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DOE OSTI2024

Understanding the Impact of Fuel on Surfactant Microstructure of Firefighting Foam

Abstract Aqueous film-forming foam is being phased out due to the environmental impacts of fluorinated surfactants contained in the firefighting foams. To develop an environmentally friendly firefighting foam, it is important to understand the factors controlling the firefighting performance of surfactants. Fuel transport through foam has been considered as a dominant mechanism for foam collapse. Therefore, the impact of fuels (heptane, octane and trimethylbenzene (TMB)) on surfactant microstructure was studied for three different types of surfactants (Capstone, Glucopon, and siloxane) that have applications in firefighting foam. Multiple techniques were used to identify the microstructure and interfacial properties of surfactants with and without exposure to liquid fuel. The ignition time of fuel vapor through foam and solubility of fuel through liquid surfactant solution were measured as well. This work shows fuel solubility has an impact on the surfactant microstructure and interfacial properties. In addition, fuel solubility and vapor pressure affect the ignition time of fuel vapors.

Engineering↗

DOE OSTI2024

An experimental and chemical kinetic modeling study of 4-butoxyheptane combustion

Here, the combustion kinetics of a novel oxygenated bioblendstock for diesel, 4-butoxyheptane (4-BH), was investigated experimentally using a flow reactor and a heated, high-pressure shock tube. The flow reactor experiments employed oxygen as the oxidizer and helium as the diluent with oxidation conducted at atmospheric pressure and 10 bar for temperatures from 400 to 1000 K at 20-K intervals. The fuel, oxidizer, and diluent flow rates were varied at different temperatures to maintain a constant initial fuel mole fraction of 1000 ppm, with stoichiometric equivalence ratio, and a residence time of 2.0 s. The reacted gas was fed to two separate GC systems that could qualitatively and quantitatively detect product species. Additionally, real fuel-air ignition delay time (IDT) data were collected using a heated, high-pressure shock-tube facility. Fuel lean (φ = 0.5) and stoichiometric (φ = 1.0) mixtures were investigated at 10 atm as well as at 30 atm for the fuel lean case for temperatures between 847 and 1259 K. A detailed chemical kinetics mechanism was developed to model the product distribution from the flow reactor and IDTs from the shock tube. The proposed model was able to predict the double NTC behavior in flow reactor experiments reasonably well. Model predictions at low temperatures were observed to be highly sensitive to the rate constants of ketohydroperoxide (KHP) decomposition in the case of the OOH group in α position which were modeled based on existing literature studies on ethers. It was noted that in the absence of theoretical or experimental studies, the rate constants for KHP decomposition used in the literature were empirically set. Additional studies are required to address the gap in model prediction obtained in this study and to reduce the uncertainty in kinetics models for ether oxidation. Predicted product concentrations and IDTs showed some quantitative agreement with experimental data, but the overall reactivity of the IDTs is underpredicted. Additionally, significant deviation is observed for the IDT results at 10 atm for the stoichiometric case with minor deviations for the other cases. The reaction pathways to the missing products were then further analyzed theoretically through quantum-mechanical calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Long duration battery sizing, siting, and operation under wildfire risk using progressive hedging

Battery sizing and siting problems are computationally challenging due to the need to make long-term planning decisions that are cognizant of short-term operational decisions. This paper considers sizing, siting, and operating batteries in a power grid to maximize their benefits, including price arbitrage and load shed mitigation, during both normal operations and periods with high wildfire ignition risk. Here we formulate a multi-scenario optimization problem for long duration battery storage while considering the possibility of load shedding during Public Safety Power Shutoff (PSPS) events that de-energize lines to mitigate severe wildfire ignition risk. To enable a computationally scalable solution of this problem with many scenarios of wildfire risk and power injection variability, we develop a customized temporal decomposition method based on a progressive hedging framework. Extending traditional progressive hedging techniques, we consider coupling in both placement variables across all scenarios and state-of-charge variables at temporal boundaries. This enforces consistency across scenarios while enabling parallel computations despite both spatial and temporal coupling. The proposed decomposition facilitates efficient and scalable modeling of a full year of hourly operational decisions to inform the sizing and siting of batteries. With this decomposition, we model a year of hourly operational decisions to inform optimal battery placement for a 240-bus WECC model in under 70 min of wall-clock time.

