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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Micro-Quantification of Helium-3 and Helium-4 in TPBAR Components

This report documents the method development for measuring helium isotopes in micrometer-sized samples of tritium producing burnable absorption rod (TPBAR) components. Helium isotopes were measured as a tracer for tritium, which decays to 3 He with a half-life of 12.33 years. Getter and cladding materials from the TPBARs were analyzed, as they are designed to trap tritium. Therefore, constraining the diffusivity of tritium through these materials is of key importance. To first establish the reliability of the noble gas mass spectrometer, a reference gas with a relative 4 He/ 3 He ratio of 1000 was pre-mixed. This standard was measured several times to ensure measurements were reproducible. Unirradiated and irradiated getter and cladding samples of TPBARs were cut into 1-100 µm 3 cubes and analyzed for 3 He and 4 He content. The unirradiated materials had helium content equal to or less than that of the measured instrument background. Irradiated cladding also had instrument background levels of helium while irradiated getters had elevated levels of 3 He, interpreted to be the decay product of tritium. No diffusion of 4 He was observed in any of these materials, however, indicating that the 3 He detected in the irradiated getter was produced in situ after tritium diffusion and decay. These findings validate this method as a way to trace tritium diffusion in reactor materials.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2023

Sample Preparation Methods for Targeted Single-Cell Proteomics

We compared three cell isolation and two proteomic sample preparation methods for single-cell and near-single-cell analysis. Whole blood was used to quantify hemoglobin (Hb) and glycated-Hb (gly-Hb) in erythrocytes using targeted mass spectrometry and stable isotope-labeled standard peptides. Each method differed in cell isolation and sample preparation as follows: 1) FACS and automated preparation in one-pot for trace samples (autoPOTS); 2) limited dilution via microscopy and a novel rapid one-pot sample preparation method that circumvented the need for the solid-phase extraction, low-volume liquid handling instrumentation and humidified incubation chamber; and 3) CellenONE-based cell isolation and the same one-pot sample preparation method used for limited dilution. Only the CellenONE device routinely isolated single-cells from which Hb was measured to be 540–660 amol per red blood cell (RBC), which was comparable to the calculated SI reference range for mean corpuscular hemoglobin (390–540 amol/RBC). FACSAria sorter and limited dilution could routinely isolate single-digit cell numbers, to reliably quantify CMV-Hb heterogeneity. Finally, we observed that repeated measures, using 5–25 RBCs obtained from N = 10 blood donors, could be used as an alternative and more efficient strategy than single RBC analysis to measure protein heterogeneity, which revealed multimodal distribution, unique for each individual.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Developing a Nuclear Quality Assurance Compliant Design Methodology for Neutronic Analysis of Xe-100 Design

The primary objective of this work is to develop a design methodology compliant with nuclear quality assurance standards for the Xe-100 neutronic design verification studies. To achieve this, a Monte Carlo model of the Xe-100 reactor was constructed using the exclusion principle, transformation technique, and universe-based level specification following Idaho National Laboratory (INL) NQA level-1 compliant standards and an NQA-1 compliant version of MCNP6. The model encompasses the entire reactor core structures, including the upper plenum, core region, and lower plenum sections, along with all sub-components. The active core section was represented using the spectral regions, each comprising a particular fuel composition and temperature averaged over the considered zone, calculated by X-energy using Very Superior Old Programs (VSOP). Additionally, a component-wise temperature map was implemented into the model, not only for the core region but also for the structural components. Temperature-dependent cross-section libraries, along with thermal scattering law libraries, generated using INL NQA-1 compliant version of NJOY21, were utilized for each isotope in the burnt fuel and the structural materials. Furthermore, the volume of each modeled component was estimated using a stochastic approach with the ray tracing method in MCNP and criticality calculations were performed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Coupled Decay Heat and Thermal Hydraulic Capability for Loss-of-Coolant Accident Simulations

