We demonstrate the value of inner-shell X-ray absorption spectroscopy for dense-plasma atomic physics and explore the coupling between constraint of the thermodynamic state and constraint of ionization-potential depression models. Synthetic K-shell absorption spectra are generated along a radius from a point-like core and analyzed using different ionization-potential depression models. Within this synthetic analysis framework, we identify plasma conditions (Te=400 eV, ρ=40 g/cm3) accessible by spherical implosions where K-shell absorption spectra discriminate between models if the material temperature is measured to a precision of 20%. The analysis is extensible to a finite-sized core and can be used to guide future studies of ionization-potential depression, informing material and radiative properties of matter in fusion plasmas and stellar interiors.

Experiments today can compress solids near isentropically to pressures approaching 100 × 106 atmospheres; however, determining the temperature of such matter remains a major challenge. Extended x-ray absorption fine-structure (EXAFS) spectroscopy is one of the few techniques sensitive to the bulk temperature of highly compressed solid matter, and the validity of this temperature measurement relies on constraining the local ion structure from the EXAFS spectrum. At high-energy-density (HED) conditions, the local ion structure often becomes distorted, which must be accounted for during the EXAFS analysis. Described here is a technique, using a parametrized ion-distribution model to directly analyze EXAFS spectra that provides a better constraint on the local structure than traditional second- or third-order cumulant expansion techniques at HED conditions. The parametrized ion-distribution model is benchmarked by analyzing EXAFS spectra from nickel molecular-dynamics simulations at ∼100 GPa and shown to provide a 10%–20% improvement in constraining the cumulants of the true ion distribution.

X-ray radiography is a technique frequently used to diagnose convergent high-energy-density (HED) systems, such as inertial confinement fusion implosion, and provides unique information that is not available through self-emission measurements. We investigate the scope and limits of that information using a radiography simulation combined with the Bayesian inference workflow. The accuracy of density reconstruction from simulated radiographs of spherical implosions driven with 27 kJ laser energy is assessed, including the increase or decrease in accuracy due to the addition of Lagrangian marker layers, Poisson noise, and improved prior information. This work is the first to present the full uncertainty distributions inferred from radiography analysis in HED systems and demonstrates the importance of constructing the full posterior probability density, as opposed to a point estimate, due to the modal structure of the likelihood surface introduced by typical experimental noise sources. This general methodology can be used both for robust analysis of radiographic data and for an improved design of radiography experiments by modeling the full experimental system.

Austenitic stainless steel, type 316, absorbs significant quantities of tritium into the near surface ( $ < 1 ~\mu \text{m}$ ) on exposure to tritium containing gases at room temperature. The tritium concentrations that develop in the near-surface region ( $ < 1 ~\mu \text{m}$ ) are shown to persist for several years without changing. The current work shows the effect of heat treatments on the near-surface tritium-concentration profiles in stainless steel. Identical stainless-steel samples were exposed to tritium at room temperature and then were heated to different temperatures between 100 °C and 300 °C for 2 h under a stagnant argon atmosphere. After this initial preheating, the concentration profiles in the first $10 ~\mu \text{m}$ were measured by using a combination of a ZnCl2 wash and an etching procedure. Tritium was thermally released by heating the samples to 550 °C to measure the residual tritium present in the bulk of the sample. The data show two dominant features. First, preheating causes tritium to migrate both out of the sample and deeper than > $1 ~\mu \text{m}$ into the bulk. This effect increases with increasing temperature. Second, the depletion of tritium from the near surface does not occur until a temperature of 200 °C.

At the Laboratory for Laser Energetics' Omega Laser Facility, thin plastic shells were directly driven with ∼20 kJ resulting in a time-integrated x-ray yield of ∼1012 ph/eV/sr at 7 keV. Using temporally, spatially, and spectrally discriminating diagnostics, three x-ray emission phases were identified: corona emission produced by the laser ablation of the shell, core stagnation, and afterglow emission due to the expanding hot material after stagnation. The newly measured corona and afterglow emission phases account for ∼25% of the total x-ray signal and produce x-ray emission at a different time or larger radius than previously considered. The resulting implications of this additional emission for x-ray absorption fine structure spectroscopy are discussed. Finally, improvements to the laser drive intensity and uniformity produced a factor-of-2 increase in total x-ray emission while decreasing the size of the stagnated core.

We acquired high resolution images of laser driven cylindrical implosion experiments using a Fresnel zone plate (FZP), a diffraction driven lens composed of alternating opaque and transparent rings, on the OMEGA laser at the Laboratory for Laser Energetics in Rochester, NY, USA. Our FZP geometrical properties were designed for a standard 25x magnification and include 700 zones of 900 nm thick gold, minimum zone width of 40 nm, and a lens radius of 56 μm to focus an energy spectral peak at 6.127 keV emitted from a Manganese backlighter. This design was informed by our new Python-implemented forward model that considers 4 diffractive orders and a realistic x-ray spectrum to characterize the spatial resolution of FZP systems. The model supports two methods of exploring FZP designs: optimization via the SciPy library and algorithmic differentiation via the PyTorch library and its neural network module.

