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At least 19 records

NRC Reactor Operating Experience Analysis and Trend Summary: 2022 Update

This report presents a summary of the Nuclear Regulatory Commission (NRC) reactor operating experience analyses with data through 2022 as well as the reliability and frequency trends identified in the 2022 update reports for component performance study, loss of offsite power analysis, initiating events analysis, and system study provided on the NRC Reactor Operating Experience Results and Databases website (https://nrcoe.inl.gov/).

99 GENERAL AND MISCELLANEOUS↗

NRC Reactor Operating Experience Analysis and Trend Summary: 2024 Update

This report presents a summary of the Nuclear Regulatory Commission’s (NRC’s) reactor operating experience analyses with data through 2024 as well as the reliability and frequency trends identified in the 2024 update reports for the component performance studies, loss-of-offsite power analysis, initiating events analysis, and system studies provided on the NRC Reactor Operating Experience Results and Databases website (https://nrcoe.inl.gov/).

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

User’s Manual for RESRAD-RDD&IND Code Version 2: Vol. 2—User’s Guide for RESRAD-RDD&IND Code

Version 2.0 of the RESRAD-RDD&IND computer code is designed to support the implementation of protective action guides (PAGs) after a nuclear emergency incident including a radiological dispersal device (RDD) and/or an improvised nuclear device (IND) incident (EPA 2017). Eight different group types, addressing various decisions, are available for selection. The RESRAD-RDD&IND code calculates radiological doses, stay times, etc., for the selected group that the user wishes to focus on. (That is, the results for all the groups are not calculated simultaneously, and the input for those other groups do not matter, although some parameter values are shared between groups.) Version 2.0 has a user-friendly interface so that the RESRAD-RDD&IND code can be used with minimal training. For example, the user can select the major characteristics of the problem-event type, source term, and decision type from the left side of the interface and then calculate the results with the default assumptions for the exposure scenarios. More in-depth analysis would include specifying site-specific exposure scenario characteristics in the right side of the interface. The procedures for data entry and results viewing are self-explanatory. This is because common window maneuvering features and text instructions were incorporated in the interface design. General and context-specific help are available to aid users entering parameter values, as well. The RESRAD-RDD&IND computer code gives the user the option to select either an RDD or IND incident for analysis. For an RDD event analysis, 11 radionuclides (Am-241, Cf-252, Cm-244, Co-60, Cs-137, Ir-192, Po-210, Pu-238, Pu-239, Ra-226, and Sr-90) are included. These 11 radionuclides are the radionuclides most likely used for an RDD. More than 90 radionuclides can be selected for an IND event analysis. Initial default concentrations are provided for 44 radionuclides for a uranium-fueled IND event. These 44 radionuclides are those that would contribute significantly to the radiation dose associated with a uranium-fueled bomb detonation. The radionuclides generated from ingrowth of these 44 initial radionuclides are also automatically included in the analysis. Pu-239, Cs-134m, Ru-105, and Rb-89 and their progeny can be selected for analysis if they are detected and their concentrations are determined. This user’s guide, which is Volume 2 of the User’s Manual for RESRAD-RDD&IND Code Version 2, provides instructions to users on how to install the RESRAD-RDD&IND code, navigate the interface, and use the various features, including those discussed above, to set up an analysis and view/print the results in text outputs. Volume 1 of the User’s Manual for RESRAD-RDD&IND Code Version 2 (Yu et al. 2026), which contains descriptions of the methodology and theoretical basis for dose modeling and the mathematical equations implemented in the code, can be accessed and viewed through the Help menu in the code or can be downloaded from the RESRAD website (https://resrad.evs.anl.gov).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Applying AI/ML Techniques to U.S. Nuclear Operating Experience Program

