamic and transient processes in warm dense matter

In this paper, we discuss some of the key challenges in the study of time-dependent processes and non-equilibrium behaviour in warm dense matter. We outline some of the basic physics concepts that have underpinned the definition of warm dense matter as a subject area in its own right and then cover, in a selective, non-comprehensive manner, some of the current challenges, pointing along the way to topics covered by the papers presented in this volume. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Assessment of the electron-proton energy relaxation rates extracted from molecular dynamics simulations in weakly-coupled hydrogen plasmas

Electron-proton energy relaxation rates are assessed using molecular dynamics (MD) simulations in weakly-coupled hydrogen plasmas. To this end, we use various approaches to extract the energy relaxation rate from MD-simulated temperatures, and we find that existing extracting approaches may yield results with a sizable discrepancy larger than the variance between analytical models, which is further verified by well-known case studies. Present results show that two of the extracting approaches can produce identical results, which is attributed to a proper treatment of relaxation evolution. To discriminate the use of various methods, an empirical criterion with respect to initial plasma temperatures is proposed, which can self-consistently explain the cases considered. In addition, for a transient electron-proton plasma, we show that it is possible to extrapolate the Coulomb logarithm from that derived by initial plasma parameters in a single MD calculation, which is reasonably consistent with previous MD data. Our results are helpful to obtain accurate MD-based energy relaxation rates.

Nonequilibrium band occupation and optical response of gold after ultrafast XUV excitation

Free electron lasers offer unique properties to study matter in states far from equilibrium as they combine short pulses with a large range of photon energies. In particular, the possibility to excite core states drives new relaxation pathways that, in turn, also change the properties of the optically and chemically active electrons. Here, we present a theoretical model for the dynamics of the nonequilibrium occupation of the different energy bands in solid gold driven by exciting deep core states. The resulting optical response is in excellent agreement with recent measurements and, combined with our model, provides a quantitative benchmark for the description of electron-phonon coupling in strongly driven gold. Focusing on sub-picosecond time scales, we find essential differences between the dynamics induced by XUV and visible light.

Energy Relaxation and Electron-Phonon Coupling in Laser-Excited Metals

The rate of energy transfer between electrons and phonons is investigated by a first-principles framework for electron temperatures up to Te = 50,000 K while considering the lattice at ground state. Two typical but differently complex metals are investigated: aluminum and copper. In order to reasonably take the electronic excitation effect into account, we adopt finite temperature density functional theory and linear response to determine the electron temperature-dependent Eliashberg function and electron density of states. Of the three branch-dependent electron-phonon coupling strengths, the longitudinal acoustic mode plays a dominant role in the electron-phonon coupling for aluminum for all temperatures considered here, but for copper it only dominates above an electron temperature of Te = 40,000 K. The second moment of the Eliashberg function and the electron phonon coupling constant at room temperature Te=315 K show good agreement with other results. For increasing electron temperatures, we show the limits of the T=0 approximation for the Eliashberg function. Our present work provides a rich perspective on the phonon dynamics and this will help to improve insight into the underlying mechanism of energy flow in ultra-fast laser-metal interaction.

Temperature relaxation in strongly-coupled binary ionic mixtures

New facilities such as the National Ignition Facility and the Linac Coherent Light Source have pushed the frontiers of high energy-density matter. These facilities offer unprecedented opportunities for exploring extreme states of matter, ranging from cryogenic solid-state systems to hot, dense plasmas, with applications to inertial-confinement fusion and astrophysics. However, significant gaps in our understanding of material properties in these rapidly evolving systems still persist. In particular, non-equilibrium transport properties of strongly-coupled Coulomb systems remain an open question. Here, we study ion-ion temperature relaxation in a binary mixture, exploiting a recently-developed dual-species ultracold neutral plasma. We compare measured relaxation rates with atomistic simulations and a range of popular theories. Our work validates the assumptions and capabilities of the simulations and invalidates theoretical models in this regime. This work illustrates an approach for precision determinations of detailed material properties in Coulomb mixtures across a wide range of conditions.

Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory

We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum Monte Carlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.

Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte Carlo simulations

We systematically investigate finite-size effects in the dynamic structure factor S(q,ω) of the uniform electron gas obtained via the analytic continuation of ab initio path integral Monte Carlo data for the imaginary-time density-density correlation function F(q,τ). Using the recent scheme by Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255001], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as N=14 electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.

Nonlinear Electronic Density Response in Warm Dense Matter

Warm dense matter (WDM)-an extreme state with high temperatures and densities that occurs, e.g., in astrophysical objects-constitutes one of the most active fields in plasma physics and materials science. These conditions can be realized in the lab by shock compression or laser excitation, and the most accurate experimental diagnostics is achieved with lasers and free electron lasers which is theoretically modeled using linear response theory. Here, we present first ab initio path integral Monte Carlo results for the nonlinear density response of correlated electrons in WDM and show that for many situations of experimental relevance nonlinear effects cannot be neglected.

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter

The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.

Interatomic Potential in the Nonequilibrium Warm Dense Matter Regime

We present a new measurement of lattice disassembly times in femtosecond-laser-heated polycrystalline Au nanofoils. The results are compared with molecular dynamics simulations incorporating a highly optimized, embedded-atom-method interatomic potential. For absorbed energy densities of 0.9-4.3  MJ/kg, the agreement between the experiment and simulation reveals a single-crystal-like behavior of homogeneous melting and corroborates the applicability of the interatomic potential in the nonequilibrium warm dense matter regime. For energy densities below 0.9  MJ/kg, the measurement is consistent with nanocrystal behavior where melting is initiated at the grain boundaries.