1Department of Physics and Astronomy, University of Rochester, Rochester, New York, 14627, USA 2Laboratory for Laser Energetics, University of Rochester, Rochester, New York, 14627, USA 3Department of Mechanical Engineering, University of Rochester, Rochester, New York, 14627, USA 4Lawrence Livermore National Laboratory, Livermore, California 94550, USA 5Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139

Experiments performed at the Laboratory for Laser Energetics with a continuous-wave (cw) x-ray source and on the OMEGA and OMEGA EP Laser Systems [Boehly et al., Opt. Commun. 133, 495 (1997) and Waxer et al., Opt. Photonics News 16, 30 (2005)] have utilized a Fresnel zone plate (FZP) to obtain x-ray images with a spatial resolution as small as ∼1.5 μm. Such FZP images were obtained with a charge-coupled device or a framing camera at energies ranging from 4.5 keV to 6.7 keV using x-ray line emission from both the cw source and high-intensity, laser-beam-illuminated metal foils. In all cases, the resolution test results are determined from patterns and grids backlit by these sources. The resolutions obtained are shown to be due to a combination of the spectral content of the x-ray sources and detector resolution limited by the magnification of the images (14× to 22×). High-speed framing cameras were used to obtain FZP images with frame times as short as ∼30 ps. Double-shell implosions on OMEGA were backlit by laser-irradiated Fe foils, thus obtaining a framing-camera-limited, FZP-image resolution of ∼3 μm-4 μm.

Convergent high-energy-density (HED) experimental platforms are used to study matter under some of the most extreme conditions that can be produced on Earth, comparable to the interior of stars. There are many challenges in using these systems for fundamental measurements currently being addressed by new analysis methods, such as the combination of a reduced physics model and Bayesian inference, allowing a self-consistent inference of physical quantities with a robust error analysis. These methods in combination with simple (as compared to inertial confinement fusion implosions) implosion platforms, which can be modified to show sensitivity to different physical mechanisms of interest, are used to study the physical properties of matter under extreme conditions. This work discusses a subset of implosion targets for studying opacity effects, electron–ion equilibration, and thermal conductivity and, as an example, a system consisting of a thick-shelled, gas-filled laser-direct-drive implosion is used to show how a reduced model and Bayesian inference can help inform experimental design decisions such as diagnostic choice. It is shown that for this system that a combination of neutron and x-ray self-emission diagnostics is critical for constraining the details of the thermodynamic states in the system and that the conductivity exponent in a Spitzer like framework can be constrained to the 30% level in deuterium at gigabar conditions. This process can be applied to many HED systems to make underlying model assumptions explicit and facilitate experimental design and analysis.

High-pressure equation of state and isentropic sound speed data for fluid silicon to pressures of 2100 GPa (21 Mbar) are reported. Principal Hugoniot measurements were performed using impedance matching techniques with alpha-quartz as the reference. Sound speeds were determined by time correlating imposed shock-velocity perturbations in both the sample (Si) and reference material (alpha-quartz). A change in shock velocity versus particle velocity (u(s)-u(p)) slope on the fluid silicon principal Hugoniot is observed at 200 GPa. Density functional theory based quantum molecular dynamics simulations suggest that both an increase in ionic coordination and a 50% increase in average ionization are coincident with this experimentally observed change in slope.

Energy flow and balance in convergent systems beyond petapascal energy densities controls the fate of late-stage stars and the potential for controlling thermonuclear inertial fusion ignition. Time-resolved x-ray self-emission imaging combined with a Bayesian inference analysis is used to describe the energy flow and the potential information stored in the rebounding spherical shock at 0.22 PPa (2.2 Gbar or billions of atmospheres pressure). This analysis, together with a simple mechanical model, describes the trajectory of the shell and the time history of the pressure at the fuel-shell interface, ablation pressure, and energy partitioning including kinetic energy of the shell and internal energy of the fuel. The techniques used here provide a fully self-consistent uncertainty analysis of integrated implosion data, a thermodynamic-path independent measurement of pressure in the petapascal range, and can be used to deduce the energy flow in a wide variety of implosion systems to petapascal energy densities.

The Guderley model of a self-similar imploding shock based on the group invariance of the flow equations is a powerful tool in understanding the behavior of converging shock waves. Two modifications described here improve the predictions of observable quantities in spherical-shock wave experiments. First, a noninfinite boundary condition is established by the isentropic release of the outer pressure. Second, a two-temperature system of ions and electrons allows description of higher temperatures while conserving energy and without perturbing the overall hydrodynamics of the solution. These modifications of the Guderley model improve the prediction of the observables in laser driven spherical shock experiments in reference to a one dimensional (1-D) hydrodynamics code.

Laser-driven ion acceleration is of great interest across a range of disciplines with potential applications including the fast ignition approach to inertial confinement fusion and proton therapy. The most robust acceleration mechanisms studied to date however, based on target normal sheath acceleration (TNSA), do not satisfy the emittance, flux and ion energy requirements for direct applications.

A technique for measuring residual motion during the stagnation phase of an indirectly driven inertial confinement experiment has been implemented. This method infers a velocity from spatially and temporally resolved images of the X-ray emission from two orthogonal lines of sight. This work investigates the accuracy of recovering spatially resolved velocities from the X-ray emission data. A detailed analytical and numerical modeling of the X-ray emission measurement shows that the accuracy of this method increases as the displacement that results from a residual velocity increase. For the typical experimental configuration, signal-to-noise ratios, and duration of X-ray emission, it is estimated that the fractional error in the inferred velocity rises above 50% as the velocity of emission falls below 24 μm/ns. By inputting measured parameters into this model, error estimates of the residual velocity as inferred from the X-ray emission measurements are now able to be generated for experimental data. Details of this analysis are presented for an implosion experiment conducted with an unintentional radiation flux asymmetry. The analysis shows a bright localized region of emission that moves through the larger emitting volume at a relatively higher velocity towards the location of the imposed flux deficit. This technique allows for the possibility of spatially resolving velocity flows within the so-called central hot spot of an implosion. This information would help to refine our interpretation of the thermal temperature inferred from the neutron time of flight detectors and the effect of localized hydrodynamic instabilities during the stagnation phase. Across several experiments, along a single line of sight, the average difference in magnitude and direction of the measured residual velocity as inferred from the X-ray and neutron time of flight detectors was found to be ∼13 μm/ns and ∼14°, respectively.