Optical conductivity of warm dense matter within a wide frequency range using quantum statistical and kinetic approaches

Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity; absorption, emission, and scattering of radiation; charged particles stopping; and further macroscopic properties. Different approaches to the dielectric function and the related dynamical collision frequency are compared in a wide frequency range. The high-frequency limit describing inverse bremsstrahlung and the low-frequency limit of the dc conductivity are considered. Sum rules and Kramers-Kronig relation are checked for the generalized linear response theory and the standard approach following kinetic theory. The results are discussed in application to aluminum, xenon, and argon plasmas.

Figure 1

Temperature dependence of the real (a) and the imaginary (b) part of the DF $\varepsilon \left(\omega \right)$ and the absorption coefficient $A$ (c) at a frequency of 3.09 eV. The coupling parameters ${\mathrm{\Gamma }}_{\mathrm{ei}}$ and ${\mathrm{\Gamma }}_{\mathrm{deg}}$ and degeneracy parameter $\mathrm{\Theta }$ are given in (d). The vertical dotted line denotes the Fermi energy. The models used are given in the legend; see Table 1 for explanations.

Figure 2

The same as in Figs. 1–1 and the electron-ion effective collision frequency ${\nu }_{\mathrm{eff}}$ (d) for a slightly extended temperature range. Not all models are shown again. Some additional models are added.

Figure 3

Real (a),(c) and imaginary (b),(d) parts of the generalized Drude-like collision frequency ${\nu }_{\mathrm{Dr}}\left(\omega \right)$ (87) as function of the laser frequency radiating solid-density aluminum plasma at $T_{\mathrm{i}}=T=300$ eV considered in different frequency ranges. The models used are given in the legend; see Table 1 for explanations and asymptotic formulas in Sec. 2e.

Figure 4

The same as in Fig. 3. The models used are different and given in the legend; see Table 1 for explanations.

Figure 5

Real and imaginary parts of the generalized Drude-like collision frequency ${\nu }_{\mathrm{Dr}}\left(\omega \right)$ (87), as functions of the laser frequency radiating solid-density aluminum plasma at $T_{\mathrm{i}}=T=20$ eV. The models used are given in the legend; see Table 1 for explanations.

Figure 6

The same as in Fig. 5. The models used are different and given in the legend; see Table 1 for explanations.

Figure 7

Dimensionless dc conductivity ${\sigma }^{*}$ [Eq. (88)] as a function of the coupling parameter ${\mathrm{\Gamma }}_{\mathrm{ei}}$ for dense argon and xenon plasmas at temperature $T=T_{\mathrm{i}}\approx 25000$ K. Experimental points of Ivanov et al. [92] and Shilkin et al. [93] for xenon and argon plasmas are shown by large markers and calculations using LRT and KT models are depicted by (marked) lines; see legend and Table 1 for explanations.

Figure 8

Reflectivity $R$ as a function of the free electron density $n_{\mathrm{e}}$ obtained from shock wave experiments on xenon plasmas, $T=T_{\mathrm{i}}\approx 30000$ K. Experimental data [94] are shown by large markers: red squares for wavelength $\lambda =1.06\mu \mathrm{m}$; green triangles for $\lambda =0.694\mu \mathrm{m}$; blue circles for $\lambda =0.532\mu \mathrm{m}$. Marked lines (with the same colors and markers for the same $\lambda$) show the LRT calculations (model ${\mathrm{RSB}\text{−}2+\mathrm{PS}}_{EC}+\text{ee}$); dotted lines show the same, but without the restriction of the screening radius from below by $R_0$ (model ${\mathrm{SB}\text{−}2+\mathrm{PS}}_{EC}+\text{ee}$).

Figure 9

Ratio $\alpha =A/A_{\mathrm{st}}$ as function of ratio ${\kappa }_S=L_S/l_s$ of a plasma with linear ramp of its density profile for different wavelengths $\lambda$ in $\mu \mathrm{m}$. Different electron densities are considered: $n=1.5,3,6\times {10}^{21}{\mathrm{cm}}^{-3}$ for thick, medium, and thin curves, respectively. The calculations in the limit of weak plasma absorption by formula (95) are shown by solid curves, but only as long as $n/n_c>1$. Numerical calculations with absorption determined by the three-moment screened Born approximation for xenon plasmas with $T=T_{\mathrm{i}}=30000$ K are shown by dashed curves.

Figure 10

The same as in Fig. 8, but with the account of a nonzero value of $\mathrm{Re}\left\{\delta {\varepsilon }_{\mathrm{b}}\left(\omega \right)\right\}$ in the calculations (solid marked lines). A constant value $\mathrm{Re}\left\{\delta {\varepsilon }_{\mathrm{b}}\left(\omega \right)\right\}=0.7$ was used in all calculations.