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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Radiation hardened beam instrumentations for multi-Mega-Watt beam facilities

The radiation hardened beam instrumentations workshop was held on February 3rd and 4th, 2022 to identify the technological challenges on the beam instrumentation for multi-Mega-Watt (MW) beam facilities. We invited a speaker from a high energy neutrino beam facility (CERN, Fermilab and J-PARC), a collider detector group (CERN and Fermilab), a neutron spallation source facility (ESS, J-PARC and SNS), and a rare-isotope beam facility (FRIB). Although, the operational beam parameter for each institution is unique due to their different physics goals, we realize that there is a common issue on the beam instrumentation. Therefore, it will be tackled by a collaborative R&D effort among facilities. We summarize an output from the workshop in the paper, and propose a possible R&D for the future radiation hardened beam instrumentations with a global effort.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Modernizing the SNS Control System

The Spallation Neutron Source at Oak Ridge National Laboratory has been operating since 2006. An upgrade to double the machine power from 1.4 MW to 2.8 MW is currently underway and a project to add a second target station is in the preliminary design phase. While each project will add the controls needed for their specific scope, the existing control system hardware, software, and infrastructure require upgrades to maintain high availability and ensure the system will meet facility requirements into the future. While some systems have received new hardware due to obsolescence, much of the system is original apart from some maintenance and technology refresh. Software will also become obsolete and must be upgraded for sustainability. Further, requirements for system capacity can be expected to increase as more subsystems upgrade to smarter devices capable of higher data rates. This paper covers planned improvements to the integrated control system with a focus on reliability, sustainability, and future capability.

White, Karen S.↗
DOE OSTI2022

Progress on Machine Learning for the SNS High Voltage Converter Modulators

The High-Voltage Converter Modulators (HVCM) used to power the klystrons in the Spallation Neutron Source (SNS) linac were selected as one area to explore machine learning due to reliability issues in the past and the availability of large sets of archived waveforms. Progress in the past two years has resulted in generating a significant amount of simulated and measured data for training neural network models such as recurrent neural networks, convolutional neural networks, and variational autoencoders. Applications in anomaly detection, fault classification, and prognostics of capacitor degradation were pursued in collaboration with the Jefferson Laboratory, and early promising results were achieved. This paper will discuss the progress to date and present results from these efforts.

Pappas, Chris↗
DOE OSTI2022

Design Enhancements for the SNS RFQ Coaxial Coupler

The H⁻ ion linear accelerator at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory operates with reliability that routinely surpasses 90% during scheduled beam operation. With the ambitious goal of eventually achieving at least 95% availability, several upgrade and improvement projects are ongoing. One such project is the modification of the coaxial couplers that transfer radio frequency (RF) power to the accelerator’s Radio Frequency Quadrupole (RFQ). The proposed modification utilizes stub sections and capacitive coupling to construct a physically separable assembly with DC isolation. With a separated coupler assembly, the section that includes the magnetic coupling loop can be permanently mounted to the RFQ which would eliminate the need to re-adjust the couplers after maintenance activities, upgrades, and repairs. Additionally, the modified design would provide increased multipaction suppression with DC biasing and potentially lower thermal gradients across the device. This paper presents the design and simulation results of the project.

Toby, George↗
DOE OSTI2023

Development of Large-Volume-Diamond Anvil Cell for Neutron Diffraction: The Neutron Diamond Anvil Cell Project at ORNL

10 years ago, Dave Mao, director of EFree (energy frontier research in extreme environments), a DOE energy frontier recognized the importance of neutron science for energy research. The subsequent establishment of a neutron group within EFree lead to the establishment of an “Instrument Development Team” for SNAP, the High-Pressure beamline at the Spallation Neutron Source at Oak Ridge National Laboratory in Tennessee. The idea was to develop novel high pressure techniques to expand the pressure range for neutron diffraction. A goal was set to reach half megabar levels (50 GPa), which at the time was considered as extremely challenging. Here we will give a brief overview of the developments during the last decade in this novel area of research. Fortunately, during this period multi carat diamond anvils have become available mainly by the chemical vapor deposition process (CVD), making research in this pressure range and beyond rather routine. This paper shows the latest developments in large anvil designs, compact multiple ton diamond cells and some examples of high-quality neutron diffraction patterns of sample sizes far below conventional levels.

