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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.

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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: I. Fully vibrationally-resolved electronic excitation of H 2 $X^1Σ^+_g)$

Here, we present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of molecular hydrogen suitable for implementation in collisional-radiative models. The adiabatic-nuclei molecular convergent close-coupling method is used to calculate cross sections for excitation of all bound vibrational levels and dissociative excitation of the B 1 Σ u + , C 1 Π u , E F 1 Σ g + , B ′ 1 Σ u + , G K 1 Σ g + , I 1 Π g , J 1 Δ g , D 1 Π u , H 1 Σ g + , b 3 Σ u + , c 3 Π u , a 3 Σ g + , e 3 Σ u + , d 3 Π u , h 3 Σ g + , g 3 Σ g + , i 3 Π g , and j 3 Δ g electronic states from all –14 bound vibrational levels of the ground electronic ($\text{X}$ $^1&#x3A3^+_g$) state. The data set consists of cross sections from threshold to 500 eV for over 5000 transitions, representing all possible electronic and vibrational transitions between the state and the –3 singlet and triplet states (where refers to the united-atoms-limit principle quantum number). The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Theoretical level energies, radiative lifetimes and transitions in W IX

The atomic states of the W IX (W{sup 8+}) tungsten ion lying below the W{sup 9+} ionisation threshold have been studied theoretically, employing the multiconfiguration Dirac–Hartree–Fock method with configuration interaction. The level electronic structures and their energies are presented. The electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) radiative transitions have been computed in order to calculate the radiative lifetimes of given states. Transition wavelengths, energies, and decay rates are also presented for selected high-intensity E1 transitions. The configuration interaction method was applied to estimate electron correlation effects. The aim of the present research was to fill a lack of atomic data for low-charged tungsten ions, which may be useful in low-temperature plasma diagnostics and may form the base for collisional–radiative modelling of spectra for low-charged tungsten ions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: II. Fully vibrationally-resolved electronic excitation of the isotopologues of H 2 (X 1 $Σ^{+}_{g}$)

Here, we present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of the isotopologues of molecular hydrogen (D 2 , T 2 , HD, HT, and DT) initially in the ground electronic state. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 500 eV for excitation of all bound vibrational levels and dissociative excitation of the B 1 $Σ^{+}_{g}$, C 1 Π u , EF 1 $Σ^{+}_{g}$, B' 1 $Σ^{+}_{g}$, GK 1 $Σ^{+}_{g}$, I 1 Π g , J 1 Δ g , D 1 Π u , H 1 $Σ^{+}_{g}$, b 1 $Σ^{+}_{g}$, c 3 Π u , a 3 $Σ^{+}_{g}$, e 3 $Σ^{+}_{u}$, d 3 Π u , h 3 $Σ^{+}_{g}$, g 3 $Σ^{+}_{g}$, i 3 Π g , and j 3 Δ g electronic states from all bound vibrational levels of the ground electronic (X 1 $Σ^{+}_{g}$) state. Including the previously-published MCCC e-H2 cross sections the data set contains cross sections for over 60,000 electronic and vibrational transitions. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: IV. Vibrationally-resolved ionization of the ground and excited electronic states

Here, we present a comprehensive set of vibrationally-resolved cross sections for electron-impact ionization of molecular hydrogen and its isotopologues (H 2 , D 2 , T 2 , HD, HT, and DT) in both the ground and excited electronic states. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 1000 eV for ionization of the ground and excited vibrational levels of the X 1 Σ$^{+}_{g}$, B 1 Σ$^{+}_{u}$, C 1 π u , EF 1 Σ$^{+}_{g}$, a 3 Σ$^{+}_{g}$, and c 3 π u electronic states, representing all states with united-atoms-limit principle quantum number n=1–2. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Aggregation in bottom-up vulnerability assessments and equity implications: The case of Jordanian households’ water supply

