Equation of State of CO_{2} Shock Compressed to 1 TPa.

Equation-of-state (pressure, density, temperature, internal energy) and reflectivity measurements on shock-compressed CO_{2} at and above the insulating-to-conducting transition reveal new insight into the chemistry of simple molecular systems in the warm-dense-matter regime. CO_{2} samples were precompressed in diamond-anvil cells to tune the initial densities from 1.35 g/cm^{3} (liquid) to 1.74 g/cm^{3} (solid) at room temperature and were then shock compressed up to 1 TPa and 93 000 K. Variation in initial density was leveraged to infer thermodynamic derivatives including specific heat and Gruneisen coefficient, exposing a complex bonded and moderately ionized state at the most extreme conditions studied.

Direct-drive measurements of laser-imprint-induced shock velocity nonuniformities.

Perturbations in the velocity profile of a laser-ablation-driven shock wave seeded by speckle in the spatial beam intensity (i.e., laser imprint) have been measured. Direct measurements of these velocity perturbations were recorded using a two-dimensional high-resolution velocimeter probing plastic material shocked by a 100-ps picket laser pulse from the OMEGA laser system. The measured results for experiments with one, two, and five overlapping beams incident on the target clearly demonstrate a reduction in long-wavelength (>25-µm) perturbations with an increasing number of overlapping laser beams, consistent with theoretical expectations. These experimental measurements are crucial to validate radiation-hydrodynamics simulations of laser imprint for laser direct drive inertial confinement fusion research since they highlight the significant (factor of 3) underestimation of the level of seeded perturbation when the microphysics processes for initial plasma formation, such as multiphoton ionization are neglected.

Shock Compression of Liquid Deuterium up to 1 TPa.

We present laser-driven shock compression experiments on cryogenic liquid deuterium to 550 GPa along the principal Hugoniot and reflected-shock data up to 1 TPa. High-precision interferometric Doppler velocimetry and impedance-matching analysis were used to determine the compression accurately enough to reveal a significant difference as compared to state-of-the-art ab initio calculations and thus, no single equation of state model fully matches the principal Hugoniot of deuterium over the observed pressure range. In the molecular-to-atomic transition pressure range, models based on density functional theory calculations predict the maximum compression accurately. However, beyond 250 GPa along the principal Hugoniot, first-principles models exhibit a stiffer response than the experimental data. Similarly, above 500 GPa the reflected shock data show 5%-7% higher compression than predicted by all current models.

Breakdown of Fermi Degeneracy in the Simplest Liquid Metal.

We are reporting the observation of the breakdown of electrons' degeneracy and emergence of classical statistics in the simplest element: metallic deuterium. We have studied the optical reflectance, shock velocity, and temperature of dynamically compressed liquid deuterium up to its Fermi temperature T_{F}. Above the insulator-metal transition, the optical reflectance shows the distinctive temperature-independent resistivity saturation, which is prescribed by Mott's minimum metallic limit, in agreement with previous experiments. At T>0.4 T_{F}, however, the reflectance of metallic deuterium starts to rise with a temperature-dependent slope, consistent with the breakdown of the Fermi surface. The experimentally inferred electron-ion collisional time in this region exhibits the characteristic temperature dependence expected for a classical Landau-Spitzer plasma. Our observation of electron degeneracy lifting extends studies of degeneracy to new fermionic species-electron Fermi systems-and offers an invaluable benchmark for quantum statistical models of Coulomb systems over a wide range of temperatures relevant to dense astrophysical objects and ignition physics.

Erratum: Measurement of Body-Centered-Cubic Aluminum at 475 GPa [Phys. Rev. Lett. 119, 175702 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.175702.

Measurement of Body-Centered-Cubic Aluminum at 475 GPa.

Nanosecond in situ x-ray diffraction and simultaneous velocimetry measurements were used to determine the crystal structure and pressure, respectively, of ramp-compressed aluminum at stress states between 111 and 475 GPa. The solid-solid Al phase transformations, fcc-hcp and hcp-bcc, are observed at 216±9 and 321±12 GPa, respectively, with the bcc phase persisting to 475 GPa. The high-pressure crystallographic texture of the hcp and bcc phases suggests close-packed or nearly close-packed lattice planes remain parallel through both transformations.

Absolute calibration of the OMEGA streaked optical pyrometer for temperature measurements of compressed materials.

