Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Hot dense plasma”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Direct Observation of Enhanced Electron-Phonon Coupling in Copper Nanoparticles in the Warm-Dense Matter Regime

Warm-dense matter (WDM) is a highly-excited state that lies at the confluence of solids, plasmas, and liquids and that cannot be described by equilibrium theories. The transient nature of this state when created in a laboratory, as well as the difficulties in probing the strongly-coupled interactions between the electrons and the ions, make it challenging to develop a complete understanding of matter in this regime. Here in this work, by exciting isolated ~8 nm nanoparticles with a femtosecond laser below the ablation threshold, we create uniformly-excited WDM. We then use photoelectron spectroscopy to track the instantaneous electron temperature and directly extract the strongest electron-ion coupling observed experimentally to date. By directly comparing with state-of-the-art theories, we confirm that the superheated nanoparticles lie at the boundary between hot solids and plasmas, with associated strong electron-ion coupling. This is evidenced both by the fast energy loss of electrons to ions, as well as a strong modulation of the electron temperature by acoustic oscillations in the nanoparticle. This work demonstrates a new route for experimental exploration and theoretical validation of the exotic properties of WDM.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Symmetric fielding of the largest diamond capsule implosions on the NIF

We present results for the largest diamond capsule implosions driven symmetrically on the National Ignition Facility (NIF) (inner radius of ~1050 μm) without the use of cross beam transfer in cylindrical Hohlraums. We show that the methodology of designing Hohlraum parameters in a semi-empirical way using an extensive database resulted in a round implosion. In addition, we show that the radiation flux symmetry is well controlled during the foot of the pulse and that swings in P2 symmetry between the inflight dense shell and hot spot are within ±4 μm and that swings around peak compression are also within the symmetry specification of ±4 μm. We observed a stronger dependence of symmetry on the capsule scale than previously observed and also observed enhanced inner beam propagation for experiments using a gas fill density of 0.3 mg/cm 3 and 1000 μm inner radius capsules. We have observed sufficient symmetry and mass remaining at near full NIF power and energy, up to 480 TW and 1.9 MJ, with little laser–plasma interactions (low laser backscattered light) and predict that this design could support extended NIF energy of up to 2.1 MJ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A pushered capsule implosion as an alternate approach to the ignition regime for inertial confinement fusion

We report in inertial confinement fusion, the threshold for ignition is a highly dynamic quantity as the sources and sinks of power in the hot spot can vary rapidly. In this article, we consider the ignition condition as a race between heating and disassembly rates and make use of a prior solution to the fusion hot-spot thermodynamics to develop a Lawson-like ignition criteria for pressure × confinement time (p-τ) vs temperature. Low-Z capsule designs reach the temperature for this threshold using as much of the shell as feasible as ablator but then are limited in τ by low stagnated mass. An alternate approach, the pushered single shell (PSS) design [D. D.-M. Ho, S. MacLaren, and Y. Wang, “High-yield implosions via radiation trapping and high rho-R,” paper presented at the 60th Annual Meeting of the APS Division of Plasma Physics, 2018], introduces a dense inner layer of Mo-Be alloy that is smoothly graded outward to pure Be, increasing the confinement time at stagnation and lowering the temperature requirement at the ignition threshold. Here, we describe a PSS ignition design for the National Ignition Facility and use the theory as well as simulations to compare it with the low-Z capsule approach. Additionally, we show how an adjustment to the design is used to anticipate the effects of mixing at the fuel–ablator interface.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Influence of mass ablation on ignition and burn propagation in layered fusion capsules

