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

TL;DR

This work tackles the challenge of modeling two-temperature, strongly coupled plasmas by developing a thermodynamically consistent multi-temperature statistical framework in the adiabatic-electron limit. It derives the first two-temperature quantum Ornstein-Zernike (QOZ) relations and their Hypernetted-Chain (HNC) closure, and builds a two-temperature two-component plasma (2TTCP) model based on an average-atom (AA) approach, validated against two-temperature DFT-MD simulations. Key contributions include the explicit two-temperature Dyson/OZ structure, a practical HNC closure for multi-temperature systems, and an AA-driven 2TTCP that reproduces ionic structure and transport (including viscosity, diffusion, and ion thermal conductivity) in non-equilibrium plasmas. This framework enables rapid, ab initio-consistent predictions of structure and transport in non-equilibrium dense plasmas, with relevance to inertial confinement fusion and high-energy-density experiments.

Abstract

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.

Figures (7)

• Figure 1: The AA produced pair potential \ref{['eq:uII_eff']} (solid lines), and Yukawa pair potential (dashed) with Thomas-Fermi screening using a $\langle Z \rangle$ from the AA model. Higher electron temperatures are the right most lines. The radial distance on the $x-axis$ is normalized to the ion sphere radius $a_I = (n_I 4\pi/3)^{-1/3}.$
• Figure 2: Ion-ion radial distribution function for Aluminum at solid density $2.7 {\rm g/cm}^3$ and fixed $T_I=1$ eV, with increasing electron temperature from left to right, a) LTE: $T_e=1$ eV ($\langle Z \rangle=3.00$), b)$T_e=3$ eV ($\langle Z \rangle=3.00$), c)$T_e=10$ eV ($\langle Z \rangle=3.02$), d)$T_e=30$ eV ($\langle Z \rangle=4.35$). We show DFT-MD (black plus), classical MD with our 2TTCP pair potential, and HNC with bridge function computations for the 2TTCP (blue solid), the YOCP (red dashed), and the OCP (purple dotted).
• Figure 3: The viscosity of $2.7$ g/cm$^3$ aluminum from the IYVM Johnson2024, which is refitted from MURILLO200849 to better match high temperature scaling.
• Figure 4: Aluminum self diffusion at 2.7 $g/$cm$^3$ for varying electron temperature at $T_I=1$ eV extracted from our PPMD simulations (squares with error bars), our DFT-MD runs with three (black pluses) and eleven (cyan triangles) valence electrons. Also shown are the equilibrium models QOFMD (blue crosses) and PAMD (red circles) from PhysRevLett.116.075002.
• Figure 5: Aluminum self diffusion at 2.7 $g/$cm$^3$ for varying electron temperature at two different ion temperatures, $5$ eV (orange) and $10$ eV (green) extracted from our PPMD simulations (squares with error bars). Also shown is an AA model from HOU201721 (open diamonds) and the equilibrium models QOFMD (blue crosses) and PAMD (red circles) from PhysRevLett.116.075002.