Boehler, Reinhard↗
DOE OSTI2011

Phase Space Coating in Synchrotons: Some Applications

Phase-space painting to produce very high intensity beam in synchrotrons is one of the widely studied topics in accelerator physics. A remarkable example of this is multi-turn beam injection by transverse phase-space painting in spallation sou rces. Use of barrier buckets at synchrotron storage rings has paved way for further advancements in this field. The Fermilab Recycler, antiproton storage ring, has been augmented with multipurpose broad-band barrier rf systems. Recently we have developed a longitudinal phase-space coating technique over already e-cooled high intensity low longitudinal antiproton beam and demonstrated with beam experiments. This method is extended to map the incoherent synchrotron tune of beam particles in a barrier bucket . Here I review various phase-space painting techniques being used in particle accelerators including some new schemes developed using barrier rf systems and possible new applications.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

HIGH-LOW FIDELITY THERMAL HYDRAULIC COUPLING USING AI/MACHINE LEARNING ALGORITHMS

The primary goal of the US Department of Energy (DOE) office of Nuclear Energy Integrated Energy Systems (IES) program is to develop the tools and framework for coupling multi-scale and multi-physical thermal and electrical energy usage and storage systems. High- and low-fidelity (high–low) coupling is a key feature of multi-scale, multi-component systems and has been an important focus of research in the nuclear energy community for the past two decades. An essential feature of demonstrating the capability to couple high-fidelity and low-fidelity systems for real-time applications are surrogate/reduced order models (ROM). For the purposes of this study, surrogate models are essentially Blackbox models, typically developed using supervised Machine learning (ML) algorithms. The surrogate models can be used to mimic the response of high-fidelity models to represent large historical datasets and coupled with more general low-fidelity system models distributed as Functional Mock-up Interface (FMI) or Functional Mock-up Units (FMU) modules. The example is demonstrated with Spallation Neutron Source (SNS) First Target Station flow loop data. The flow loop is a liquid mercury loop with a pump, piping, heat exchange, and internal heat generation in the target window. This work elucidates some of the potential benefits and future needs of developing tools for high–low system coupling of energy systems.

Williams, Wesley↗
DOE OSTI2022

Benchmarking and Exploring Parameter Space of the 2-Phase Bubble Tracking Model for Liquid Mercury Target Simulation

High intensity proton pulses strike the Spallation Neutron Source (SNS)’s mercury target to provide bright neutron beams. These strikes deposit extensive energy into the mercury and its steel vessel. Prediction of the resultant loading on the target is difficult when helium gas is intentionally injected into the mercury to reduce the loading and to mitigate the pitting damage on the vessel. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. We present a study comparing the measured target strains in the SNS target station with the simulation results of the solid mechanics simulation framework. We investigate a wide range of various physical model parameters, including the number of bubble families, bubble size distribution, viscosity, surface tension, etc. to understand their impact on simulation accuracy. Our initial findings reveal that using 8-10 bubble families in the model renders a simulation strain envelope that covers the experimental ones. Further optimization studies are planned to predict the strain response more accurately.

Lin, Lianshan↗
DOE OSTI2012

MYRRHA a multi-purpose hybrid research reactor for high-tech applications

MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) is the flexible experimental accelerator driven system (ADS) in development at SCK-CEN. MYRRHA is able to work both in subcritical (ADS) as in critical mode. In this way, MYRRHA will allow fuel developments for innovative reactor systems, material developments for generation IV (GEN IV) systems, material developments for fusion reactors, radioisotope production and industrial applications, such as Si-doping. MYRRHA will also demonstrate the ADS full concept by coupling the three components (accelerator, spallation target and subcritical reactor) at reasonable power level to allow operation feedback, scalable to an industrial demonstrator and allow the study of efficient transmutation of high-level nuclear waste. MYRRHA is based on the heavy liquid metal technology and so it will contribute to the development of lead fast reactor (LFR) technology and in critical mode, MYRRHA will play the role of European technology pilot plant in the roadmap for LFR. In this paper the historical evolution of MYRRHA and the rationale behind the design choices is presented and the latest configuration of the reactor core and primary system is described. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2012