After decades of research, recent laser-driven inertial fusion experiments have demonstrated rapid progress toward achieving thermonuclear ignition using capsule designs with cryogenic fuel layers. The ignition physics for these layered capsules involves a complex interplay between the dynamically forming hot spot and the dense surrounding fuel. Using analytic theory and numerical simulations, we demonstrate that the mass ablation rate into the hot spot depends sensitively upon the temperature of the dense fuel, resulting in ablative inflows up to [Formula: see text] faster than previous estimates. This produces an enthalpy flux into the hot spot that plays a critical role in controlling the hot spot temperature, the ignition threshold, and the subsequent burn propagation. The net influence of mass ablation on the ignition threshold is regulated by a dimensionless parameter that depends upon the temperature of the dense fuel. As a consequence, the ignition threshold is sensitive to any mechanism that heats the dense fuel, such as neutrons or radiation emitted from the hot spot. These predictions are confirmed using radiation-hydrodynamic simulations for a series of capsules near ignition conditions. This analysis may have relevance for understanding the variable performance of recent experiments and for guiding new capsule designs toward higher fusion yields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Report Summarizing the Mechanical Properties of a Large ODS Ferritic Alloy Ingot by Forging at High Temperatures for Future Mother Tube Production

Oxide dispersion strengthened (ODS) ferritic alloys are considered the benchmark fuel cladding and core structural material in advanced nuclear energy reactors that require high-temperature strength and creep properties and resistance to radiation damage. The ODS ferritic alloys including 14YWT are produced by mechanical alloying (MA), which is time-consuming and is associated with high manufacturing costs that are not beneficial to being used in advanced nuclear energy reactors. This report summarizes the accomplishments in FY24 in the INM program for producing an ODS ferritic alloy by high-deformation, high-temperature processing of reactive and ferritic alloy powders for advanced reactor fuel cladding applications. Following four hot forging experiments, it was concluded that several significant challenges were encountered that were difficult to overcome. These challenges were related to using high annealing temperatures for pressure assisted sintering processes to produce dense microstructures, but the high annealing temperatures result in long range diffusion of Ti through the bcc Fe lattice and react with the YIG particles that are distributed on the prior surfaces of the ferritic alloy powders. In addition, it was determined that the high deformations induced by forging at high temperatures were not very effective for fracturing the reactive YIG particles into smaller particles and distributing them into the interior of the ferritic alloy powders. Spark plasma sintering was attempted for shortening the time at high temperatures, which led to full densification but the microstructure characterization results still showed that Ti atoms diffused over long distances in the bcc Fe lattice and reacted with the YIG particles. Finally, a short 30 minute high intensity ball milling experiment was conducted on blended 14WT and YIG powders for inducing severe deformations that caused the initially spherical powders of 14WT decorated with the YIG particles on the surfaces to transform to flakes and fracturing of YIG particles into smaller particles that were incorporated into the bcc Fe lattice. Two forgings were performed with the high intensity milled powders: first annealing for 20 minutes at 850ºC followed by forging and second annealing for 20 minutes at 1,100ºC followed by forging. At 850ºC, Ti atoms are effectively immobile, thus allowing for densification albeit incomplete. The deformation by forging after annealing for 20 minutes at 1,100ºC favored dynamic recrystallization processes that led to nano-size grains with very high stored energy due to high dislocation density. The corresponding VH data showed significant hardening that correlated with estimated strengthening of ~1650 MPa. This hybrid processing approach combining high intensity ball milling of powder with annealing and forging showed the most promise for producing an oxide dispersing strengthened ferritic alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Four-dimensional QCD equation of state with multiple chemical potentials

Here, we construct a four-dimensional version of the equation of state (EoS) model neos, neos-4d, as a function of the temperature and chemical potentials of baryon, electric charge, and strangeness for the hot and dense quantum chromodynamics (QCD) matter created in relativistic nuclear collisions. This EoS enables multiple conserved charge current evolution in a relativistic fluid. Input from lattice QCD simulations and a hadron resonance gas model is considered for constructing the equation of state. We investigate its applicability to the relativistic hydrodynamic description of nuclear collisions and present a method for efficient numerical implementation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Equation of state of hot, dense magnesium derived with first-principles computer simulations