Experiments in high-energy-density physics often use optical pyrometry to determine temperatures of dynamically compressed materials. In combination with simultaneous shock-velocity and optical-reflectivity measurements using velocity interferometry, these experiments provide accurate equation-of-state data at extreme pressures (P > 1 Mbar) and temperatures (T > 0.5 eV). This paper reports on the absolute calibration of the streaked optical pyrometer (SOP) at the Omega Laser Facility. The wavelength-dependent system response was determined by measuring the optical emission from a National Institute of Standards and Technology-traceable tungsten-filament lamp through various narrowband (40-nm-wide) filters. The integrated signal over the SOP's ∼250-nm operating range is then related to that of a blackbody radiator using the calibrated response. We present a simple closed-form equation for the brightness temperature as a function of streak-camera signal derived from this calibration. Error estimates indicate that brightness temperature can be inferred to a precision of <5%.

Publisher's Note: Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA [Phys. Rev. Lett. 117, 025001 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.025001.

Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA.

A record fuel hot-spot pressure P_{hs}=56±7 Gbar was inferred from x-ray and nuclear diagnostics for direct-drive inertial confinement fusion cryogenic, layered deuterium-tritium implosions on the 60-beam, 30-kJ, 351-nm OMEGA Laser System. When hydrodynamically scaled to the energy of the National Ignition Facility, these implosions achieved a Lawson parameter ∼60% of the value required for ignition [A. Bose et al., Phys. Rev. E 93, 011201(R) (2016)], similar to indirect-drive implosions [R. Betti et al., Phys. Rev. Lett. 114, 255003 (2015)], and nearly half of the direct-drive ignition-threshold pressure. Relative to symmetric, one-dimensional simulations, the inferred hot-spot pressure is approximately 40% lower. Three-dimensional simulations suggest that low-mode distortion of the hot spot seeded by laser-drive nonuniformity and target-positioning error reduces target performance.

Temperature measurements of shocked silica aerogel foam.

We present recent results of equation-of-state (EOS) measurements of shocked silica (SiO_{2}) aerogel foam at the OMEGA laser facility. Silica aerogel is an important low-density pressure standard used in many high energy density experiments, including the novel technique of shock and release. Due to its many applications, it has been a heavily studied material and has a well-known Hugoniot curve. This work then complements the velocity and pressure measurements with additional temperature data providing the full EOS information within the warm dense matter regime for the temperature interval of 1-15 eV and shock velocities between 10 and 40 km/s corresponding to shock pressures of 0.3-2 Mbar. The experimental results were compared with hydrodynamic simulations and EOS models. We found that the measured temperature was systematically lower than suggested by theoretical calculations. Simulations provide a possible explanation that the emission measured by optical pyrometry comes from a radiative precursor rather than from the shock front, which could have important implications for such measurements.

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

Accurate knowledge of the optical properties of a warm dense deuterium-tritium (DT) mixture is important for reliable design of inertial confinement fusion (ICF) implosions using radiation-hydrodynamics simulations. The opacity of a warm dense DT shell essentially determines how much radiation from hot coronal plasmas can be deposited in the DT fuel of an imploding capsule. Even for the simplest species of hydrogen, the accurate calculation of their opacities remains a challenge in the warm-dense matter regime because strong-coupling and quantum effects play an important role in such plasmas. With quantum-molecular-dynamics (QMD) simulations, we have derived a first-principles opacity table (FPOT) of deuterium (and the DT mixture by mass scaling) for a wide range of densities from ρ(D)=0.5 to 673.518g/cm(3) and temperatures from T=5000K up to the Fermi temperature T(F) for each density. Compared with results from the astrophysics opacity table (AOT) currently used in our hydrocodes, the FPOT of deuterium from our QMD calculations has shown a significant increase in opacity for strongly coupled and degenerate plasma conditions by a factor of 3-100 in the ICF-relevant photon-energy range. As conditions approach those of classical plasma, the opacity from the FPOT converges to the corresponding values of the AOT. By implementing the FPOT of deuterium and the DT mixture into our hydrocodes, we have performed radiation-hydrodynamics simulations for low-adiabat cryogenic DT implosions on the OMEGA laser and for direct-drive-ignition designs for the National Ignition Facility. The simulation results using the FPOT show that the target performance (in terms of neutron yield and energy gain) could vary from ∼10% up to a factor of ∼2 depending on the adiabat of the imploding DT capsule; the lower the adiabat, the more variation is seen in the prediction of target performance when compared to the AOT modeling.