As the nuclear energy industry considers ways to achieve improved economics in the current fleet of light-water reactors (LWRs), one possible approach is to operate each cycle for longer durations. This causes a greater portion of the fuel to be burned and reduces the frequency of outages, which ultimately reduces the cost to operate the reactor. However, this also leads to higher burnup fuels than has traditionally been allowed in these reactors. Thus, there are concerns about integrity of high-burnup (HBu) fuel, especially during accident conditions such as loss-of-coolant accidents (LOCAs), as shown by Capps et al.. To investigate these concerns, advanced modeling and simulation capabilities are being leveraged to determine the susceptibility of HBu fuel to fuel fragmentation, relocation, and dispersion (FFRD). Improvements have previously been made to fuel performance capabilities to more accurately model these phenomena; multiphysics simulations have also been conducted to determine the power and burnup histories of the HBu fuel, which are needed as inputs for the fuel performance calculations. Most recently, new statistical approaches have been developed to identify a subset of fuel rods that have greater FFRD susceptibility, reducing the total number of fuel performance simulations required. Prior LOCA simulations have relied on the TRACE systems code, which can model the core and primary loop during accident conditions. TRACE includes many models for various aspects of the primary loop, but two sets of models are important for this report. First, TRACE uses a lumped-fuel approach for modeling the core. This approximates the ~50,000 fuel rods in the core with a much smaller number of rods. The rods can be lumped in various ways as determined by the user. For example, one lumped rod may be used to represent all rods in an assembly, sometimes with an additional rod representing the hottest fuel rod. However, due to runtime constraints and complexity of modeling, a more common approach is to group several assemblies or larger regions of the core into single lumped rods. These lumping schemes apply not only to fuel rods but to flow channels as well. Second, TRACE has several different models for treating decay heat, ranging from pregenerated decay heat curves based on an ANSI/ANS-5.1 standard (hereinafter abbreviated simply as ANSI) to explicit time-dependent heat inputs from the user. None of these models account for differences in isotopics between different rods, which is an approximation the work in this report seeks to eliminate. This report focuses on the implementation of coupled decay heat capabilities in the Virtual Environment for Reactor Applications (VERA) code suite to address a gap identified in previous LOCA simulations. This constitutes an improvement for both the lumped-fuel and decay heat models in TRACE. VERA has been developed to perform high-fidelity, whole-core multiphysics simulations for LWRs. Previously, during the Consortium for Advanced Simulation of LWRs (CASL) program, the emphasis was on providing accurate steady-state analysis—with a secondary focus on reactivity insertion accident (RIA) analysis—to address operational challenges in the nuclear energy industry. Under the Department of Energy (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, these capabilities are being extended to a broader range of transient analyses with the goal of quantifying the risk of fuel failures such as FFRD. To properly model such conditions with VERA, decay heat calculations have been integrated with the multiphysics to enable rod-by-rod thermal hydraulic (TH) conditions to be driven by the decay heat in long-running accidents such as LOCAs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

