First-principles opacity table of warm dense deuterium for inertial-confinement-fusion applications

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 study of L-shell iron and chromium opacity at stellar interior temperatures

Recently developed free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter has been applied for studying L-shell opacity of iron and chromium at T=182 eV. We use Mermin-Kohn-Sham density functional theory with a ground-state and a fully-temperature-dependent generalized gradient approximation exchange-correlation (XC) functionals. It is demonstrated that the role of XC at such a high-T is negligible due to the total free energy of interacting systems being dominated by the noninteracting free-energy term, in agreement with estimations for the homogeneous electron gas. Our DFT predictions are compared with the radiative emissivity and opacity of the dense plasma model, with the real-space Green's function method, and with experimental measurements. Good agreement is found between all three theoretical methods, and in the bound-continuum region for Cr when compared with the experiment, while the discrepancy between direct DFT calculations and the experiment for Fe remains essentially the same as for plasma-physics models.

Probing atomic physics at ultrahigh pressure using laser-driven implosions

Spectroscopic measurements of dense plasmas at billions of atmospheres provide tests to our fundamental understanding of how matter behaves at extreme conditions. Developing reliable atomic physics models at these conditions, benchmarked by experimental data, is crucial to an improved understanding of radiation transport in both stars and inertial fusion targets. However, detailed spectroscopic measurements at these conditions are rare, and traditional collisional-radiative equilibrium models, based on isolated-atom calculations and ad hoc continuum lowering models, have proved questionable at and beyond solid density. Here we report time-integrated and time-resolved x-ray spectroscopy measurements at several billion atmospheres using laser-driven implosions of Cu-doped targets. We use the imploding shell and its hot core at stagnation to probe the spectral changes of Cu-doped witness layer. These measurements indicate the necessity and viability of modeling dense plasmas with self-consistent methods like density-functional theory, which impact the accuracy of radiation transport simulations used to describe stellar evolution and the design of inertial fusion targets.

Atoms and molecules under extreme temperature and pressure can be investigated using dense plasmas achieved by laser-driven implosion. Here the authors report spectral change of copper in billions atmosphere pressure that can only be explained by a self-consistent approach.

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.

PhaseX: an X-ray phase-contrast imaging simulation code for matter under extreme conditions

We present PhaseX, a simulation code for X-ray phase-contrast imaging (XPCI), specially dedicated to the study of matter under extreme conditions (of pressure and density). Indeed, XPCI can greatly benefit the diagnosis of such states of matter. This is due to the noticeable contrast enhancement obtained thanks to the exploitation of both attenuation and phase-shift of the electromagnetic waves crossing the sample to be diagnosed. PhaseX generates synthetic images with and without phase contrast. Thanks to its modular design PhaseX can adapt to any imaging set-up and accept as inputs objects generated by hydrodynamic or particle-in-cell codes. We illustrate Phase-X capabilities by showing a few examples concerning laser-driven implosions and laser-driven shock waves.

Time-dependent density functional theory applied to average atom opacity

We focus on studying the opacity of iron, chromium, and nickel plasmas at conditions relevant to experiments carried out at Sandia National Laboratories [J. E. Bailey et al., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. We calculate the photoabsorption cross sections and subsequent opacity for plasmas using linear-response time-dependent density functional theory (TD-DFT). Our results indicate that the physics of channel mixing accounted for in linear-response TD-DFT leads to an increase in the opacity in the bound-free quasicontinuum, where the Sandia experiments indicate that models underpredict iron opacity. However, the increase seen in our calculations is only in the range of 5%-10%. Further, we do not see any change in this trend for chromium and nickel. This behavior indicates that channel mixing effects do not explain the trends in opacity observed in the Sandia experiments.

Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas

We present a free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin-Kohn-Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo-Greenwood optic data with a single atom in simulation cell calculations to close the photon energy gap between the L and K edges and extend the K-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo-Greenwood calculations with AIMD snapshots. Kubo-Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the L edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-Z materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomenon of redshift-to-blueshift in K-L (1s→2p) and K-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of 1s→2p to the K-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.

