Session JO03: HED: Warm Dense Matter Theory

Plasma Waves and the Compressibility of Warm Dense Hydrogen

Recent experiments on single- and double-shocked liquid deuterium[1,2] have provided new evidence for increased compressibility of hydrogen compared to theoretical models in the warm-dense-matter regime between 200 and 1000 GPa. We show that a specific heat contribution from plasma waves, not explicitly included in the theoretical models, is sufficient to explain the discrepancy. 

Equation of State for Dense Plasmas using the Multiple Scattering Method

 

Electronic structure methods for hot, dense plasmas often use density functional theory (DFT) with major additional approximations.  For example, orbital-free DFT currently uses functionals that do not recover discrete core states, while average atom methods model one atom in an averaged plasma.  Here we use the so-called multiple scattering method to solve the Kohn-Sham DFT equations for dense plasmas.  The method is all-electron and does not use pseudo-potentials.  We find that equation of state calculations result in good agreement with other state-of-the-art methods, and find that computational cost does not increase with temperature, allowing access to very high temperature, non-degenerate systems.   

An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter

Wave packet molecular dynamics (WPMD) is a computationally fast tool used to model warm dense matter systems [1]. WPMD is a non-adiabatic method that employs many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigate three of the main approximations in most variants of WPMD: a limited basis set, estimations of exchange, and dearth of correlation [2]. We examine each of these approximations through simulation of atomic and molecular hydrogen in addition to a dense hydrogen plasma. The most significant improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match the experimental pressures of dense hydrogen. The semi-empirical scaling parameters are necessary to correct the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

      1. R. A. Davis et al. Phys. Rev. Research. 2, 4 (2020).

      2. W. A. Angermeier and T. G. White, Plasma 4, 294 (2021).

Molecular Dynamics Simulations of Inelastic X-Ray Scattering from Shocked Copper

By taking the spatial and temporal Fourier transforms of the coordinates of the atoms in molecular dynamics simulations conducted using an embedded-atom-method potential, we calculate the inelastic scattering of x-rays from copper single-crystals shocked along [001] to pressures of up to 70 GPa. Above the Hugoniot elastic limit (HEL), we find that the copious stacking faults generated at the shock front introduce strong quasi-elastic scattering (QES) that competes with the inelastic scattering signal, which remains discernible within the first Brillouin zone; for specific directions in reciprocal space outside the first zone, the QES dominates the inelastic signal overwhelmingly. The synthetic scattering spectra we generate from our Fourier transforms suggest that energy resolutions of order 10~meV would be required to distinguish inelastic from quasi-elastic scattering within the first Brillouin zone of shock-loaded copper. We further note that high-resolution inelastic scattering also affords the possibility of directly measuring particle velocities via the Doppler shift. These simulations are of relevance to future planned inelastic scattering experiments at x-ray Free Electron Laser (FEL) facilities.   

Development of a new Quantum Trajectory Molecular Dynamics Framework

The dynamic properties of a warm dense matter (WDM) system is strongly influenced by electron dynamics. Therefore, there is a need for computational methods which explicitly treat the electron dynamics, while still scalable and independent on any equilibrium assumptions, for the ability to model ongoing experimental efforts. We present an extension of the wave packet molecular dynamic scheme, where the electron state has an arbitrary Gaussian form, increasing the degree of freedom in the model and allowing for anisotropy in collisional dynamics and molecular bonds. The model employs a generalised scheme for the computation of short-range interactions, Ewald summation and Pauli interactions. The highly parallelised molecular dynamics framework LAMMPS has been utilized for the implementation of the model, with the intention to allow investigations of larger-scale systems. We present both ground state as well as the thermodynamic properties of the model, specialising in hydrogen systems.   

Dissipation and effective interaction on the dynamic structure factor of warm dense matter

The relative impact of dissipation and the effective ionic interaction on the ionic dynamic structure factor is examined. Two disparate physically based models of dissipation, which can differ numerically by orders of magnitude, are used in molecular dynamics. We find a negligible impact on the amplitudes of the dynamic structure factors for physically realistic parameter values from both models. We then examine the effective ionic interaction by varying its strength, the size of the atomic core (through a pseudopotential) and the screening model. We find that ``diffusive" peaks in the dynamic structure factor are very sensitive to the form of the ionic interaction, and this sensitivity arises primarily from atomic physics through the pseudopotential. This suggests that it would be useful to employ the measured zero-frequency dynamic structure factor $S_{ii}(k,0)$ as a constraint on the effective interaction, which in turn can be used to compute physical properties.   

