arXiv subjects

Nathaniel R. Shaffer

Publications and source records attributed to Nathaniel R. Shaffer.

11 recordsLinked to original sources

arXiv2026

Plasma Conductivity from Warm Dense Matter to the Spitzer Limit Using Mean-Force Kinetic Theory

A theoretical model is developed to compute electronic transport coefficients extending from warm and dense to hot and dilute plasma conditions. This kinetic theory-based approach models strong Coulomb correlations by treating interactions using the potential of mean force, electron degeneracy using the Uehling-Uhlenbeck equation, and diffraction by computing cross sections quantum mechanically. The result provides a fast and accurate means to compute electrical conductivity,thermal conductivity and electrothermal coefficients, including contributions from electron-electron interactions. The model enables accurate calculation of materials properties in many warm dense matter systems, including inertial confinement fusion, stellar evolution, and high energy density plasma experiments.

physics.plasm-ph↗

arXiv2026

Kinetic Theory for Electronic Transport Properties of Warm Dense Matter: Chapman-Enskog Solution of the Uehling-Uhlenbeck Equation

A kinetic theory is developed to describe the electrical conductivity, thermal conductivity, and electrothermal coefficients in warm dense plasmas. It models electron degeneracy using the Uehling-Uhlenbeck equation, diffraction by computing scattering cross sections quantum mechanically, and strong coupling by treating the scattering events using the potential of mean force. A key advancement detailed here is the development of a Chapman-Enskog solution of the Uehling-Uhlenbeck equation for hydrodynamic transport coefficients. The result is a model which accurately predicts transport coefficients spanning from warm dense matter conditions through hot dilute plasmas, including the influence of electron-electron interactions. Results are compared with quantum molecular dynamics simulations, experiments, and other models. The present method is able to capture the ''Spitzer'' terms in the classical plasma limit, while also capturing the correct degenerate limit. The transition between these limits in the warm dense matter regime is explained in terms of the availability of states for electron scattering.

physics.plasm-ph↗

arXiv2024

Quantum Ornstein-Zernike Theory for Two-Temperature Two-Component Plasmas

Laboratory plasma production almost always preferentially heats either the ions or electrons, leading to a two-temperature state. High-fidelity modeling of these systems can be achieved with density functional theory molecular dynamics in the two-temperature, adiabatic electron limit. Motivated by this, we construct a statistical mechanics framework for the multi-temperature system that is theoretically consistent with the ab initio calculation. We proceed to derive multi-temperature quantum Ornstein-Zernike equations for the first time. We then construct a two-temperature two-component plasma model using the average atom and compute the radial distribution function, viscosity, ion thermal conductivity, and ion self-diffusion. We verify that we recover the ionic structure and self-diffusion of density functional molecular dynamics simulations.

physics.plasm-ph↗

arXiv2022

Dense plasma opacity via the multiple-scattering method

The calculation of the optical properties of hot dense plasmas with a model that has self-consistent plasma physics is a grand challenge for high energy density science. Here we exploit a recently developed electronic structure model that uses multiple scattering theory to solve the Kohn-Sham density functional theory equations for dense plasmas. We calculate opacities in this regime, validate the method, and apply it to recent experimental measurements of opacity for Cr, Ni, and Fe. Good agreement is found in the quasicontinuum region for Cr and Ni, while the self-consistent plasma physics of the approach cannot explain the observed difference between models and the experiment for Fe.

physics.plasm-ph↗

arXiv2020

New Conductive Opacities for White Dwarf Envelopes

Thanks to their continuous cooling and relative simplicity, white dwarf stars are routinely used to measure the ages of stellar populations. The usefulness of white dwarfs as cosmochronometers depends on the availability of accurate cooling models. A key ingredient of those models are the conductive opacities, which largely govern the cooling rate. In this work, we present improved conductive opacities for the regime of moderate coupling and moderate degeneracy that characterizes an important portion of the envelopes of DA and DB white dwarfs. We find differences of up to a factor 3 between our calculations and the commonly used opacities of Cassisi et al. (2007), which we attribute to an improved account of electron-electron scattering. The cooling models are strongly affected by those changes in the conductive opacities: the age of a 4000 K white dwarf can be reduced by as much as 2 Gyr. We provide analytical fits to our new opacities to facilitate the implementation of this important effect in white dwarf evolution codes.

astro-ph.SR↗

arXiv2020

A Model of Electron Transport in Dense Plasmas Spanning Temperature Regimes

We present a new model of electron transport in warm and hot dense plasmas which combines the quantum Landau-Fokker-Planck equation with the concept of mean-force scattering. We obtain electrical and thermal conductivities across several orders of magnitude in temperature, from warm dense matter conditions to hot, nondegenerate plasma conditions, including the challenging crossover regime between the two. The small-angle approximation characteristic of Fokker-Planck collision theories is mitigated to good effect by the construction of accurate effective Coulomb logarithms based on mean-force scattering, which allows the theory to remain accurate even at low temperatures, as compared with high-fidelity quantum simulation results. Electron-electron collisions are treated on equal footing as electron-ion collisions. Their accurate treatment is found to be essential for hydrogen, and is expected to be important to other low-Z elements. We find that electron-electron scattering remains influential to the value of the thermal conductivity down to temperatures somewhat below the Fermi energy. The accuracy of the theory seems to falter only for the behavior of the thermal conductivity at very low temperatures due to a subtle interplay between the Pauli exclusion principle and the small-angle approximation as they pertain to electron-electron scattering. Even there, the model is in fair agreement with ab initio simulations.

