Unified description of linear screening in dense plasmas

Improved Ionization Potential Depression Model Incorporating Dynamical Structure Factors and Electron Degeneracy for Non-Ideal Plasma Composition

In this work, we present an improved model for ionization potential depression (IPD) in dense plasmas that builds upon the approach introduced by Lin et al., which utilizes a dynamical structure factor (SF) to account for ionic microfield fluctuations. The main refinements include the following: (1) replacing the Wigner-Seitz radius with an ion-sphere radius, thereby treating individual ionization events as dynamically independent; (2) incorporating electron degeneracy through a tailored interpolation between Debye-Hückel and Thomas-Fermi screening lengths. Additionally, we solve the Saha equation iteratively, ensuring self-consistent determination of the ionization balance and IPD corrections. These modifications yield significantly improved agreement with recent high-density and high-temperature experimental data on warm dense aluminum, especially in regimes where strong coupling and partial degeneracy are crucial. The model remains robust over a broad parameter space, spanning temperatures from 1 eV up to 1 keV and pressures beyond the Mbar range, thus making it suitable for applications in high-energy-density physics, inertial confinement fusion, and astrophysical plasma research. Our findings underscore the importance of accurately capturing ion microfield fluctuations and electron quantum effects to properly describe ionization processes in extreme environments.

Impact of Quantum Non-Locality and Electronic Non-Ideality on the Shannon Entropy for Atomic States in Dense Plasma

The influence of the collective and quantum effects on the Shannon information entropy for atomic states in dense nonideal plasma was investigated. The interaction potential, which takes into account the effect of quantum non-locality as well as electronic correlations, was used to solve the Schrödinger equation for the hydrogen atom. It is shown that taking into account ionic screening leads to an increase in entropy, while taking into account only electronic screening does not lead to significant changes.

Photo-plasmonic effect as the hot electron generation mechanism

Based on the effective Schrödinger-Poisson model a new physical mechanism for resonant hot-electron generation at irradiated half-space metal-vacuum interface of electron gas with arbitrary degree of degeneracy is proposed. The energy dispersion of undamped plasmons in the coupled Hermitian Schrödinger-Poisson system reveals an exceptional point coinciding the minimum energy of plasmon conduction band. Existence of such exceptional behavior is a well-know character of damped oscillation which in this case refers to resonant wave-particle interactions analogous to the collisionless Landau damping effect. The damped Schrödinger-Poisson system is used to model the collective electron tunneling into the vacuum. The damped plasmon energy dispersion is shown to have a full-featured exceptional point structure with variety of interesting technological applications. In the band gap of the damped collective excitation,depending on the tunneling parameter value, there is a resonant energy orbital for which the wave-like growing of collective excitations cancels the damping of the single electron tunneling wavefunction. This important feature is solely due to dual-tone wave-particle oscillations, characteristics of the collective excitations in the quantum electron system leading to a resonant photo-plasmonic effect, as a collective analog of the well-known photo-electric effect. The few nanometer wavelengths high-energy collective photo-electrons emanating from the metallic surfaces can lead to a much higher efficiency of plasmonic solar cell devices, as compared to their semiconductor counterpart of electron-hole excitations at the Fermi energy level. The photo-plasmonic effect may also be used to study the quantum electron tunneling and electron spill-out at metallic surfaces. Current findings may help to design more efficient spasers by using the feature-rich plasmonic exceptional point structure.

Yukawa-Friedel-tail pair potentials for warm dense matter applications

Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard N-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the nonparametric force-matched potentials from N-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multispecies warm dense matter.

Energy band structure of multistream quantum electron system

In this paper, using the quantum multistream model, we develop a method to study the electronic band structure of plasmonic excitations in streaming electron gas with arbitrary degree of degeneracy. The multifluid quantum hydrodynamic model is used to obtain N-coupled pseudoforce differential equation system from which the energy band structure of plasmonic excitations is calculated. It is shown that inevitable appearance of energy bands separated by gaps can be due to discrete velocity filaments and their electrostatic mode coupling in the electron gas. Current model also provides an alternative description of collisionless damping and phase mixing, i.e., collective scattering phenomenon within the energy band gaps due to mode coupling between wave-like and particle-like oscillations. The quantum multistream model is further generalized to include virtual streams which is used to calculate the electronic band structure of one-dimensional plasmonic crystals. It is remarked that, unlike the empty lattice approximation in free electron model, energy band gaps exist in plasmon excitations due to the collective electrostatic interactions between electrons. It is also shown that the plasmonic band gap size at first Brillouin zone boundary maximizes at the reciprocal lattice vector, G, close to metallic densities. Furthermore, the electron-lattice binding and electron-phonon coupling strength effects on the electronic band structure are discussed. It is remarked that inevitable formation of energy band structure is a general characteristics of various electromagnetically and gravitationally coupled quantum multistream systems.

