Equation of State Measurements of Warm Dense Carbon Using Laser-Driven Shock and Release Technique

We present a new approach to equation of state experiments that utilizes a laser-driven shock and release technique combined with spatially resolved x-ray Thomson scattering, radiography, velocity interferometry, and optical pyrometry to obtain independent measurements of pressure, density, and temperature for carbon at warm dense matter conditions. The uniqueness of this approach relies on using a laser to create very high initial pressures to enable a very deep release when the shock moves into a low-density pressure standard. This results in material at near normal solid density and temperatures around 10 eV. The spatially resolved Thomson scattering measurements facilitate a temperature determination of the released material by isolating the scattering signal from a specific region in the target. Our results are consistent with quantum molecular dynamics calculations for carbon at these conditions and are compared to several equation of state models.

Figure 1

Schematic of the XRTS target set. The driven target sits inside the larger cone inside a small gold cap and consists of a plastic (CH) ablator, a graphite or diamond sample, and a silica (${\mathrm{SiO}}_2$) aerogel disc. The second smaller gold cones contain Ni and V backlighted foils for XRTS and radiography measurements, respectively, coated on top of a Be filter on the inner side of the cone. Laser beams then illuminate the driven target and the ablator from the inside of each Au cone. The XRTS target also includes Ta pinholes on top of each backlighter to collimate the x rays. The VISAR target is identical but has no backlighter cones or pinholes and includes a $40\text{−}\mu \mathrm{m}$ step on the back side of the aerogel disc.

Figure 2

X-ray scattering data from shock-released diamond at high drive. The best-fit conditions were $T_e=13\pm 2\mathrm{eV}$, $n_e=2.6\pm 0.2\times {10}^{23}{\mathrm{cm}}^{-3}$, and $Z=2.25\pm 0.15$. The error bars were determined by a ${\chi }^2$ fit (inserted image).

Figure 3

An example of released diamond radiography image showing transmitted intensity (a) compared to a mass density plot from two-dimensional (2D) FLASH simulation (b). The 2D simulations confirm that the transverse effects in WDM conditions within the release wave are negligible.

Figure 4

Comparison of data sets with EOS models, including SESAME [14, 15] and QMD simulations by Kwon et al. [4]. The graphite low drive data point ($T_e=11.0\pm 2\mathrm{eV}$, $7.00\pm 0.78\mathrm{Mbar}$, and $\rho =3.0\pm 0.2\mathrm{g}/{\mathrm{cm}}^3$) is compared with isochores from the SESAME table 7832 for graphite, 7831 for liquid carbon Inferno model, and QMD simulations at $3.0\mathrm{g}/{\mathrm{cm}}^3$ (a), while the diamond data points for low ($T_e=5.5\pm 3\mathrm{eV}$, $P=3.79\pm 0.64\mathrm{Mbar}$, and $\rho =2.8\pm 0.2\mathrm{g}/{\mathrm{cm}}^3$) and high drive ($13\pm 2\mathrm{eV}$, $7.32\pm 0.67\mathrm{Mbar}$, and $2.3\pm 0.2\mathrm{g}/{\mathrm{cm}}^3$) are compared with isochores from SESAME table 7830 for diamond and 7831 for liquid carbon at $2.3\mathrm{g}/{\mathrm{cm}}^3$ and $2.8\mathrm{g}/{\mathrm{cm}}^3$. The diamond data are also compared with results from the QMD simulations calculated for the measured temperatures and densities for each data point showing an excellent agreement.