Bottom-up methods for water resources modeling rely on acceptability thresholds to find, through a response surface, which deeply uncertain futures lead to system failure. They commonly treat water users as aggregate actors, which may preclude analysis of the equity impacts of interventions. This paper explores how aggregation choices for large groups of water users lead to different policy recommendations in response surface assessments. Herein, two aggregation methods with varying parameters are considered: percentile satisfaction targets and generalized mean. A 2-dimensional stress-test assessment across groundwater availability and population is applied to household water supply in Jordan. The study compares six different policies covering supply enhancement and rebalancing, using a country-wide multi-agent model that characterizes households across socioeconomic strata. For different aggregation levels, policies are ordered by their associated robustness index. Results show that aggregation choices may modify response surfaces as much as policy changes and strongly determine policy preference. Modifying allocation rules can substantially reduce the disparity in household vulnerability. Preferences defined by aggregation intervals provide a finer understanding of trade-offs among water users and may improve deliberation over equity under deep uncertainty.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Tree growth, transpiration, and water-use efficiency between shoreline and upland red maple (Acer rubrum) trees in a coastal forest

Coastal shoreline forests are vulnerable to seawater exposure, the impacts of which will increase due to sea-level rise, but the longterm adaption strategies and vulnerability of coastal forests are not well understood. We used whole-tree transpiration, leaf water potential, tree-ring width, and tree-ring d13C (a proxy for intrinsic water use efficiency, iWUE) to examine the long-term adaption strategies of red maple (Acer rubrum) trees at the coastal interface (i.e., shoreline) and nearby upland in Maryland, USA. Red maple trees that grew along the shoreline and were exposed to slightly saline water (up to two PSU) had higher transpiration rates than those growing in the nearby upland forest during a wet year, but these differences disappeared during a normal precipitation year. Shoreline trees grew more slowly than upland trees over the last four decades, but these growth differences have disappeared in the last six years. Shoreline and upland trees had similar variation in iWUE, indicating that higher transpiration rates of the seawater exposed trees did not translate into differences in water use efficiency. There were no differences in predawn and midday water potential between upland and shoreline trees, suggesting no water stress occurs in shoreline trees. These findings indicate that urrent soil salinity is below the threshold to constrain coastal red maple physiological activities.

Wang, Wenzhi↗
DOE OSTI2022

Predicting spring green-up across diverse North American grasslands

Vegetation phenology influences many ecosystem and climate processes, such as carbon uptake and energy and water cycles. Thus, understanding drivers of vegetation phenology is crucial for predicting current and future impacts of climate change on ecological systems. Existing models can accurately predict the date of spring green-up in temperate forests but tend to perform poorly in grassland systems. We hypothesize this is because most do not incorporate water availability, a primary limiting factor for grassland plants. In this study, we used long-term datasets of digital imagery from the PhenoCam Network of 43 diverse North American grassland sites (195 site-years) to test existing spring phenology models, as well as develop several new models that incorporate precipitation or soil moisture (53 models). As a result, most of the new models performed substantially better, with the best model requiring sufficient accumulated precipitation followed by warm temperatures to trigger spring onset (root mean square error, RMSE, between predicted and observed dates = 16.0 days). Importantly, the best model performed well across all grassland types using a single set of parameters, from temperate to arid grasslands. Since plants are adapted to their local climates, model performance was further improved when parameters were independently optimized for four separate climate regions (RMSE = 10.4 days). Therefore, both sufficient precipitation and temperature are required for grassland green-up, but optimal thresholds vary by region. Running the top model with projected climate data (representative concentration pathway 8.5) suggests that, depending on the climate region, spring onset will occur up to 12 days earlier within 100 years in temperature-limited sites, but the trend is unclear for precipitation-limited sites (3.5 ± 8.0 days later). This new phenology model improves our ability to understand and predict grassland dynamics, with implications for both current and future ecosystem processes related to carbon and water cycling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Turbulence regimes in the nocturnal roughness sublayer: Interaction with deep convection and tree mortality in the Amazon