Temperature Equilibration due to Charge State Fluctuations in Dense Plasmas

The charge states of ions in dense plasmas fluctuate due to collisional ionization and recombination.  As these fluctuations modify the ion interaction potential, over a cycle of ionization and recombination they can lead to an exchange of energy between the ions and free electrons.

 

In this work, we develop a theory for electron-ion energy transfer due to charge state fluctuations. Combining the theory with a random walk approach for the fluctuations, we present calculations for experimentally accessible plasmas. We find that the energy exchange rate from this novel mechanism could be comparable to, or even exceed, the rate due to direct electron-ion collisions. Furthermore, this mechanism is predicted to exhibit a complex dependence on the temperature and ionization state of the plasma. This could contribute to our understanding of significant variation in experimental measurements of equilibration times.   

Electronic stopping in warm dense matter using Ehrenfest dynamics and time-dependent density functional theory

Ehrenfest dynamics with time-dependent density functional theory (TDDFT) provides a framework for first-principles calculations of electronic stopping power that has been successfully applied in the solid state in numerous contexts. Its use in the warm dense regime has not been as widely studied, in part due to the computational expense of treating a large number of thermally occupied orbitals. In this talk, we examine some of the challenges associated with scaling Ehrenfest+TDDFT into the warm dense regime. We first consider isochorically heated aluminum, which allows us to study the impact of the pseudization of the L-shell under conditions in which it is increasingly thermally depleted. We then consider all-electron calculations of liquid-like deuterium and carbon to study the impact of finite-size effects and configurational averaging as a function of projectile energy. We conclude by taking the lessons we have learned to the analysis of electronic stopping in deuterium/beryllium mixtures relevant to fusion experiments. Throughout, we work within the context of validating average-atom models for the elemental systems and providing benchmark data for mixtures. We also report on some of the computational aspects of these calculations, which are among the largest of their kind.   

Investigating the Stopping Power of Warm Dense Plasmas using Time-Dependent Mixed Density-Functional Theory (TD-mDFT)

Charged particle stopping power in warm dense plasmas has applications to inertial confinement fusion and astrophysics. In recent studies [1-3], time-dependent density functional theory (TD-DFT) in both the Kohn-Sham (KS) and orbital-free (OF) formalism has been used to investigate the charged particle stopping power of high energy density plasmas. A new method of combining deterministic with stochastic KS-DFT has been developed [4] and denoted as mixed-DFT (mDFT). The TD version of mDFT is now used to investigate the charged particle stopping power of dense plasmas above and below the Fermi temperature. We will show how TD-mDFT calculations for the stopping power of dense carbon plasmas converge to TD-KS-DFT and TD-OF-DFT results within the temperature range. From these ab initio methods, we will present the comparisons of these results to establish the credibility of the TD-mDFT method.

[1] R. J. Magyar, et al., Contrib. Plasma Phys. 56, 459 (2016).

[2] Y. H. Ding, et al., Phys. Rev. Lett. 121, 145001 (2018).

[3] A. J. White et al., Phys. Rev. B 98, 144302 (2018).

[4] A. J. White et al, Phys. Rev. Lett. 125, 055002 (2020).   

Bound-bound features in x-ray Thomson scattering signals

Warm dense matter (WDM) experiments rely on diagnostic techniques such as x-ray Thomson scattering, where plasmonic features in the inelastic scattering spectrum are sensitiveto electronic temperature. Typical approaches to thermometry are based on the applicationof detailed balance to red- and blue-shifted plasmons, but various sources of uncertaintiespose challenges for this method. We propose peaks arising from bound-bound transitions, i.e., scattering into thermally depleted core orbitals, as alternative diagnostic features whichwe predict to become increasingly prominent at high temperatures. For the cases of iron and aluminum isochorically heated to 1 eV and 20 eV, our first-principles, real-time time-dependent density functional theory calculations validate an average atom model modifiedto treatd-band electrons as quasibound states. This work lays the foundation for accurate diagnostic tools as higher temperatures become accessible on XFEL platforms.   