Idaho National Laboratory (INL) has provided technical assistance to the U.S. Nuclear Regulatory Commission (NRC) in reliability and risk analysis including the operating experience (OpE) program since the 1980s. The U.S. nuclear OpE program provides input parameters to the NRC Standardized Plant Analysis Risk models and the industry probabilistic risk assessment (PRA) models. While earlier PRA focuses were on at-power, internal event analysis, the risks from external hazards and during low power shutdown (LPSD) operation could be significant and the needs to develop LPSD PRA and external hazards PRA are on the rise. One issue in developing LPSD PRA is the reasonable estimation of shutdown initiative event (SDIE) frequencies. INL has developed and is maintaining an SDIE database for the NRC. However, this database is based on the reviewing of Licensee Event Reports (LERs), which is believed to be only a subset of “actual” shutdown initiating events occurred in the industry. This paper investigates a new approach to identify and characterize shutdown initiating events from the Institute of Nuclear Power Operations (INPO) industry database using machine learning techniques. The main process in this approach is to find out the relationship between key words in event descriptions and the SDIE categories as in the NRC SDIE database. The relationship can then be applied to the INPO database and search for SDIEs.

99 GENERAL AND MISCELLANEOUS↗

Backup Power Performance of Solar-plus-Storage Systems during Routine Power Interruptions: A Case Study Application of Berkeley Lab’s PRESTO Model

This technical brief estimates the expected performance of a solar photovoltaic and energy storage system (PVESS) for providing backup power during short-duration power interruption events, accounting for the unpredictable nature of those events. The analysis relies on the Power Reliability Event Simulation TOol (PRESTO), a publicly available model developed by Berkeley Lab to simulate the occurrence of short-duration power interruption events at the county-level. A separate storage dispatch model is then used to simulate PVESS operation and backup performance for each of the large number of interruption events produced by PRESTO. In performing this simulation, the analysis accounts for how the customer operates its battery on a day-to-day basis—in this case, we assume the battery is cycled each day in response to time-of-use rates—and how that, in turn, impacts the battery’s state of charge at the beginning of each interruption event. The analysis presented here is intended to demonstrate an application of the PRESTO model as well as to illustrate some of the key determinants of PVESS backup power performance during short-duration power interruption events. The analysis focuses initially on a typical single-family home in Maricopa County, Arizona, and includes a limited set of scenarios related to system sizing, backup power configuration, and whether the customer charges its battery storage system from the grid during normal operating conditions. The analysis also presents comparative results for two other counties, in Massachusetts (Middlesex) and California (Los Angeles), illustrating how regional differences in climate, interruption patterns, and retail rate structures can affect PVESS performance as a backup power source. In the conclusions, we highlight a number of other important considerations for evaluating PVESS backup power capabilities.

14 SOLAR ENERGY↗

Fracture Network Prediction Using Physics-based Machine Learning Algorithms

In recent years, systematic CO2 injection into geological reservoirs across the U.S. has gained traction as a strategy to mitigate greenhouse gas emissions. This approach necessitates precise monitoring to ensure secure containment, minimize risks, and optimize storage management. Our study leverages machine learning (ML) techniques to advance the understanding of CO2 injection processes, focusing on the Illinois Basin. Over a three-year injection period, we analyzed microseismic data, identifying 19 temporal intervals with significant bottom-hole pressure changes. By partitioning microseismic events into these intervals and estimating b-values, we revealed over 100 clusters of events related to fracture initiation or reactivation. Advanced spatial analysis highlighted horizontally-oriented fractures along the NNW-SSE axis. This quantification of fracture networks informs dynamic injection scheduling, work-over strategies, and risk assessments, enhancing carbon capture, utilization, and storage (CCUS) operations. Additionally, our methodology offers valuable insights for oil and gas operations and geothermal development, supporting fracture-based monitoring and risk mitigation.

Kumar, Abhash↗

Analysis of Narrow Bipolar Events Using Mode Decomposition Methods

Multi-resolution analysis methods can reveal the underlying physical dynamics of nonstationary signals, such as those from lightning. In this paper we demonstrate the application of two multi-resolution analysis methods: Ensemble Empirical Mode Decomposition (EEMD) and Variational Mode Decomposition (VMD) in a comparative way in the analysis of electric field change waveforms from lightning. EEMD and VMD decompose signals into a set of Intrinsic Mode Functions (IMFs). The IMFs can be combined using distance and divergence metrics to obtain noise reduction or to obtain new waveforms that isolate the physical processes of interest while removing irrelevant components of the original signal. We apply the EEMD and VMD methods to the observations of three close Narrow Bipolar Events (NBEs) that were reported by Rison et al. The ΔE observations reveal the occurrence of complex oscillatory processes after the main NBE sferic. We show that both EEMD and VMD are able to isolate the oscillations from the main NBE, with VMD being more effective of the two methods since it requires the least user supervision. The oscillations are found to begin at the end of the NBEs' downward fast positive breakdown and appear to be produced by a half-wavelength standing wave within a weakly-conducting resonant ionization cavity left behind in the wake of the streamer-based NBE event. In conclusion, additional analysis shows that one of the NBEs was likely initiated by an energetic cosmic ray shower, and also corrects a misinterpretation in the literature that fast breakdown is an artifact of NBE-like events in interferometer observations.