Using two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, we derive the equation of state of magnesium in the regime of warm dense matter, with densities ranging from 0.43 to 86.11 g cm –3 and temperatures from 20,000 K to 5×10 8 K. These conditions are relevant for the interiors of giant planets and stars as well as for shock compression measurements and inertial confinement fusion experiments. Here, we study ionization mechanisms and the electronic structure of magnesium as a function of density and temperature. We show that the L shell electrons, 2s and 2p energy bands, merge at high densities. This results in gradual ionization of the L-shell with increasing density and temperature. In this regard, Mg differs from MgO, which is also reflected in the shape of its principal shock Hugoniot curve. For Mg, we predict a single broad pressure-temperature region, where the shock compression ratio is approximately 4.9. Mg thus differs from Si and Al plasmas that exhibit two well-separated compression maxima on the Hugoniot curve for L and K shell ionizations. Finally, we study multiple shocks and effects of preheat and precompression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Observations of anomalous x-ray emission at early stages of hot-spot formation in deuterium-tritium cryogenic implosions

In DT cryogenic implosions, hot-spot x-ray self-emission is observed to begin at a larger shell radius than is predicted by a 1-D radiation-hydrodynamic implosion model. Laser-imprint is shown to explain the observation for a low-adiabat implosion. Furthermore, for more-stable implosions the data are not described by the imprint model and suggest there are additional sources of decompression of the dense fuel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Overview of ASDEX upgrade results in view of ITER and DEMO

Experiments on ASDEX Upgrade (AUG) in 2021 and 2022 have addressed a number of critical issues for ITER and EU DEMO. A major objective of the AUG programme is to shed light on the underlying physics of confinement, stability, and plasma exhaust in order to allow reliable extrapolation of results obtained on present day machines to these reactor-grade devices. Concerning pedestal physics, the mitigation of edge localised modes (ELMs) using resonant magnetic perturbations (RMPs) was found to be consistent with a reduction of the linear peeling-ballooning stability threshold due to the helical deformation of the plasma. Conversely, ELM suppression by RMPs is ascribed to an increased pedestal transport that keeps the plasma away from this boundary. Candidates for this increased transport are locally enhanced turbulence and a locked magnetic island in the pedestal. The enhanced D-alpha (EDA) and quasi-continuous exhaust (QCE) regimes have been established as promising ELM-free scenarios. Here, the pressure gradient at the foot of the H-mode pedestal is reduced by a quasi-coherent mode, consistent with violation of the high-n ballooning mode stability limit there. This is suggestive that the EDA and QCE regimes have a common underlying physics origin. In the area of transport physics, full radius models for both L- and H-modes have been developed. These models predict energy confinement in AUG better than the commonly used global scaling laws, representing a large step towards the goal of predictive capability. A new momentum transport analysis framework has been developed that provides access to the intrinsic torque in the plasma core. In the field of exhaust, the X-Point Radiator (XPR), a cold and dense plasma region on closed flux surfaces close to the X-point, was described by an analytical model that provides an understanding of its formation as well as its stability, i.e., the conditions under which it transitions into a deleterious MARFE with the potential to result in a disruptive termination. With the XPR close to the divertor target, a new detached divertor concept, the compact radiative divertor, was developed. Here, the exhaust power is radiated before reaching the target, allowing close proximity of the X-point to the target. No limitations by the shallow field line angle due to the large flux expansion were observed, and sufficient compression of neutral density was demonstrated. With respect to the pumping of non-recycling impurities, the divertor enrichment was found to mainly depend on the ionisation energy of the impurity under consideration. In the area of MHD physics, analysis of the hot plasma core motion in sawtooth crashes showed good agreement with nonlinear 2-fluid simulations. This indicates that the fast reconnection observed in these events is adequately described including the pressure gradient and the electron inertia in the parallel Ohm’s law. Concerning disruption physics, a shattered pellet injection system was installed in collaboration with the ITER International Organisation. Thanks to the ability to vary the shard size distribution independently of the injection velocity, as well as its impurity admixture, it was possible to tailor the current quench rate, which is an important requirement for future large devices such as ITER. Progress was also made modelling the force reduction of VDEs induced by massive gas injection on AUG. The H-mode density limit was characterised in terms of safe operational space with a newly developed active feedback control method that allowed the stability boundary to be probed several times within a single discharge without inducing a disruptive termination. Regarding integrated operation scenarios, the role of density peaking in the confinement of the ITER baseline scenario (high plasma current) was clarified. The usual energy confinement scaling ITER98(p,y) does not capture this effect, but the more recent H20 scaling does, highlighting again the importance of developing adequate physics based models. Advanced tokamak scenarios, aiming at large non-inductive current fraction due to non-standard profiles of the safety factor in combination with high normalised plasma pressure were studied with a focus on their access conditions. A method to guide the approach of the targeted safety factor profiles was developed, and the conditions for achieving good confinement were clarified. Based on this, two types of advanced scenarios (‘hybrid’ and ‘elevated’

