Ab initio calculation of shocked xenon reflectivity

Reflectivity of shocked compressed xenon plasma is calculated within the framework of the density functional theory approach. Dependencies on the frequency of incident radiation and on the plasma density are analyzed. The Fresnel formula for the reflectivity is used. The longitudinal expression in the long-wavelength limit is applied for the calculation of the imaginary part of the dielectric function. The real part of the dielectric function is calculated by means of the Kramers-Kronig transformation. The results are compared with experimental data. The approach for the calculation of plasma frequency is developed.

Figure 1

Dependence of reflectivity $R$ on the electron concentration $n_e$ at $\lambda =694$ nm. The solid line corresponds to the case of collisionless plasma, where there is a cutoff of reflectivity at the plasma frequency. The red stars are the experimental data [18]. The dashed black line corresponds to the reflectivities calculated by the Drude formula with the static collisional frequency [22].

Figure 2

Dependencies of function $S$ on the upper limit ${\omega }_{\max }$ at various densities $\rho$.

Figure 3

Dependencies of plasma frequency on density of xenon plasma. Pentagons correspond to values of ${\omega }_p$ calculated by using Drude formula (13). Squares are results calculated with formula (16). Circles are estimates of plasma frequencies obtained in Refs. [18, 22]. Arrows indicate the values of the frequencies, which correspond to the wavelengths 1064, 694, and 532 nm.

Figure 4

An example of the electron density of states at $\rho =1.6$ ${\text{g/cm}}^3$.

Figure 5

Dependencies of the shocked xenon plasma reflectivity on the plasma density at various values of wavelengths. The experimental data [17, 18, 19, 20] are depicted by stars. The squares correspond to the calculation data. The arrows indicate the values of the plasma density where the frequency of incident radiation and the plasma frequency coincide with each other.

Figure 6

Dependencies of the reflectivity on the plasma density at the wavelength 1064 nm. The solid line is the case of collisionless plasma. The dashed line corresponds to the reflectivities calculated by the Drude formula with the static collisional frequency [22]. The dash-dot line is the Drude model with a wide wave front as a fitting parameter [22, 24, 25, 26]. The stars are the experimental data [17]. The pentagons connected by the dashed line are results or Ref. [34]; the circles connected by the dashed line are results of Ref. [34] with band-gap corrections; the squares connected by the solid line are the results of this work. The arrows indicate the plasma density where the frequency of the incident radiation equals to the plasma frequency.

Figure 7

Reflectivities calculated in the DFT framework with the Kubo-Greenwood formula at various densities: The pentagons connected by the dashed line are the results of Ref. [34], and the diamond are results of this work.