Radiation flow through an inhomogeneous medium is critical in a wide range of physics and astronomy applications, from transport across cloud layers on the Earth to the propagation of supernova blast waves producing ultraviolet and X-ray emission. Radiation interacts with matter, driving hydrodynamic feedback that further alters the radiation characteristics (energy and angular distribution). This paper reviews the current state of the art in the modeling of inhomogeneous radiation transport, subgrid models developed to capture this often-unresolved physics, and the experiments designed to improve our understanding of these models. This paper focuses on simulations based on upcoming experiments designed to test this physics. We present a series of detailed simulations (both single-clump and multi-clump conditions) probing the dependence on the physical properties of the radiation front (e.g., radiation energy) and material characteristics (specific heat, opacity, clump densities). We find that, unless the radiation pressure is high, the clumps will heat and then expand, effectively cutting off the radiation flow. The expanding winds can also produce shocks that generates high-energy emission. We compare our detailed simulations with some of the current subgrid prescriptions, identifying some of the limitations of these current models.

Precise characterization of experimental radiation flow is required to validate the high energy density physics models, numerical methods, and codes that are used to simulate radiation-hydrodynamics phenomena such as thermal radiation transport in stochastic media. The Cassio code is used to simulate thermal radiation flow through inhomogeneous, stochastic-media-foam configurations containing optically thick clumps dispersed within an optically thin background aerogel. Cassio can model small inhomogeneous problems directly, but most problems require approximations to meet computer limitations on run-times and memory usage. Various examples of these approximations are methods that produce, in one calculation, an ensemble-averaged solution and associated standard deviation; reduced spatial dimensionality with approximate geometries; and full material homogenization with no geometric detail. Cassio simulations are used to design experiments at the OMEGA-60 Laser Facility that can measure the radiation flow using the spatially resolved COAX absorption spectroscopy diagnostic. The experimental platforms flow radiation through foam targets ranging from a background-only aerogel, to a single configuration of a specified stochastic medium, to a fully homogenized foam of the background and clump materials. Under constant total clump mass, larger clumps (here, larger than 10 μm diameter) will mix more slowly with the background such that the bulk radiation flow is faster than it would be in a fully homogenized material. The COAX platform can be used to infer temperature and density profiles in both the background material and clumps, simultaneously, and therefore to differentiate radiation flow in a range of stochastic and homogeneous media.

This work provides a numerical study of how double shell capsule deformations caused by drive asymmetries and fabrication imperfections affect implosion symmetry and neutron yield. Hydrodynamics simulations are performed in two dimensions and focus on low-mode deformations that are caused by corresponding asymmetries in the Hohlraum drive, component offsets, and ablator joint gaps. By providing a parameter study of these features, our goal is to understand the dominant sources for inner shell deformation and yield degradation. The discussed capsules are composed of an aluminum ablator with a chromium inner shell. The latter encloses a carbon-deuterium foam ball that serves as fuel. We find that for clean capsules, even-numbered low-mode asymmetries in the drive are imprinted on the ablator and smoothly transferred to the inner shell during shell collision. The resulting deformation of the inner shell is more pronounced with larger fuel radius, while the yield is inversely proportional to the amplitude of the drive asymmetry and varies by factors ≤4 in comparison with clean simulations. Capsule component offsets in the vertical direction and ablator thickness nonuniformity result in p1-type deformations of the imploding inner shell. Finally, joint gaps have the largest effect in deforming the ablator and inner shell and degrading yield. While small gap widths (1 μm) result in prolate inner shells, larger gap widths (4 μm) cause an oblate deformation. More importantly, capsules with a small outer gap (1 μm) experience a dramatic drop in yield, typically <3% of a clean simulation.

Both radiation flows and shocks have been extensively studied in the laboratory in the past few decades due to their critical roles in many astrophysical and high-energy density physics processes. In the Radishock experiment, a halfraum-powered radiation wave is driven into a low-density foam and interacts with an ablatively driven, counter-propagating shock. The interacting waves produce a spike in energy density with a temperature greater than the local temperature of the individual waves. As in the successful predecessor experiment, COAX, the primary diagnostic uses absorption spectroscopy at many locations down the cylindrical target, enabling a spatial temperature inference of the radiation wave and its interactions with the shock. Combined with a radiography diagnostic that is capable of imaging the shock and interaction features, we are able to study and inform model predictions of the interaction spike phenomenon. We describe the underlying physics behind the shock interactions with the radiation front and the implications of this experimental study for a broad range of astrophysical phenomena.

