A Kinetic Model for Electron-Ion Transport in Warm Dense Matter

TL;DR

This paper develops a quantum kinetic model incorporating Coulomb coupling effects for electron-ion transport in Warm Dense Matter, predicting relaxation times and conductivity with good agreement to simulations.

Contribution

It introduces a quantum generalization of a classical Coulomb coupling model using a potential of mean force from the quantum Ornstein-Zernike equation, including exchange and correlation effects.

Findings

Predicted relaxation times and conductivity for solid density aluminum plasma.

Model spans classical to degenerate plasma regimes.

Results agree with recent quantum molecular dynamics simulations.

Abstract

We present a model for electron-ion transport in Warm Dense Matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although this model has been derived rigorously in the classical limit [S.D. Baalrud and J. Daligault, Physics of Plasmas 26, 8, 082106 (2019)], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. By solving the Uehling-Uhlenbeck equation for electron-ion relaxation rates, we predict the momentum and temperature relaxation time and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.