Overview of SNS accelerator shielding analyses

The Spallation Neutron Source is an accelerator driven neutron scattering facility for materials research. During all phases of SNS development, including design, construction, commissioning and operation, extensive neutronics work was performed in order to provide adequate shielding, to assure safe facility operation from radiation protection point of view, and to optimize performance of the accelerator and target facility. Presently, most of the shielding work is concentrated on the beam lines and instrument enclosures to prepare for commissioning, safe operation and adequate radiation background in the future. Although the accelerator is built and in operation mode, there is extensive demand for shielding and activation analyses. It includes redesigning some parts of the facility, facility upgrades, designing additional structures, storage and transport containers for accelerator structures taken out of service, and performing radiation protection analyses and studies on residual dose rates inside the accelerator. (authors)

43 PARTICLE ACCELERATORS↗
DOE OSTI2013

Handling Radioactive Waste from the Proton Accelerator Facility at the Paul Scherrer Institut (PSI) - Always Surprising? - 13320

The Paul Scherrer Institut (PSI) is the largest national research centre in Switzerland. Its multidisciplinary research is dedicated to a wide field in natural science and technology as well as particle physics. In this context, PSI is operating, amongst others, a large proton accelerator facility since more than 30 years. In two cyclotrons, protons are accelerated to high speeds and then guided along roughly 100 m of beam line to three different target stations to produce secondary particles like mesons and neutrons for experiments and a separately beam line for UCN. The protons induce spallation processes in the target materials, and also at other beam loss points along the way, with emission of protons, neutrons, hydrogen, tritium, helium, heavier fragments and fission processes. In particular the produced neutrons, due to their large penetration depth, will then interact also with the surrounding materials. These interactions of radiation with matter lead to activation and partly to contamination of machine components and the surrounding infrastructures. Maintenance, operation and decommissioning of installations generate inevitably substantial amounts of radioactive operational and dismantling waste like targets, magnets, collimators, shielding (concrete, steel) and of course secondary waste. To achieve an optimal waste management strategy for interim storage or final disposal, radioactive waste has to be characterized, sorted and treated. This strategy is based on radiation protection demands, raw waste properties (size, material, etc.), and requirements to reduce the volume of waste, mainly for legal and economical reasons. In addition, the radiological limitations for transportation of the waste packages to a future disposal site have to be taken into account, as well as special regulatory demands. The characterization is a task of the waste producer. The conditioning processes and quality checks for radioactive waste packages are part of an accredited waste management process of PSI, especially of the Section Dismantling and Waste Management. Strictly proven and accepted methods needed to be developed and enhanced for safe treatment, transport, conditioning and storage. But in the field of waste from research activities, individual and new solutions have to be found in an increasingly growing administrative environment. Furthermore, a wide variety of components, with a really large inventory of radioactive nuclides, has to be handled. And there are always surprising challenges concerning the unusual materials or the nuclide inventory. In case of the operational and dismantling radioactive accelerator waste, the existing conditioning methods are in the process of a continuous enhancement - technically and administratively. The existing authorized specifications of conditioning processes have to be extended to optimize and fully describe the treatment of the inevitably occurring radioactive waste from the accelerator facility. Additional challenges are the changes with time concerning the legal and regulatory requirements - or do we have to consider it as business as usual? This paper gives an overview of the current practices in radioactive waste management and decommissioning of the existing operational accelerator waste. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Overview on Analyses of Dose Rates During RID Parts Removal/Exchange

One of the most irradiated Spallation Neutron Source (SNS) accelerator components is ring injection dump (RID), which is located downstream of the accumulator ring injection section. The unstripped and only partially stripped H- beam is discarded in the injection into the accumulator ring and is redirected to the RID, which is about 5% of the full beam current. According to the accelerator operation plan, the beam stop and the window assemblies of the existing RID will be removed and replaced, when they have reached their end-of-life. This procedure, which includes multiple steps, is scheduled to take place during facility maintenance period in January 2023.In order to support job planning and meet ALARA requirements during removal and exchange of the components, dose rates for each stage of exchange operation are calculated.

Popova, Irina I.↗
DOE OSTI2021

Experience with Inner Reflector Plug exchange in SNS

The Inner Reflector Plug (IRP) is a central component of the Spallation Neutron Source target monolith, which houses the mercury target and four liter-sized neutron moderator units. It is exposed to high-level radiation fields during routine operation and builds up significant activity. The IRP needs to be replaced due to moderator neutron poison and decoupler burn-out, which is used for shaping neutron pulses. The first IRP exchange took place in March 2018. The old IRP was extracted from the target monolith, providing space for the new one. It was split into three segments, each of which was handled separately. The lowest section of the IRP is the largest segment in size and in activity and is temporarily stored on-site for cool down before conduction post irradiation examination. In support of planning the replacement activities, a wide range of activation and transport analyses were performed. This included calculating isotope inventories and the radiation fields for each segment as it is extracted in storage casks, and the radiation field from the empty IRP pit in the target monolith. While the replacement was taking place, measurements were performed and later on compared to the calculations. During these studies, it was discovered that a significant contributor to the radiation field from the lower IRP segment is from photo-neutrons. Photo-nuclear physics was added to the analyses and calculated results compared well with measured dose rates.