Double shell inertial confinement fusion is a concept for achieving robust thermonuclear burn that uses dense metal shells to compress deuterium-tritium (DT) fuel to fusion conditions. Double shell implosions are typically indirectly driven and involve a target that consists of a low-Z ablator, a foam layer, and a high-Z pusher surrounding the DT fuel. The goal of the campaign is to achieve a volumetric burn as radiation losses from the DT fuel are trapped by the opaque high-Z shell. The overall performance of double shell implosions relies on the efficient collisional transfer of kinetic energy between layers. The efficiency of this transfer (and therefore the overall performance of a given implosion) is degraded by the presence of low-mode asymmetries. P2 asymmetries are often observed in spatially resolved 2D radiographs of nominal double shell implosions. This work discusses three such experiments: one with an oblate P2 asymmetry, one with a prolate P2 asymmetry, and one with an approximate spherical symmetry. After performing a shape analysis of the oblate and prolate implosions to quantify asymmetries, these experimental results were compared with the results of hydrodynamic simulations for the two experiments. Differences between the experiment and simulation were then used to design an approximately spherical implosion by altering the incident laser cone fraction. Radiographs from the experiment that implemented the modified cone fraction show evidence of an implosion that is approximately spherical until bang time. This design is intended to serve as a point design for future studies that will seek to optimize various aspects of the double shell target.

Spectral diagnostics provide a powerful probe of high energy-density physics experiments. By shining an x-ray source on a target, absorption features can be used to determine accurate temperature profiles of that target material. Many studies produce a single temperature/density measurement by fitting these observed spectra. This paper demonstrates how, by leveraging detailed simulations, we can not only measure the average temperature and density, but the full density and temperature profiles. To do so, we must conduct a careful analysis of the uncertainties in the diagnostic measurement. We discuss the characteristics and associated uncertainties of the spectral diagnostic used in the COAX, Radishock and OuTi experiments, ultimately demonstrating how these detailed studies increase the potential of this powerful probe.

The Radishock platform studies the interaction between a radiation wave and a counter-propagating shockwave within a Ti-laden silica aerogel foam using x-ray absorption spectroscopy and point-projection backlighter radiography from the COAX platform [1]. The radiation wave is produced by a laser-driven halfraum, and the shock wave via a directly-driven ablator. These experiments can provide insight into supernova shock breakout emission where the radiation flow breaking out of the star interacts with the circumstellar medium and the relative velocity between this breakout and the medium dictates the degree of heating in the shock. In our Radishock experiments, the radiation flow is not apparent in the radiographic diagnostic and can be directly observed only via the absorption spectroscopy diagnostic, which provides a measure of temperature and position. On the other hand, the shockwave launched from the ablator side of the target is observed in the radiographs, and we extract the full 2D shock front contour using computer vision techniques [2]. In the course of this analysis, we found features present in the late time interaction shots which were not present in the radiation wave only, shockwave only, and early time interaction shots. These features appear to be ablation driven off of the shock front by the interaction with the radiation wave, and it provides an indirect means of probing the radiation wave radiographically, and a direct means of probing the interaction itself.