New insights into Mn 2+ and Mg 2+ inhibition of calcite growth

Impurity ion and isotope partitioning into carbonate minerals provide a window into the molecular processes occurring at the fluid-mineral interface during crystal growth. Here, we employ calcium isotope fractionation together with process-based modeling to elucidate the mechanisms by which two divalent cations with starkly contrasting compatibility, magnesium and manganese, inhibit calcite growth and incorporate into the mineral lattice. Calcite growth inhibition by Mg 2+ is log-linear and K Mg is on the order of 0.02–0.03 throughout the range of {Mg 2+ }/{Ca 2+ } studied here (0.01–2.6). Mn 2+ exhibits much stronger log-linear growth rate inhibition at low Mn 2+ concentrations (fluid {Mn 2+ }/{Ca 2+ } = 0.001–0.02). Mn 2+ is readily incorporated into the calcite lattice to form a calcite-rhodochrosite solid solution, with large partition coefficients (K Mn 4.6–15.6) inversely correlated to growth rate. For both Mn 2+ and Mg 2+ , calcium isotope fractionation is found to be invariant with {Me 2+ }/{Ca 2+ } despite more than an order of magnitude decline in growth rate. This invariant Δ 44/40 Ca suggests that the presence of Mn 2 + or Mg 2+ does not significantly change the relative rates of Ca 2+ attachment and detachment at kink sites during growth, indicative of a dominantly kink blocking inhibition mechanism. Because the partitioning behavior dictates that Mn 2+ must attach to the surface significantly faster than Ca 2+ , attachment of Mn 2+ is likely to be as a non-monomer species such as an ion pair or possibly a larger polynuclear cluster. We propose that calcite growth rate inhibition by Mn is determined by the kinetics of carbonate attachment at Mn-occupied kink sites, potentially due to slow re-orientation kinetics of carbonate ions that have formed an inner-sphere complex with Mn 2+ at the surface but must reorient to incorporate into the lattice. We demonstrate that patterns in Mg 2+ partitioning and inhibition behavior are broadly consistent with growth inhibition driven by slow Mg 2+ -aquo complex dehydration relative to Ca 2+ but argue that this mechanism likely represents one endmember scenario, seen in Mg-calcite growth at low supersaturations and net precipitation rates. During growth at faster net precipitation rates, some portion of Mg 2+ is likely incorporated as a partially hydrated or otherwise complexed species, but calcite growth remains significantly inhibited by the kinetics of CO 3 2- attachment at Mg 2+ kink sites. These findings suggest a hybrid classical/nonclassical growth mechanism whereby Ca 2+ incorporates largely as a free ion at kink sites while Mn 2+ and some portion of Mg 2+ are incorporated via non-monomer attachment. This pattern may be generalizable; trace constituent cations with aquo-complex desolvation rates significantly slower than the mineral growth rate preferentially incorporate as a non-monomer species during otherwise classical crystal growth.

58 GEOSCIENCES↗
DOE OSTI2025

Investigation of U content in J-swipe/PIC samples

This final report documents the results of an evaluation of the U content in J-swipes for the International Atomic Energy Agency (IAEA). J-swipes are manufactured with inked numbers (1–30) and U backgrounds that are considered consistent across different lots and manufacturing times. These characteristics make them ideal for use by IAEA inspectors for pre-inspection check samples to ensure inspectors are not cross-contaminating sites. However, recent work has found elevated U concentrations in the inked numbers compared with the J-swipe material. To determine whether the inked numbers correlate with the U backgrounds, triplicate U content measurements were made on Swipes 1, 2, 11, 22, and 28. Triplicates of each swipe were processed through the standard chemistry used by the Oak Ridge National Laboratory Network of Analytical Laboratories team and analyzed for U content by isotope dilution via multicollector inductively coupled plasma mass spectrometry. Finally, samples were made by mass consisting of only ink areas and only cotton swipe material to determine the trace element differences between the cotton and the ink.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Global Gyrokinetic Simulations of Isotope Effects under Ambipolar Electric Fields and Advances Toward Whole-Volume Modeling

We review global gyrokinetic simulation studies on plasma transport in the Large Helical Device using XGC-S. XGC-S is an extended version of X-point Gyrokinetic Code for stellarators and has been progressively verified throughout the code development process. Verification tests of neoclassical transport successfully demonstrate the generation of an ambipolar electric field due to ripple-trapped particles. We perform quasi-linear analyses of the ion temperature gradient mode under the influence of the ambipolar electric field. The results reveal that the ambipolar electric field and the heavy hydrogen component in mixed isotope plasmas can lead to the favorable isotope effect observed in recent deuterium experiments. We also present recent efforts in code development toward whole-volume simulations, including the helical divertor region. A mesh generation scheme based on field-line tracing and the construction of curved surfaces perpendicular to the magnetic field would be promising for global field calculations in the whole-volume simulations.