54 ENVIRONMENTAL SCIENCES↗

Characterization of nuclear breakup as a function of hard-scattering kinematics using dijets measured by ATLAS in p+Pb collisions

This Letter analyzes the sensitivity of event geometry estimators to the initial-state kinematics of hard scattering in proton–lead collisions. This analysis uses dijets as a proxy for the parton–parton scattering configuration, correlating it with event geometry estimators, namely the energy deposited in the Zero-Degree Calorimeter and the transverse energy recorded in the Forward Calorimeter in the Pb-going direction. The analysis uses data recorded by the ATLAS detector at the Large Hadron Collider with a nucleon–nucleon center-of-mass energy of 8.16 TeV, corresponding to an integrated luminosity of 56 nb − 1 . The jets are measured within the pseudorapidity interval −2.8 < η < 4.5, where positive η values correspond to the direction of the proton beam. Results are presented as a function of the Bjorken-x of the parton originating from the proton, xp . Both event geometry estimators are found to be dependent on xp , with the energy deposited in the Zero-Degree Calorimeter about six times less sensitive to xp compared with the transverse energy deposited in the Forward Calorimeter.

Aad, G↗

The Role of Subcloud Mesoscale Convergence in Sculpting Convective Updraft Width and Depth

The initiation of deep moist convection is governed in part by the horizontal width of updrafts near cloud base, which limits the deleterious effects of entrainment-driven dilution on buoyant thermals ascending through the free troposphere. However, the factors controlling cloud-base updraft width, which in turn dictates cloud depth, are not well understood. We track the evolving three-dimensional structure of the mesoscale subcloud forcing for vertical motion and near-cloud thermodynamic ingredients within a high-resolution ensemble of simulations of seven realistic daytime orographic convection initiation events to determine their relative roles in controlling cloud width and depth. Statistical analysis of approximately 5000 cloudy updraft samples indicates that the most important contributors to the width of cloudy updrafts across the ensemble are the depth and magnitude of the subcloud mesoscale ascent. However, the depth achieved by clouds is more consistently predicted by the near-cloud ambient relative humidity within the lower to middle free troposphere and convective available potential energy. Therefore, although the width of cloudy updrafts may be partly set at low levels by the mesoscale vertical mass and moisture flux, the likelihood of deep moist convection is governed by the generation of positive buoyancy within cumulus thermals and entrainment-driven dilution that reduces it. The persistence of the low-level mesoscale vertical forcing locally consolidates and vertically transports boundary layer moisture, helping to reduce updraft dilution. However, these factors vary in relative impacts on cloudy updrafts across individual cases, indicating multiple pathways for deep convection initiation.

Convective storms↗

Hazard and risk analysis framework for nuclear power plant–based integrated energy systems

