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DOE OSTI2020

Improving Elemental Ratio Measurements on Uranyl Fluoride with NanoSIMS

Measurements on samples of calcined uranyl fluoride (UO 2 F 2 ) using Raman spectroscopy, electron microscopy with elemental analysis, and secondary ion mass spectrometry (SIMS) indicate four facts. First, UO 2 F 2 undergoes a previously unreported oxidation reaction beginning around 350 °C in air. The resulting oxidation compound is likely similar to U 3 O 8 /UO 3 , but presently represents a novel chemical species. Second, variations in F/U ratio across samples as measured by electron microscopy with x-ray spectroscopy correlate with variations in F/U ratio as measured with the NanoSIMS 50L instrument. Third, simple mixed powders of LaF 3 +U 3 O 8 are not sufficiently homogeneous to act as a high F+U content standard material. Fourth, additional method development for determining the bulk F/U ratio using an alternative technique is necessary to further develop analytical standards.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Influence of Spatter on Porosity, Microstructure, and Corrosion of Additively Manufactured Stainless Steel Printed Using Different Island Size

Specimens of 316 L stainless steel were printed using laser powder bed fusion (LPBF), a popular metal additive manufacturing (AM) technique, with varying island sizes. Not many researchers have considered the impact of spatter while optimizing LPBF printing parameters. In this research, the influence of spatter was considered while also investigating the effect of varied island size on the microstructure, surface roughness, microhardness, and corrosion resistance of LPBF-316 L. No correlation was observed between surface roughness or microhardness and minor variations in island size. However, a correlation was drawn between varied island sizes and porosity in LPBF-316 L. The specimens associated with larger island sizes showed significantly enhanced corrosion resistance due to fewer manufacturing defects and reduced porosity, attributed to the minimal influence of the spatter. Based on analysis, the LPBF parameters were revised, which lead to superior corrosion resistance of LPBF-316 L, attributed to high density and reduced porosity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Demonstration of CFD to support the coupled analysis of a reactor pressure vessel subjected to pressurized thermal shock

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended duration or under accident condition. As one of the most significant components of a reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Aging degradation mechanisms (e.g. thermo-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The prediction of the temperature field is achieved by using computational fluid dynamics (CFD) simulation. In this report, a demonstration CFD standalone simulation is performed to support coupled analysis for Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS). The study use a simplified computational domain to represents a real RPV. The purpose of the study is to demonstrate the transient temperature response of RPV to ECC injection. The CFD model is built in a robust and efficient way for further coupled calculation. The next steps of this work, including the coupled thermal and tensor mechanics capabilities using Cardinal are expected to be complete by the end of FY21 for the demo problem. After this, into FY22, the capability will be demonstrated for a realistic RPV.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Variability and associated uncertainty in image analysis for soiling characterization in solar energy systems

The accumulation of soiling on photovoltaic modules and on the mirrors of concentrating solar power systems causes non-negligible energy losses with economic consequences. These challenges can be mitigated, or even prevented, through appropriate actions if the magnitude of soiling is known. Particle counting analysis is a common procedure to characterize soiling, as it can be easily performed on micrographs of glass coupons or solar devices that have been exposed to the environment. Particle counting does not, however, yield invariant results across institutions. The particle size distribution analysis is affected by the operator of the image analysis software and the methodology utilized. The results of a round-robin study are presented in this work to explore and elucidate the uncertainty related to particle counting and its effect on the characterization of the soiling of glass surfaces used in solar energy conversion systems. An international group of soiling experts analyzed the same 8 micrographs using the same open-source ImageJ software package. The variation in the particle analyses results were investigated to identify specimen characteristics with the lowest coefficient of variation (CV) and the least uncertainty among the various operators. The mean particle diameter showed the lowest CV among the investigated characteristics, whereas the number of particles exhibited the largest CV. Additional parameters, such as the fractional area coverage by particles and parameters related to the distribution's shape yielded intermediate CV values. These results can provide insights on the magnitude inter-lab variability and uncertainty for optical and microscope-based soiling monitoring and characterization.