25 ENERGY STORAGE↗

DOE OSTI2024

Skeletal reaction models for methane combustion

A local-sensitivity-analysis technique is employed to generate new skeletal reaction models for methane combustion from the foundational fuel chemistry model (FFCM-1). Here, the sensitivities of the thermo-chemical variables with respect to the reaction rates are computed via the forced-optimally time dependent (f-OTD) methodology. In this methodology, the large sensitivity matrix containing all local sensitivities is modeled as a product of two low-rank time-dependent matrices. The evolution equations of these matrices are derived from the governing equations of the system. The modeled sensitivities are computed for the auto-ignition of methane at atmospheric and high pressures with different sets of initial temperatures, and equivalence ratios. These sensitivities are then analyzed to rank the most important (sensitive) species. A series of skeletal models with different number of species and levels of accuracy in reproducing the FFCM-1 results are suggested. The performances of the generated models are compared against FFCM-1 in predicting the ignition delay, the laminar flame speed, and the flame extinction. The results of this comparative assessment suggest the skeletal models with 24 and more species generate the FFCM-1 results with an excellent accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Examining experimental nitrogen-based emissions trends from ammonia/diesel and ammonia/hydrogen/diesel combustion

Ammonia has garnered interest as an alternative fuel for power sectors with heavy payload and distance requirements, such as shipping. In this study, ammonia was used in a dual-fuel compression-ignition combustion strategy to overcome some of its technical barriers, using a diesel pilot to ignite a premixed mixture of ammonia and air. Mixtures of premixed ammonia and hydrogen were also explored to evaluate whether the inclusion of hydrogen improves nitrogen-based emissions from the combustion process. A single-cylinder version of a Cummins ISB 6.7 L engine platform was used to experimentally study these effects at various global air/fuel ratios and hydrogen energy fractions. Hydrogen inclusion produced pronounced NOx and N2O emissions, while inclusion of trapped residuals increased N2O but reduced NOx. The two most recent and relevant mechanisms available in the literature—those from Xu and Zhang-Ren-Kokjohn—were used in a chemical kinetics analysis to examine the observed differences in the NOx trends from two dual-fuel ammonia/diesel datasets: (1) in which a portion of the premixed ammonia was substituted with hydrogen and (2) in which the effect of hot trapped residuals was evaluated with only ammonia/air premixed mixtures. The analysis with both mechanisms showed agreement with experimental trends; however, contributions from thermal vs. fuel-borne NOx pathways showed disagreement. A reaction pathway analysis showed that the HNO to NO pathway was the key to NO formation in the mixture.

Tyrewala, Daanish [ORNL] (ORCID:0000000208599324)↗

DOE OSTI2024

Potential Adoption and Benefits of Co-Optimized Multimode Engines and Fuels for U.S. Light-Duty Vehicles