Basic Plasma Phenomena and Gas Discharges↗
DOE OSTI2020

Is the Kok effect a respiratory phenomenon? Metabolic insight using 13 C labeling in Helianthus annuus leaves

The Kok effect is a well-known phenomenon in which the quantum yield of photosynthesis changes abruptly at low light. This effect has often been interpreted as a shift in leaf respiratory metabolism and thus used widely to measure day respiration. However, there is still no formal evidence that the Kok effect has a respiratory origin. Here, both gas exchange and isotopic labeling were carried out on sunflower leaves, using glucose that was 13 C-enriched at specific C-atom positions. Position-specific decarboxylation measurements and NMR analysis of metabolites were used to trace the fate of C-atoms in metabolism. Decarboxylation rates were significant at low light (including above the Kok break point) and increased with decreasing irradiance below 100 µmol photons m –2 s –1 . The variation in several metabolite pools such as malate, fumarate or citrate, and flux calculations suggest the involvement of several decarboxylating pathways in the Kok effect, including the malic enzyme. Our results show that day respiratory CO 2 evolution plays an important role in the Kok effect. Furthermore, the increase in the apparent quantum yield of photosynthesis below the Kok break point is also probably related to malate metabolism, which participates in maintaining photosynthetic linear electron flow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Real-time gross actinide monitoring in extreme (10 6 :1) beta-gamma background fluid streams using mini-ATMFDs

Real-time, trace alpha activity monitoring in extreme mixed radiation fields is a well-known challenge in fission product-rich streams containing mixtures of beta-gamma-alpha radiation-emitting isotopes, arising due to the extreme 10 6 :1 ratio of background beta-gamma vs. alpha radiation activity levels. This paper presents results from a novel approach to addressing this challenge, based on Tensioned Metastable Fluid Detector (TMFD) sensing technology. An acoustically driven technique was developed and tested at Purdue University (using dissolved Rn-Po and U-chain alpha emitters), and validated (with dissolved Pu) at Savannah River National Laboratory for real-time monitoring of alpha activity in the 100–10,000 dpm/mL range.

Environmental Monitoring↗
DOE OSTI2023

Realistic application of short-lived fission product delayed neutron, gamma-ray analysis for simultaneous nondestructive trace quantification of U, Pu mixtures on cellulose swipes

Detection and characterization of fissile traces are of interest to the international nuclear nonproliferation community, including the International Atomic Energy Agency. Pre-inspection check samples are analyzed by neutron activation analysis at the High Flux Isotope Reactor operated by the Oak Ridge National Laboratory under the umbrella of the IAEA Network of Analytical Laboratories. The simultaneous quantification of U and Pu mixtures was accomplished using the combined delayed neutron (DN) delayed gamma-ray (DG) method to analyze cellulose swipes with actinide loading <1ng in a blind field trial. The total fissile quantity was measured by the DN counts and the relative proportions of U, Pu were determined by calibration of the 104 Tc / 141 Ba fission product count ratio using known mixtures. The DNDG method demonstrated high accuracy in flagging the presence of 239 Pu in uranium down to <100 pg mass loading. In conclusion, peak significance tests helped to control false positive Pu flagging and simultaneous quantification of U and Pu loading was accomplished on samples that passed the significance tests.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Metal Organic Complexation in Seawater: Historical Background and Future Directions

The speciation of most biologically active trace metals in seawater is dominated by complexation by organic ligands. This review traces the history of work in this area, from the early observations that showed surprisingly poor recoveries using metal preconcentration protocols to the present day, where advances in mass spectroscopy and stable isotope geochemistry are providing new insights into the structure, origin, fate, and biogeochemical impact of organic ligands. Many long-standing hypotheses about the specific biological origin of ligands such as siderophores in seawater are finally being validated. This work has revealed the complexity of organic complexation, with multiple ligands and, in some cases, timescales of ligand exchange that are much slower than originally thought. The influence of organic complexation on scavenging is now a key parameter in biogeochemical models of biologically essential metals, especially iron. New insights about the sources and sinks of ligands are required to enhance the usefulness of these models.