Calculating Opacity in Hot, Dense Matter Using Second-Order Electron-Photon and Two-Photon Transitions to Approximate Line Broadening

Calculations of the opacity of hot, dense matter require models for plasma line broadening. However, the most general theories are too complex to calculate directly and some approximation is inevitably required. The most widely used approaches focus on the line center, where a Lorentzian shape is obtained. Here, we demonstrate that in the opposite limit, far from the line center, the opacity can be expressed in terms of second-order transitions, such as electron-photon and two-photon processes. We suggest that this insight could form the basis for a new approach to improve calculations of opacity in hot, dense matter. Preliminary calculations suggest that this approach could yield increased opacity away from absorption lines.

Time-Resolved XUV Opacity Measurements of Warm Dense Aluminum

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion research. However, theoretical predictions in the challenging dense plasma regime are conflicting and there is a dearth of accurate experimental data to allow for direct model validation. Here we present time-resolved transmission measurements in solid-density Al heated by an XUV free-electron laser. We use a novel functional optimization approach to extract the temperature-dependent absorption coefficient directly from an oversampled pool of single-shot measurements, and find a pronounced enhancement of the opacity as the plasma is heated to temperatures of order of the Fermi energy. Plasma heating and opacity enhancement are observed on ultrafast timescales, within the duration of the femtosecond XUV pulse. We attribute further rises in the opacity on ps timescales to melt and the formation of warm dense matter.

Correlations between conduction electrons in dense plasmas

Most treatments of electron-electron correlations in dense plasmas either ignore them entirely (random phase approximation) or neglect the role of ions (jellium approximation). In this work, we go beyond both these approximations to derive a formula for the electron-electron static structure factor which properly accounts for the contributions of both ionic structure and quantum-mechanical dynamic response in the electrons. The result can be viewed as a natural extension of the quantum Ornstein-Zernike theory of ionic and electronic correlations, and it is suitable for dense plasmas in which the ions are classical and the conduction electrons are quantum-mechanical. The corresponding electron-electron pair distribution functions are compared with the results of path integral Monte Carlo simulations, showing good agreement whenever no strong electron resonance states are present. We construct approximate potentials of mean force which describe the effective screened interaction between electrons. Significant deviations from Debye-Hückel screening are present at temperatures and densities relevant to high-energy density experiments involving warm and hot dense plasmas. The presence of correlations between conduction electrons is likely to influence the electron-electron contribution to the electrical and thermal conductivity. It is expected that excitation processes involving the conduction electrons (e.g., free-free absorption) will also be affected.

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.

Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well-Defined Initial State

We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth-order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a superposition of Lewis dot resonance structures.

Continuum Lowering and Fermi-Surface Rising in Strongly Coupled and Degenerate Plasmas

Continuum lowering is a well known and important physics concept that describes the ionization potential depression (IPD) in plasmas caused by thermal- or pressure-induced ionization of outer-shell electrons. The existing IPD models are often used to characterize plasma conditions and to gauge opacity calculations. Recent precision measurements have revealed deficits in our understanding of continuum lowering in dense hot plasmas. However, these investigations have so far been limited to IPD in strongly coupled but nondegenerate plasmas. Here, we report a first-principles study of the K-edge shifting in both strongly coupled and fully degenerate carbon plasmas, with quantum molecular dynamics calculations based on the all-electron density-functional theory. The resulting K-edge shifting versus plasma density, as a probe to the continuum lowering and the Fermi-surface rising, is found to be significantly different from predictions of existing IPD models. In contrast, a simple model of "single-atom-in-box," developed in this work, accurately predicts K-edge locations as ab initio calculations provide.