Popova, Irina I.↗
DOE OSTI2023

Overview on Shielding Analyses for the VENUS Instrument at SNS

VENUS, a world‐class versatile neutron imaging instrument, is under construction and is expected to be completed and ready to start commissioning in 2023. The range of cold to epithermal neutrons at SNS will give users of VENUS access to novel imaging methods, as well as to significantly improved existing methods. The instrument is being built on beam line 10 at Spallation Neutron Source (SNS) First Target Station (FTS) facing a decoupled poisoned hydrogen moderator. Instrument design, which includes optics, Front-End components and instrument enclosure components and shape started over 10 years ago and during this time had significant changes. All changes were supported by neutronics analyses to provide adequate shielding for both Front-End and instrument enclosure.Final optics design will provide the field of view (FOV) at the detector position (where the image is formed) to be as high as 0.20 by 0.20 m. Both the beam, which contains a large fraction of high-energy neutrons, and the desire for a large footprint on the detector are challenges for shielding design and budget, because the driving cost for the instrument is the beam line and enclosure shielding. For cost reason VENUS baseline design is optimized with respect to both the instrument cave footprint and its wall thickness, and Front-End shielding is tailored along the beam. Analyses are performed with the Monte Carlo particle transport code MCNPX version 2.7.0 to make choices on materials, thicknesses and configurations of the shielding. Numerous calculations are performed to meet space and coast constrain and to satisfy instrument physics needs and to comply with radiation protection requirements.

Gallmeier, Franz X.↗
DOE OSTI2017

Challenges and Recent Developments of Neutron Non-Destructive Assay with UO{sub 2}F{sub 2}-Bearing Materials - 17336

In the enrichment process of an operating Gaseous Diffusion Plant (GDP), such as the Portsmouth and Paducah facilities, UF6 gas will immediately hydrolyze forming the chemical compound UO{sub 2}F{sub 2} (Uranyl Fluoride). This mostly happens in Alumina (Al{sub 2}O{sub 3}) traps where the UF6 adsorbs to moistened Alumina pellets forming a UO{sub 2}F{sub 2} layer around the pellet. Similarly, NaF.UF{sub 6} absorption traps produce the complex Na{sub 2}UF{sub 8} which also hydrolyzes when exposed to moist air. UO{sub 2}F{sub 2} can also be formed in many other processes where UF6 gas comes into contact with moisture within structures and objects such as pipes, converters compressors and coolers. When the structures are refurbished, or designated for D and D, UO{sub 2}F{sub 2}-bearing objects are generated both in situ and ex situ requiring fissile (U-235) characterization. In addition, ex situ waste streams are generated when UO{sub 2}F{sub 2}-bearing materials are placed in drummed or boxed waste containers. Gamma spectroscopy Non-Destructive Assay (NDA) is commonly utilized to characterize UO{sub 2}F{sub 2}-bearing waste but generally has high associated Total Measurement Uncertainties (TMU's) and, in some cases, Data Quality Objectives (DQO's) cannot be met. In addition, high UO{sub 2}F{sub 2} mass loadings, such as hold-up materials, require gamma modeling when infinitely thick to the Uranium energy lines. A common neutron NDA technique, or method, is to exploit the neutrons generated from the F-19(a, n)Na-22 reaction which has an appreciable reaction cross-section. The isotopes of Uranium are a-emitters, and, in particular, U-234 has a significantly higher a-decay reaction cross-section leading to a significant relative neutron Specific Activity (nSA). Neutron NDA is appealing since, in some cases, it has potentially lower TMU's than gamma NDA and neutron detector slabs facilitate surrounding large, complex-shaped, objects. Characterizing UO{sub 2}F{sub 2}-bearing waste for fissile content using neutrons generated from U-234, requires the U-235/U-234 ratio as well as the enrichment as well as the corresponding nSA's. It is also noted that U-238 has a considerable, relative, spontaneous fission nSA and this is a higher concern for low-enrichments where the mass of U-238 dominates. Additional neutron interfering elements include cosmic-ray induced spallation within the objects and background from other, in situ, UO{sub 2}F{sub 2}-bearing objects. In this paper we present the challenges and recently developed hardware and algorithmic strategies for quantifying fissile mass both in situ and ex situ using neutron NDA that works in conjunction to gamma spectroscopy NDA, or process knowledge, for objects and drummed/boxed waste containing UO{sub 2}F{sub 2}-bearing materials leading to minimal TMU's and achievable DQO's. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Feasibility Studies on a Hexagonal-Lattice Core for a World-Class Cold Neutron Source

