First-principles equation-of-state table of beryllium based on density-functional theory calculations

Laser-direct-drive fusion target design with a high-Z gradient-density pusher shell

Laser-direct-drive fusion target designs with solid deuterium-tritium (DT) fuel, a high-Z gradient-density pusher shell (GDPS), and a Au-coated foam layer have been investigated through both 1D and 2D radiation-hydrodynamic simulations. Compared with conventional low-Z ablators and DT-push-on-DT targets, these GDPS targets possess certain advantages of being instability-resistant implosions that can be high adiabat (α≥8) and low hot-spot and pusher-shell convergence (CR_{hs}≈22 and CR_{PS}≈17), and have a low implosion velocity (v_{imp}<3×10^{7}cm/s). Using symmetric drive with laser energies of 1.9 to 2.5MJ, 1D lilac simulations of these GDPS implosions can result in neutron yields corresponding to ≳50-MJ energy, even with reduced laser absorption due to the cross-beam energy transfer (CBET) effect. Two-dimensional draco simulations show that these GDPS targets can still ignite and deliver neutron yields from 4 to ∼10MJ even if CBET is present, while traditional DT-push-on-DT targets normally fail due to the CBET-induced reduction of ablation pressure. If CBET is mitigated, these GDPS targets are expected to produce neutron yields of >20MJ at a driven laser energy of ∼2MJ. The key factors behind the robust ignition and moderate energy gain of such GDPS implosions are as follows: (1) The high initial density of the high-Z pusher shell can be placed at a very high adiabat while the DT fuel is maintained at a relatively low-entropy state; therefore, such implosions can still provide enough compression ρR>1g/cm^{2} for sufficient confinement; (2) the high-Z layer significantly reduces heat-conduction loss from the hot spot since thermal conductivity scales as ∼1/Z; and (3) possible radiation trapping may offer an additional advantage for reducing energy loss from such high-Z targets.

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

A wide-range (0 to 1044.0 g/cm^{3} and 0 to 10^{9} K) equation-of-state (EOS) table for a CH_{1.72}O_{0.37}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.

Development of a Multiphase Beryllium Equation of State and Physics-based Variations

We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.

Structure and dynamics of warm dense aluminum: a molecular dynamics study with density functional theory and deep potential

We perform a systematic study on the structure and dynamics of warm dense aluminum (Al) at temperatures ranging from 0.5 to 5.0 eV with molecular dynamics utilizing both density functional theory (DFT) and the deep potential (DP) method. On one hand, unlike the Thomas-Fermi kinetic energy density functional (KEDF), we find that the orbital-free DFT method with the Wang-Teter non-local KEDF yields properties of warm dense Al that agree well with the Kohn-Sham DFT method, enabling accurate orbital-free DFT simulations of warm dense Al at relatively low temperatures. On the other hand, the DP method constructs a deep neural network that has a high accuracy in reproducing short- and long-ranged properties of warm dense Al when compared to the DFT methods. The DP method is orders of magnitudes faster than DFT and is well-suited for simulating large systems and long trajectories to yield accurate properties of warm dense Al. Our results suggest that the combination of DFT methods and the DP model is a powerful tool for accurately and efficiently simulating warm dense matter.

Direct-drive double-shell implosion: A platform for burning-plasma physics studies

Double-shell ignition designs have been studied with the indirect-drive inertial confinement fusion (ICF) scheme in both simulations and experiments in which the inner-shell kinetic energy was limited to ∼10-15 kJ, even driven by megajoule-class lasers such as the National Ignition Facility. Since direct-drive ICF can couple more energy to the imploding shells, we have performed a detailed study on direct-drive double-shell (D^{3}S) implosions with state-of-the-art physics models implemented in radiation-hydrodynamic codes (lilac and draco), including nonlocal thermal transport, cross-beam energy transfer (CBET), and first-principles-based material properties. To mitigate classical unstable interfaces, we have proposed the use of a tungsten-beryllium-mixed inner shell with gradient-density layers that can be made by magnetron sputtering. In our D^{3}S designs, a 70-μm-thick beryllium outer shell is driven symmetrically by a high-adiabat (α≥10), 1.9-MJ laser pulse to a peak velocity of ∼240 km/s. Upon spherical impact, the outer shell transfers ∼30-40 kJ of kinetic energy to the inner shell filled with deuterium-tritium gas or liquid, giving neutron-yield energies of ∼6 MJ in one-dimensional simulations. Two-dimensional high-mode draco simulations indicated that such high-adiabat D^{3}S implosions are not susceptible to laser imprint, but the long-wavelength perturbations from the laser port configuration along with CBET can be detrimental to the target performance. Nevertheless, neutron yields of ∼0.3-1.0-MJ energies can still be obtained from our high-mode draco simulations. The robust α-particle bootstrap is readily reached, which could provide a viable platform for burning-plasma physics studies. Once CBET mitigation and/or more laser energy becomes available, we anticipate that break-even or moderate energy gain might be feasible with the proposed D^{3}S scheme.

Atom-in-jellium equations of state in the high-energy-density regime

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.

Ab Initio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for ab initio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the ab initio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.