Exploring a diverse portfolio of technologies for decarbonization is crucial to understanding the potential impacts of different technological solutions and their associated environmental implications. Using high-octane, high-sensitivity biofuel blends in co-optimized multimode engines can increase engine efficiency and reduce vehicle emissions. Here, the multimode engine research focuses on the benefits of light-duty vehicle engines, which can operate in multiple modes depending on the vehicle's load. Low-temperature combustion can improve efficiency and reduce emissions (such as those from oxides of nitrogen and particulate matter) during low-load operation, while spark ignition performance is maintained in high-load operation. These advanced engines can be optimized to run on blends of biobased fuels. This analysis models scenarios for potential market adoption of co-optimized multimode vehicles fueled by three different bioblendstocks: ethanol, isopropanol, and isobutanol. An integrated modeling approach is used to forecast the energy and environmental impacts of the deployment of co-optimized multimode vehicles and fuels in the light-duty sector over the 2020-to-2050 time horizon. The multidisciplinary approach combines vehicle sales modeling, system dynamics modeling of the biorefining industry, and life cycle assessment to estimate the emissions and energy benefits. The models consider market forces such as consumer preferences for vehicle attributes, biofuel supply and demand dynamics subject to biorefinery capacity build-out and bioresource constraints, and forecasted changes to the U.S. bulk energy system over time. Market adoption of co-optimized vehicles is evaluated across a wide parameter space for incremental vehicle cost and engine efficiency improvement. This analysis reveals that the deployment of co-optimized multimode fuels and vehicles results in up to a 5% reduction in annual sector-wide life cycle greenhouse gas (GHG) emissions by 2050, relative to a business-as-usual scenario, but is also indicates environmental trade-offs, such as higher life cycle water-use. Emission benefits could potentially increase beyond 2050, as the new technologies penetrate the market and gain a foothold. Results also show that, under certain circumstances, vehicles with engines co-optimized for use with high-octane, high-sensitivity biofuel blends can be cost-competitive with conventional gasoline, while reducing GHG emissions. Our modeling results indicate that co-optimized multimode fuels and engines can be strategically leveraged in tandem with electrification to decarbonize the light-duty sector. Co-optimized vehicles could play a role in the early years of the time horizon, while electric vehicles (EVs) could become more competitive in the later years, highlighting the complementary benefits of these technologies for GHG reductions.

Oke, Doris↗

DOE OSTI2024

The impact of low-mode symmetry on inertial fusion energy output in the burning plasma state

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Spatiotemporal dynamics of fast electron heating in solid-density matter via XFEL

Abstract High-intensity, short-pulse lasers are crucial for generating energetic electrons that produce high-energy-density (HED) states in matter, offering potential applications in igniting dense fusion fuels for fast ignition laser fusion. High-density targets heated by these electrons exhibit spatially non-uniform and highly transient conditions, which have been challenging to characterize due to limitations in diagnostics that provide simultaneous high spatial and temporal resolution. Here, we employ an X-ray Free Electron Laser (XFEL) to achieve spatiotemporally resolved measurements at sub-micron and femtosecond scales on a solid-density copper foil heated by laser-driven fast electrons. Our X-ray transmission imaging reveals the formation of a solid-density hot plasma localized to the laser spot size, surrounded by Fermi degenerate, warm dense matter within a picosecond, and the energy relaxation occurring within the hot plasma over tens of picoseconds. These results validate 2D particle-in-cell simulations incorporating atomic processes and provide insights into the energy transfer mechanisms beyond current simulation capabilities. This work significantly advances our understanding of rapid fast electron heating and energy relaxation in solid-density matter, serving as a key stepping stone towards efficient high-density plasma heating and furthering the fields of HED science and inertial fusion energy research using intense, short-pulse lasers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Wildfire and power grid nexus in a changing climate

Global wildfire events have had increasingly severe impacts in recent years, particularly in the western USA, driven by extreme fire-weather conditions, fuel accumulation and multiple ignition sources. Wildfires sparked by power lines tend to be larger and more destructive, as they often occur during high winds, which accelerate the spread of fires. Moreover, efforts to contain wildfires frequently result in power outages, causing considerable economic disruption. Here, in this Review, we examine wildfire risks related to power-line-induced ignitions, infrastructure damage, climate-induced environmental impacts, grid operational risks, real-time grid management risks, vegetation management risks, and financial and funding risks in the context of a changing climate and their interdependence with power grid infrastructures. We then explore the resilience of power grids under wildfire threats, looking at risk analysis, prediction and mitigation strategies. The Review also shares practical insights and experiences in the USA to inform researchers, policymakers and industry professionals.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Security constrained optimal power shutoff for wildfire risk mitigation

