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DOE OSTI2021

FY21 Status report on the CMVB and CNWG International Collaborations

The ART-GCR Methods area includes an international collaboration work package that covers the tasks defined for the Computational Methods Validation and Benchmark (CMVB)and Civil Nuclear Energy Research and Development Working Group (CNWG) projects. This report summarizes the status of the FY21 tasks and planned FY22 DOE contributions. The CMVB Project Arrangement (PA) is not yet formally approved by all signatories, and no work has therefore been performed in FY21 at INL related to this activity. The CNWG activities inFY21 consisted of the simulation of the High Temperature Test Reactor (HTTR) Loss Of Forced Cooling (LOFC) experimental with the Idaho National Laboratory (INL) codes Griffin, BISON and RELAP-7 based on the Multiphysics Object-Oriented Simulation Environment (MOOSE).It was found that the multiphysics coupled suite is capable of simulating all the important phenomena occurring during the Depressurized Loss of Forced Cooling (DLOFC) experiments showing promising agreement with the measurements given the number of uncertainties and approximations introduced into the model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Southeast Regional Carbon Sequestration Partnership Phase III Overview of Accomplishments (SECARB Phase III Final Report)

The Southeast Regional Carbon Sequestration Program (SECARB) is a carbon management program established in 2003 and managed by the Southern States Energy Board (SSEB). SECARB is one of seven regional carbon sequestration partnerships formed by the Department of Energy (DOE). The seven partnerships form a national network of more than 400 organizations covering 43 states and four Canadian provinces with expertise in the areas of carbon capture, transportation, and storage. The SECARB program was funded by DOE and cost-sharing partners. The primary goal of SECARB was to identify major sources of carbon emissions, characterize the geology of a 13-state region, determine the most promising options for commercial deployment of carbon dioxide (CO 2 ) sequestration technologies in the South, and validate the technology options through carefully executed field testing through 2017. This report summarizes significant Phase III accomplishments and is organized by task as established within the SECARB Phase III Statement of Project Objectives (SOPO). This document does not provide an exhaustive overview of individual tasks. Rather, this report provides an overview of programmatic accomplishments and a timeline of events. Where applicable, hyperlinks to specific project deliverables are provided.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Software Quality Assurance for EBR-II Fuels Irradiation and Physics Database (FIPD)

The Fuels Irradiation and Physics Database (FIPD) is an ongoing DOE project on archival of the EBR-II metal-alloy fuel irradiation experiments. As part of its use in support of license applications, the Quality Assurance Program Plan (QAPP) was drafted and endorsed by NRC in an effort to demonstrate its compliance with regulatory expectations. Software Quality Assurance (SQA) for the physics portion of FIPD is intended to qualify the calculated quantities such as fuel and cladding temperatures, neutron fluence and axially varying burnup estimates for irradiated fuel elements. This report covers the initial evaluation of SQA status of three neutron physics and thermo-fluid codes (REBUS, RCT and SE2RCT) that form the basis of calculated quantities for as-irradiated characteristics of the tested metallic fuel elements. The report also introduces an SQA plan to address the identified deficiencies. The REBUS, RCT, and SE2RCT codes are all part of the Argonne Reactor Code (ARC) code system. There is considerable knowledge and experience on REBUS and RCT but relatively less on SE2RCT. During FY2021, efforts focused on an assessment of how the data in the EBR-II Physics and Analysis DataBase (PADB) is generated with SE2RCT and used in FIPD. Additional tasks included considerations of uncertainties for power estimates in REBUS and RCT calculations and their impact on the combined RCT methodology. The RCT software usage in FIPD was assessed this year and the input/output details studied. A “requirements” document was created that identifies the key features of the RCT software being used in FIPD that need to have SQA documentation. A brief discussion on the history of RCT and its input is included in this report along with the basic SQA roadmap laid out in the requirements document. The SE2RCT software usage in FIPD is still being studied noting that there is no current manual. As part of the work done this year, two bugs were identified in the SE2RCT software which have a minor impact on the accuracy of the results it produces. No requirements document has been created, but one identified feature of SE2RCT being used that needs verification was its fuel pin temperature calculation. The work completed this year confirms that the approximations which will be included in the software verification report for SE2RCT are accurate. In addition to software quality assurance work for RCT and SE2RCT, an automated verification framework is proposed to simplify the software quality assurance process. The purpose of this framework is to streamline code verification and documentation while minimizing repetitive tasks for code developers and reviewers. The reduction of repeated input (between reference solution, software, and documentation input) throughout the SQA process reduces potential for human errors during the preparation of the supporting software quality records. The automation of the verification and documentation process proposed for this project leverages the existing verification structure already in place for the SAS4A/SASSYS-1 code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Autonomous Inspection of Geologic Repositories: Current State of the Art and Future Directions