Employing integrated energy systems (IESs) with nuclear power plants (NPPs) can improve NPP utilization by leveraging dedicated thermal and electric power delivery, but it may also increase operational safety risks. This paper presents a framework to identify and quantify hazards and risks for such IESs. The framework combines accidentology to review past industrial accidents with failure modes and effects analysis (FMEA) to identify potential future incidents. Hydrogen explosion and toxic chemical release hazards are of particular concern. Explosion consequences are quantified using the Bauwens-Dorofeev (Bauwens) and trinitrotoluene equivalent mass (TNT-EM) methods, while chemical release consequences are computed using the Gaussian atmospheric dispersion method. Operational disturbances from direct electrical and thermal integration that may affect NPP safety are modeled using probabilistic risk analysis (PRA). Hazards and risks are then evaluated for regulatory compliance. The framework is applied to IESs comprising pressurized or boiling water reactors supplying three levels of thermal and electrical power to industrial customers. Case studies include high-temperature steam electrolysis hydrogen plants of varying capacities and a synthetic fuel production plant. Sensitivity analysis examines piping component failures in the PRA model as a precursor to cost estimation for thermal extraction line design. Additionally, Fussel-Vessely (FV) and risk increase importance (RII) measures identify risk-informed design improvements for the thermal extraction system. FMEA highlights hazards such as loss of offsite power, prompt loss of electrical load, loss of thermal output, and immediate steam diversion, in addition to hydrogen explosions and toxic chemical releases. Both Bauwens and TNT-EM methods suggest maintaining several hundred meters of separation between the NPP and hydrogen facility to mitigate explosion risks. PRA results show a maximum initiating event frequency increase of 1.15% and an overall risk increase of 0.28%. Importance measure analysis identifies upstream pipe leak isolation components as critical. Evaluating the results against safety regulations, it is concluded that hazards and risks can be managed to comply with regulations through risk-informed thermal and electrical connection designs, component selection, maintenance programs, and safe separation distances between NPPs and integrated industrial facilities.

08 - HYDROGEN↗

Development of a novel bunch oscillation recorder with RFSoC technology

The SuperKEKB accelerator is designed to achieve unprecedented luminosity levels, but this goal is currently hindered by Sudden Beam Loss (SBL) events. These events not only obstruct luminosity improvement but also pose a significant risk to accelerator components, the Belle II detectors, and the superconducting focusing system, potentially leading to severe damage and quenching of the superconducting system. Here, to address this critical challenge, we have developed a novel Bunch Oscillation Recorder (BOR) based on RFSoC technology. The BOR has demonstrated high precision with a position resolution of 0.03 mm, making it a powerful tool for real-time beam monitoring. In its initial deployment, the BOR successfully recorded multiple SBL events, providing valuable data for further analysis. By strategically positioning BORs at the suspected points of SBL origin, we aim to directly identify sources of beam instability. We anticipate that this portable, high-speed BOR monitor will play a crucial role in resolving the SBL issue, ultimately helping achieve SuperKEKB's luminosity targets.

Beam diagnostics↗

Λ polarization from vortex rings as the medium response for jet thermalization

We performed a systematic study on the formation of vorticity rings as the process for jet thermalization in the medium created in high-energy nuclear collisions. In this work, we expanded our previous analysis to a more realistic framework by considering noncentral events and fluctuations in the initial condition. We simulate the formation and evolution of the flow vortex structure in a relativistic viscous hydrodynamic model and study the sensitivity of the proposed “ring observable” (ℛ$^{𝑡}_{Λ}$) that can be measured experimentally through the polarization of Λ hyperons. We show that this observable is robust with respect to fluctuating initial conditions to capture the jet-induced vortex flow signal and further study its dependence on different model parameters, such as the jet's velocity, position, the fluid's shear viscosity, and the collision centrality. The proposed observable is associated with the formation of vorticity in a quark-gluon plasma, showing that the measurement of particle polarization can be a powerful tool to probe different properties of jet-medium interactions and to understand better the polarization induced by the transverse and longitudinal expansions of the medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Prioritizing Uncertainties in Hydrogen Contribution to Risk in Post-Crash Outcomes for Rail

This report presents analysis from Sandia National Laboratories predicting contributions to risk associated with the use of hydrogen technology for rail. Event sequence diagrams are used to describe possible accident scenarios and progressions. Initiating event frequencies and branch event probabilities for each scenario are quantified with uncertainty using distributions fit to Federal Railroad Administration and U.S. Department of Transportation Pipeline and Hazardous Materials Safety Administration data on applicable accidents from 2000 to 2020. Uncertainty is propagated through the event sequence diagram to estimate the frequency and conditional probability of accident end states. The analysis identifies four scenarios with significant contributions to risk from hydrogen that are predicted to occur relatively frequently, which may inform priorities for reducing uncertainty. These scenarios are 1) overpressure events resulting from collisions with hydrogen release due to mechanical damage and delayed ignition, 2) jet fire events resulting from collisions with hydrogen release due to mechanical damage and immediate ignition, 3) jet fires resulting from fire or explosion initiating events involving the hydrogen tank and correct operation of the thermally-activated pressure relief device (TPRD) subsequent to the thermal insult, and 4) pressure burst resulting from fire or explosion initiating events involving the hydrogen tank and failure of the TPRD. Delayed and immediate hydrogen ignition probabilities are identified as being highly uncertain and potential candidates for reducing conservatism in the predicted frequencies for these two scenarios.