14 SOLAR ENERGY↗

DOE OSTI2026

Genetic analyses of leaf traits in an interspecific Zoysia japonica × Zoysia matrella F2 population

Zoysiagrass (Zoysia spp.) is an important warm-season turfgrass cultivated across tropical, subtropical, and temperate regions of the world. The genus is characterized by the presence of salt-secreting glands on the adaxial leaf surface, which contribute to its high salt tolerance. In this study, we analyzed an interspecific F2 population, derived from selfing an F1 from a cross between Z. japonica acc. Meyer and Z. matrella acc. PI 231146, for variation in adaxial salt gland density, leaf width, and vein count. Using composite interval mapping with a previously constructed genetic map as a framework, we identified three quantitative trait loci (QTL) for leaf width, two QTL for vein count, and two QTL for salt gland density. We complemented the QTL analysis with bulked segregant RNA-seq (BSR-seq) to identify shared genomic regions and candidate genes for leaf width and salt gland density. BSR-seq identified four trait-associated regions, but only a single region identified for leaf width on Chr08 overlapped with a QTL for the same trait. We highlight putative candidate genes underlying the leaf width and salt gland density QTL and discuss their potential roles in leaf development. Together, the QTL and candidate genes provide an important resource for breeding stress-resilient Zoysia germplasm.

Pradhan, Shreena [University of Georgia, Athens]↗

DOE OSTI2022

An experimental and kinetic modeling study of the pyrolysis of isoprene, a significant biogenic hydrocarbon in naturally occurring vegetation fires

Isoprene dominates the carbon flux emitted by vegetation and constitutes 40% of non-methane biogenic emissions worldwide. Despite pyrolysis experiments at temperatures above 1000 K showing a link between isoprene combustion and aromatic species formation, comprehensive mechanistic research on isoprene is scarce in the literature. Here, in this work, we carry out an experimental and theoretical study to build, for the first time, a chemical kinetic model describing isoprene pyrolysis. The formation of polycyclic aromatic hydrocarbon (PAH) precursor species, often observed in vegetation fire plumes, is partially explained by isoprene pyrolysis experiments and theoretical modeling. Molecular dynamics (MD) simulations unveil reaction pathways from allylic isoprenyl radicals to allene and cyclopentadiene (CPD) intermediates, two relevant species detected in the experiments. Rate constants for these identified pathways are calculated using variational transition state theory to update the kinetic model, which is validated against single-pulse shock tube (SPST), and jet-stirred reactor (JSR) experimental data in the temperature range of 850–1690 K. The kinetic model presents satisfactory agreement with the SPST experimental data, and a reaction pathway analysis shows that association of propargyl radicals results in benzene formation. The JSR pathway analysis also identifies the prominent reactions for CPD, benzene, styrene, and toluene formation. Our model does not reproduce the CPD experimental profiles, indicating that additional studies are necessary. Overall, our findings advance the understanding of isoprene pyrolysis and its related atmospheric pollutants in naturally occurring vegetation fires where smoldering and oxygen-deficient combustion processes are present.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Effects of secondary void-initiating particles on the steady-state crack growth resistance of high-strength steel

In this investigation, we focus on the dependence of stable crack growth resistance, as measured by the short-rod fracture toughness test, on secondary void-initiating particles such as AlN and Ti-based grain-refining precipitates in a variety of high-strength steels with tempered martensitic microstructures. The model developed by Ritchie and Thompson is modified to illustrate the significant amounts of toughening that can result from the refinement of secondary particles. Analysis of the data suggests that material strength is a predominant factor in increasing the short-rod fracture toughness relative to linear-elastic measures of initiation fracture toughness, but the extent of toughening is limited by the size and number density of secondary particles in the microstructure. The variation in estimates of secondary microvoid initiation and growth strains with precipitate size reinforce the notion that primary fracture at non-metallic inclusions and secondary fracture at smaller particles occur as sequential processes with a degree of concurrence that is dependent on the state of precipitation in both particle dispersions. Toughening in this connection is maximized by increases in microvoid growth strain that result from decreases in the size and areal number density of secondary void-initiating particles. Finally, the occurrence of transient instabilities during crack extension in short-rod specimens is explained with a phenomenological model that relates crack growth stability to natural variations in the dispersion of secondary void-initiating particles in the microstructure.