Geological repositories for nuclear waste, including spent nuclear fuel, present a significant challenge for traditional International Atomic Energy Agency (IAEA) safeguards tools due to their inaccessibility and demanding operational conditions. The IAEA has been working closely with Member State organizations currently involved in repository construction and planning, including Euratom, the Finnish and Swedish regulatory authorities, and relevant facility operators. However, the verification challenge remains unsolved, and there persists an out- standing need for tools and approaches that will help the IAEA verify that no nuclear material is diverted from a repository environment. The challenge is also not static. Activities must encompass verification of the design, prior to and during the construction/operation phase, and post backfill. Throughout these various phases, it is imperative that the IAEA maintains a continuity of knowledge (CoK) of all material including information on material inventory and flow. This paper highlights these challenges and outlines how they might be addressed by using remote or autonomous vehicles. Specifically, we discuss the current state of the art in robotic autonomy for known or partially known environment mapping and patrolling, as well as shared autonomy, where humans collaborate with closed loop autonomation to complete tasks. We explore the feasibility of using rovers for these verification tasks, along with the challenges associated with system implementation. Hardware and software suggestions are provided based on the adoption of similar technologies in other comparable areas and ability to close technical gaps. Lastly, human-robotic interactions are considered based on the challenges of the environment of the repository and effective deployment and continued operation of the robot system.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Big Adaptive Rotor Phase I Final Report

The Big Adaptive Rotor (BAR) project was initiated by the U.S. Department of Energy (DOE) in 2018 with the goal of identifying novel technologies that can enable large (>100 meter [m]) blades for low-specific-power wind turbines. Five distinct tasks were completed to achieve this goal: 1. Assessed the trends, impacts, and value of low-specific-power wind turbines; 2. Developed a wind turbine blade cost-reduction road map study; 3. Completed research-and-development opportunity screening; 4. Performed detailed design and analysis; and, 5. Assessed low-cost carbon fiber. These tasks were completed by the national laboratory team consisting of Sandia National Laboratories (Sandia), the National Renewable Energy Laboratory (NREL), and Lawrence Berkeley National Laboratory.

17 WIND ENERGY↗

DOE OSTI2021

Atrial Model Development and Prototype Simulations; Final Report for CRADA No. TC02224.0

This project was a collaborative effort between Lawrence Livermore National Security, LLC as manager and operator of Lawrence Livermore National Laboratory (LLNL) and Amgen, Inc. ("Amgen"), to develop a capability to computationally evaluate the importance and roles of different ion channels in atrial fibrillation. The first phase of this collaboration was to implement the atrial model, run prototype simulations, and analyze the results. Two No-Cost Time Extension (NCTE) requests were executed for this project. The first NCTE was executed on April 1, 2016, and extended the CRADA project for an additional two months to allow enough time to complete the tasks and deliverables, due to a delay in the start of the project. A second NCTE was executed on June 28, 2016, extending the project by three months, through November 3, 2016, to allow enough time to complete the final tasks and deliverables as well as negotiate a CRADA extension. The actual duration of this project was fourteen months. Amgen was unable to obtain budget approval to extend the CRADA past November 3, 2016. All of the deliverables for this CRADA project were successfully completed according to schedule.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Developing Accelerated Test Protocols and Tuning Microstructures of the Common Materials to Improve Robustness, Reliability, and Endurance of SOFC Cells