Abstract Electric grid faults are increasingly the source of ignition for major wildfires. To reduce the likelihood of such ignitions in high risk situations, utilities use preemptive de‐energization of power lines, commonly referred to as Public Safety Power Shutoffs (PSPS). Besides raising challenging trade‐offs between power outages and wildfire safety, PSPS removes redundancy from the network at a time when component faults are likely to happen. This may leave the network particularly vulnerable to unexpected line faults that may occur while the PSPS is in place. Previous works have not explicitly considered the impacts of these outages. To address this gap, the Security Constrained Optimal Power Shutoff problem is proposed which uses post‐contingency security constraints to model the impact of unexpected line faults when planning a PSPS. This model enables, for the first time, the exploration of a wide range of trade‐offs between both wildfire risk and pre‐ and post‐contingency load shedding when designing PSPS plans, providing useful insights for utilities and policy makers considering different approaches to PSPS. The efficacy of the model is demonstrated using the EPRI 39‐bus system as a case study. The results highlight the potential risks of not considering security constraints when planning PSPS and show that incorporating security constraints into the PSPS design process improves the resilience of current PSPS plans.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

The advanced evolution of massive stars

The nuclear rates for reactions involving 12 C and 16 O are key to computing the energy release and nucleosynthesis evolution of massive stars during their advanced burning phases. Ultimately, these burning rates shape the stellar structure and evolution and influence the nature of the compact objects produced at the end of the stellar life. We explore the implications of new nuclear reaction rates from both experimental and theoretical studies for 12 C(α, γ) 16 O, 12 C+ 12 C, 12 C+ 16 O, and 16 O+ 16 O reactions for massive stars. Our goal is to investigate how the chemical structure and nucleosynthesis evolve from the He-exhaustion stage to the O-burning phase and how these processes influence the ultimate stellar fate. We computed rotating and non-rotating models for stars of different masses at solar metallicity. We used the stellar evolution code GENEC, which includes a large network of nuclear reactions and isotopes involved in advanced phases, as well as updated rates for 12 C(α,γ) 16 O. For the three fusion reactions involving 12 C and 16 O, we considered new rates following a data-driven fusion suppression scenario (hereafter HIN(RES)) and new theoretical rates obtained with time-dependent Hartree-Fock (TDHF) calculations. The updated 12 C(α, γ) 16 O rates mainly impact the chemical structure evolution changing the 12 C/ 16 O ratio at He-exhaustion and have little effect on the CO core mass. This variation in the 12 C/ 16 O ratio is in some cases critical for predicting the final fate of the model, which is very sensitive to 12 C abundance, and in particular the 20 M ⊙ remnant may change from a black hole to a neutron star. The He-burning (C-burning) lifetime is also decreased (increased) by about −2% (+15%). The combined new rates for 12 C+ 12 C and 16 O+ 16 O fusion reactions according to the HIN(RES) model lead to shorter C- and O-burning lifetimes by ≈ − 10%, and −50%, respectively, and shift the ignition conditions to higher temperatures and densities. In contrast, the theoretical TDHF rates primarily affect C-burning, increasing its duration by about 30% and lowering the ignition temperature. These changes modify the chemical structure of the core, the size and duration of C-burning shells, and hence their compactness. They also impact the central and shell nucleosynthesis (by ±1 dex and by factors of ±2–10, respectively), while 12 C+ 16 O reaction rates variations remain the least important.