Cold neutrons have kinetic energies less than 5 meV and wavelengths greater than 4 Α. They can be transported over tens of meters through super-reflecting neutron guides with minimal losses. Cold neutrons are used to investigate the structure of larger molecular systems such as biological materials, polymers and aggregates, due to their preferential interaction with light elements and general ignorance towards heavy ones. Intense beams of cold neutrons are obtained from slowing down a source of thermal energy neutrons - which may be from either a research reactor or spallation neutron source - through some cryogenic moderator such as liquid hydrogen or deuterium. The present reactor at the NIST Center for Neutron Research (NCNR) - NBSR - is such a cold neutron source (CNS) facility which provides cold neutron beams for over 2,000 scientists performing various experiments annually. Feasibility studies on a replacement reactor for the NBSR are underway at NCNR with the primary purpose of optimized cold neutron production. Low enriched uranium (LEU) fuel is required for the new reactor to conform to nuclear non-proliferation agreements. The low thermal power rate of 20 MW is taken as a priority with a fuel cycle length designated as 30 days. A horizontal split compact core with a large D{sub 2}O reflector tank is currently proposed and studied, with the expectation of achieving much better cold neutron performance than the present NIST reactor (NBSR). A preliminary core design has been completed using MCNP6 modeling and simulation. The physics performance characteristics of the proposed new core indicate that the new design is competitive with the most notable existing advanced cold neutron sources. In previous studies, only rectangular shaped fuel elements were considered because they have similar external dimensions as the NBSR fuel elements. However, from a compact core standpoint, a square lattice is not the most effective geometry for a tight configuration. Moreover, the previous studies also showed that the square lattice of the fuel elements left little room to accommodate vertical insertion blade-type control elements. As a result, all control blades had to reside in the D{sub 2}O reflector, which made the design cumbersome (in that case the control blades must penetrate the reflector tank) and neutronically uneconomical. In this summary, a preliminary feasibility study on a hexagonal core lattice is performed to render an alternative geometry for the new reactor (HEX core) to provide sufficient space for the control elements. The identical LEU fuel (U{sub 3}Si{sub 2}/Al) with U-235 enrichment 19.75% is used in the new design. The maximum thermal power and fuel management scheme remain the same as the previous investigations (three 30-day cycled batches for each batch of three fuel elements). The horizontal split compact core concept is also applied in the hexagonal lattice core design, with the objective of creating maximum thermal flux traps between the split core halves. A detailed description of the model for the hexagonal lattice core is presented in the following section. The HEX core design achieves a number of successes over the previous split-core design. Given that much of the motivation of this work was based on implementation of control blades into a concept which lacked them, it is notable that neutron economy was well-preserved in the process of achieving conservatively effective reactivity control; start-up k{sub eff} was in fact increased by 0.23% and peak thermal flux increased by ∼25%. A useful metric in determining the efficacy of resources towards creating an environment for the production of cold neutrons - dubbed the 'quality factor' (QF) - is the ratio of peak thermal neutron flux in a system to the total thermal power produced. Because HEX core's objectives are very focused in comparison to existing research reactors, it is fitting to pursue a design which out-performs all others in terms of some specific performance metric, namely this QF term. While HFIR remains the greatest cold neutron source in the world, it does so through use of HEU fuel (which will be replaced with LEU in the near future), and suffers a greater level of fast neutron contamination that is expected from the HEX design. The new core design achieves these successes due to the hexagonal lattice fuel arrangement, a 13.5% reduction in cladding mass, and a 13.1% reduction in fuel element volume. In spite of a 5.5% reduction in fuel mass, no compromises in reactor performance were noted. Provided the favorable characteristics shown of the control blade design, refueling intervals longer than the prescribed 30 days may be considered. It can be speculated that with these quantitative benefits, the overall capital and continuous costs of the HEX core design will be less than the previously proposed split-core concept.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2016