Geochemistry & Geophysics↗
DOE OSTI2022

An automated workflow that generates atom mappings for large‐scale metabolic models and its application to Arabidopsis thaliana

SUMMARY Quantification of reaction fluxes of metabolic networks can help us understand how the integration of different metabolic pathways determines cellular functions. Yet, intracellular fluxes cannot be measured directly but are estimated with metabolic flux analysis (MFA), which relies on the patterns of isotope labeling of metabolites in the network. The application of MFA also requires a stoichiometric model with atom mappings that are currently not available for the majority of large‐scale metabolic network models, particularly of plants. While automated approaches such as the Reaction Decoder Toolkit (RDT) can produce atom mappings for individual reactions, tracing the flow of individual atoms of the entire reactions across a metabolic model remains challenging. Here we establish an automated workflow to obtain reliable atom mappings for large‐scale metabolic models by refining the outcome of RDT, and apply the workflow to metabolic models of Arabidopsis thaliana . We demonstrate the accuracy of RDT through a comparative analysis with atom mappings from a large database of biochemical reactions, MetaCyc. We further show the utility of our automated workflow by simulating 15 N isotope enrichment and identifying nitrogen (N)‐containing metabolites which show enrichment patterns that are informative for flux estimation in future 15 N‐MFA studies of A. thaliana . The automated workflow established in this study can be readily expanded to other species for which metabolic models have been established and the resulting atom mappings will facilitate MFA and graph‐theoretic structural analyses with large‐scale metabolic networks.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

MRDIS Case Study

The Mobile Radiation Detection and Identification System (MRDIS) is a large mobile scanner that inspects containers in transit from cargo ships for radiological materials. The MRDIS platform operates as a two-part system with one MRDIS using a plastic Polyvinyl Toleune (synthetic polymer) for primary detection and another MRDIS that uses spectroscopic detectors for secondary isotopic identification. MRDIS can operate either independently or as part of a team, depending on the needs of the port. MRDIS is controlled by a human operator, who searches the computer monitor for any traces of radiological materials when the containers pass through the center of the system. Each MRDIS can also feed data into a central system or collect data on its own for additional material analysis. The system integrates radiation detection, radioisotope identification, an optical character recognition system, occupancy/speed sensors, wireless communications, and data processing capabilities to discern what specific radiological materials are of particular interest. In addition, Sandia engineers created a detailed set of requirements for subsequent models, allowing for faster implementation of additional detection systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Physics Division Strategic Plan Fiscal Years 2020-2024

The vision of the Physics Division (PHY) at Argonne National Laboratory is to continue enhancing its role as a world-leading institution in basic nuclear physics research and its applications. Key to this vision is for PHY to continue to safely and effectively operate and evolve the capabilities of the Argonne Tandem Linac Accelerator System (ATLAS) facility to best serve its users. ATLAS is the Department of Energy (DOE) accelerator facility for low-energy nuclear physics research. The research carried out by PHY covers many themes in contemporary science but can be distilled into five areas of focus. These themes are interconnected, with continuously evolving synergies between the various groups and facilities in PHY and the broader Laboratory. This five-year strategic plan serves to illustrate our current capabilities and new directions related to these five areas of focus (ATLAS also develops an independent strategic plan): Accelerator research and design. The goal of this theme is to design, fabricate, test, and implement novel accelerator systems, with a focus on high-intensity ion and electron systems. These R&D activities have led to enhancements in the ATLAS accelerator system. Among others, the division’s accelerator systems are in use or planned for use at Fermilab, the Advanced Photon Source, and in a broad variety of applications at the Facility for Rare Isotope Beams (FRIB). Atom trapping and fundamental symmetries. The goal of this theme is to explore and exploit the uses of advanced laser cooling and trapping techniques to manipulate atoms. There are three main areas of focus. First is in the application of the atom trap trace analysis (ATTA) technique for age determination of groundwater and ice by using radio-krypton dating. The next two trapping-based programs involve tests of fundamental symmetries in nature: the cooling and trapping of radium-225 with the aim of determining limits on an observation of its electric dipole moment and precision measurements of the beta decay properties of helium-6 to set limits on the tensor coupling constant. This is complemented by measurements of similar properties in lithium-8 and boron-8. Nuclear astrophysics. The goal of this theme is to enhance our understanding of how elements are created in the universe via explosive nucleosynthesis and how stars evolve. To meet the challenges of this theme, many of the capabilities of ATLAS are being enhanced, including the development of new beams through a new in-flight separator (RAISOR) and the anticipated neutron-generator upgrade of the Californium Rare Isotope Breeder Upgrade facility (nuCARIBU). These are coupled to state-of-the-art instruments such as the Canadian Penning Trap, Helical Orbit Spectrometer, Gammasphere, GRETINA, Multi-Sampling Ionization Chamber, the Fragment Mass Analyzer, and Argonne Gas-filled Fragment Analyzer, and a new low-background experimental area for decay studies. Nuclear structure. The goal of this theme is to understand the structure of nuclei, both stable and radioactive, in terms of single-particle properties, their shapes, and the dynamics governing reactions between them. These include questions such as what are the limits of nuclear stability and what are the properties of super heavy nuclei. As with the nuclear astrophysics theme, the capabilities of ATLAS, guided by the ATLAS user community, are continuously being enhanced to this end. The Division has strategic initiatives to play a leading role in the development of instrumentation and research programs at the FRIB. Quantum chromodynamics (QCD) and hadron physics. The goal of this theme is to lead major research programs focused on revealing the quark and gluon structure of protons, neutrons, nuclei, and short-lived mesons and baryons. These involve major programs at Jefferson Lab, Fermilab, and smaller facilities. They are complemented by theoretical endeavors centered on the question of how hadrons and their properties emerge from QCD. Out of these activities arise strategic initiatives to play a major role in the forthcoming Electron-Ion Collider (EIC).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