Benchmarking Conductivities from Average Atom Methods to Density Functional Theory for Warm Dense Matter

Accurate and efficient calculations of electrical conductivities of warm dense matter (WDM) enable design and interpretation of laboratory WDM experiments. In this context, average atom (AA) methods commonly use the Ziman framework, which gives widely varying predictions depending on, e.g., models chosen for the ion-ion static structure factor and scattering cross sections. Here, we benchmark and constrain AA results against density functional theory (DFT) calculations with the Kubo-Greenwood formula. We consider solid-density beryllium at temperatures of 0.1, 0.5, and 1 eV and compare densities of state, dielectric functions, and dynamic conductivities. We find good agreement for frequencies above 5 eV and explore first-principles approaches for modeling electron-ion and electron-electron couplings affecting the low-frequency Drude contribution. This work forms a crucial component of broader efforts to benchmark and improve AA methods.   

Improved First-Principles Equation-of-State Table of Deuterium for High-Energy-Density Science Applications

We present an improved first-principles equation-of-state (iFPEOS) table of deuterium covering densities 10^-3 < r < 1.6×10³ g/cm³ and temperatures 800 K < T < 256 MK. iFPEOS is based on the latest theoretical developments in quantum treatment of ions and electrons within the ab initio molecular dynamics driven by density-functional-theory approach. For an improved description of the electronic structure across temperature regimes, iFPEOS employs a meta-generalized-gradient-approximation free-energy exchange-correlation density functional with explicit temperature dependence. Nuclear quantum effects are taken into account via path-integral molecular dynamics. Comparing iFPEOS to other equation-of-state (EOS) models and latest experimental measurements we find that iFPEOS provides an improved agreement with experimental data for pressures up to 200 GPa and temperatures up to 60,000 K. For higher pressures and temperatures, however, iFPEOS predicts lower compressibility and higher sound speed along the Hugoniot, compared to experiment, thereby further confirming the systematic disagreement between theory and experiment in this regime.   

Static Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics.

Experimental setups as well as theoretical modeling of Warm Dense Matter (WDM) heavily rely on linear response theory. However, Dornheim et. al.  [Phys. Rev. Lett.125, 085001 (2020)] showed that assuming the linear regime is not always justified for WDM. We use the ab initio Path-Integral Monte-Carlo (PIMC) technique to obtain exact results for the harmonically perturbed homogeneous electron gas. A thorough analysis for different perturbation amplitudes is carried out. The corresponding density response reveals resonances at higher harmonics of the perturbation frequency. Furthermore, the induced density response as a function of the perturbation strength unveils that the dominant term beyond linear response is the second harmonic. We show that the nonlinear density response is highly sensitive to exchange–correlation effects, rendering it a potentially valuable new diagnostic tool. The results signify the importance of response contributions beyond the linear regime to accurately model WDM.   

Comparison of Equations of State for Warm and Hot Dense Matter from REODP and PIMC Modeling

Equations of State (EOS), transport and spectral properties of Warm and Hot Dense Matter (WDM and HDM denoted here as High Energy Density Matter (HEDM)) calculated from first principles are of great importance for understanding the processes in large planets, laser ablation, and inertial confinement fusion. The HEDM regime includes states of matter near solid density and at temperatures ~1 - 100 eV (WDM) and ~0.1 - 10 keV (HDM). A path integral Monte Carlo (PIMC) method is usually employed for calculating the EOS of HEDM. This is a statistical sampling approach that requires high computational time even for a single temperature-density point. The Hartree-Fock-Slater - Collisional-Radiative Steady-State (HFS-CRSS) model implemented in the Radiative Emissivity and Opacity of Dense Plasmas (REODP) code [Miloshevsky et al. PRE 92 (2015) 033109] is used to predict the EOS of HEDM. The internal energy and pressure for a large set of temperature-density points are computed within seconds on a desktop computer. Comparisons of the EOS for warm and hot dense carbon and other materials obtained from the REODP and PIMC models show very good agreement for wide ranges of temperature and density.   

A Many-Body Extension to Madelung Quantum Hydrodynamics

In this talk we derive a many-body quantum-hydrodynamic model from first principles in the spirit of Madelung. We obtain exact time-dependent 3-D fluid equations that satisfy wave function symmetry or anti-symmetry, then obtain simplified forms for the cases of single permanent and Slater determinant with orthonormal basis functions. We show that, neglecting correlations and assuming many degenerate plane-wave electrons in the uniform limit, electron dynamics are governed by basic Euler equations with a mean-field Hartree interaction, Thomas–Fermi pressure, and Dirac exchange potential.