Publications

The Integrated Tiger Series (ITS) generates a database containing energy deposition data. This data, when stored on an Exodus file, is not typically suitable for analysis within Sierra Mechanics for finite element analysis. The its2sierra tool maps data from the ITS database to the Sierra database. This document provides information on the usage of its2sierra.

This report provides documentation for the Sandia Toolkit (STK) modules. STK modules are intended to provide infrastructure that assists the development of computational engineering software such as finite-element analysis applications. STK includes modules for unstructured-mesh data structures, reading/writing mesh files, geometric proximity search, and various utilities. This document contains a chapter for each module, and each chapter contains overview descriptions and usage examples. Usage examples are primarily code listings which are generated from working test programs that are included in the STK code-base. A goal of this approach is to ensure that the usage examples will not fall out of date.

The effective management of plastic waste streams to prevent plastic land and water pollution is a growing problem that is also one of the most important challenges in polymer science today. Polymer materials that are stable over their lifetime and can also be cheaply recycled or repurposed as desired could more easily be diverted from waste streams. However, this is difficult for most commodity plastics. It is especially difficult to conceive this with intractable, cross-linked polymers such as rubbers. In this work, we explore the utility of microencapsulated Grubbs’ catalysts for the in-situ depolymerization and reprocessing of polybutadiene (PB) rubber. Second-generation Hoveyda-Grubbs catalyst (HG2) contained within glassy thermoplastic microspheres can be dispersed in PB rubber below the microsphere’s glass transition temperature (Tg) without adverse depolymerization, evidenced by rubber with and without these microspheres obtaining similar shear storage moduli of ≈16 and ≈28 kPa, respectively. The thermoplastic’s Tg can be used to tune the depolymerization temperature, via release of HG2 into the rubber matrix. For example, using poly(lactic acid) (PLA) vs polysulfone results in an 85 and 162 °C depolymerization temperature, respectively. Liquefaction of rubber to a mixture of small molecules and oligomers is demonstrated using a 0.01 mol % catalyst loading using PLA as the encapsulant. At that same catalyst loading, depolymerization occurs to a greater extent in comparison to two ex-situ approaches, including a conventional solvent-assisted method, where it occurs at roughly twice the extent at each given catalyst loading. In addition, depolymerization of the microsphere-loaded rubbers was demonstrated for samples stored under nitrogen for 23 days. Lastly, we show that the depolymerized products can be reprocessed back into solid rubber with a shear storage modulus of ≈32 kPa. Thus, we envision that this approach could be used to recycle and reuse cross-linked rubbers at the end of their product lifetime.

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High Energy Arcing Faults (HEAFs) are hazardous events in which an electrical arc leads to the rapid release of energy in the form of heat, vaporized metal, and mechanical force. In Nuclear Power Plants, these events are often accompanied by loss of essential power and complicated shutdowns. To confirm the probabilistic risk analysis (PRA) methodology in NUREG/CR-6850, which was formulated based on limited observational data, the NRC led an international experimental campaign from 2014 to 2016. The results of these experiments uncovered an unexpected hazard posed by aluminum components in or near electrical equipment and the potential for unanalyzed equipment failures. Sandia National Laboratories (SNL), in support of the NRC work, collaborated with NIST, BSI, KEMA, and NRC to support the full-scale HEAF test campaign in 2022. SNL provided high speed visible and infrared video/data of ten tests that collected data from HEAFs originated on copper and aluminum buses inside switchgears and bus ducts. Part of the SNL scope was to place cameras with high-speed data collection at different vantage points within the test facility to provide NRC a more complete and granular view of the test events.

A major difficulty in the analysis of molecular-level simulations is that macroscopic flow quantities are inherently noisy due to molecular fluctuations. An important example for turbulent flows is the kinetic energy dissipation rate. Traditionally, this quantity is calculated from gradients of the macroscopic velocity field, which exacerbates the noise problem. The inability to accurately compute the dissipation rate makes meaningful comparison of molecular-level and continuum simulation results a serious challenge. Herein, we extend previously developed coarse-graining theories to derive an exact molecular-level expression for the dissipation rate, which would circumvent the need to compute gradients of noisy fields. Although the exact expression cannot feasibly be implemented in Sandia’s direct simulation Monte Carlo (DSMC) code SPARTA, we utilize an approximate “hybrid” approach and compare it to the conventional gradient-based approach for planar Couette flow and the two-dimensional Taylor-Green vortex, demonstrating that the hybrid approach is significantly more accurate. Finally, we explore the possibility of adopting a Lagrangian approach to calculate the energy dissipation rate.

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A collection of MATLAB functions and class definitions called System Workflow Tools (SWFT) are available to semi-automate steps in the simulation process. Some of these steps are often simple and routine for smaller finite element models, but if done directly by an analyst can quickly become labor intensive, cumbersome, and error prone for larger, system level models. Some of SWFT’s capabilities demonstrated in this report includes writing Sierra input decks and processing Quantities of Interest (QOI) from results files. SWFT also writes scripts in order to utilize other software programs such as Cubit (separating system level CAD into subassemblies and components, creating nodesets and sidesets), DAKOTA (ensemble management), and ParaView (contour plots and animations). Detailed commands and workflows from mesh generation to report generation are provided as examples for analysts to utilize SWFT capabilities.

