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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Thermo-Mechanical Distortion of Tungsten-Coated Steel During High Heat Flux Testing Using Plasma Arc Lamps

An experimental setup and a test section were designed and fabricated for high heat flux testing (HHFT) of neutron-irradiated specimens using water-wall plasma arc lamps. Because of the radiological considerations and limitations of reactor irradiation, the size of the test articles was limited to disks less than 10 mm in diameter. The specimen was clamped onto an actively cooled block, and clamping allowed the insertion of several thermocouples on the back surface of the specimen through a copper (Cu) block. Five vacuum plasma sprayed tungsten (W)–coated F82H steel specimens were subjected to HHFT. Surface profilometry measurements, which were conducted after HHFT, revealed central bowing of the top W surface. This type of residual distortion occurred for all of the specimens, and the larger the specimens were, the larger was the distortion.In an attempt to understand specimen distortion and address the science questions related to the testing of subsize specimens during HHFT, a simplified thermo-mechanical model was developed. By using a measured temperature in the Cu as an isothermal boundary condition, the model eliminated the need for coupling cooling fluid flow models with stress models, greatly simplifying the analysis. The main variable in the proposed model is hC, i.e., the thermal contact conductance between the F82H and the Cu washer. Inelastic properties, including hardening properties, were considered for F82H steel and Cu. Numerical simulation results demonstrated a buildup of residual deformation during HHFT and a very complex state of stress and deformation during typical heat flux (HF) cycling. Additionally, hoop stress evolution during a high heat flux cycle reveals that F82H at an interface with W would be mainly in compression during HF application and experienced a transition to a tension state during cooldown. Also, specimen distortion evolves during each HF cycle, as the specimen bows downward during HF application and upward during the cooldown period between HF cycles. The final specimen distortion, i.e., upward bowing of the specimen center, was qualitatively predicted for hC values of 4000 to 5000 W/(m 2 ·K). This hC range of values, for which bulging is obtained, is at the lower spectrum of the range of values for hC, consistent with the low thermal contact conductance expected from the unpolished F82H surface.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Microstructure, electrical resistivity, and tensile properties of neutron-irradiated Cu–Cr–Nb–Zr

High strength, high conductivity copper alloys that can resist creep at high temperatures are one of the primary candidates for efficient heat exchangers in fusion reactors. Cu–Cr–Nb–Zr (CCNZ) alloys, which were designed to improve the strength and creep life of ITER Cu–Cr–Zr (CCZ) reference alloys, have been found to have comparable electrical conductivity and tensile properties to CCZ alloys. The measured creep rupture times for these improved alloys is about ten times higher than the ITER reference alloys at 90–125 MPa at 500 °C. However, the effects of neutron irradiation on these alloys, and the ensuing material properties, have not been studied; thus, their utility in a fusion reactor environment is not well understood. This study characterizes the room temperature mechanical and electrical properties of a neutron-irradiated CCNZ alloy and compares them to a neutron-irradiated ITER reference heat sink CCZ alloy. Tensile specimens were neutron irradiated in the High Flux Isotope Reactor (HFIR) to 5 dpa between 250 °C and 325 °C. Post-irradiation characterization included electrical resistivity measurements, hardness, and tensile tests. Microstructural evaluation used scanning electron microscopy, energy dispersive x-ray spectroscopy, and atom probe tomography to characterize the irradiation-produced changes in the microstructure and investigate the mechanistic processes leading to post-irradiation properties. Transmutation calculations were validated with composition measurements from atom probe data and used to calculate contributions to the increased electrical resistivity measured after irradiation. Comparisons with CCZ alloys in the same irradiation heat found that the post-irradiated CCNZ and CCZ alloys had comparable electrical resistivity. Although CCNZ alloys suffered more irradiation hardening than CCZ, the overall tensile behavior deviated very little from non-irradiated values in the temperature range studied.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Irradiation hardening and ductility loss of Eurofer97 steel variants after neutron irradiation to ITER-TBM relevant conditions