08 HYDROGEN↗

Applying Automated Detectors for Regional Infrasound Signals to Global Networks: A Case Study Using the 2022 Hunga Tonga Volcanic Eruption

The January 15, 2022 Tonga Hunga volcanic eruption was the largest event to be recorded across the International Monitoring System infrasound network. Signals from the eruption were identified at all 53 operational stations by International Data Centre analysts. This report contains descriptors for signal detection bulletins produced by infrasound researchers at Sandia National Laboratories and Los Alamos National Laboratory. Manual detection bulletins were produced by laboratory staff. Automated detection bulletins were produced using automated infrasound processing tools developed at both laboratories. Initial results are provided to evaluate the utility of extending tools developed for regional infrasound event analysis to global-scale events.

58 GEOSCIENCES↗

Data-driven modeling of dynamic occupant thermostat override behavior for demand response applications

Buildings consume nearly 40% of global energy and produce similar emissions. Whiletechnological advances address efficiency, occupant behavior causes energy use variations up to 300% between identical buildings. This gap between predicted and actual building performance impacts building design, operations, and grid demand management programs. Through analyses of smart thermostat data from 1,400 single-occupant homes, the researchdemonstrates that occupants respond to 8°F thermostat setpoint changes within a median of 15 minutes, while 2°F changes trigger responses within a median of 30 minutes. This highlights an understudied temporal relationship between thermostat setbacks and response time of occupant behaviors. Models of such behavior dynamics are required to incorporate occupant impacts into building performance simulation. A key contribution of this dissertation is the Thermal Frustration Theory (TFT), which positsthat thermal discomfort driven behaviors are caused by the time-accumulation of discomfort, not simply a temperature deviation threshold or a delay from an initiating event. Using a dataset of 634 thermostats, each with 25+ manual setpoint changes, a comparative analysis of TFT and comfort zone and a delayed response theories demonstrated that personalized TFT models better predict when manual setpoint change occur. This was measured by the area under the curve statistical measure (AUC); all three models perform similarly by a Matthews Correlation Coefficient measure. Higher AUC performance is especially important for modeling occupant behavior in demand response programs where false negatives of rare occupant interactions could adversely affect grid stability. EnergyPlus based simulations were conducted with TFT-derived occupant models, demonstrating the ability to identify parameters of known TFT models from only data observable with smart thermostats, even under the presence of noise from routine overrides. Overall, the dissertation highlights that thermostat interactions are neither static,instantaneous, nor driven solely by the environment. Instead, temporal accumulation of discomfort and routine-based behavior play important roles. The methodology and results offer a pathway towards more accurate modeling of human-building interactions for policy assessment, building design, and demand response programs.

Sharma, Kunind [Northeastern University] (ORCID:00↗

Hazards and Probabilistic Risk Assessments of a Light-Water Reactor Coupled with Industrial Facilities

This report provides a roadmap and toolkit for site-specific risk assessments across a broad range of industrial customers co-located with nuclear power plants (NPPs). This report builds upon the body of work sponsored by the Department of Energy (DOE) Light-Water Reactor Sustainability (LWRS) Flexible Plant Operation and Generation Pathway that presented hazards assessment and generic probabilistic risk assessments (PRAs) for the addition of a heat extraction system (HES) to light-water reactors co-located with hydrogen production facilities. The report expands the hazards assessments to include other industrial facilities: an oil refinery, a methanol plant, a synthetic fuel (synfuel) plant, the production of synthetic gas (syngas) as part of the methanol and synfuel plants, and wood pulp and paper mills. All these facilities are specified through industrial process and requirements research performed by national laboratories, universities, and interaction with industry. Many of the processes used in this report are pre-conceptual designs to use for decarbonization of the current technology facilities. A process of failure modes and effects analysis (what can go wrong) and accidentology (what has historically gone wrong) was used to determine the hazards presented to the NPP by the addition of the HES and the industrial customer. Chemical properties of feedstocks and products are summarized as part of the hazards assessment. Example analysis procedures are provided for each of the hazard types identified. These deterministic analyses can be used to assess adherence to licensing criteria. They can also be used to meet other safety goals like protection of the public, workers, or industrial facility equipment. The probabilistic analysis consisted of three sizes of HESs modeled in a PRA to assess the impact on the initiating events (IE) and results of the PRA. The PRA results conclude that the resulting increases in IE frequencies are below the limits required for small changes to existing NPPs under 10 CFR 50.59.

