Reflectivity of Shock Compressed Xenon Plasma

Experimental results [1] for the reflection coefficient of shock-compressed dense Xenon plasmas at pressures of 1.6 – 17 GPa and temperatures around 30 000 K using a laser beam with λ = 1.06 μm are compared with calculations based on different theoretical approaches to the dynamical collision frequency. It is found that a reasonable description can be given assuming a spatial electron density profile corresponding to a finite width of the shock wave front of about 2 · 10−6 m. 1 Reflectivity measurements Experiments with an explosively driven generator of shock waves to produce dense nonideal Xenon plasmas were reported in [1]. The reflectivity was measured using a laser system with the wave length λl = 1.06 μm. The results of the experiments are shown in Tab. 1. The thermodynamic parameters of the plasma were determined from the measured shock wave velocity. The plasma composition was calculated within a chemical picture [2]. Working with a grand canonical ensemble [3] virial corrections have been taken into account due to charge-charge interactions (Debye approximation). Short range repulsion of atoms and ions (including multiply charged positive ions) was considered via second and third virial coefficients within a virial expansions. In the parameter range of the shock wave experiments, derivations of up to 20 % for the composition have been obtained depending on the approximations for the equation of state. This is within the accuracy of the experimental values of the reflectivity. P/ GPa T/ K ρ/ g cm−3 ne/ cm−3 na/cm−3 R 1.6 30050 0.51 1.8×1021 6.1×1020 0.096 3.1 29570 0.97 3.2×1021 1.4×1021 0.12 5.1 30260 1.46 4.5×1021 2.2×1021 0.18 7.3 29810 1.98 5.7×1021 3.5×1021 0.26 10.5 29250 2.70 7.1×1021 5.4×1021 0.36 16.7 28810 3.84 9.1×1021 8.6×1021 0.47 Tab. 1: Experimental results for the reflectivity R of Xenon plasmas at given parameter values: pressure P , temperature T , mass density ρ, free electron number density ne and density of neutral atoms na. 2 Contrib. Plasma Phys. vol (year) num It was suggested that the measurement of reflectivity allows to determine the concentration of free electrons in the plasma. However, investigating these data [1], it was not possible to find a direct relationship between the values of free electron density ne and the reflectivity R. The reflection coefficient increases smoothly with the free electron density. It approaches only slowly values characteristic for metals, although the critical density for metallic behaviour n e = 1.02×1021cm−3, where the plasma frequency, ωpl = √ nee/( 0me) with me the electron mass, coincides with the frequency ωl of the probing laser pulse, is exceeded even at the lowest density. However, this critical density is taken from the RPA approximation for the dielectric function in the long–wavelength limit = 1−ω2 pl/ω l where total reflection occurs due to a vanishing dielectric function. Taking collisions into account this will be smoothed out. On the other hand, a sharp boundary between plasma and undisturbed gas in front of shock wave is assumed. In [1], the spatial structure of the ionizing shock wave was discussed, showing three characteristic zones, which may influence the electromagnetic wave propagation. In a precursor zone, the gas is heated, but the influence on the wave propagation is small. In the region of the shock wave front a steep increase of the free electron density is expected. The width of the wave front is determined by relaxation processes in the plasma. It was estimated to be of the order d ≈ 10−7 m [1], which is one order of magnitude less than the laser wave length. Under this condition d/λ 1, the laser beam reflection was assumed to be determined by the electron properties of the plasma behind the shock wave front. An expression derived from the Fresnel formula in the long–wavelength limit R(ω) = ∣∣∣∣ √ (ω)− 1 √ (ω) + 1 ∣∣∣∣ 2 (1) was applied where the frequency ω has to be taken at the laser frequency ωl = 1.8 · 10 Hz. The complex frequency–dependent dielectric permittivity (ω) = 1 + i 0ω σ(ω) = 1− ω 2 pl ω[ω + iν(ω)] (2) has been related to the dynamical conductivity σ(ω) or the dynamical collision frequency ν(ω). The Drude formula σ(ω) = 0 ω 2 pl ν(0)− iω (3) follows if the collision frequency is taken in the static limit ν(0) = 0ω 2 pl/σ(0) relating it to the static conductivity σ(0). Different expressions for σ(0) have been considered in [1], but no satisfying explanation of the experimental results has been given there. As will be seen in the following discussion, the Drude model is not an appropriate approximation under the experimental conditions considered. In the present work, improvements in the calculation of the dielectric function as well as considerations concerning the shape of the wave front will be discussed to find a consistent theoretical approach to the measured reflectivities. H. Reinholz, Plasma Reflectivity 3 2 Reflection by a step-like plasma front In this section, we investigate the reflection coefficient at a shock wave front where its width d shall be neglected. According to the Fresnel formula, the reflection coefficient at a step-like plasma front [4] R(ω) = ∣∣∣∣1− Z(ω) 1 + Z(ω) ∣∣∣∣ 2