Dynamic electron-ion collisions and nuclear quantum effects in quantum simulation of warm dense matter

The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas

The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)10.1088/1367-2630/17/7/073017] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows us to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K<T_{e}<10^{9}K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.

Temperature relaxation in dense plasmas

We present a model to calculate temperature-relaxation rates in dense plasmas. The electron-ion interaction potential and the thermodynamic data of interest are provided by an average-atom model. This approach allows the study of the temperature relaxation in a two-temperature electron-ion system.

Measurement of Electron-Ion Relaxation in Warm Dense Copper

Experimental investigation of electron-ion coupling and electron heat capacity of copper in warm and dense states are presented. From time-resolved x-ray absorption spectroscopy, the temporal evolution of electron temperature is obtained for non-equilibrium warm dense copper heated by an intense femtosecond laser pulse. Electron heat capacity and electron-ion coupling are inferred from the initial electron temperature and its decrease over 10 ps. Data are compared with various theoretical models.

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy, which we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3-18.6  g cm(-3), 5.0×10(5)-1.3×10(8)  K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

Ab initio approach to model x-ray diffraction in warm dense matter

It is demonstrated how the static electron-electron structure factor in warm dense matter can be obtained from density functional theory in combination with quantum Monte Carlo data. In contrast to theories assuming well-separated bound and free states, this ab initio approach yields also valid results for systems close to the Mott transition (pressure ionization), where bound states are strongly modified and merge with the continuum. The approach is applied to x-ray Thomson scattering and compared to predictions of the Chihara formula whereby we use the ion-ion and electron-ion structure from the same simulations. The results show significant deviations of the screening cloud from the often applied Debye-like form.

Electron-ion equilibration in ultrafast heated graphite

We have employed fast electrons produced by intense laser illumination to isochorically heat thermal electrons in solid density carbon to temperatures of ∼10,000  K. Using time-resolved x-ray diffraction, the temperature evolution of the lattice ions is obtained through the Debye-Waller effect, and this directly relates to the electron-ion equilibration rate. This is shown to be considerably lower than predicted from ideal plasma models. We attribute this to strong ion coupling screening the electron-ion interaction.

Reduced coupled-mode approach to electron-ion energy relaxation

We present a reduced model for the energy transfer via coupled collective modes in two-temperature plasmas based on quantum statistical theory. The model is compared with exact numerical evaluations of the coupled-mode (CM) energy transfer rate and with alternative reduced approaches over a range of conditions in the warm dense matter (WDM) and inertial confinement fusion (ICF) regimes. Our approach shows excellent agreement with an exact treatment of the CM rate and supports the importance of the coupled-mode effect for the temperature and energy relaxation in WDM and ICF plasmas. We find that electronic damping of collective ion density fluctuations is crucial for correctly describing the mode spectrum and, thus, the energy exchange. The reduced CM approach is studied over a wide parameter space, enabling us to establish its limits of applicability.

Dynamic ion structure factor of warm dense matter

The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from ab initio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be insufficient to describe the data. An extended Mermin approach, a hydrodynamic model, and the method of moments with local constraints are capable of reproducing the numerical results but have rather limited predictive powers as they all need some numerical data as input. The method of moments is found to be the most promising.

Observation of inhibited electron-ion coupling in strongly heated graphite

Creating non-equilibrium states of matter with highly unequal electron and lattice temperatures (T(ele)≠T(ion)) allows unsurpassed insight into the dynamic coupling between electrons and ions through time-resolved energy relaxation measurements. Recent studies on low-temperature laser-heated graphite suggest a complex energy exchange when compared to other materials. To avoid problems related to surface preparation, crystal quality and poor understanding of the energy deposition and transport mechanisms, we apply a different energy deposition mechanism, via laser-accelerated protons, to isochorically and non-radiatively heat macroscopic graphite samples up to temperatures close to the melting threshold. Using time-resolved x ray diffraction, we show clear evidence of a very small electron-ion energy transfer, yielding approximately three times longer relaxation times than previously reported. This is indicative of the existence of an energy transfer bottleneck in non-equilibrium warm dense matter.

Velocity relaxation in a strongly coupled plasma

Collisional relaxation of Coulomb systems is studied in the strongly coupled regime. We use an optical pump-probe approach to manipulate and monitor the dynamics of ions in an ultracold neutral plasma, which allows direct measurement of relaxation rates in a regime where common Landau-Spitzer theory breaks down. Numerical simulations confirm the experimental results and display non-Markovian dynamics at early times.

Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas

We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical two-body potentials and a generalized Lenard-Balescu (GLB) theory capable of treating multicomponent weakly coupled plasmas. The GLB is used in two modes: (1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction and (2) with the classical (ℏ→0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough. In addition, we show that classical calculations with statistical potentials derived from the exact quantum two-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.

Short-time electron dynamics in aluminum excited by femtosecond extreme ultraviolet radiation

The femtosecond dynamics of the electrons in aluminum after an intense extreme ultraviolet pulse is investigated by Monte Carlo simulations. Transient distributions of the conduction band electrons show an almost thermalized, low-energy part and a high-energy tail. Constructing emission spectra from these data, we find excellent agreement with measurements. The radiative decay mainly reflects the colder part of the distribution, whereas the highly excited electrons dominate the bremsstrahlung spectrum. For the latter, we also find good agreement between predicted and measured energy scales.