Ten Eurofer97 steel variants, produced by non-standard fabrication-processing routes and modified alloying chemistries, were studied by neutron irradiations in the high flux isotope reactor. The irradiations were performed to ITER-TBM relevant conditions of ~255–350 °C, 2.94–3.24 dpa. We quantified the irradiation-induced degradation of the steels using mechanical property tests. All the steels suffered from irradiation hardening, where a significant increase in Vickers microhardness and yield stress (σ YS ) occurred, accompanied with severe loss of tensile elongation. The extent of hardening was material dependent. For T irr = 300±30 °C, most steels showed σ YS increase in the range of ~30% to as high as ~66%, except for a low temperature tempered steel with σYS increase below 15%. Despite large losses in elongation, most failures were ductile. Significant post-necking ductility was retained with reduction in area (RA) between 65–75%, but <50% for low temperature tempered steels. The ultimate tensile stress to yield stress (σ UTS /σ YS ) ratios decreased significantly after irradiation, highlighting irradiation-induced strain hardening capacity reduction. No major effect of irradiation on the plastic instability stress (σ PIS ) and true fracture stress of the steels was observed. By comparing the tensile stresses in true stress units and with literature, the results suggest that RAFM steel designing should target materials with a large separation between σ PIS and σ YS , to ensure the materials can maintain large work hardening and uniform deformation capability after irradiation. The tensile data of the steels additionally revealed a compelling evidence of an inverse trend between the change in RA and increase in σ YS of the neutron irradiated Eurofer97 type steels.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Degradation of electrical resistivity of tungsten following shielded neutron irradiation

A major challenge for heat transfer in nuclear materials is to ensure thermal mobility after high amounts of neutron irradiation. Tungsten is widely selected as a heat transfer material in fusion reactors. In metals, thermal conductivity is dominated by electrons’ ability to transfer energy. Neutron irradiation generates point defects, clusters, and solid transmutation (e.g.rhenium and osmium in tungsten), which inhibit electron motion. The purpose of this work is to quantify the irradiation-induced change in electron mobility and deconvolute transmutation and microstructural effects on observed changes to electron mobility. Single and polycrystalline tungsten were fast neutron irradiated in the High Flux Isotope Reactor at Oak Ridge National Laboratory to doses between 0.2 and 0.7 displacements per atom (dpa) and temperatures from 500 °C to 1000 °C. Grain growth was observed in all samples. Microstructure and transmutation were quantified. The geometric orientation of samples with elongated grains has been shown to affect electrical resistivity. A mathematical model was developed and used to deconvolute solid-solution transmutation, grain, and temperature-dependent lattice effects on resistivity. At ~0.4 dpa at ~590 °C, the combined resistivity degradation due to voids, vacancies, interstitials, and dislocations is estimated to be greater than the contribution from solid solution Re transmutation, which is greater than the contribution from grain boundaries. At doses of ~0.7 dpa at ~750 °C, solid solution Re contributions are greater than all other effects combined. As a result, this work establishes a basis to predict the effects of irradiation temperature and transmutation on thermal properties of tungsten and highlights the importance of irradiation temperature.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Deterministic modelling of the SPERT IV reactor transients using the multi-physics capability of WIMS

The ANSWERS WIMS reactor physics code is being developed for whole core multi-physics modelling. The established neutronics capability for lattice calculations has recently been extended to be suitable for whole core modelling of Small Modular Reactors (SMRs). A whole core transport, SP3 or diffusion flux solution is combined with fuel assembly resonance shielding. An integrated thermal hydraulic solver permits temperature and density variations to feedback to the neutronics calculation. This capability can be applied to both steady state and time dependent transient problems. Nuclear reactor design and safety case development requires assessment of a range of reactor transients, to inform both normal operation limitations and accident scenario analysis. This paper presents new methodology developed in WIMS to couple the core neutronics to the integrated core thermal hydraulics solver for the simulation of reactor transients in whole core models. To support the validation of the multi-physics capability of WIMS, this capability has been applied to the reactivity insertion transient experiments performed in the plate fuelled SPERT-IV reactor. This study employs WIMS using the whole core solver MERLIN, which calculates the time-dependent flux distribution and magnitude, coupled to ARTHUR, which solves for the time-dependent thermal hydraulics solution, and provides thermal feedback via the cross sections generated by GEOM, which performs resonance shielding calculations and generates cross section data for the plate geometry. This spatial kinetics model, with dynamic cross section generation, allows for variations in the temperature and neutron flux profile with time.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Failure evaluation of neutron-irradiated SiC/SiC composites by underwater acoustic emission