This work is built on our prior work where we found that phase transformation in praseodymium nickelates, e.g. Pr 2 NiO 4 (PNO) and (Pr 1-x Nd x ) 2 NiO 4 (PNNO), can be electrochemically driven, and is substantially faster when compared to thermal annealing studies. The first task aims at an attempt to further accelerate the phase transformation in the oxygen electrode by alternating the current input in the cells, which lead to the development of accelerated test protocols (ATPs). ATPs showed up to 60x faster phase transformation and up to 10x faster performance degradation in (Pr 0.50 Nd 0.50 ) 2 NiO 4 electrodes, when compared to long-term operation under constant current density. Furthermore, the phase stable Nd 2 NiO 4 and (La 0.6 Sr 0.4 )(Co 0.8 Fe 0.2 )O 3 (LSCF6482) electrodes were tested in full cells under ATPs, and showed up to 10x faster performance degradation within 1,100 hours in a comparison with long-term thermal annealing studies and electrochemical operation under constant current density. The second task aims at the quantification of the contributions of cell components to the total impedance of a solid oxide fuel cell (SOFC) using electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT). Specifically, the role of gas composition at both anode and cathode was systematically studied, aiming at deconvoluting, identifying and quantifying the contributions of different electrode processes. This was achieved by first tuning the partial pressure of H 2 at the anode and subsequently varying the partial pressure of O 2 at the cathode. The results suggest that, while DRT offers a viable way of deconvoluting different times distributions, additional attention is needed before assigning a peak to a specific electrode process due to the significant overlap of the contributions from the cathode and the anode. Density function theory studies show that both Pr-vacancies and O-defects play a key role on the activity and stability for nickelates towards oxygen reduction reaction. The resident O-interstitials and oxygen ions in the PrO layer form peroxide (O 2 2- ) nearby Pr vacancies. The O 2 2- limits oxygen-ion transport due to the required additional energy to break its O-O bond. We further calculated the formation and segregation energies for different Ln ions (La, Pr, Nd, Pm, Sm, Gd, Tb, Dy, and Ho) in PNO and CeO 2 (111) surfaces. In addition to Nd, Pm and La are suggested as potential dopants in PNO to enhance it stability without decomposition due to their more negative formation energies, lower diffusion energies, and positive separation energies.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

SECARB-USA: Needs Assessment Framework for Storage Complexes

The goal of this task is to develop an assessment to identify data needed to advance geologic storage projects, with a focus on the SECARB region. The GCCC team considers the needs of CO2 source, storage, and utilization operators and stakeholders, finance and insurance institutions, state and local government relators and agencies, property owners, local stakeholders at prospective storage complexes, and environmental non-governmental organizations (NGOs). Many of these needs are spelled out in the requirements of the Class VI permit. However, at the initial stages of project development, the workflow will not start with permit writing. A number of other factors must be evaluated prior to this major investment. The team’s goal in this report is to inventory the range of typical needs for a wide variety of projects. For subsequent tasks, the team will consider how these needs vary among projects and through the stages of investment, so that project developers can plan the early stages of capitalization.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Integrated TBC/EBC for SiC Fiber Reinforced SiC Matrix Composites for Next Generation Gas Turbines (Final Report)

In this ambitious project, a significant challenge preventing widespread use of ceramic matrix composites in hot section components of gas power generating turbines was addressed. Hot section components made from SiC fiber reinforced SiC matrix composites (SiC/SiC composites), have the potential to achieve a combined cycle energy efficiency of above 65%. To achieve this efficiency, the temperature of the combustion gases on the turbine component surface is expected to reach as high as ~1700ºC (3100ºF). However, SiC/SiC composites suffer from volatilization at high temperature under high velocity steam environment – typical in a turbine hot chamber. This integrated collaborative project, between two research groups at Clemson University and a team of engineers and scientists at GE Gas Power, focused on design, fabrication and evaluation of a new graded environmental barrier coating. Using the excellent compositional tailorability of polymer derived ceramics (PDCs), we developed an integrated EBC/BC that smoothly transitions from bottom SiC/SiC bond interface to hermetic sesquioxide (Y 2 O 3 ) top surface. This smooth compositional transition avoided the sharp CTE mismatch at interfaces to greatly reduce the thermal stress. The developed EBC is compatible with and bonds well with the bond coat that GE uses. The top hermetic oxide surface ensures low oxygen transportation and volatilization rates under the high velocity steam environment. The graded microstructure with increasing sesquioxide concentration also decreases the amount of Si and C elements near the top hermetic sesquioxide layer. Coatings made using a process suitable for manufacturing – atmospheric plasma spraying was demonstrated. The microstructure of coatings made using this process were fully characterized. Finally, the performance of these coatings was investigated under the most demanding conditions for this application. Specifically, high temperature, high velocity steam exposure; thermal shock test; and thermal cycling tests. The graded coatings performed exceptionally well in all these tests. Specific suggestions for future development in this area have also been identified. In addition to the excellent technical progress, this project helped initiate a robust collaboration between the research groups at Clemson and GE Gas Power. It also provided a high-quality learning and mentoring opportunity for the three post-doctoral research associates and two UG students at Clemson University who worked on this project. All proposed tasks, sub-tasks were completed, and all milestones achieved.