We investigated the influence of seasonality and proximity to the forest canopy on nocturnal turbulence regimes in the roughness sublayer of a Central Amazon forest. Since convective systems of different scales are common in this region, we also analyzed the effect of extreme wind gusts (propagated from convective downdrafts) on the organization of the turbulence regimes, and their potential to cause the mortality of canopy trees. Our data include high-frequency winds, temperature and ozone concentration at different heights during the dry and wet seasons of 2014. In addition, we used critical wind-speed data derived from a tree-winching experiment and a modeling study conducted in the same study site. Two different turbulence regimes were identified at three heights above the canopy: a weakly stable (WS) and a very stable regime (VS). The threshold wind speeds that mark the transition between turbulence regimes were larger during the dry season and increased as a function of the height above the canopy. The turbulent fluxes of sensible heat and momentum during the WS accounted for 88% of the entire nighttime flux. Downdrafts occurred only in the WS and favored a fully coupled state of wind flow along the canopy profile. The destructive potential of winds was four times higher than on nights without downdrafts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Effects of forest structural and compositional change on forest microclimates across a gradient of disturbance severity

Forest structural diversity and community composition are key in regulating forest microclimates. When disturbance affects structural diversity or composition, forest microclimates may be altered due to changes in soil temperature, soil water content, and light availability. It is unclear however which structural or compositional components, when changed or to what extent, result in microclimatic change. To address this question, we used data from a large scale, manipulative stem-girdling experiment in northern, lower Michigan—the Forest Resilience and Threshold Experiment (FoRTE). FoRTE follows a factorial design with multiple levels of disturbance severity (0, 45, 65, 85%) based on targeted reductions in gross leaf area index via stem-girdling induced mortality. These disturbance severity treatments are applied in two ways: either as top-down (largest trees are killed) or bottom-up (small to medium trees killed) treatments. We examined how multiple components of structural diversity and community composition changed as a product of disturbance severity and type, and then tested for resulting effects on forest microclimates (light availability, soil temperature, and soil water), using a multivariate, Random Forest framework. We found that measures of community composition (species richness, species evenness, and Shannon-Wiener Diversity Index) and stand structure (basal area, standard deviation of DBH, tree size diversity) declined more following disturbance than did measures of canopy cover, heterogeneity, arrangement, or height. However, when changes in each variable from pre- to post-disturbance, measured as log change, were employed in a multivariate, Random Forest regression framework, structural diversity measures of heterogeneity (rugosity, top rugosity), cover (canopy cover), and arrangement (porosity) were the most influential variables, but with differences among bottom-up and top-down treatments We found that the death of large trees from disturbance impacts soil temperature, water, and light environments more substantially and uniformly across disturbance gradients than does the death of smaller trees. Furthermore, our results have implications for both statistical and process-based modeling of forest disturbance.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Multivariate environmental and trait-based controls of transpiration in the Central Amazon Rainforest

Tropical forest tree mortality is increasing due to more severe droughts, yet our understanding of how tree traits and life strategies are linked to drought stress has been limited by measurement scarcity. The BIONTE (BIOmass and NuTrient Experiment) near Manaus, Brazil hosts one of the world’s largest sap flow installations, with sensors in 90 canopy trees across a wood density gradient monitored since June 2022. The 2023 El Niño drought provided a unique opportunity to evaluate how water availability impacts tree transpiration. An interpretable machine learning framework was used to study the complex interactions between transpiration and multiple environmental variables such as soil water availability and vapor pressure deficit (VPD), and how these interactions vary with wood density and individual trees. We found varying responses of transpiration from different trees during the El Niño drought. Transpiration generally increased with temperature, with stronger effects in wetter areas and in trees with low to medium wood density. However, this response was modulated by stomatal sensitivity to VPD, which constrained transpiration under high atmospheric demand, particularly in intermediate-moisture area. The inflection in transpiration rate at high temperatures (>32°C) underscores the role of stomatal and hydraulic regulation in limiting water loss and protecting trees from excessive evaporative demand. Analysis of soil water contribution to transpiration revealed unimodal patterns in wetter area, with peak contributions near 0.45 cm 3 cm -3 of surface soil water and declining or flat responses beyond that threshold, suggesting a shift from water- to energy-limited transpiration. In contrast, drier areas exhibited limited transpiration sensitivity to soil water conditions and minimal trait-based variation in VPD responses, indicating supply-limited conditions. Despite higher wood density trees being generally more resilient, this study shows diverse tree drought resilience, prompting further investigation into the specific traits and dynamics between environmental variables in regulating transpiration and other physiological processes in trees.