Here, understanding the statistical properties of mechanical properties of non-irradiated and neutron-irradiated SiC/SiC composites is essential for component design. This study aims to evaluate the detailed damage accumulation behavior of composites focusing on two fracture parameters: proportional limit stress (PLS) and acoustic emission (AE) onset stress. The developmental underwater AE technique, which is benefit in non-contact in-situ failure monitoring method during mechanical testing and in handle of the irradiated material, was first applied to evaluate damage accumulation behavior. Two types of chemical vapor infiltration SiC/SiC composites were used: one reinforced with Hi-Nicalon Type-S SiC fiber and one reinforced with Tyranno-SA3 SiC fiber in the form of satin-woven 2D fabrics with pyrolytic carbon interface. Neutron irradiation in the High Flux Isotope Reactor at Oak Ridge National Laboratory reached a fluence of 30 dpa at a temperature of 620–670°C. Four-point flexural tests were conducted to evaluate post-irradiation strength. Weibull statistics did not suggest marked degradation of composite strength. Detailed failure behavior evaluated by AE demonstrated no irradiation-induced change of the AE onset stress (i.e., crack initiation equivalent stress). Failure probability analysis suggests that increasing the reliability of composites (i.e., the Weibull modulus rather than strength itself) is essential to expanding the design margin and benefiting from a probabilistic design approach.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accurate Fe–He machine learning potential for studying He effects in BCC-Fe

Nanostructured Ferritic Alloys (NFAs) containing oxide nanoparticles are prospective advanced structural materials in future fusion reactors. Lacking fusion neutron sources with an adequate flux, modeling is critical to understand radiation damage in the NFAs, including helium effects. Machine learning interatomic potentials (MLPs) have been demonstrated to be capable of describing atomic interactions in chemically complex systems with comparable accuracy to density functional theory (DFT) but with much less computational costs. Hence, MLPs are chosen to study He bubble accumulation in chemically complex NFAs. As a preliminary step, we develop a Fe–He potential, based on ~10,000 atomic configurations. The developed MLP accurately predicts the bulk properties of BCC-Fe compared to DFT, including the lattice constant (2.832 Å), elastic constants (c 11 = 271 GPa, c 12 = 141, c 44 = 93), and phonon frequencies (maximum error < 3.5%). The MLP predicts He binding energies in He n V bubbles and He n clusters with a mean absolute error (MAE) of only ~70 meV, which is ~3 to ~5 times smaller than the MAE of binding energies estimated using empirical potentials. The MLP also accurately predicts the migration barrier of interstitial He (64 meV). Furthermore, the MLP correctly predicts the maximum number of He atoms (critical size) at which a He n V bubble (He n cluster) can kick-out a self-interstitial atom (SIA), forming a bigger He n V 2 bubble (He n V bubble). Subsequently, we use the MLP to perform molecular dynamics simulations to investigate the effect of temperature on the critical size of He n V bubbles and He n clusters. We find that the critical size decreases with increasing temperature — indicating that smaller bubbles and clusters can kick-out an SIA at higher temperatures, thereby escalating the He bubble growth. We report the current Fe–He MLP can be further developed to include all chemical interactions in NFAs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Understanding the effect of specimen size on the properties of fine-grain isotropic nuclear graphite for irradiation studies: Physical, electrical, thermal properties

Programs at Oak Ridge National Laboratory are investigating the effects of neutron irradiation in the High Flux Isotope Reactor (HFIR) on properties of fine-grain nuclear graphites. Specimens were irradiated in the HFIR flux trap, which required using specimens that are smaller than the sizes recommended by ASTM standards. Here, this work has investigated whether subsized specimens can be used to reliably determine the measured physical (density, elastic moduli, and electrical resistivity) and thermal properties (coefficient of thermal conductivity and thermal conductivity). The results show the specimen sizes in this investigation had a minimal influence on any of the measured properties. Even for the properties where size influenced the measured value (density and thermal conductivity), an explanation is provided, and the consequences can be accounted for in post-irradiation results. This work demonstrated that using subsized specimens for physical and thermal property measurements is suitable when necessary for fine-grain isotropic graphite.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The microstructure effects on irradiation response of ferritic – martensitic steels

