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

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 averageatom 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.

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

“…Another fundamental property of the UEG is the arXiv:2106.00973v1 [physics.comp-ph] 2 Jun 2021 momentum distribution function n(k), which is highly important for the development of accurate models for the computation of different transport properties of WDM [80]. At finite temperatures, the first results have been presented by Militzer et al [81,82] based on approximate restricted path integral Monte Carlo (PIMC) simulations.…”