Unified description of linear screening in dense plasmas

Electron screening of ions is among the most fundamental properties of plasmas, determining the effective ionic interactions that impact all properties of a plasma. With the development of new experimental facilities that probe high-energy-density physics regimes ranging from warm dense matter to hot dense matter, a unified framework for describing dense plasma screening has become essential. Such a unified framework is presented here based on finite-temperature orbital-free density functional theory, including gradient corrections and exchange-correlation effects. We find a new analytic pair potential for the ion-ion interaction that incorporates moderate electronic coupling, quantum degeneracy, gradient corrections to the free energy, and finite temperatures. This potential can be used in large-scale “classical” molecular dynamics simulations, as well as in simpler theoretical models (e.g., integral equations and Monte Carlo), with no additional computational complexity. The new potential theoretically connects limits of Debye-Hückel–Yukawa, Lindhard, Thomas-Fermi, and Bohmian quantum hydrodynamics descriptions. Based on this new potential, we predict ionic static structure factors that can be validated using x-ray Thomson scattering data.

Figure 1

Screening lengths ${\lambda }_{\pm }$ and ${\gamma }_{+}$ for EGS (green, solid line) compared to ${\lambda }_{\text{TF}}$ for TF-Y (blue, dotted line) and ${\lambda }_{\text{D}}$ for DH (blue, dashed line). The top panel shows the lengths as a function of $T_e$ with the fixed mean electron density being $n_0={10}^{22}{\mathrm{cm}}^{-3}$, while the bottom panel shows the lengths as a function of $n_0$ with the fixed temperature $T_e=1$ eV. The bifurcation points on each EGS curve correspond to the monotonic-oscillatory transition.

Figure 2

Comparison of free electron density deviations from the mean, $n_0$, about a point impurity at the origin for TF-Y (blue, dashed) and EGS (green, solid), where $n_0={10}^{22}{\mathrm{cm}}^{-3}$ and $T_e=5$ eV. The inset is the same plot on a semilog scale. Note that EGS correctly predicts $\delta n\left(0\right)$ to be a finite cusp, and as $r\to \infty$, it predicts a lower electron density. These effects arise due to the fact that the Kirzhnits correction (12) penalizes not only gradients but also low densities.

Figure 3

Phase space regions of screening model validity for Be. Unscreened Coulombic interactions lose validity for temperatures and densities below ${\lambda }_{\text{TF}}=a_i$ (white line), and similarly, the Yukawa interaction loses validity below ${\lambda }_{+}={\lambda }_{-}$ (black lines). For the latter condition, we have shown the cases with (dashed, black line) and without (solid, black line) local field corrections. Behind these curves, a color plot of ${\Gamma }_{ee}$ is shown to demonstrate regions of strong e-e coupling.

Figure 4

Radial distribution function (a) and static structure factor (b) comparisons between TF-Y (blue, dashed line) and EGS (green, solid line) models for Al. In each case, we have set $Z^{*}=3$, $n_i=6\times {10}^{22}{\mathrm{cm}}^{-3}$, and $T_e=0.5$ eV. The EGS potential predicts a lower repulsion between ions than the TF-Y model due to the reduced electron densities near the ionic centers; however, the overall screening effects are enhanced from the diminished densities in the far field.