Ab initio simulations and measurements of the free-free opacity in aluminum

The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10 eV.

Figure 1

Experimental setup for the opacity measurement on the Artemis facility.

Figure 2

Measurement of the transmission through the Al step target for the 15th laser harmonic around 24 eV. The top panels show the spatial intensity distribution of the HHG beam without a target (full beam), and the transmitted intensity through the step target. The natural log of the ratio of the two yields the total absorption [see Eq. (2)], which when plotted in 3D to illustrate that the steps of the target are clearly visible in the absorption measurement.

Figure 3

Observed transmission of the 15th harmonic through the Al step target sample. Following Eq. (2) we perform a linear fit to the five data points to extract $\kappa \left(\omega \right)$ (the slope), $\alpha \left(\omega \right)$ (the $y$ intercept), and related errors. Fitted lines corresponding to the largest and smallest slopes are shown.

Figure 4

Comparison of the equation of state for solid density, warm dense Al as predicted following our MD simulations, confirming consistency with previously published average-atom and multicentred Kohn-Sham calculations [30].

Figure 5

Spectral function for the $2p$ bound state and the lowest lying continuum state for $T=15$ eV. Restriction to single shot ${\mathrm{G}}_0{\mathrm{W}}_0$ combined with a finite-order Padé approximant for the analytic continuation results in broad quasiparticle peaks lacking clear satellite features.

Figure 6

(a) Calculated opacity for room temperature Al along with our own measurements and those of previous studies. (b) LFC increases absorption between the plasma frequency and the L-edge, while the primary effect of the ${\mathrm{G}}_0{\mathrm{W}}_0$ correction is to shift the energy of the L-shell reducing the opacity.

Figure 7

Calculated opacity for equilibrated warm dense Al up to $T=15\mathrm{eV}$ along with the single data point of Kettle et al. ($T_e\approx 1\mathrm{eV}$).

Figure 8

Comparison of our calculated opacity with the inverse bremsstrahlung (IB) model of Ref. [10] at high temperatures. Our results appear to approach the IB model both in slope and absolute value.