42 ENGINEERING↗

DOE OSTI2021

Dynamic Mode Decomposition of Random Pressure Fields over Bluff Bodies

Fluctuating surface pressures on a bluff body exposed to a boundary layer flow generally are characterized as a spatiotemporally varying random field. In this paper, a dynamic mode decomposition (DMD) was applied to extract dominant features embedded in these random pressure fields. Utilizing an unsupervised machine learning algorithm, spatial modes and their temporal variations were grouped into different clusters at scales, e.g., macro, meso, and micro. A proper orthogonal decomposition (POD) of the experimental data was carried out to observe commonalities and distinctive perspectives each decomposition offers. Here, a comprehensive examination of the DMD/POD for their convergence criteria, data sufficiency, and modal components analysis was conducted. The physical interpretation of the spatiotemporal pressure field based on these decomposition schemes was discussed. At different scales, the DMD modes can capture the evolution of aerodynamic features, e.g., convection of vortices (or vortex tubes) and other structures. The distribution of energy among these three broad scales also reflects an energy cascade in pressure fluctuations akin to turbulence.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Identifying dominant environmental predictors of freshwater wetland methane fluxes across diurnal to seasonal time scales

While wetlands are the largest natural source of methane (CH 4 ) to the atmosphere, they represent a large source of uncertainty in the global CH 4 budget due to the complex biogeochemical controls on CH 4 dynamics. Here we present, to our knowledge, the first multi-site synthesis of how predictors of CH 4 fluxes (FCH4) in freshwater wetlands vary across wetland types at diel, multiday (synoptic), and seasonal time scales. In this work we used several statistical approaches (correlation analysis, generalized additive modeling, mutual information, and random forests) in a wavelet-based multi-resolution framework to assess the importance of environmental predictors, nonlinearities and lags on FCH4 across 23 eddy covariance sites. Seasonally, soil and air temperature were dominant predictors of FCH4 at sites with smaller seasonal variation in water table depth (WTD). In contrast, WTD was the dominant predictor for wetlands with smaller variations in temperature (e.g., seasonal tropical/subtropical wetlands). Changes in seasonal FCH4 lagged fluctuations in WTD by ~17 ± 11 days, and lagged air and soil temperature by median values of 8 ± 16 and 5 ± 15 days, respectively. Temperature and WTD were also dominant predictors at the multiday scale. Atmospheric pressure (PA) was another important multiday scale predictor for peat-dominated sites, with drops in PA coinciding with synchronous releases of CH 4 . At the diel scale, synchronous relationships with latent heat flux and vapor pressure deficit suggest that physical processes controlling evaporation and boundary layer mixing exert similar controls on CH 4 volatilization, and suggest the influence of pressurized ventilation in aerenchymatous vegetation. In addition, 1- to 4-h lagged relationships with ecosystem photosynthesis indicate recent carbon substrates, such as root exudates, may also control FCH4. By addressing issues of scale, asynchrony, and nonlinearity, this work improves understanding of the predictors and timing of wetland FCH4 that can inform future studies and models, and help constrain wetland CH 4 emissions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Simulation of Premixed and Partially Premixed Jet-in-Crossflow Flames at High Pressure

In this paper, we explore the operational map of a lean axial-staged combustor of premixed and partially premixed reacting jet-in-crossflow flames at high -pressure (5 atm). This study attempts to expand the data to relatively high pressure and could significantly aid scaling to real gas turbine engine conditions at 20–30 atm. High-speed camera, particle image velocimetry (PIV), CH* chemiluminescence, temperature, and pressure measurements were taken and processed to allow accurate reconstruction of six operating points relative to computational fluid dynamics (CFD) simulations under minimal adjustments. Variation of lean main stage (φ = 0.575 and 0.73) and rich jet (φ = 1.1, 4, and 8) equivalence ratio has been investigated for a four mm axial jet. The fully premixed flames were found to be controlled by the crossflow temperature before ignition and the crossflow oxygen content during combustion. Analysis of flame shape and position for the partially premixed operating points describes a lee stabilized as well as a more unsteady windward flame branch. Adjustment of added jet fuel and crossflow temperature along with its corresponding oxygen level is required to attain a compact flame body. Here, the risk of delaying combustion progress is significantly increased at a richer jet φ = 8 and an overshooting, spatially divided flame was attained with a main stage φ = 0.73. Control toward a compact flame body is critical to allow combustion at reasonable reaction rate.