Helium-3 Production via Lithium-6 Activation in an Accelerator-Driven Reactor

In this paper, the possibility of using an accelerator-driven subcritical reactor to produce helium-3 is explored. Current supply of helium-3 in the United States is running low. Helium-3 has many applications in neutron detection, high-energy physics, and national security, and has a growing demand in the scientific community for its properties. The main source of helium-3 in the United States is from dismantling nuclear arms, where tritium is allowed to decay into helium-3. There are no current, significant future plans for increasing helium-3 production. However, the projected demand of this isotope is expected to increase dramatically, with greater research into aneutronic fusion, and allotments of helium for the Spallation Neutron Source, and ITER expected in years to come. Tritium, with a half-life of 12.3 years, will take time to decay to helium-3, which means production needs to start now to counter the future deficit. This helium-3 production system sets out to be an economical, and safe solution for this future deficit. A zirconium-lithium mixture is utilized as a target for breeding helium-3. Specifically, the target rods will consist of lithium aluminate pellets with diameters ranging from 100 to 500 microns, dispersed within a zirconium matrix. Lithium targets in pellet form were chosen over a solid rod, or annulus, in order to reduce self-shielding effects within the lithium, and to further facilitate tritium loading and containment within the zirconium. Additionally, a stainless steel 316 cladding surrounds the target rods, to further reduce outgassing of helium. The core is made up of 6480 fuel pins, enriched to 4.75% wt% U-235/U, and 3660 lithium pins in mixed assemblies arranged in hexagonal lattices, with the lithium enriched to 75% lithium-6, and a total lithium loading of approximately 70 kg. An accelerator is used as a neutron source, firing 800 MeV protons at a liquid lead target loop. Neutronics analysis and burnup calculation were performed with the aid of MCNP6. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2016

Uncertainty Quantification of Spatial Correction Factor for Sjoestrand Method due to Cross-section Data

Accelerator-driven System (ADS), which couples a subcritical core with a spallation neutron source, is proposed as a nuclear transmutation technology to reduce the radioactive half-life of high-level waste. To maintain a safe operation in ADS, the core should be kept in subcritical state. Thus, the subcritical state of the core must be quantified through measurement of subcriticality, which is a quantitative margin from critical state. The area ratio method, or the Sjoestrand method, is one of the subcriticality measurement techniques applicable to the ADS. In this method, the absolute value of subcriticality can be obtained by analyzing the temporal variation of neutron density in the core due to the periodic injection of neutron pulses. In practice, the value of subcriticality is measured by the temporal variation of neutron count rate detected by a detector in the core. Time integrals of count rates due to prompt and delayed neutrons A{sub p} and A{sub d}, are measured. Then, the ratio of A{sub p} to A{sub d}, which is called as the area ratio, yields negative reactivity -ρ, i.e. subcriticality, in dollar units: A{sub p}/A{sub d} ≅ -ρ/β{sub eff'} (1) where β{sub eff} is the effective delayed neutron fraction. Equation (1) represents the basic idea of the Sjoestrand method. Note, however, that Eq. (1) is approximately derived using the point kinetics model. In an actual subcritical system, the measured area ratio is not necessarily equal to the exact value of subcriticality in dollar units, due distortion by spatial higher-order modes. Hence, in the actual measurement, this spatial effect is corrected by a spatial correction factor such as the Bell and Glasstone correction factor (the Bell factor), or by extraction of the fundamental mode (so-called the extrapolated area ratio method). In addition, there is an effect due to the neutron detector materials (e.g. {sup 3}He(n,p) and {sup 235}U(n,f)). These effects must be considered in the correction of the measured area ratio. In this study, we focused on the uncertainty of Bell factor. The Bell factor f is defined by the ratio of the area ratio to the subcriticality as follows: f ≡ -[ρ/β{sub eff}]/[A{sub p}/A{sub d}] (2) The Bell factor f can be evaluated by a core analysis. By multiplying the measured area ratio by the Bell factor?, the spatial higher-order mode effect in the area ratio can be corrected. However, the uncertainty of the Bell factor due to uncertainties of cross-section data (covariance data) has not been quantitatively evaluated so far. In this study, we propose a method to quantify the uncertainty of the Bell factor in an actual core analysis. As a feasibility study, the uncertainty quantification is carried out in a simple one-dimensional subcritical core system. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