Microstructural optimization to achieve greater mechanical strength has been one of the focuses in ferritic–martensitic steels development. However, these optimized microstructures’ effects on the radiation response are not well known. In this work, two ferritic–martensitic steels (9Cr-NbMo and 9Cr-Ta) underwent neutron irradiation in the High Flux Isotope Reactor, and their room-temperature post-irradiation tensile properties and microstructure evolutions were investigated and compared. These two steels exhibit similar pre-irradiation tensile behavior, and their yield strengths are higher than that of other ferritic–martensitic steels by about 200–250 MPa. Microstructural characterization on pre-irradiated materials reveals a smaller grain size in 9Cr-Ta (2.8 ± 0.3 μm in 9Cr-Ta versus 4.3 ± 0.5 μm in 9Cr-NbMo) but higher dislocation density and precipitate density in 9Cr-NbMo. As is common for ferritic–martensitic steels at low irradiation temperatures (less than about 0.45T m ), irradiation-induced hardening at 400 °C was observed for both alloys. Irradiation at 490 °C causes the two alloys to exhibit different tensile behavior: 9Cr-Ta softens by 208 MPa in yield stress, whereas 9Cr-NbMo maintains strength. Additionally, microstructural characterizations were performed, including precipitate growth, dislocation, and defect formation. Using the barrier hardening model for microstructure–property correlation, the softening in irradiated 9Cr-Ta is primarily attributed to the significant dislocation recovery, while the strength lost from the slight dislocation recovery in 9Cr-NbMo was compensated by the additional strength from the irradiation-induced cavities. The microstructure effect (primarily precipitate, dislocation and boundary) on the radiation response is discussed herein.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Reactor cell neutron dose for the molten salt breeder reactor conceptual design

The private sector’s interest in the active development of molten salt reactors has led to the need to develop and test advanced modeling and simulation tools to analyze various advanced reactor types under numerous conditions. This paper discusses the effort undertaken to model the Oak Ridge National Laboratory (ORNL) Molten Salt Breeder Reactor (MSBR) design using ORNL’s Shift Monte Carlo code. The MSBR model integrates a Monte Carlo N-Particle (MCNP) MSBR core model with an MCNP model that was generated from a CAD model of the external components and the reactor building, which was subsequently run in Shift. This paper focuses on development of the fully integrated model and its use in performing neutron transport calculations in the reactor cell area. This model is intended to aid in understanding radiological dose conditions during operation, as well as the iron dpa rates in the reactor vessel. The neutron biological dose rates and flux calculated in the reactor cell are much higher in the MSBR than in typical light-water reactors. The implications of these results and future work are also discussed in this paper.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

A charged particle transport approximation for thick and thin plasmas

In this work, we will construct a simple method to be utilized in the interpretation of the properties of a thin plasma from a study of the transport of charged particles through it. We do so by first demonstrating how charged particle fluxes encode local plasma information in their spectra for sufficiently thick plasmas and then propose how to extend that analysis to the thin plasma limit where the extensive geometry cannot be neglected through arguments from scale separation. We provide a numerical treatment of the transport problem and demonstrate that it is in good agreement with the approximation we present. Finally, we utilize both the numerical solution and our novel approximation to study the impact of the extensive scale of the plasma on the yield and flux normalized high-energy neutron spectra resulting from the upscattering of charged fuel ions. Using this analysis, we show that (after controlling for fusion yield) for the same uniform densities and temperatures, larger plasmas have higher magnitude but softer reaction-in-flight (RIF) neutron spectra relative to smaller plasmas. This is because larger plasmas retain more knocked-on suprathermal ions within their bulk and can downscatter them to lower average energies, while smaller plasmas allow a larger fraction of high energy particles to “range out” of the system prior to substantial downscattering or inducing an RIF reaction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Analysis of Design Alternatives of Actively Cooled RF Window for MPEX