Influence of dissipation and effective interaction on the dense plasma dynamic structure factor

The ionic dynamic structure factor is examined to assess the relative roles of dissipation and the effective ionic interaction. 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. 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.

Machine Learning Discovery of Computational Model Efficacy Boundaries

Computational models are formulated in hierarchies of variable fidelity, often with no quantitative rule for defining the fidelity boundaries. We have constructed a dataset from a wide range of atomistic computational models to reveal the accuracy boundary between higher-fidelity models and a simple, lower-fidelity model. The symbolic decision boundary is discovered by optimizing a support vector machine on the data through iterative feature engineering. This data-driven approach reveals two important results: (i) a symbolic rule emerges that is independent of the algorithm, and (ii) the symbolic rule provides a deeper understanding of the fidelity boundary. Specifically, our dataset is composed of radial distribution functions from seven high-fidelity methods that cover wide ranges in the features (element, density, and temperature); high-fidelity results are compared with a simple pair-potential model to discover the nonlinear combination of the features, and the machine learning approach directly reveals the central role of atomic physics in determining accuracy.

Modeling hydration-mediated ion-ion interactions in electrolytes through oscillating Yukawa potentials

Classical Poisson-Boltzmann theory represents a mean-field description of the electric double layer in the presence of only Coulomb interactions. However, aqueous solvents hydrate ions, which gives rise to additional hydration-mediated ion-ion interactions. Experimental and computational studies suggest damped oscillations to be a characteristic feature of these hydration-mediated interactions. We have therefore incorporated oscillating Yukawa potentials into the mean-field description of the electric double layer. This is accomplished by allowing the decay length of the Yukawa potential to be complex valued. Ion specificity emerges from assigning individual strengths and phases to the Yukawa potential for anion-anion, anion-cation, and cation-cation pairs as well as for anions and cations interacting with an electrode or macroion. Excluded volume interactions between ions are approximated by replacing the ideal gas entropy by that of a lattice gas. We derive mean-field equations for the Coulomb and Yukawa potentials and use their solutions to compute the differential capacitance for an isolated planar electrode and the pressure that acts between two planar, like-charged macroion surfaces. Attractive interactions appear if the surface charge density of the macroions is sufficiently small.

Multicomponent mutual diffusion in the warm, dense matter regime

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

Ion friction at small values of the Coulomb logarithm

Transport properties of high-energy-density plasmas are influenced by the ion collision rate. Traditionally, this rate involves the Coulomb logarithm, lnΛ. Typical values of lnΛ are ≈10-20 in kinetic theories where transport properties are dominated by weak-scattering events caused by long-range forces. The validity of these theories breaks down for strongly coupled plasmas, when lnΛ is of order one. We present measurements and simulations of collision data in strongly coupled plasmas when lnΛ is small. Experiments are carried out in the first dual-species ultracold neutral plasma (UNP), using Ca^{+} and Yb^{+} ions. We find strong collisional coupling between the different ion species in the bulk of the plasma. We simulate the plasma using a two-species fluid code that includes Coulomb logarithms derived from either a screened Coulomb potential or a the potential of mean force. We find generally good agreement between the experimental measurements and the simulations. With some improvements, the mixed Ca^{+} and Yb^{+} dual-species UNP will be a promising platform for testing theoretical expressions for lnΛ and collision cross-sections from kinetic theories through measurements of energy relaxation, stopping power, two-stream instabilities, and the evolution of sculpted distribution functions in an idealized environment in which the initial temperatures, densities, and charge states are accurately known.

Excess pressure and electric fields in nonideal plasma hydrodynamics

Nonideal plasmas have nontrivial space and time correlations, which simultaneously impact both the excess thermodynamic quantities as well as the collision processes. However, hydrodynamics models for designing and interpreting nonideal plasma experiments, such as inertial-confinement fusion experiments, typically neglect electrodynamics, although some models include electric fields indirectly through a generalized Fick's law. However, because most transport models are not computed self-consistently with the equation of state, there is double counting of the forces in the excess thermodynamic quantities and the collision terms. Here we employ the statistical mechanical hydrodynamic theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)JCPSA60021-960610.1063/1.1747782] to examine inhomogeneous, nonideal plasmas that contain electric fields. We show that it is not possible to simultaneously separate terms that correspond to electric fields and excess pressure; rather, these quantities arise from the same interparticle Coulomb forces. Moreover, new terms associated with nonlocality appear in the presence of strong inhomogeneities.

