First-principles equation of state of CHON resin for inertial confinement fusion applications

A wide-range (0 to 1044.0 g/${\mathrm{cm}}^3$ and 0 to ${10}^9$ K) equation-of-state (EOS) table for a ${\mathrm{CH}}_{1.72}{\mathrm{O}}_{0.37}{\mathrm{N}}_{0.086}$ quaternary compound has been constructed based on density-functional theory (DFT) molecular-dynamics (MD) calculations using a combination of Kohn-Sham DFT MD, orbital-free DFT MD, and numerical extrapolation. The first-principles EOS data are compared with predictions of simple models, including the fully ionized ideal gas and the Fermi-degenerate electron gas models, to chart their temperature-density conditions of applicability. The shock Hugoniot, thermodynamic properties, and bulk sound velocities are predicted based on the EOS table and compared to those of C-H compounds. The Hugoniot results show the maximum compression ratio of the C-H-O-N resin is larger than that of CH polystyrene due to the existence of oxygen and nitrogen; while the other properties are similar between CHON and CH. Radiation hydrodynamic simulations have been performed using the table for inertial confinement fusion targets with a CHON ablator and compared with a similar design with CH. The simulations show CHON outperforms CH as the ablator for laser-direct-drive target designs.

Figure 1

A snapshot of the 50-atom CHON unit cell after KS-DFT-MD simulations at 1.2 g/${\mathrm{cm}}^3$ and 1000 K, which consists of a C-H-O-N frame and a ${\mathrm{H}}_2$ molecule. Edges of the periodic cell are shown with gray lines. Brown, cream, red, and blue spheres represent C, H, O, and N atoms, respectively.

Figure 2

Temperature-density grid of the EOS data for CHON produced in this work. The data at densities below 0.025 g/${\mathrm{cm}}^3$ are extrapolated based on the Redlich-Kwong fit of data between 0.1 and 1.0 g/${\mathrm{cm}}^3$ and therefore not shown for clarity. “bC”: bare Coulomb.

Figure 3

Fit of (a) low-density (up to 1.2 g/${\mathrm{cm}}^3$) pressures and (b) energies data (empty squares) to a Redlich-Kwong model along different isotherms (line-crosses).

Figure 4

(a) Internal energy and (b) pressure of CHON along different isochores considered in this study. “bC”: bare Coulomb. Gray lines denote corresponding values for a fully ionized ideal gas. The energies have been uniformly lifted by 310 eV/50-atom cell to ensure positive values for the logarithmic plot.

Figure 5

Matching KS (blue) and OF (red) data in (a) energy and (b) pressure along selected isochores in this work. Data shown are relative to values of fully ionized ideal gas (denoted by $E_0$ and $P_0$ and shown with black dotted horizontal lines). Blue diamonds and squares denote calculations using PAW and bare-Coulomb potentials, respectively. Different isochores have been shifted apart for clarity.

Figure 6

(a) Internal energy and (b) pressure of CHON along different isotherms considered in this study. “bC”: bare Coulomb. Gray lines represent the fully ionized ideal gas value. Black lines denote the Fermi degenerate electron gas values at zero K.

Figure 7

Comparison in pair-correlation functions from OF-DFT-MD and KS-DFT-MD calculations of CHON at selected densities and 250 000 K. The different sets of curves have been shifted apart for clarity. “bC”: bare-Coulomb.

Figure 8

(a) Pressure- and (b) temperature-compression ratio Hugoniot of CHON compared with that of CH from KS/OF calculations and those of C–H compounds, O, and N from FPEOS.

Figure 9

(a) Heat capacity, (b) Grüneisen parameter, (c) thermal expansivity, and (d) bulk sound velocity of CHON as functions of temperature along selected isochores and the principal Hugoniot. Corresponding properties of pure CH along the polystyrene Hugoniot and calculated based on the FPEOS database [12, 13, 48] are shown in dark-gray solid curves for comparison. In (a) and (b), the horizontal gray dashed lines denote the corresponding values of a fully ionized ideal gas.

Figure 10

Target assemblies using (a) CH or (b) CHON as the ablator, and (c) laser pulse shape used in our LILAC simulations.

Figure 11

Comparison in the time evolution of (a) laser absorption fraction and (b) implosion velocity between targets using CH or CHON as the ablator.

Figure 12

Comparison in (a) areal density and (b) neutron yield at later time of the implosion when using targets with CH or CHON ablators.

Figure 13

Energy differences between PAW and bare-Coulomb calculations for single snapshots as a function of (a) density and (b) electronic temperature. In (a), the electronic temperature is 1000 K in all cases except 17.5 g/${\mathrm{cm}}^3$, which includes results from extra calculations at 15,625 K or using a $2\times 2\times 2$ $k$ mesh, as compared to only using the $\mathrm{\Gamma }$ point in other cases. Differences between (a) and (b) at comparable density-temperature conditions are negligible and are due to differences in snapshots and detailed settings of the calculations. “bC”: bare-Coulomb.

Figure 14

Comparison in (a),(b) pressure and (c),(d) energy calculated by KS calculations using different potentials. Results in (a) and (c) are based on single-snapshot KS-DFT calculations for the same structures and electronic temperatures as Fig. 13. Results in (b) and (d) are based on KS-DFT-MD calculations at 25 g/${\mathrm{cm}}^3$. “bC”: bare-Coulomb.

Figure 15

(a) Tuning parameters $\gamma$ determined in this study for CHON at different densities. The matching temperature is shown in the legend. (b) Relative differences in pressure between OF- and KS-DFT MD at the matching condition.

Figure 16

(a) Pressures and (b) internal energies at relatively low densities along four different isotherms. KS-DFT(-MD) data are shown with diamond symbols for comparison.