The Materials Plasma Exposure eXperiment (MPEX) has been designed as a linear plasma divertor simulator in order to address plasma material interaction (PMI) science for next-generation fusion devices. It will have the capability to test neutron irradiated samples with plasma fluxes of greater than 10 24 m -2 s -1 . It is expected to operate steady state for up to 10 6 s to consider PMI affects through reactor end of life. The conceptual design of MPEX was completed in 2019, with preliminary design having begun in 2020. The plasma source for MPEX is a helicon antenna, where the energized helical antenna sits outside of the vacuum in order to minimize impurities in the plasma. It is expected to receive up to 200 kW of continuous power, and so the antenna and the window must be actively cooled. The water-cooled copper antenna has been operated at full power on the Proto-MPEX device (which is a test facility to demonstrate the plasma source and heating systems). The water-cooled window, however, is a novel component that must meet numerous competing requirements. It requires a low dielectric loss to allow the Radio Frequency (RF) power to create the plasma within the vacuum boundary. It must be structurally robust to handle the significant heat flux from the plasma and any heat from dielectric coupling. It must be compatible with the coolant (preferably water). It requires a vacuum seal that minimizes impurities into the plasma and does not compromise the structural integrity of the window. Two window designs have been tested. Results from these tests, where temperatures are measured and heat fluxes inferred from infrared camera data, have been correlated with thermal-structural simulations. When these simulations are extrapolated to the full power steady-state heat fluxes that are expected in MPEX, the designs do not appear to have the necessary structural robustness. This study explores design alternatives for the MPEX helicon antenna window, presents analysis results for several of the alternatives, and shows a viable solution that satisfies the requirements for MPEX operation.

Tipton Jr, Joseph↗
DOE OSTI2021

Sensitivity of future liquid argon dark matter search experiments to core-collapse supernova neutrinos

Future liquid-argon DarkSide-20k and Argo detectors, designed for direct dark matter search, will be sensitive also to core-collapse supernova neutrinos, via coherent elastic neutrino-nucleus scattering. This interaction channel is flavor-insensitive with a high-cross section, enabling for a high-statistics neutrino detection with target masses of ~50 t and ~360 t for DarkSide-20k and Argo respectively. Thanks to the low-energy threshold of ~0.5 keVnr achievable by exploiting the ionization channel, DarkSide-20k and Argo have the potential to discover supernova bursts throughout our galaxy and up to the Small Magellanic Cloud, respectively, assuming a 11-M progenitor star. In this work, we report also on the sensitivity to the neutronization burst, whose electron neutrino flux is suppressed by oscillations when detected via charged current and elastic scattering. Finally, the accuracies in the reconstruction of the average and total neutrino energy in the different phases of the supernova burst, as well as its time profile, are also discussed, taking into account the expected background and the detector response.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Actinide targets for the synthesis of superheavy nuclei

The use of heavy actinide targets, including 243 Am, 240,242,244 Pu, 245,248 Cm, 249 Bk, and 249 Cf, irradiated by intense heavy ion beams of 48 Ca has resulted in a significant expansion of the periodic table since 2000, including the discovery of five new heaviest elements and more than 50 new isotopes. These actinide materials can only be produced by intense neutron irradiation in very high flux reactors followed by chemical processing and purification in specialized hot cell facilities available in only a few locations worldwide. This paper reviews the reactor production of heavy actinides, the recovery and chemical separation of actinide materials, and the preparation of actinide targets for superheavy element experiments. The focus is on 248 Cm, 249 Bk, mixed 249–251 Cf, and 254 Es, including current availabilities and new production processes. The impacts of new facilities, including the Superheavy Element Factory at Dubna, accelerator and separator upgrades at RIKEN, and proposed upgrades to the High Flux Isotope Reactor at Oak Ridge are also described. Examples of recent superheavy element research are discussed as well as future opportunities for superheavy research using actinide targets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Conceptual design of HFIR irradiation experiment for material compatibility study on liquid Sn divertor