03 NATURAL GAS↗

DOE OSTI2023

Spatiotemporal Variability of Electric System Reliability Metrics

As urbanization continues to grow, urban density also rises, placing significant stress on critical infrastructure. Cities often face challenges in investing in new infrastructure or upgrading existing ones. One area of infrastructure that has come under strain is the electric grid, leading to prolonged power outages. According to data from the U.S. Energy Information Administration, the average duration of power outages has steadily doubled from 2013 to 2021, primarily due to extreme weather events. The IEEE has developed a series of reliability metrics to assess the reliability of the electric system. However, these metrics are only applied at the utility level, making it challenging to comprehend the variations in these indices at finer spatial resolutions and, consequently, evaluate reliability at the non-utility level. In this study, we leveraged electric outage data collected at 15-minute intervals at the county level to estimate electric system reliability over a six-year period using a novel data analysis approach. Our findings reveal a gradual decline in reliability in the U.S. Southwest compared to national averages. Furthermore, the duration of outages per customer per event has significantly decreased in large portions of California and Florida. These discoveries can be valuable for utility companies as they seek to pinpoint regional anomalies and plan for prioritized remediation efforts.

Singh, Nagendra↗

DOE OSTI2025

Evolved Gas Analysis–Mass Spectrometry Exposes Polymer Network Structures

Polymer network structures in epoxy thermosets play an important role in the final thermoset material properties. However, analytical characterization of these network structures is difficult due to their amorphous nature. In this work, the application of evolved gas analysis–mass spectrometry (EGA-MS) to characterize the polymer network structures of bisphenol A (BPA)-based thermosets is demonstrated. Analytical characterization of the polymer network structures is accomplished by monitoring the Product-Specific Kinetics (PSK) of BPA monomer formation during thermal degradation investigations. We relate observed differences in the activation energy (E a ) of BPA monomer formation to the local packing environment around the BPA monomer units within the polymer network. Variations in the local environment related to the polymer networks manifest qualitatively as broadening in the thermal profile of the BPA monomer evolution and quantitatively as changes in the activation energy (E a ). Three BPA thermoset formulations were investigated; two amine-cured thermoset with 4,4′-diaminodiphenylmethane (DDM) or poly(propylene glycol) bis(2-amino-propyl ether) (PPG400) and a homopolymerized thermoset via curing with Epikure 3253 catalyst (3253). Results revealed that the 3253 thermoset contained two distinct packing densities in the polymer network, while DDM and PPG400 thermosets had uniform distributions of packing densities. Results from the DDM thermoset revealed a gradually decreasing E a , while the apparent E a of PPG400 was consistent over the entire degradation. Furthermore, these differences in E a were concluded to stem from the flexibility of the corresponding polymer networks and the ability of the network components to rearrange and occupy formed voids. Due to the minimal sample required for analysis (100–200 μg), this EGA-MS technique has great potential for postproduction evaluation of composite parts to identify changes in the polymer networks from use and aging, which could signal compromised performance.

Degradation↗

DOE OSTI2020

Persistent Protein Motions in a Rugged Energy Landscape Revealed by Normal Mode Ensemble Analysis

Proteins are allosteric machines that couple motions at distinct, often distant, sites to control biological function. Low-frequency structural vibrations are a mechanism of this long-distance connection and are often used computationally to predict correlations, but experimentally identifying the vibrations associated with specific motions has proved challenging. Spectroscopy is an ideal tool to explore these excitations, but measurements have been largely unable to identify important frequency bands. The result is at odds with some previous calculations and raises the question what methods could successfully characterize protein structural vibrations. Here we show the lack of spectral structure arises in part from the variations in protein structure as the protein samples the energy landscape. However, by averaging over the energy landscape as sampled using an aggregate 18.5 μs of all-atom molecular dynamics simulation of hen egg white lysozyme and normal-mode analyses, we find vibrations with large overlap with functional displacements are surprisingly concentrated in narrow frequency bands. These bands are not apparent in either the ensemble averaged vibrational density of states or isotropic absorption. However, in the case of the ensemble averaged anisotropic absorption, there is persistent spectral structure and overlap between this structure and the functional displacement frequency bands. We systematically lay out heuristics for calculating the spectra robustly, including the need for statistical sampling of the protein and inclusion of adequate water in the spectral calculation. The results show the congested spectrum of these complex molecules obscures important frequency bands associated with function and reveal a method to overcome this congestion by combining structurally sensitive spectroscopy with robust normal mode ensemble analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Elucidating the role of surface species in CO oxidation catalyzed by boron nitride nanotube supported transition metal oxides