Drought↗
DOE OSTI2021

Trajectory of Growth of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Variants in Houston, Texas, January through May 2021, Based on 12,476 Genome Sequences

Certain genetic variants of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are of substantial concern because they may be more transmissible or detrimentally alter the pandemic course and disease features in individual patients. SARS-CoV-2 genome sequences from 12,476 patients in the Houston Methodist health care system diagnosed from January 1 through May 31, 2021 are reported here. Prevalence of the B.1.1.7 (Alpha) variant increased rapidly and caused 63% to 90% of new cases in the latter half of May. Eleven B.1.1.7 genomes had an E484K replacement in spike protein, a change also identified in other SARS-CoV-2 lineages. Compared with non–B.1.1.7-infected patients, individuals with B.1.1.7 had a significantly lower cycle threshold (a proxy for higher virus load) and significantly higher hospitalization rate. Other variants [eg, B.1.429 and B.1.427 (Epsilon), P.1 (Gamma), P.2 (Zeta), and R.1] also increased rapidly, although the magnitude was less than that in B.1.1.7. Twenty-two patients infected with B.1.617.1 (Kappa) or B.1.617.2 (Delta) variants had a high rate of hospitalization. Breakthrough cases (n = 207) in fully vaccinated patients were caused by a heterogeneous array of virus genotypes, including many not currently designated variants of interest or concern. Finally, in the aggregate, this study delineates the trajectory of SARS-CoV-2 variants circulating in a major metropolitan area, documents B.1.1.7 as the major cause of new cases in Houston, TX, and heralds the arrival of B.1.617 variants in the metroplex.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Reliability metrics and their management implications for open pond algae cultivation

The prevalence of contaminating organisms in outdoor algae cultivation, with the often-associated dramatic crop failures, necessitates the need for metrics describing production system reliability. Standard metrics for algae cultivation reliability are critically needed to be able to map improvements in operational parameters, but do not currently exist. In this work, we present a set of standard metrics including mean time to failure (MTTF) and mean time between failures (MTBF) as the basis for the calculation of pond failure rate (FR) and reliability coefficient (RC). Metrics associated with the numbers of contaminating organisms such as abundance ratio (AR), prevalence of infection (PI), and mean intensity of infection (MII) are also relevant. These metrics, based on measured experimental values of outdoor pond performance during the Algae Testbed Public-Private Partnership (ATP3) Unified Field Studies (UFS), provide a basis for quantifying pond failure and provide insight into potential pond management and contaminant mitigation strategies. From these reliability metrics applied to this dataset, we are able to link operational parameters, such as harvest frequency and inoculum source, to pond reliability for different algae strains and seasons, and from an assessment of AR, provide contamination thresholds beyond which a culture may be unrecoverable. Ultimately, the implementation of widely-practiced and simple-to-calculate algae pond reliability metrics calculated from rapid and easy to collect data or observations will reduce risk and uncertainty in large-scale algae deployment and aid in the development of integrated pest management (IPM) strategies.

09 BIOMASS FUELS↗
DOE OSTI2020

Initial development of an RIA envelope for dispersed nuclear fuel

A reactivity insertion accident (RIA) is a design basis accident in which reactivity is rapidly injected as a result of a control rod ejection or blade drop scenario. The resultant power increase can result in fuel rod failure and subsequent release of radioactive material into the reactor’s primary system. For light water reactors, failure under RIAs is typically a result of fuel melt, pellet-cladding interaction, or rod over-pressurization. Fuel melt occurs when the fuel system is unable to transport heat out of the fuel system. Pellet-cladding interaction occurs when an aggressive fuel pellet expansion pushes on an embrittled cladding beyond its strain limit. Rod over-pressurization occurs when a fuel rod exceeds the critical heat flux and departs from nucleate boiling, causing the rod internal pressure to rapidly increase, exceeding the systems pressure, and balloon until it bursts. To prevent failure, regulators have developed safety requirements that limit the injected enthalpy based on the state of the fuel system. However, dispersed fuel could enable the removal or relaxation of regulator-imposed safety criteria. Dispersed fuel embeds fuel particles in a highly conductive metal. Dispersed particles can have a particle radius of 1 µm to greater than 100 µm. Traditional fuel systems are plagued by poor thermal conductivity, especially at higher burnups, thus reducing the ability of the fuel system to respond to an RIA. However, dispersed fuel could improve the ability of the fuel system to transport injected energy away from the fissile material and into the coolant more efficiently. Furthermore, dispersing the fuel particles mitigates hard contact that typically occurs in the traditional zirconium-uranium dioxide fuel system, thus removing pellet-cladding mechanical interaction as a potential failure mechanism. This paper evaluates fuel particles dispersed in a metal matrix using the BISON fuel performance code to develop an initial failure threshold based on melt temperature of the fuel particle and/or cladding material as a function of fission density for beginning-of-life and end-of-life conditions. BISON results show that (1) reducing the size of the particles allows fission density to increase as a function of time, (2) particle-to-particle proximity must be considered to evaluate the limiting conditions, and (3) improving the fuel particle thermal conductivity improves thermal performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Direct Bayesian inference for fault severity assessment in Digital-Twin-Based fault diagnosis