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Boride-based Ceramic Super-high Temperature Thermocouples in Harsh Environments (Final Scientific/Technical Report)

An electromotive force (emf) can be generated along a temperature gradient between the cold end and hot end of a thermoelectric material, termed the Seebeck effect. Based on the Seebeck effect, metallic alloys have been extensively employed to detect temperatures for centuries, named thermocouples. However, commercially available thermocouple alloys suffer from limitations, such as oxidation, chemical degradation, and poor long-term stability under high-temperature harsh environments. This DOE-funded project aimed to develop high-temperature, chemically tolerant thermocouples suitable for operation in extreme environments relevant to semiconducting thermoelectric materials. The research focused on boride-based semiconducting thermoelectric compounds as candidates for next-generation thermocouples with enhanced oxidation resistance, chemical stability, and thermal robustness under conditions representative of charcoal-fired electricity facilities. During the funded years, boride materials were synthesized using an arc-plasma technique under ambient air and argon atmospheres, enabling scalable and cost-effective production compared with conventional boride fabrication methods. The synthesized borides were processed into nanostructured powders, followed by consolidation into dense bulk materials using a spark plasma sintering (SPS) bottom-up approach. Comprehensive characterization was performed, including microstructural analysis, electrical transport measurements, and optical and thermal property evaluation. Both p-type and n-type boride electric legs were fabricated and integrated into boride-based thermocouples. The thermal and irradiation stabilities of the boride nanomaterials and bulk thermoelectric materials were systematically evaluated to assess suitability for long-term operation in harsh environments. Additionally, 12 students were broadly hands-on trained spanning the full research workflow, including word processing and technical editing (e.g., LATEX for manuscript and poster preparation), data collection and analysis (using Python and related libraries and hardware interfaces), sample preparation (including arc-plasma synthesis and spark plasma sintering), and advanced characterization techniques (such as X-ray diffraction, UV–vis spectroscopy, electron microscopy, differential thermal analysis (DTA), and Seebeck coefficient measurements, etc). Overall, this project demonstrated the feasibility of boride-based thermoelectric materials as durable high-temperature thermocouples, providing a promising pathway toward robust temperature sensing technologies aligned with DOE energy infrastructure and extreme-environment monitoring needs.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2022

Knock-on deuteron imaging for diagnosing the morphology of an ICF implosion at OMEGA

Knock-on deuteron imaging is a new diagnostic technique that is being implemented at the OMEGA laser facility to diagnose the morphology of an inertial confinement fusion (ICF) implosion. It utilizes the fact that some of the neutrons from deuterium–tritium (DT)-fusion reactions generated in the central hot-spot of an ICF implosion elastically scatter deuterons as they traverse the surrounding shell layer. The energy of these “knock-on” deuterons depends on the scattering angle, where the most energetic deuterons are forward-scattered and probe the shape of the central hot-spot, while lower-energy deuterons are made by side-scattering or slowing down in the fuel and carry information about the distribution of the dense DT-fuel layer surrounding the hot-spot. The first proof-of-concept tests have been conducted successfully. In these tests, three penumbral imagers with different views on an implosion recorded deuterons scattered from the dense shell of DT-gas-filled deuterated plastic shell implosions with prescribed offsets. Data from these experiments are presented here, along with novel analysis techniques that iteratively reconstruct the deuteron source from the data. Reconstructed hot-spot and shell radii agree with 1D hydro simulations and indicate a P1 asymmetry in the direction of the offset. A comparison of coaxial deuteron and x-ray images suggests the presence of a mix between the hot-spot and shell on the order of 15 μm. This new diagnostic capability will allow us to study asymmetries in unprecedented detail at OMEGA.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Use of tritium-rich fuel to improve the yield of layered deuterium/tritium inertial fusion capsules