Structural characteristics of strongly coupled ions in a dense quantum plasma

The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjölander (STLS) approximation. Different cross-checks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at r_{s}>1, where r_{s} is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.

A viscous quantum hydrodynamics model based on dynamic density functional theory

Dynamic density functional theory (DDFT) is emerging as a useful theoretical technique for modeling the dynamics of correlated systems. We extend DDFT to quantum systems for application to dense plasmas through a quantum hydrodynamics (QHD) approach. The DDFT-based QHD approach includes correlations in the the equation of state self-consistently, satisfies sum rules and includes irreversibility arising from collisions. While QHD can be used generally to model non-equilibrium, heterogeneous plasmas, we employ the DDFT-QHD framework to generate a model for the electronic dynamic structure factor, which offers an avenue for measuring hydrodynamic properties, such as transport coefficients via x-ray Thomson scattering.

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.

Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons

Nonlinear ion-acoustic waves are analyzed in a nonrelativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite-temperature quantum kinetic theory in the long-wavelength limit. The dispersion relation of the obliquely propagating electrostatic waves in magnetized quantum plasma with arbitrary degeneracy of electrons is obtained. Using the reductive perturbation method, the corresponding Zakharov-Kuznetsov equation is derived, describing obliquely propagating two-dimensional ion-acoustic solitons in a magnetized quantum plasma with degenerate electrons having an arbitrary electron temperature. It is found that in the dilute plasma case only electrostatic potential hump structures are possible, while in dense quantum plasma, in principle, both hump and dip soliton structures are obtainable, depending on the electron plasma density and its temperature. The results are validated by comparison with the quantum hydrodynamic model including electron inertia and magnetization effects. Suitable physical parameters for observations are identified.

Atomic bound state and scattering properties of effective momentum-dependent potentials

Effective classical dynamics provide a potentially powerful avenue for modeling large-scale dynamical quantum systems. We have examined the accuracy of a Hamiltonian-based approach that employs effective momentum-dependent potentials (MDPs) within a molecular-dynamics framework through studies of atomic ground states, excited states, ionization energies, and scattering properties of continuum states. Working exclusively with the Kirschbaum-Wilets (KW) formulation with empirical MDPs [C. L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834 (1980)0556-279110.1103/PhysRevA.21.834], optimization leads to very accurate ground-state energies for several elements (e.g., N, F, Ne, Al, S, Ar, and Ca) relative to Hartree-Fock values. The KW MDP parameters obtained are found to be correlated, thereby revealing some degree of transferability in the empirically determined parameters. We have studied excited-state orbits of electron-ion pair to analyze the consequences of the MDP on the classical Coulomb catastrophe. From the optimized ground-state energies, we find that the experimental first- and second-ionization energies are fairly well predicted. Finally, electron-ion scattering was examined by comparing the predicted momentum transfer cross section to a semiclassical phase-shift calculation; optimizing the MDP parameters for the scattering process yielded rather poor results, suggesting a limitation of the use of the KW MDPs for plasmas.

Ionic transport in high-energy-density matter

Ionic transport coefficients for dense plasmas have been numerically computed using an effective Boltzmann approach. We have developed a simplified effective potential approach that yields accurate fits for all of the relevant cross sections and collision integrals. Our results have been validated with molecular-dynamics simulations for self-diffusion, interdiffusion, viscosity, and thermal conductivity. Molecular dynamics has also been used to examine the underlying assumptions of the Boltzmann approach through a categorization of behaviors of the velocity autocorrelation function in the Yukawa phase diagram. Using a velocity-dependent screening model, we examine the role of dynamical screening in transport. Implications of these results for Coulomb logarithm approaches are discussed.

Unified Concept of Effective One Component Plasma for Hot Dense Plasmas

Orbital-free molecular dynamics simulations are used to benchmark two popular models for hot dense plasmas: the one component plasma (OCP) and the Yukawa model. A unified concept emerges where an effective OCP (EOCP) is constructed from the short-range structure of the plasma. An unambiguous ionization and the screening length can be defined and used for a Yukawa system, which reproduces the long-range structure with finite compressibility. Similarly, the dispersion relation of longitudinal waves is consistent with the screened model at vanishing wave number but merges with the OCP at high wave number. Additionally, the EOCP reproduces the overall relaxation time scales of the correlation functions associated with ionic motion. In the hot dense regime, this unified concept of EOCP can be fruitfully applied to deduce properties such as the equation of state, ionic transport coefficients, and the ion feature in x-ray Thomson scattering experiments.