For applications in condition-based maintenance of nuclear systems, the assessment of fault severity is crucial. In this work, we developed a framework that allows for direct inference of the probability distributions of possible faults in a system. Here, we employed a model-based approach with model residuals generated from analytical redundancy relations provided by physics-based models of the system components. From real-time sensor readings, the values of the model residuals can be calculated, and the posterior probability distributions of the faults can be computed directly using the methods of Bayesian networks. From the posterior distribution of each fault, one can estimate the fault probability based on a chosen threshold and assess the severity of the fault. By eliminating the discretization and simplifications in middle steps, this approach allows us to leverage the available computational resources to provide more accurate fault probability estimates and severity assessments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM +. For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed. The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. In conclusion, given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

DNS↗
DOE OSTI2025

Graphite waste classification and disposal cost estimation for high temperature gas and salt reactors

As high-temperature reactor designs progress to demonstration, managing the radioactive wastes from these systems presents unique challenges. This work explores the irradiated graphite source term produced by three reactor designs: The Modular High Temperature Gas reactor (MHTGR), a pebble-bed High Temperature Gas Reactor (pb-HTGR), and a Fluoride-cooled High-temperature Reactor (FHR). We predicted a C-14 concentration of 4.3 Ci/m 3 for the MHTGR, 1.2 Ci/m 3 for the pebble bed HTGR, and 2.5 Ci/m 3 for the gFHR after 20 years of operation. The final C-14 concentration highly depended on the graphite nitrogen impurity, a major precursor for C-14. The C-14 concentration in all reactor types exceeded the 0.8 Ci/m3 threshold, resulting in a Class C waste classification. The costs associated with accepting the graphite after 20 years in a low-level waste disposal facility were projected to be 255 dollars per kWe for the MHTGR, 248 dollars per kWe for the pb-HTGR, and 56.8 dollars per kWe for the FHR.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Efficient Computation of Doppler-Broadened Elastic Scattering Kernel Moments Using Ladder-Operator Formulation

Anefficient routine for computing Legendre moments of the Doppler-broadened elastic scattering kernel, including resonance scattering effects, has been implemented in the ISOXML module of Griffin. Isotropic scattering in the center-of-mass system and the ideal gas model for target motion are assumed. A ladder-operator formulation is introduced to compute all Legendre moments from order 0 to N simultaneously, enabling near-linear scaling of computational cost with respect to the maximum Legendre order. A physics-based strategy for constructing outgoing energy grids has also been developed, in which a tailored base grid is combined with adaptive refinement to maintain accuracy while limiting the number of outgoing energy points. For energies between resonances, a constant cross-section model is employed to further reduce computational cost. In addition, a quantitative criterion is derived to determine isotope-wise cut-off incident energies based on a prescribed up-scattering probability coverage. For 238U, up to incident energies of approximately 75, 230, and 661 eV at 294, 900, and 2500 K (corresponding to a 2% up-scattering probability threshold), computation of P0 kernels requires 1–8 s and computation of P0–P5 kernels requires 0.4–4 min using a single thread, while maintaining 1–3% relative error in up-scattering probability. These results demonstrate that the proposed formulation enables accurate and computationally practical Doppler-broadened kernel generation for online multigroup cross-section production in Griffin.

Doppler-broadening↗