03 NATURAL GAS↗

DOE OSTI2021

Development of Enabling Technologies for a Pressurized Dry Feed Oxy-Coal Reactor

Researchers at Brigham Young University (3 faculty, 9 graduate students, and 35 undergraduate students) completed this 5-year research program with the main objective to build and test a 100 kWth pressurized dry-feed oxy-coal combustor (POC). This objective was achieved through the development and testing of a unique pressurized dry coal fluidization feed system that operates in conjunction with a pressurized oxycoal combustor. The project included a series of R&D tasks, including design, modeling, bench-scale testing, construction, safety reviews, and reactor testing which are detailed in this report. BYU researchers were supported in some modeling tasks by project partners Reaction Engineering International (REI) and CPFD Software.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2021

Home Energy Professionals Certifications ISO/IEC 17024: 2021 Policies and Procedures Manual

The U.S. Department of Energy (DOE) enlisted its National Renewable Energy Laboratory (NREL) to coordinate the development of a framework for new certifications in the weatherization and home performance industry. The Home Energy Professional certifications support DOE's Weatherization Assistance Program (WAP) and the broader residential home performance industry through the credentialing process of defined job task analysis for energy auditors and quality control inspectors. The HEP certifications are not intended to supplant or infringe upon any existing industry-recognized credentials, however, the WAP and the home performance industry have utilized the advanced HEP certifications to promote quality work and standardized job task analysis since 2010. On an ongoing basis, NREL brings industry practitioners and subject matter experts together to develop, review, and revise the certification schemes in accordance with the International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC) 17024 standard, "Conformity assessment - General requirements for bodies operating certification of persons" (ISO/IEC 17024). This handbook covers the policies and procedures for the process of developing, maintaining, and validating the certification schemes. Each policy and procedure includes the relevant ISO/IEC 17024 section at the beginning.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Measurement of radiolytic hydrogen generation and impact of drying treatments on reactor exposed and surrogate aluminum materials

Technical challenges associated with dry storage of Aluminum-clad Spent Nuclear Fuel (ASNF) include a need to better understand the potential extent of gaseous molecular hydrogen (H 2 ) production through radiolytic degradation of the aluminum (oxy)hydroxide films present on ASNF. The characterization of radiolytic gas generation from ASNF (oxy)hydroxide layers has been identified as a key knowledge gap which poses a technical challenge to the long-term storage of ASNF. Task 2 of the action plan for the extended (>50 years) dry storage of ASNF addresses this gap. Previous radiolysis studies performed under Task 2 established baseline estimates of H 2 generation rates from the attendant hydrated oxides. The results confirmed that net radiolytic H 2 production has a dependency on absorbed gamma dose, as well as relative humidity and cover gas composition (air, nitrogen, and argon). Further experiments revealed that the physisorbed water on the samples may significantly impact the radiolytic H 2 yield. This phenomenon complicates the determination of H 2 generation rates for hydrated oxides, which may lead to inaccurate modeling predictions of the long-term H 2 yields in sealed storage systems containing ASNF, particularly when compared to spent fuel casks which have undergone some drying process intended to remove physically- and chemically-bound water. This report describes the testing methods utilized and the hydrogen generation results obtained in an investigation of the effects of gamma irradiation on aluminum materials for a variety of (oxy)hydroxide surface compositions and drying conditions. The testing methods included small-area aluminum material testing in ampules, and large-area aluminum material testing in steel vessels. Test material preparation, irradiation, and radiolytic H 2 measurement methods are summarized. The measured H 2 concentrations, which reflect the variable initial hydrated inventory and drying treatments, are compared to one another as well as to previously published data, to identify the primary factors affecting radiolytic H 2 generation rates and potential equilibrium H 2 concentrations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Results for the September Bimonthly Calendar Year 2021 Tank 50 Salt Solution Sample

In this Technical Report, the chemical and radionuclide contaminant results from the 2021 September bimonthly sample of Tank 50 salt solution are presented in tabulated form. The information from this characterization will be used by Savannah River Remediation (SRR) for the transfer of aqueous waste from Tank 50 to the Saltstone Production Facility (SPF), where the waste will be treated and disposed in the Saltstone Disposal Facility. This Technical Report compares results, where applicable, to SPF Waste Acceptance Criteria (WAC) Limits and Targets that were established at the time the Tank 50 sample was obtained. The chemical and radionuclide contaminant results from the characterization of the 2021 September bimonthly sampling of Tank 50 were requested by SRR personnel via a Task Technical Request (TTR) and details of the testing are presented in the Savannah River National Laboratory (SRNL) Task Technical and Quality Assurance Plan (TTQAP). This Technical Report is the TTR deliverable relating Salt Solution Analysis from the SRR request.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Saltstone Third Quarter Calendar Year 2021 (3QCY21) Toxicity Characteristic Leading Procedure (TCLP) Results