physics.plasm-ph↗

arXiv2020

Correlations Between Conduction Electrons in Dense Plasmas

Most treatments of electron-electron correlations in dense plasmas either ignore them entirely (random phase approximation) or neglect the role of ions (jellium approximation). In this work, we go beyond both these approximations to derive a new formula for the electron-electron static structure factor which properly accounts for the contributions of both ionic structure and quantum-mechanical dynamic response in the electrons. The result can be viewed as a natural extension of the quantum Ornstein-Zernike theory of ionic and electronic correlations, and it is suitable for dense plasmas in which the ions are classical and the conduction electrons are quantum-mechanical. The corresponding electron-electron pair distribution functions are compared with the results of path integral Monte Carlo simulations, showing good agreement whenever no strong electron resonance states are present. We construct approximate potentials of mean force which describe the effective screened interaction between electrons. Significant deviations from Debye-Hückel screening are present at temperatures and densities relevant to high energy density experiments involving warm and hot dense plasmas. The presence of correlations between conduction electrons is likely to influence the electron-electron contribution to the electron and thermal conductivity. It is expected that excitation processes involving the conduction electrons (e.g., free-free absorption) will also be affected.

physics.plasm-ph↗

arXiv2019

The Barkas Effect in Plasma Transport

Molecular dynamics simulations reveal that a fundamental symmetry of plasma kinetic theory is broken at moderate to strong Coulomb coupling: the collision rate depends on the signs of the colliding charges. This symmetry breaking is analogous to the Barkas effect observed in charged-particle stopping experiments and gives rise to significantly enhanced electron-ion collision rates. It is expected to affect any neutral plasma with moderate to strong Coulomb coupling such as ultracold neutral plasmas (UNP) and the dense plasmas of ICF and laser-matter interaction experiments. The physical mechanism responsible is screening of binary collisions by the correlated plasma medium, which causes an asymmetry in the dynamics of large-angle scattering. Because the effect pertains only to close interactions, it is not predicted by traditional transport models based on cut-off Coulomb collisions or linear dielectric response. A model for the effective screened interaction potential is presented that is suitable for the coupling strengths achieved in UNP experiments. Transport calculations based on this potential and the effective potential kinetic theory agree with simulated relaxation rates and predict that the Barkas effect can cause up to a 70% increase in the electron-ion collision rate at the conditions of present UNP experiments. The influence of the Barkas effect in other transport processes is also considered.

physics.plasm-ph↗

arXiv2017

Pair Correlation Functions of Strongly Coupled Two-Temperature Plasma

Using molecular dynamics simulations, we perform the first direct tests of three proposed models for the pair correlation functions of strongly coupled plasmas with species of unequal temperature. The models are all extensions of the Ornstein-Zernike/hypernetted-chain theory used to good success for equilibrium plasmas. Each theory is evaluated at several coupling strengths, temperature ratios, and mass ratios for a model plasma in which the electrons are positively charged. We show that the model proposed by Seuferling, Vogel, and Teopffer [Phys. Rev. A 40, 323 (1989)] agrees well with molecular dynamics over a wide range of mass and temperature ratios, as well as over a range of coupling strength similar to that of the equilibrium HNC theory. The SVT model also correctly predicts the strength of interspecies correlations and exhibits physically reasonable long-wavelength limits of the static structure factors. Comparisons of the SVT model with the Yukawa OCP model are used to show that ion-ion pair correlations are well described by the YOCP model up to $Γ_e \approx 1$, beyond which it rapidly breaks down.

physics.plasm-ph↗

arXiv2016

Thermodynamic State Variables in Quasi-Equilibrium Ultracold Neutral Plasma

The pressure and internal energy of an ultracold plasma in a state of quasi-equilibrium are evaluated using classical molecular dynamics simulations. Coulomb collapse is avoided by modeling electron-ion interactions using an attractive Coulomb potential with a repulsive core. We present a method to separate the contribution of classical bound states, which form due to recombination, from the contribution of free charges when evaluating these thermodynamic state variables. It is found that the contribution from free charges is independent of the choice of repulsive core length-scale when it is sufficiently short-ranged. The partial pressure associated with the free charges is found to closely follow that of the one-component plasma model, reaching negative values at strong coupling, while the total system pressure remains positive. This pseudo-potential model is also applied to Debye-Hückel theory to describe the weakly coupled regime.

physics.plasm-ph↗

arXiv2016

Effective Potential Theory for Diffusion in Binary Ionic Mixtures

Self-diffusion and interdiffusion coefficients of binary ionic mixtures are evaluated using the Effective Potential Theory (EPT), and the predictions are compared with the results of molecular dynamics simulations. We find that EPT agrees with molecular dynamics from weak coupling well into the strong coupling regime, which is a similar range of coupling strengths as previously observed in comparisons with the one-component plasma. Within this range, typical relative errors of approximately 20% and worst-case relative errors of approximately 40% are observed. We also examine the Darken model, which approximates the interdiffusion coefficients based on the self-diffusion coefficients.

physics.plasm-ph↗