Boron nitride nanotube (BNNT) is considered a highly promising catalyst support due to its outstanding thermal stability and chemical inertness. These characteristics make BNNT an attractive alternative for high-temperature applications. However, most studies to date have focused on incorporating platinum group metals (PGMs) to achieve high activity. Although BNNT-supported PGM catalysts are highly effective, their scarcity and high cost hinder widespread use in industrial processes. In this study, BNNT-supported transition metal oxides (TMO x /BNNT; TM = Fe, Co, Ni, and Cu) catalysts were investigated, and CO oxidation was applied as a model reaction to evaluate their catalytic performance. Several characterization techniques, including SEM-EDX, TEM, SXRD, H 2 -TPR, and XPS, were employed to examine their physicochemical properties. Notably, the particle size of the metal oxides differed significantly depending on the metal type. This variation is primarily attributed to the inherent metal–support interactions and the thermodynamic stability of each oxide during synthesis. These properties also affected catalytic activity, and various parameters, such as oxygen mobility and redox behavior, played important roles in determining performance. Finally, in situ DRIFTS, CO-TPSR, reaction-order analysis, and 18 O 2 isotope-labeling experiment were used to investigate the reaction mechanism. In conclusion, the findings provide insights into the design of cost-effective BNNT-supported catalysts and highlight their potential applicability in oxidation reactions.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Theoretical Kinetics Predictions for Reactions on the NH 2 O Potential Energy Surface

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH 2 O potential energy surface, including the NH 2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH 3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (~0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical–radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H 2 channel contributes 10% of the total NH 2 + O flux at combustion temperatures, although this channel is not included in modern NH 3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH 3 oxidation and NO x formation. Finally, the present results for NH 2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH 3 and thermal DeNO x .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Remote Sensing of Tundra Ecosystems Using High Spectral Resolution Reflectance: Opportunities and Challenges

Abstract Observing the environment in the vast regions of Earth through remote sensing platforms provides the tools to measure ecological dynamics. The Arctic tundra biome, one of the largest inaccessible terrestrial biomes on Earth, requires remote sensing across multiple spatial and temporal scales, from towers to satellites, particularly those equipped for imaging spectroscopy (IS). We describe a rationale for using IS derived from advances in our understanding of Arctic tundra vegetation communities and their interaction with the environment. To best leverage ongoing and forthcoming IS resources, including National Aeronautics and Space Administration’s Surface Biology and Geology mission, we identify a series of opportunities and challenges based on intrinsic spectral dimensionality analysis and a review of current data and literature that illustrates the unique attributes of the Arctic tundra biome. These opportunities and challenges include thematic vegetation mapping, complicated by low‐stature plants and very fine‐scale surface composition heterogeneity; development of scalable algorithms for retrieval of canopy and leaf traits; nuanced variation in vegetation growth and composition that complicates detection of long‐term trends; and rapid phenological changes across brief growing seasons that may go undetected due to low revisit frequency or be obscured by snow cover and clouds. We recommend improvements to future field campaigns and satellite missions, advocating for research that combines multi‐scale spectroscopy, from lab studies to satellites that enable frequent and continuous long‐term monitoring, to inform statistical and biophysical approaches to model vegetation dynamics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A North Atlantic synthetic tropical cyclone track, intensity, and rainfall dataset

Tropical Cyclones (TCs) cause significant socio-economic damages to the US and Caribbean coastal regions annually, making it important to understand TC risk at the local-to-regional scales. However, the short length of the observed record and the substantial computational expense associated with high-resolution climate models make it difficult to assess TC risk using either approach. To overcome these challenges, we developed a database of synthetic TCs using the Risk Analysis Framework for Tropical Cyclones (RAFT). The database includes 40,000 synthetic TC tracks, along-track intensities and storm-induced precipitation. TC tracks generated in RAFT are in reasonable agreement with the observed spatial distribution of TC tracks and basin-scale TC statistics. Specifically, along the coast, spatial variations in TC crossing probability and extreme winds upon landfall are well-reproduced by RAFT with R-squared values of 0.81 and 0.73, respectively. In summary, the synthetic TC database constructed with RAFT provides a reasonable pathway for the robust assessment of North Atlantic TC wind and rainfall risks.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Simultaneous compression and opacity data from time-series radiography with a Lagrangian marker

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. Additionally, if the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