abundances↗

DOE OSTI2026

Violent mergers revisited: The origin of the fastest stars in the Galaxy

Binary systems of two carbon-oxygen white dwarfs are one of the most promising candidates for the progenitor systems of Type Ia supernovae. Violent mergers, where the primary white dwarf ignites when the secondary white dwarf smashes into it while being disrupted on its last orbit, were the first double degenerate merger scenario proposed that ignites dynamically. However, violent mergers likely contribute only a few percent to the total Type Ia supernova rate and do not yield normal Type Ia supernova light curves. Here we revisit the scenario, simulating a violent merger with better methods and, in particular, a more accurate treatment of the detonation. We find good agreement with previous simulations but with one critical difference: The secondary white dwarf being disrupted and accelerated towards the primary white dwarf and impacted by its explosion does not fully burn, and its core survives as a bound object. The explosion leaves behind a 0.16 M ⊙ star travelling 2800 km/s, making it an excellent (and so far the only) candidate to explain the origin of the fastest observed hypervelocity stars. We also show that before the explosion, 5 × 10 −3 M ⊙ of material predominantly consisting of helium, carbon, and oxygen had already been ejected at velocities above 1000 km/s. Finally, we argue that if a violent merger made the hypervelocity stars D6-1 and D6-3 and violent mergers require the most massive primary white dwarfs in binaries of two carbon-oxygen white dwarfs, there has to be a much larger population of white dwarf mergers with slightly lower mass primary white dwarfs. Because this population likely represents ≫10% of the Type Ia supernovae rate, it can essentially only give rise to normal Type Ia supernovae.

Astronomy and AstroPhysics↗

DOE OSTI2024

What next: Further implosion space exploration on the path to NIF extended yield capability

We present quantitative motivations and assessments of various proposed and ongoing directions to further improving yields and target gain of igniting indirect-drive implosions at the National Ignition Facility (NIF). These include increasing compression and confinement time, improving hohlraum and ablator efficiency, and further increasing peak power and laser energy. 1D hydroscaled simulations, augmented by analytic 1D theory, have been used to project yield improvements for each of these implosion optimization tracks, normalized to the best current performing 4 MJ shot. At current NIF capabilities of 2.2 MJ, 450 TW, we project several paths could reach 15 MJ yield levels. We also expect several key implosion physics questions will be addressed in attempting to reach this yield level. These include demonstrating to what extent lower adiabat designs leading to higher compression will increase gain and efficiency, and whether we can reduce residual kinetic energy and ablator-fuel mix that is probably limiting the current burn-up fraction. For an envisaged NIF upgrade to EL = 3 MJ at fixed 450 TW peak power, scaling capsule size and fuel thicknesses faster than pure hydroscaling should allow for yields that could reach up to 60–80 MJ, depending on the efficiency gains realized in increasing deuterium-tritium fuel thickness, reducing hohlraum losses, and switching to lower Z ablators. The laser-plasma instability and beam transmission scaling in these larger hohlraums is shown to be favorable if the spot size is increased with hohlraum scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Self-generated magnetic fields in the hot spot of direct-drive cryogenic implosions at Omega

This work reports that Biermann self-generated magnetic fields of ≈200 MG and Hall parameters of ≈1.5 are produced in the stagnation phase of direct-drive cryogenic implosions at Omega. The magnetic fields produce a drop of 2.4% in fusion yield and 1% in ion temperature. A quantitative estimate of the effect of self-generated magnetic fields on yield and ion temperature is essential, since direct measurements of these fields are not available. Reconstructed simulations of the 50 Gbar implosions, with all the stagnation measurements reproduced simultaneously by a combination of mid- and low-mode asymmetries as degradation mechanisms [Bose et al., Phys. Plasmas 25, 062701 (2018)], are used to obtain the estimates. The magnetic fields cause a decrease in yield due to the Righi–Leduc heat flow, which exceeds any benefits from heat flow suppression due to magnetization. It is important to note that both direct-drive Omega-scale implosions and indirect-drive National Ignition Facility (NIF)-scale implosions [Walsh et al., Phys. Rev. Lett. 118, 155001 (2017)] produce similar estimates for the magnetic field strength, and both show a decrease in fusion yield, with the Righi–Leduc transport as the loss mechanism. However, the yield degradation at Omega is small and lower by ≈5× compared to the indirect-drive ignition-scale NIF estimate.