Liquid Sn is one of the promising coolants for liquid surface divertor concept of fusion reactors. However, the compatibility between liquid Sn and structural materials is an important issue that has to be addressed, because liquid Sn is extremely corrosive to steels at high temperatures. The corrosion may be mitigated when a protective Al2O 3 layer is formed on the surface of alumina forming steels. However, the effect of neutron irradiation on the integrity of protective layer is not made clear so far. Japan and US joint research project “FRONTIER” started in 2019 to investigate the material compatibility under neutron irradiation. The purpose of the present study is to develop the conceptual design of the irradiation test capsule which enables material compatibility tests for the alumina forming steels - liquid metal systems under neutron irradiation in the High Flux Isotope Reactor at Oak Ridge National Laboratory, TN, USA. The three dimensional drawing of capsule structure was then developed. The validity of the material selections for the capsule design was investigated by means of corrosion tests of SiC, Si3N4, Ti, and Mo in liquid Sn at 773 K for 262 hr.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

High Data Rate Detector for Neutron Reflectometer

Neutron reflectometers are a class of instruments that employ neutron diffraction for measuring the structure of thin films. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, polymer and surfactant adsorption, structure of thin film magnetic systems, biological membranes, etc. Such instruments are considered to be one of the most important in the neutron science field. Newer facilities place growing demands on the count rate capability of the specialized neutron detectors required. Proportional Technologies completed the Phase I effort successfully with a fully operational prototype detector built at PTI and tested at the CG1A neutron beam of the High Flux Isotope Reactor (HFIR, Oak Ridge, TN). The prototype incorporated 3 panels of 14 copper-walled cells each (total of 42 cells), each lined with 1.3 μm of 10B4C. The detector was tested for efficiency, spatial resolution, count rate linearity, uniformity, overlap and scatter. Testing revealed stable operation, uniform response across cells, and successful resolution of individual cells. The maximum count rate tested in the 3 panels combined was 590 kHz, limited by a deadtime of about 1 μs in the digital electronics. The local rate measured in a single cell showed no deadtime losses up to 810 cps/mm2, indicating that a rate of 20 Mhz can be supported in the 308-cell detector planned for Phase II.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Sensitivity of future liquid argon dark matter search experiments to core-collapse supernova neutrinos

Future liquid-argon DarkSide-20k and ARGO detectors, designed for direct dark matter search, will be sensitive also to core-collapse supernova neutrinos, via coherent elastic neutrino-nucleus scattering. This interaction channel is flavor-insensitive with a high-cross section, enabling for a high-statistics neutrino detection with target masses of $\sim$50~t and $\sim$360~t for DarkSide-20k and ARGO, respectively. Thanks to the low-energy threshold of $\sim$0.5~keV$_{nr}$ achievable by exploiting the ionization channel, DarkSide-20k and ARGO have the potential to discover supernova bursts throughout our galaxy and up to the Small Magellanic Cloud, respectively, assuming a 11-M$_{\odot}$ progenitor star. We report also on the sensitivity to the neutronization burst, whose electron neutrino flux is suppressed by oscillations when detected via charged current and elastic scattering. Finally, the accuracies in the reconstruction of the average and total neutrino energy in the different phases of the supernova burst, as well as its time profile, are also discussed, taking into account the expected background and the detector response.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part IV: PFNS and $\bar{ν}$ Uncertainty Propagation

An analytic benchmark with continuous-energy cross sections was previously derived to validate criticality calculations. Here, to extend the utility of the analytic benchmark to verify the implementation of $\bar{ν}$ and prompt fission neutron spectrum (PFNS) uncertainty propagation methods, new simplified forms that are dependent on the incident (fission-causing) neutron energy, as well as the outgoing neutron energy for the PFNS, are introduced in this work. The analytical forms for the flux and adjoint flux are derived for the extended benchmark and used to determine the 𝑘-eigenvalue sensitivity to $\bar{ν}$ and PFNS. The 𝑘-eigenvalue uncertainty due to $\bar{ν}$ and PFNS is calculated for the analytic benchmark using simplified$\bar{ν}$ and PFNS representations based on the ENDF-B/VIII.0 239 Pu evaluation. Because of the low sensitivity of the analytic benchmark to the physical PFNS, a nonphysical high-sensitivity PFNS is also presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