Inertial confinement fusion (ICF) and high-energy density (HED) physics experiments experience complicated forcing for instability growth and mix due to the ubiquitous presence of multiple shocks interacting with perturbations on multiple material interfaces. One common driver of instability growth is successive shocks from the same direction. However, there is a severe lack of analytic work and modeling validation for same-sided successive shocks since they are extremely difficult to achieve with conventional (non-HED) drivers. Successive shocks access a large instability parameter space; idealized fluid theory [K. O. Mikaelian, Phys. Rev. A 31, 410 (1985)] predicts 15 different interface evolution scenarios for a sinusoidal perturbation. Growth becomes more complex for multi-mode, compressible HED systems. The Mshock campaign is the first experiment in any fluid regime to probe a wide portion of successive shock parameter space. This is enabled by our development of a hybrid direct/indirect drive platform capable of creating independently controllable successive shocks on the National Ignition Facility. These experiments have delivered the first data capable of rigorously challenging our models and their ability to accurately capture Richtmyer–Meshkov growth under successive shocks. Single-mode and two-mode experiments have successfully demonstrated the ability to access and control the various growth scenarios of the shocked interface, including re-inversion, freeze out, and continued growth. Simulations and theoretical modeling are shown to accurately capture the experimental observations in the linear growth phase, giving us confidence in our ICF/HED design codes.

The goal of the Xflows experimental campaign is to study the radiation flow on the National Ignition Facility (NIF) reproducing the sensitivity of the temperature (±8 eV, ±23 μm) and density (±11 mg/cc) measurements of the COAX platform [Johns et al., High Energy Density Phys. 39, 100939 (2021); Fryer et al., High Energy Density Phys. 35, 100738 (2020); and Coffing et al., Phys. Plasmas 29, 083302 (2022)]. This new platform will enable future astrophysical experiments involving supernova shock breakout, such as Radishock (Johns et al., Laboratory for Laser Energetics Annual Report 338, 2020) on OMEGA-60 [Boehly et al., Rev. Sci. Instrum. 66, 508 (1995)], and stochastic media (such as XFOL on OMEGA). Greater energy and larger physical scale on NIF [Moses et al., Eur. Phys. J. D 44, 215 (2007)] will enable a greater travel distance of radiation flow, higher density, and more manufacturable foams and enable exploration of a greater range of radiation behavior than achievable in the prior OMEGA experiments. This publication will describe the baseline configuration for the Xflows experimental campaign and the roadmap to achieve its primary objectives.

The COAX platform has been used in numerous experiments to study radiation flow from a laser-driven halfraum down a low-density SiO2 foam laden with Ti, Sc, or V as spectroscopic dopants. These experiments, conducted first at OMEGA-60 and transitioning to NIF, utilize 1-D space-resolving absorption spectroscopy to characterize the radiation flow temperature to within +8eV and density within +11mg/cc. Parallel point-projection radiography measurements capture the development of the transonic and subsonic shock, and the combination strongly constrains radiation hydrodynamics simulations. This presentation will overview our body of work in this area and advertise applications to laboratory astrophysics, materials studies, and ICF.

Predicting and modeling the behavior of experiments with radiation waves propagating through low-density foams require a detailed quantification of the numerous uncertainties present. In regimes where a prominent radiative shock is produced, key dynamical features include the shock position, temperature, and curvature and the spatial distribution and temperature of the corresponding supersonic radiation wave. The COAX experimental platform is designed to constrain numerical models of such a radiative shock propagating through a low-density foam by employing radiography for spatial and shock information, Dante for characterizing the x-ray flux from the indirectly driven target, and a novel spectral diagnostic designed to probe the temperature profile of the wave. In this work, we model COAX with parameterized 2D simulations and a Hohlraum-laser modeling package to study uncertainties in diagnosing the experiment. The inferred temperature profile of the COAX radiation transport experiments has been shown to differ from simulations more than expected from drive uncertainties that have been constrained by simultaneous soft x-ray flux and radiography measurements.

radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.

In the Double Shell Inertial Confinement Fusion concept, characterizing the shape asymmetry of imploding metal shells is vital for understanding energy-efficient compression and radiative losses of the thermonuclear fuel. The Monte Carlo N-Particle MCNP® code forward models radiography of Double Shell capsule implosions using the Advanced Radiographic Capability at the National Ignition Facility. A procedure is developed for using MCNP to reconstruct density profiles from the radiograph image intensity. For a given Double Shell imploding target geometry, MCNP radiographs predict image contrast, which can help guide experimental design. In future work, the calculated MCNP synthetic radiographs will be compared with experimental radiographs to determine the radial and azimuthal density profiles of the Double Shell capsules.