Properties of warm dense polystyrene plasmas along the principal Hugoniot.

Polystyrene (CH) is often chosen as the ablator material for inertial confinement fusion (ICF) targets. Its static, dynamical, and optical properties in warm, dense conditions (due to shock compression) are important for ICF designs. Using the first-principles quantum molecular dynamics (QMD) method, we have investigated the equation of state (EOS) and optical reflectivity of shock-compressed CH up to an unprecedentedly high pressure of 62 Mbar along the principal Hugoniot. The QMD results are compared with existing experimental measurements as well as the SESAME EOS model. Although the Hugoniot pressure and/or temperature from QMD calculations agrees with experiments and the SESAME EOS model at low pressures below 10 Mbar, we have identified for the first time a stiffer behavior of shocked CH at higher pressures (>10 Mbar). Such a stiffer behavior of warm, dense CH can affect the ablation pressure (shock strength), shock coalescence dynamics, and nonuniformity growth in ICF implosions. In addition, we corrected the mistake made in literature for calculating the reflectivity of shocked CH and obtained good agreements with experimental measurements, which should lend credence to future opacity calculations in a first-principles fashion.

First-principles thermal conductivity of warm-dense deuterium plasmas for inertial confinement fusion applications.

Thermal conductivity (κ) of both the ablator materials and deuterium-tritium (DT) fuel plays an important role in understanding and designing inertial confinement fusion (ICF) implosions. The extensively used Spitzer model for thermal conduction in ideal plasmas breaks down for high-density, low-temperature shells that are compressed by shocks and spherical convergence in imploding targets. A variety of thermal-conductivity models have been proposed for ICF hydrodynamic simulations of such coupled and degenerate plasmas. The accuracy of these κ models for DT plasmas has recently been tested against first-principles calculations using the quantum molecular-dynamics (QMD) method; although mainly for high densities (ρ > 100 g/cm3), large discrepancies in κ have been identified for the peak-compression conditions in ICF. To cover the wide range of density-temperature conditions undergone by ICF imploding fuel shells, we have performed QMD calculations of κ for a variety of deuterium densities of ρ = 1.0 to 673.518 g/cm3, at temperatures varying from T = 5 × 103 K to T = 8 × 106 K. The resulting κQMD of deuterium is fitted with a polynomial function of the coupling and degeneracy parameters Γ and θ, which can then be used in hydrodynamic simulation codes. Compared with the "hybrid" Spitzer-Lee-More model currently adopted in our hydrocode lilac, the hydrosimulations using the fitted κQMD have shown up to ∼20% variations in predicting target performance for different ICF implosions on OMEGA and direct-drive-ignition designs for the National Ignition Facility (NIF). The lower the adiabat of an imploding shell, the more variations in predicting target performance using κQMD. Moreover, the use of κQMD also modifies the shock conditions and the density-temperature profiles of the imploding shell at early implosion stage, which predominantly affects the final target performance. This is in contrast to the previous speculation that κQMD changes mainly the inside ablation process during the hot-spot formation of an ICF implosion.

Measurement of high-pressure shock waves in cryogenic deuterium-tritium ice layered capsule implosions on NIF.

The first measurements of multiple, high-pressure shock waves in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility have been performed. The strength and relative timing of these shocks must be adjusted to very high precision in order to keep the DT fuel entropy low and compressibility high. All previous measurements of shock timing in inertial confinement fusion implosions [T. R. Boehly et al., Phys. Rev. Lett. 106, 195005 (2011), H. F. Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] have been performed in surrogate targets, where the solid DT ice shell and central DT gas regions were replaced with a continuous liquid deuterium (D2) fill. This report presents the first experimental validation of the assumptions underlying this surrogate technique.

Solid iron compressed up to 560 GPa.

Dynamic compression by multiple shocks is used to compress iron up to 560 GPa (5.6 Mbar), the highest solid-state pressure yet attained for iron in the laboratory. Extended x-ray absorption fine structure (EXAFS) spectroscopy offers simultaneous density, temperature, and local-structure measurements for the compressed iron. The data show that the close-packed structure of iron is stable up to 560 GPa, the temperature at peak compression is significantly higher than expected from pure compressive work, and the dynamic strength of iron is many times greater than the static strength based on lower pressure data. The results provide the first constraint on the melting line of iron above 400 GPa.