Physics↗

DOE OSTI2024

Inferring fusion nuclear burnwidths with low gain photomultiplier impulse response functions

When an inertial confinement fusion implosion is compressed, it maintains thermonuclear density and temperatures for a very short time scale, about 100 ps. The Gamma Reaction History diagnostic measures the time evolution of the fusion burn, but its temporal resolution is limited by the use of a photomultiplier tube (PMT) to amplify the photon signal. Multichannel plate-based PMTs have a fast (~120 ps) full-width at half-max impulse response function (IRF), but the time scale is similar to the incoming physics signal. An analysis routine is used to remove the effect of the PMT IRF and infer the incident fusion burnwidth. With the National Ignition Facility achieving ignition and creating much brighter signals, the PMTs are run at gains three orders of magnitude lower than nominal operation. Calibration at these settings shows the PMT IRFs get ~15% wider. Taking the gain-dependent IRF can affect the inferred nuclear burnwidths by up to ~15%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Source shape estimation for neutron imaging systems using convolutional neural networks

Neutron imaging systems are important diagnostic tools for characterizing the physics of inertial confinement fusion reactions at the National Ignition Facility (NIF). In particular, neutron images give diagnostic information on the size, symmetry, and shape of the fusion hot spot and surrounding cold fuel. Images are formed via collection of neutron flux from the source using a system of aperture arrays and scintillator-based detectors. Currently, reconstruction of fusion source geometry from the collected neutron images is accomplished by solving a computationally intensive maximum likelihood estimation problem via expectation maximization. In contrast, it is often useful to have simple representations of the overall source geometry that can be computed quickly. In this work, we develop convolutional neural networks (CNNs) to reconstruct the outer contours of simple source geometries. We compare the performance of the CNN for penumbral and pinhole data and provide experimental demonstrations of our methods on both non-noisy and noisy data.

Machine learning, neutron imaging, source reconstr↗

DOE OSTI2024

Hybrid direct drive with a two-sided ultraviolet laser

This paper presents a “hybrid” approach to direct drive inertial confinement fusion that can exploit a high-energy gas laser with two opposed beams. The target and driver are asymmetric, much like experiments performed on the National Ignition Facility, but have been designed to benefit from scale and their particular compatibility with a fusion power plant. The imploded masses (and areal densities) are increased by a factor of 12 (3) and provide a path to high-gain implosions that robustly ignite. The design also mitigates common concerns such as laser imprint and cross-beam energy transfer. We discuss the rationales for a hybrid target, the methods used to control implosion symmetry, and the implication(s) for inertial fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Comparison of tungsten versus molybdenum for double shell capsules using machine learning design optimization

Double shell targets are an alternative ignition platform for inertial confinement fusion. One design consideration for double shell targets is the choice of inner shell material to help trap radiation emitted by the hot fuel to aid ignition. Materials such as molybdenum and tungsten are of interest for the inner shell layer of the targets. While molybdenum has a lower density that could inhibit instability growth and allow for radiography and code benchmarking, tungsten has a higher density that could provide more compression and confinement. These tradeoffs have been explored using optimized designs for each material. Our previous work [Vazirani et al., “Coupling 1D xRAGE simulations with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 28, 122709 (2021); Vazirani et al., “Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 30, 062704 (2023); and Vazirani et al., “Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design,” Stat. Anal. Data Min. 17, e11698 (2024)] resulted in a multi-fidelity Bayesian optimization framework to find yield-optimized double shell target geometries. By leveraging simulations of varying fidelities (one-dimensional and two-dimensional) to inform one another, the multi-fidelity optimization was able to optimize a design in the highest fidelity with significantly fewer simulations than would be used in a systematic parameter scan. In this work, we apply the multi-fidelity Bayesian optimization to explore the optimized designs of double shell targets with molybdenum and tungsten inner shells as well as the physics producing the high performing implosions. A physics exploration of all the simulations used in this study shows trends in designs that contribute to high yields, ion temperatures, and fuel areal densities. Comparison of molybdenum and tungsten simulations shows that they can produce similar implosion conditions with different geometries, which would be important to study in experiments. Graded density layers produce varying performances with the two materials but continue to be of interest for future studies along with studies of doped inner shell materials and applied surface roughness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