US-DOE and Republic of South Africa Uranium Benchmarking: Results From Los Alamos National Laboratory (Study Report)

This report details work performed at Los Alamos National Laboratory (LANL) in support of an interlaboratory uranium (U) benchmarking collaboration between LANL, Lawrence Livermore National Laboratory (LLNL), and South African Nuclear Energy Corporation (Necsa). The goal of this interlaboratory benchmarking exercise is to compare analytical methods and data obtained on uranium reference materials CUP-2 and New Brunswick Laboratory (NBL) certified reference material (CRM) 124-2. The LANL commitments for this project include performing microwave digestion of fresh CUP-2 and CRM 124-2 powders, measuring the U isotope composition of CUP-2 and CRM 124-2 by both single-collector and multi-collector inductively coupled plasma mass spectrometry (SC-ICP-MS and MC-ICP-MS, respectively), and determining trace-element abundances in CUP-2 and CRM 124-2 by inductively coupled plasma mass spectrometry (ICP-MS). This report details the methods employed by LANL in support of these objectives and presents the data obtained during this collaborative exercise.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Field deployable trace radioisotope analysis through combined electrochemical and alpha spectroscopy methods

A method for depositing actinides directly onto a 4H-SiC Schottky barrier diode (SBD) detector as a field deployable actinides sensor was developed to enable off-site analysis, shortening the time to obtain critical information such as elements, concentration, and/or isotopic ratio related to the radiological situation. A thin film of Hg was first electrodeposited onto the Pt contact of the SiC diode, followed by chronoamperometric deposition of microgram levels of actinides under conventional control conditions. The 4H-SiC diode maintained consistent functionality through the electrodeposition process and showed resolved alpha-energy spectra that contained accurate isotopic information demonstrating the feasibility of a combined chemical and radiological sensor for field actinide detection and quantification.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Linear source method of characteristics in HELIOS2

The Studsvik Scandpower code HELIOS2 is a fast lattice transport code that has gained wide use for reactor fuel cycle analysis in commercial, regulatory, and research environments. It contains two transport solvers - Collision Probabilities (CP) and Method of Characteristics (MoC) - with a general geometry ability and generalized depletion for a variety of fuel types, experimental facilities, and isotope production applications. The HELIOS2 lattice code has been extended with the development of a linear source MoC option. The linear source equations are derived within the scope of the HELIOS2 general geometry and non-cyclic ray tracing. The implementation was tested for fine and coarse spatial mesh models of the 2D C5G7 MOX computational benchmark, which provides a pure and extreme test of a transport solver. The linear source yields at least comparable accuracy with reduced computational resource requirements relative to the flat-source approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