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

Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ∼10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ∼20%. By implementing the FPEOS table into the 1-D radiation-hydrodynamic code LILAC, we studied the EOS effects on beryllium-shell-target implosions. The FPEOS simulation predicts higher neutron yield (∼15%) compared to the simulation using the SESAME 2023 EOS table.

First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations

Using density-functional theory-based molecular-dynamics simulations, we have investigated the equation of state for silicon in a wide range of plasma density and temperature conditions of ρ=0.001-500g/cm^{3} and T=2000-10^{8}K. With these calculations, we have established a first-principles equation-of-state (FPEOS) table of silicon for high-energy-density (HED) plasma simulations. When compared with the widely used SESAME-EOS model (Table 3810), we find that the FPEOS-predicted Hugoniot is ∼20% softer; for off-Hugoniot plasma conditions, the pressure and internal energy in FPEOS are lower than those of SESAME EOS for temperatures above T ≈ 1-10 eV (depending on density), while the former becomes higher in the low-T regime. The pressure difference between FPEOS and SESAME 3810 can reach to ∼50%, especially in the warm-dense-matter regime. Implementing the FPEOS table of silicon into our hydrocodes, we have studied its effects on Si-target implosions. When compared with the one-dimensional radiation-hydrodynamics simulation using the SESAME 3810 EOS model, the FPEOS simulation showed that (1) the shock speed in silicon is ∼10% slower; (2) the peak density of an in-flight Si shell during implosion is ∼20% higher than the SESAME 3810 simulation; (3) the maximum density reached in the FPEOS simulation is ∼40% higher at the peak compression; and (4) the final areal density and neutron yield are, respectively, ∼30% and ∼70% higher predicted by FPEOS versus the traditional simulation using SESAME 3810. All of these features can be attributed to the larger compressibility of silicon predicted by FPEOS. These results indicate that an accurate EOS table, like the FPEOS presented here, could be essential for the precise design of targets for HED experiments.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K<T_{e}<10^{9}K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.

Optical Properties of Fluid Hydrogen at the Transition to a Conducting State

We use fast transient transmission and emission spectroscopies in the pulse laser heated diamond anvil cell to probe the energy-dependent optical properties of hydrogen at pressures of 10-150 GPa and temperatures up to 6000 K. Hydrogen is absorptive at visible to near-infrared wavelengths above a threshold temperature that decreases from 3000 K at 18 GPa to 1700 K at 110 GPa. Transmission spectra at 2400 K and 141 GPa indicate that the absorptive hydrogen is semiconducting or semimetallic in character, definitively ruling out a first-order insulator-metal transition in the studied pressure range.

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ=0.1to100g/cm(3) and T=1000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

Atomic and optical properties of warm dense copper

The emission of x rays from warm dense matter is of great interest for both spectroscopic diagnostics and development of intense x-ray sources. We report the results from the collisional-radiative steady-state (CRSS) modeling of atomic and optical properties of copper plasmas at near-solid and solid-state density for a range of temperatures. The CRSS model is validated against the available data on the average charge state and shifts of energy levels in aluminum and the opacity and emissivity spectra of carbon and aluminum plasmas. The average charge states, number density of ion species, and free electrons as a function of temperature are investigated for the solid-density copper plasma. Due to the dense plasma environment the four outer electrons are found to be unbounded even in the low-temperature limit ∼1eV. As the temperature changes from 1 to 100 eV, the predominant species vary from fivefold- to twelvefold-ionized copper ions. The opacity and emissivity spectra of dense copper plasmas are studied using the local thermodynamic equilibrium (LTE) and non-LTE approaches. It is found that the non-LTE effects are important in the spectral region of soft x rays emitted from the K shell. The emissivity in spectral lines is completely suppressed, indicating the importance of the energy-dissipating radiative processes in this soft x-ray region. Line broadening and redshifts of the K- and L-shell spectral lines toward higher wavelengths are observed with the increase of plasma density. These results have important implications for understanding the radiative properties of warm dense copper and can be useful for future experimental studies.