Measurement of the sound velocity and Grüneisen parameter of polystyrene at inertial confinement fusion conditions

The principal Hugoniot, sound velocity, and Grüneisen parameter of polystyrene were measured at conditions relevant to shocks in inertial confinement fusion implosions, from 100 to 1000 GPa. The sound velocity is in good agreement with quantum molecular dynamics calculations and all tabular equation of state models at pressures below 200 GPa. Above 200 GPa, the experimental results agree with two of the examined tables, but do not agree with the most recent table developed for design of inertial confinement fusion (ICF) experiments. The Grüneisen parameter increases with density below $\sim 3.1\mathrm{g}/{\mathrm{cm}}^3$ and approaches the asymptotic value for an ideal gas after complete dissociation. This behavior is in good agreement with quantum molecular dynamics results and previous work but is not represented by any of the tabular models. The discrepancy between tabular models and experimental measurement of the sound velocity and Grüneisen parameter is sufficient to impact simulations of ICF experiments.

Figure 1

(a) Schematic of multilayered flat targets consisting of Parylene-N ablator, quartz baseplate, and quartz and CH samples. (b) The raw VISAR data from shot 22092 shows a decaying shock in the quartz baseplate followed by a perturbed steady shock in the quartz and CH samples. (c) The perturbations to the quartz (red) and CH (dashed blue) shock velocities shown were used to determine the CH sound velocity. The data were averaged over four fringes (∼100 µm) in the center of the target [±50–150 µm in (b)].

Figure 2

(a) $U_s\text{−}{u}_p$ results from this work (yellow diamonds) are in good agreement with reanalyzed results from Barrios (blue squares). The new $U_S\text{−}{u}_p$ fit (solid red line) is systematically stiffer than the fit determined by Barrios (dotted black line) using an earlier version of the quartz standard. (b) The experimental results are in good agreement with QMD-based FPEOS-0516 (dashed-double-dotted black line) and the SESAME 7593 (dashed-dotted green line) EOS tables. Neither LEOS 5111 (long-dashed blue line) nor 5400 (dashed purple line) are in good agreement with the data, with LEOS 5111 being too compressible and LEOS 5400 being too incompressible at pressures below 400 GPa.

Figure 3

The isentropic sound velocity measurements (yellow diamonds) are in good agreement with QMD calculations (black circles) of the sound velocity along the Hugoniot. Both sets of data show a slight plateau in sound velocity between 400 and 500 GPa. The results also agree well with the SESAME 7593 (dashed-dotted green line) table, as well as LEOS 5111 (long-dashed blue line) for pressures >350 GPa and LEOS 5400 (dashed purple line) at low pressure. The large plateau in sound velocity exhibited in LEOS 5400 is not supported by these results, such that LEOS 5400 underpredicts the sound velocity above 200 GPa.

Figure 4

Lines and symbols same as in Fig. 3. Measurements of the polystyrene Grüneisen parameter exhibit an increase with density until reaching an approximately constant value at $\sim 3.2\mathrm{g}/{\mathrm{cm}}^3$. This behavior is in good agreement with these QMD calculations for CH and previous calculations for GDP (connected gray squares). None of the EOS tables shown agree with these results and the SESAME 7593 table is the only one where the Grüneisen parameter increases with density before reaching a nearly constant result. The LEOS 5111 table has an approximately constant Grüneisen parameter for the entire density range shown. The LEOS 5400 table exhibits behavior opposite the experimental and QMD results albeit with the maximum deviation from the asymptotic value being similar.