The principal Hugoniot, sound velocity, and Grijneisen parameter of polystyrene were measured at conditions relevant to shocks in inertial confinement fusion implosions, from 100 to 1000 GPa. The sound velocity is in good agreement with quantum molecular dynamics calculations and all tabular equation of state models at pressures below 200 GPa. Above 200 GPa, the experimental results agree with two of the examined tables, but do not agree with the most recent table developed for design of inertial confinement fusion (ICF) experiments. The Grijneisen parameter increases with density below similar to 3.1 g/cm(3) and approaches the asymptotic value for an ideal gas after complete dissociation. This behavior is in good agreement with quantum molecular dynamics results and previous work but is not represented by any of the tabular models. The discrepancy between tabular models and experimental measurement of the sound velocity and Gruneisen parameter is sufficient to impact simulations of ICF experiments.

MgO is a major constituent of the MgO-FeO-SiO2 system that comprises the Earth's mantle and that of super-Earth exoplanets. Knowledge of its high-pressure behavior is important for modeling the more complex compounds. This paper presents measurements of the principal Hugoniot, sound velocity, and temperature of MgO, shocked to pressures of 710 to 2300 GPa using laser-driven compression. The Hugoniot and temperature measurements compare favorably to previous results constraining the shock response of MgO at extreme conditions. The Gruneisen parameter was calculated from the Hugoniot and sound velocity data and was found to be underpredicted by tabular models. The sound velocity of liquid MgO is overpredicted by models implying that the quantity of partial melt required to match decreased wave speeds in ultralow velocity zones in the lower mantle may be less than previously assumed and experiments at lower-mantle pressures are needed.

The behavior of carbon at terapascal pressures (10’s of millions of atmospheres) is important to modeling ice giant planets and white dwarf stars and to designing inertial confinement fusion (ICF) experiments, where diamond is used to contain and compress the hydrogen fuel. The high-pressure shock and release responses of diamond are of particular interest to the initial stages of an ICF implosion. Measurements of these behaviors provide rigorous constraints on important paths through carbon’s equation of state. This work presents experimental Hugoniot and release data for both single-crystal diamond (SCD) and nanocrystalline diamond (NCD), which is comprised of nanometer-scale diamond grains and is 5% less dense than SCD. We find that the NCD used in ICF experiments has a stiffer Hugoniot than SCD that can be attributed to porosity. A Gr¨uneisen parameter of 1 for high-pressure fluid carbon was derived from the NCD and SCD Hugoniots and is used in Mie-Gr¨uneisen models to accurately describe the NCD and SCD release data.

Current inertial confinement fusion experiments on the National Ignition Facility (NIF) [G. H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 43, 2841 (2004)] are attempting to demonstrate thermonuclear ignition using x-ray drive by imploding spherical targets containing hydrogen-isotope fuel in the form of a thin cryogenic layer surrounding a central volume of fuel vapor [J. Lindl, Phys. Plasmas 2, 3933 (1995)]. The fuel is contained within a plastic ablator layer with small concentrations of one or more mid-Z elements, e.g., Ge or Cu. The capsule implodes, driven by intense x-ray emission from the inner surface of a hohlraum enclosure irradiated by the NIF laser, and fusion reactions occur in the central hot spot near the time of peak compression. Ignition will occur if the hot spot within the compressed fuel layer attains a high-enough areal density to retain enough of the reaction product energy to reach nuclear reaction temperatures within the inertial hydrodynamic disassembly time of the fuel mass ...

The equation of state (EOS) of carbon in its high-pressure solid and liquid phases is of interest to planetary astrophysics and inertial confinement fusion. Of particular interest are the high-pressure shock and release responses of diamond as these provide rigorous constraints on important paths through the EOS. This paper presents experimental Hugoniot and release data for both single-crystal diamond (SCD) and nanocrystalline diamond (NCD), which is comprised of nanometer-scale diamond grains and is similar to 5% less dense than SCD. We find that NCD has a stiffer Hugoniot than SCD that can be attributed to porosity. A Gruneisen parameter of similar to 1 was derived from the data, which suggests increased coordination in the high-pressure fluid carbon compared to ambient diamond.