Precision shock tuning on the national ignition facility.

Ignition implosions on the National Ignition Facility [J. D. Lindl et al., Phys. Plasmas 11, 339 (2004)] are underway with the goal of compressing deuterium-tritium fuel to a sufficiently high areal density (ρR) to sustain a self-propagating burn wave required for fusion power gain greater than unity. These implosions are driven with a very carefully tailored sequence of four shock waves that must be timed to very high precision to keep the fuel entropy and adiabat low and ρR high. The first series of precision tuning experiments on the National Ignition Facility, which use optical diagnostics to directly measure the strength and timing of all four shocks inside a hohlraum-driven, cryogenic liquid-deuterium-filled capsule interior have now been performed. The results of these experiments are presented demonstrating a significant decrease in adiabat over previously untuned implosions. The impact of the improved shock timing is confirmed in related deuterium-tritium layered capsule implosions, which show the highest fuel compression (ρR~1.0 g/cm(2)) measured to date, exceeding the previous record [V. Goncharov et al., Phys. Rev. Lett. 104, 165001 (2010)] by more than a factor of 3. The experiments also clearly reveal an issue with the 4th shock velocity, which is observed to be 20% slower than predictions from numerical simulation.

Assembly of high-areal-density deuterium-tritium fuel from indirectly driven cryogenic implosions.

The National Ignition Facility has been used to compress deuterium-tritium to an average areal density of ~1.0±0.1 g cm(-2), which is 67% of the ignition requirement. These conditions were obtained using 192 laser beams with total energy of 1-1.6 MJ and peak power up to 420 TW to create a hohlraum drive with a shaped power profile, peaking at a soft x-ray radiation temperature of 275-300 eV. This pulse delivered a series of shocks that compressed a capsule containing cryogenic deuterium-tritium to a radius of 25-35 µm. Neutron images of the implosion were used to estimate a fuel density of 500-800 g cm(-3).

Plasma-accelerated flyer-plates for equation of state studies.

We report on a new technique to accelerate flyer-plates to high velocities (∼5 km/s). In this work, a strong shock is created through direct laser ablation of a thin polyimide foil. Subsequent shock breakout of that foil results in the generation of a plasma characterized by a smoothly increasing density gradient and a strong forward momentum. Stagnation of this plasma onto an aluminum foil and the resultant momentum transfer accelerates a thin aluminum flyer-plate. The aluminum flyer-plate is then accelerated to a peak velocity of ∼5 km/s before impact with a transparent lithium fluoride (LiF) window. Simulations of the stagnating plasma ramp compression and wave reverberations within the flyer-plate suggest that the temperature at the flyer-plate impact surface is elevated by less than 50 °C. Optical velocimetry is used to measure the flyer-plate velocity and impact conditions enabling the shocked refractive index of LiF to be determined. The results presented here are in agreement with conventional flyer-plate measurements validating the use of plasma-accelerated flyer-plates for equation of state and impact studies.

Inelastic x-ray scattering from shocked liquid deuterium.

The Fermi-degenerate plasma conditions created in liquid deuterium by a laser-ablation-driven shock wave were probed with noncollective, spectrally resolved, inelastic x-ray Thomson scattering employing Cl Ly(α) line emission at 2.96 keV. These first x-ray Thomson scattering measurements of the microscopic properties of shocked deuterium show an inferred spatially averaged electron temperature of 8±5 eV, an electron density of 2.2(±0.5)×10(23) cm(-3), and an ionization of 0.8 (-0.25, +0.15). Two-dimensional hydrodynamic simulations using equation-of-state models suited for the extreme parameters occurring in inertial confinement fusion research and planetary interiors are consistent with the experimental results.

Velocity and timing of multiple spherically converging shock waves in liquid deuterium.

The fuel entropy and required drive energy for an inertial confinement fusion implosion are set by a sequence of shocks that must be precisely timed to achieve ignition. This Letter reports measurements of multiple spherical shock waves in liquid deuterium that facilitate timing inertial confinement fusion shocks to the required precision. These experiments produced the highest shock velocity observed in liquid deuterium (U(s) = 135 km/s at ∼2500 GPa) and also the first observation of convergence effects on the shock velocity. Simulations model the shock-timing results well when a nonlocal transport model is used in the coronal plasma.