The aqueous waste from Tank 50 (salt solution) is sampled quarterly for transfers to the Saltstone Production Facility (SPF). Salt solution is treated at SPF and disposed of in the Saltstone Disposal Facility (SDF). Per request of customer, X-TTR-Z-00023, Revision 0, two SDF waste form (saltstone) samples were prepared in the Savannah River National Laboratory (SRNL) from the Tank 50 Waste Acceptance Criteria (WAC) sample and Z-Area premix material for the third quarter of calendar year 2021(3QCY21). One sample contained a Full Premix which included 10:45:45 (by weight) of cement, slag and fly ash. The second sample contained 60:40 (by weight) of slag and fly ash only referred to as the “Cement-Free grout sample”. Results from this technical report support Task 2: ‘Grout Leaching Analyses’ of the Task Technical Request (TTR) prepared by Savannah River Remediation (SRR). After at least 28 days cured, a sample of each of the SDF waste forms was collected and shipped to a certified laboratory for analysis using the Toxicity Characteristic Leaching Procedure (TCLP). The 3QCY21 saltstone (Full Premix) and the Cement-Free grout samples met the South Carolina (SC) Code of Regulations for Hazardous Waste Management Regulations (HWMR) 61-79.261.24 and 61-79-268.48 requirements for a non-hazardous waste form with respect to Resource Conservation and Recovery Act (RCRA) metals and Underlying Hazardous Constituents (UHCs), and also met the SPF WAC that was in effect at the time of the tank sampling.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Pit depth analysis using automated software for three containers with complete imaging

The 3013 surveillance program is tasked with ensuring the long term safety of plutonium storage in 3013-compliant containers. One component of this task is to understand corrosion features found on the interior sidewall of the inner container closure weld region (ICCWR). To this end, three containers were selected to have laser confocal microscope (LCM) 20X imaging of the entire ICCWR. This report describes the analysis of the LCM pit depth data using the automated corrosion analysis software. The analysis included determining maximum pit depths and distributions of pit depths, volumes, and diameters for all pit features identified on the three containers. Results provided insight into possible corrosion mechanisms and were consistent with previous pit growth model predictions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Artificial Intelligence for Digital Security and Protections

Proper functioning of nuclear power plants relies on a mix of well-regulated human and machine-driven workflows. This regulation supports nuclear safety through a series of processes and many of the tasks that support these processes have a repetitive nature that make artificial intelligence (AI) informed by machine learning (ML) a potential aid in a variety of tasks. AI is being evaluated for activities that include inspections, fuel processing, monitoring, and other activities. The introduction of any new technology presents a potential new attack vector. In the case of AI/ML, there are many attacks that have already been discovered and over time the attacks can be expected to follow the growth pattern observed in cyber security. While future planning is necessary, current efforts need to be established now to predict the threat emergence over the next year 10 years and mitigate potential threats. Based on these observations, AI/ML will need to become trustworthy, which corresponds to techniques and procedures that emphasize AI explainability along with resilience techniques to data, algorithms, models, and systems. This kind of system robustness is the foundation for defenses against AI/ML-specific attacks. Attempting to look forward and take a broad view of capabilities provides input to research roadmaps and the ability to distill vulnerabilities into specific use cases may provide greater assistance in understanding the technology benefits while introducing new risks. The impact of current and future AI in three areas—capabilities, challenges, and recovery strategies—represents an initial attempt at balancing both.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Classification of Orbits in Poincare Maps Using Machine Learning

Poincare plots, also called Poincare maps, are used by plasma physicists to understand the behavior of magnetically confined plasma in numerical simulations of a tokamak. These plots are created by the intersection of field lines with a two-dimensional poloidal plane that is perpendicular to the axis of the torus representing the tokamak. A plot is composed of multiple orbits, each created by a different field line as it goes around the torus. Each orbit can have one of four distinct shapes, or classes, that indicate changes in the topology of the magnetic fields confining the plasma. Given the (x, y) coordinates of the points that form an orbit, the analysis task is to assign a class to the orbit, a task that appears ideally suited for a machine learning approach. In this paper, we describe how we overcame two major challenges in solving this problem - creating a high-quality training set, with few mislabeled orbits, and converting the coordinates of the points into features that are discriminating, despite the variation within the orbits of a class and the apparent similarities between orbits of different classes. Our automated approach is not only more objective and accurate than visual classification, but is also less tedious, making it easier for plasma physicists to analyze the topology of magnetic fields from numerical simulations of the tokamak.

97 MATHEMATICS AND COMPUTING↗