08 HYDROGEN↗

Neutron Identification Capabilities in MicroBooNE Through the Application of Machine Learning with Blips

Neutrinos (ν) are subatomic particles first observed in 1956 by LANL physicists Clyde Cowan and Frederick Reines but first theorized by Wolfgang Pauli in 1930. Neutrinos are the least massive known particle and are classified as leptons with 3 flavors corresponding to their leptonic counterparts (electron, muon, and tau). We know that they are abundant, 65 billion neutrinos travel through your fingertip every second, and elusive, a single neutrino could fly through a lightyear of lead without interacting at all. Though, there is much still unknown and a better characterization of these “ghostly” particles can give us clues as to the matter/anti-matter asymmetry in the early universe and possible glimpses into new physics. To measure a particle that is extremely light and rarely interacting, physicists have developed an extremely sensitive detector known as a Liquid Argon Time Projection Chamber (LArTPC). The fiducial volume (or TPC) is bombarded with neutrinos, some of which interact with argon (Ar) atoms to produce particles that in turn excite and ionize the Ar. The products of these are free electrons which then drift through the TPC’s applied magnetic field towards a multi-plane wire readout system. The electrons’ charge is collected at this anode and the light from the initial interactions is collected by photomultiplier tubes (PMTs). In conjunction, these mechanisms allow LArTPCs to achieve millimeter spatial resolution and sub-MeV energy thresholds. The detector of interest in this study is the MicroBooNE Experiment at Fermilab. MicroBooNE is an above ground LArTPC with dimensions of approximately 10m × 2.5m × 2.3m, about the size of a school bus. Its purpose is to study neutrinos, so to improve rates of measured ν interactions, the detector is squarely in the path of the Booster Neutrino Beam (BNB) at Fermilab. A major challenge in neutrino studies is energy reconstruction, much of the neutrino’s original energy is lost in interactions that the detector is not sensitive to, often due to low-energy products. The initial goal of this analysis was to better identify neutrons, the main source of poor energy reconstruction in neutrino events. Because neutrons are neutral particles, like neutrinos, we can only directly measure the products of their interactions in LArTPCs. Most of these products are low-energy signals and while each one contributes a negligible amount of energy, collectively these signals make up most of the lost energy in each neutrino event. We define these signals as blips; point-like, isolated depositions of charge in the detector. Blips have MeV-scale energies and are the size of a single hit (charge deposition) or a cluster of a few hits on at least two wire planes. Blips are the principal detector features used to study low-energy physics; thus, they are the key to unlocking information not only about neutrons but gamma photons, supernova and solar neutrinos as well as helping us better identify certain particles. Therefore, this analysis strives to use blips for improved neutron identification (ID) and characterization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High Flux Isotope Reactor Low-Enriched Uranium High Density Silicide Fuel Preliminary Design Update: System Transient Analysis

As a part of conversion efforts from highly enriched uranium (HEU) to low-enriched uranium (LEU) fuel under direction of the National Nuclear Security Administration of the U.S. Department of Energy, multiple proposed designs of the High Flux Isotope Reactor (HFIR) have been created and assessed regarding reactor physics performance metrics, including designs utilizing uranium silicide dispersion fuel (U3Si2-Al). This report updates the previous analyses that evaluated the nuclear safety performance of LEU fuel designs with respect to selected accident events from the HFIR Safety Analysis Report (SAR). Both the Low Density (LD) and High Density (HD) Optimized designs’ reactivity initiated accident fuel performance improved relative to the HEU fuel, attributed to greater 238 U negative Doppler feedback. However, the thermal margins for primary coolant system accidents were reduced with some acceptance criteria unable to be met. The need to resolve reduced thermal margin, open modeling items, and unresolved assumptions was identified.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