In deuterium–tritium (DT) ice layered implosions, nearly all hot spot mass at peak burn comes from the dense fuel. Accurate prediction of the fuel mass ablation, including the enthalpy associated with mass inflow into the hot spot from the dense fuel, is essential to understanding the energetics and ignition of the hot spot in layered implosions. A recently published boundary layer analysis (Daughton et al., 2023) indicates a faster mass ablation rate than in previous analyses of layered implosions. Inclusion of this effect provides a better match to simulations and leads to a new ignition threshold where the temperature of the dense fuel plays a critical role. This analysis motivates possible new directions for improved capsule performance. Here, the authors present evidence in support of one such approach: the use of tritium-rich ice to decrease 14 MeV neutron scattering and heating of the dense fuel, resulting in less mass ablation and more robust burn of the hot spot. It is found from numerical simulations that despite a less favorable D:T ratio in the ice, the use of a 40:60 D:T ratio leads to an increase in capsule yield of 17% percent compared with that of a 50:50 D:T ratio fuel for capsules resembling those of the recent N210808 ignition experiment on the NIF (Abu-Shawareb et al., 2022) and an increase of 74% compared with that of a 60:40 D:T ratio fuel capsule. Finally, these results are potentially important for modeling all layered implosions, since some degree of DT fractionization may arise naturally during the beta layering process. In addition, this physics is important for the feasibility of high-gain capsule designs that seek to minimize tritium usage, as in some inertial fusion energy concepts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Role of relativistic laser intensity on isochoric heating of metal wire targets

In a recent experimental campaign, we used laser-accelerated relativistic hot electrons to ensure heating of thin titanium wire targets up to a warm dense matter (WDM) state [EPL 114, 45002 (2016)]. The WDM temperature profiles along several hundred microns of the wire were inferred by using spatially resolved X-ray emission spectroscopy looking at the Ti Kαcharacteristic lines. A maximum temperature of ~30 eV was reached. Our study extends this work by discussing the influence of the laser parameters on temperature profiles and the optimisation of WDM wire-based generation. The depth of wire heating may reach several hundreds of microns and it is proven to be strictly dependent on the laser intensity. At the same time, it is quantitatively demonstrated that the maximum WDM temperature doesn’t appear to be sensitive to the laser intensity and mainly depends on the deposited laser energy considering ranges of 6×10 18 –6×10 20 W/cm 2 and 50–200 J.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Magnetization around mix jets entering inertial confinement fusion fuel

Engineering features are known to cause jets of ablator materials to enter the fuel hot-spot in inertial confinement fusion implosions. The Biermann battery mechanism wraps them in a self-generated magnetic field. Here we show that higher-Z jets have an additional thermoelectric magnetic source term that is not present for hydrogen jets, verified here through a kinetic simulation. It has similar magnitude to the Biermann term. We then include this in an extended magneto-hydrodynamic approach to post process an xRAGE radiation-hydrodynamic implosion simulation. The simulation includes an accurate model for the capsule fill tube, producing a dense carbon jet that becomes wrapped in a 4000 T magnetic field. A simple spherical carbon mix model shows that this insulates the electron heat conduction enough to cause contraction of the jet to an optically thick equilibrium. The denser magnetized jet hydrodynamics could change its core penetration and therefore the final mix mass, which is known to be well correlated with fusion yield degradation. Fully exploring this will require self-consistent magneto-hydrodynamic simulations. Experimental signatures of this self-magnetization may emerge in the high energy neutron spectrum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Dense Pair and Gamma-Ray Creation Using Ultra-Intense Lasers (Final Technical Report)

Lasers with intensity >1.4x10 18 W.cm -2 irradiating solid targets couple 10-50% of its energy to “hot electrons” near the critical surface, with temperature kT > mc 2 . When these hot electrons impact high-Z target ions (e.g. Au, Pt), they emit copious bremsstrahlung gamma-rays and create e + e - pairs via the Trident process. For targets thicker than ~0.1mm, the gamma-rays create secondary pairs via the Bethe-Heitler processes. The concept of using lasers to create pairs was first studied by Shearer et al (1973). Motivated by the rapid advance of short-pulse ultra-intense lasers based on chirped-pulse amplification, Liang (1994) first proposed irradiating solid Au targets with laser intensity ≥10 20 W.cm -2 to create dense e + e - pairs. Using particle-in-cell (PIC, Birdsall and Langdon, 1991) simulations, Liang et al (1998, 2002) estimated that high-energy PW lasers can in principle achieve ultra-high in-situ pair densities. Subsequent studies supported this idea and found that for gold foils thicker than ~50 μm, the pair yield is dominated by the Bethe-Heitler (BH, Heitler 1954) process. Cowan et al (1999, 2000) using the LLNL Nova PW-laser to irradiate 125μm gold foils first observed pair creation, followed by Chen et al (2009) who demonstrated copious BH pair creation using the Titan, Omega-EP and Orion lasers. However, the emerging e + /e - ratio of these experiments was ≤ few %, and the pair density was only 10 13 /cc so that the pair jet transverse size R(~mm) was < pair skin depth c/ω + (=8πn+e 2 /m) 1/2 ). This was insufficient to qualify as a bona fide ”pair plasma”.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Novel tools and observables for jet physics in heavy-ion collisions

Abstract Studies of fully-reconstructed jets in heavy-ion collisions aim at extracting thermodynamical and transport properties of hot and dense QCD matter. Recently, a plethora of new jet substructure observables have been theoretically and experimentally developed that provide novel precise insights on the modifications of the parton radiation pattern induced by a QCD medium. This report, summarizing the main lines of discussion at the 5th Heavy Ion Jet Workshop and CERN TH institute ‘Novel tools and observables for jet physics in heavy-ion collisions’ in 2017, presents a first attempt at outlining a strategy for isolating and identifying the relevant physical processes that are responsible for the observed medium-induced jet modifications. These studies combine theory insights, based on the Lund parton splitting map, with sophisticated jet reconstruction techniques, including grooming and background subtraction algorithms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Transport of an intense proton beam from a cone-structured target through plastic foam with unique proton source modeling

Laser-accelerated proton beams are applicable to several research areas within high-energy density science, including warm dense matter generation, proton radiography, and inertial confinement fusion, which all involve transport of the beam through matter. Here, we report on experimental measurements of intense proton beam transport through plastic foam blocks. The intense proton beam was accelerated by the 10 ps, 700 $\textit{J}$ OMEGA EP laser irradiating a curved foil target, and focused by an attached hollow cone. The protons then entered the foam block of density 0.38 g/cm 3 and thickness 0.55 or 1.00 mm. At the rear of the foam block, a Cu layer revealed the cross section of the intense beam via proton- and hot electron-induced Cu-K α emission. Images of x-ray emission show a bright spot on the rear Cu film indicative of a forward-directed beam without major breakup. 2D fluid-PIC simulations of the transport were conducted using a unique multi-injection source model incorporating energy-dependent beam divergence. Along with postprocessed calculations of the Cu – $K_α$ emission profile, simulations showed that protons retain their ballistic transport through the foam and are able to heat the foam up to several keV in temperature. The total experimental emission profile for the 1.0 mm foam agrees qualitatively with the simulated profile, suggesting that the protons indeed retain their beamlike qualities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

On the computation of moments in the Super-Transition-Arrays model for radiative opacity calculations

In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the calculation of averages of products of subshell populations. Here, in the present work, we discuss several aspects of the computation of such peculiar partition functions, insisting on the precautions that must be taken in order to avoid numerical difficulties. In a previous work, we derived a formula for supershell partition functions, which takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients for which we obtained a recursion relation and an explicit formula. We show that such an expansion can be combined with the recurrence relation for shifted partition functions. We also propose, neglecting the effect of fine structure as a first step, a positive-definite formula for the Super-Transition-Array moments of any order, providing an insight into the asymmetry and sharpness of the latter. The corresponding formulas are free of alternating sums. Several ways to speed up the calculations are also presented.

74 ATOMIC AND MOLECULAR PHYSICS↗