Over the past decade, cybersecurity researchers have released multiple studies highlighting the insecure nature of I&C system communication protocols. In response, standards bodies have addressed the issue by adding the ability to encrypt communications to some protocols in some cases, while control system engineers have argued that encryption within these kinds of high consequence systems is in fact dangerous. Certainly, control system information between systems should be protected. But encrypting the information may not be the best way to do so. In fact, while in IT systems vendors are concerned with confidentiality, integrity, and availability, frequently in that order, in OT systems engineers are much more concerned with availability and integrity that confidentiality. In this paper, we will counter specific arguments against encrypting control system traffic, and present potential alternatives to encryption that support nuclear OT system needs more strongly that commodity IT system needs while still providing robust integrity and availability guarantees.

This report documents the preliminary design phase of the Critical Experiment Design (CED-1) conducted as part of integral experiment request (IER) 523. The purpose of IER-523 is to determine critical configurations of 35 weight percent (wt%) enriched uranium dioxideberyllium oxide (UO₂-BeO) material with Seven Percent Critical Experiment (7uPCX) fuels at Sandia National Laboratories (Sandia). Preliminary experiment design concepts, neutronic analysis results, and proposed paths for continuing the CED process are presented. This report builds on the feasibility and justification of experimental need report (CED-0) completed in December 2021.

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. The second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

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Hydrogen diffusion in metals and alloys plays an important role in the discovery of new materials for fuel cell and energy storage technology. While analytic models use hand-selected features that have clear physical ties to hydrogen diffusion, they often lack accuracy when making quantitative predictions. Machine learning models are capable of making accurate predictions, but their inner workings are obscured, rendering it unclear which physical features are truly important. To develop interpretable machine learning models to predict the activation energies of hydrogen diffusion in metals and random binary alloys, we create a database for physical and chemical properties of the species and use it to fit six machine learning models. Our models achieve root-mean-squared errors between 98-119 meV on the testing data and accurately predict that elemental Ru has a large activation energy, while elemental Cr and Fe have small activation energies. By analyzing the feature importances of these fitted models, we identify relevant physical properties for predicting hydrogen diffusivity. While metrics for measuring the individual feature importances for machine learning models exist, correlations between the features lead to disagreement between models and limit the conclusions that can be drawn. Instead grouped feature importance, formed by combining the features via their correlations, agree across the six models and reveal that the two groups containing the packing factor and electronic specific heat are particularly significant for predicting hydrogen diffusion in metals and random binary alloys. This framework allows us to interpret machine learning models and enables rapid screening of new materials with the desired rates of hydrogen diffusion.

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Additive manufacturing of metal components enables rapid fabrication of complex geometries. However, metal additive manufacturing also introduces new morphological and microstructural characteristics which might be detrimental to component performance. Here we report the pitting corrosion properties of wrought and additively manufactured 316L stainless steel after atmospheric exposure to coastal environments and laboratory-created environments. Qualitative visualization in combination with quantitative analysis of resulting pits provided an in-depth understanding of pitting differences between wrought and additively manufactured 316L stainless steel and between coastal and laboratory-based exposure. Optical and scanning electron microscopy were utilized for visualization, while white light interferometry measured pits across approximately 5mm x 5mm areas on each sample. Post-processing of the interferometry data enables quantification of pitting attack for each sample in terms of both pit depth and pit volume. The pitting analysis introduced herein offers a new technique to compare pitting attack between different manufacturing processes and materials.

Tritium exhibits unique environmental behavior because of its potential interactions with water and organic substances. Modeling the environmental consequences of tritium releases can be relatively complex and thus an evaluation of MACCS is needed to understand what updates, if any, are needed in MACCS to account for the behavior of tritium. We examine documented tritium releases and previous benchmarking assessments to perform a model intercomparison between MACCS and state-of-practice tritium-specific codes UFOTRI and ETMOD to quantify the difference between MACCS and state of practice models for assessing tritium consequences. Additionally, information to assist an analyst in judging whether a postulated tritium release is likely to lead to significant doses is provided.

This project has identified opportunities to bring further reductions in the mass and cost of modern wind turbine blades through the use of alternative material systems and manufacturing processes. The fiber reinforced polymer material systems currently used by the wind industry have stagnated as the technology continues to mature and as a means to reduce risk while introducing new products with continually increasing blade lengths. However, as blade lengths continue to increase, the challenge of controlling blade mass becomes even more critical to enabling the associated levelized cost of energy reductions. Stiffer and stronger reinforcement fibers can help to resolve the challenges of meeting the loading demands while limiting the increase in weight, but these materials are substantially more expensive than the traditional E-glass fiber systems. One goal of this project and associated work is to identify pathways that improve the cost-effectiveness of carbon fiber such that it is the reinforcement of choice in the primary structural elements of wind blades. The use of heavy-tow textile carbon fiber material systems has been shown to reduce the blade mass by 30-31% when used in the spar cap and by up to 7% when used in edgewise reinforcement. A pultrusion cost model was developed to enable a material cost comparison that includes an accurate estimate of the intermediate manufacturing step of pultrusion for the carbon fiber composite. Material cost reductions were revealed in most cases for the heavy-tow textile carbon fiber compared to infused fiberglass. The use of carbon fiber in the edgewise reinforcement produced the most notable material cost reduction of 33% for the heavy-tow textile carbon fiber. The mass and cost savings observed when using carbon fiber in edgewise reinforcement demonstrate a clear opportunity of this design approach. A carbon fiber conversion cost model was expanded to include a characterization of manufacturing costs when using advanced conversion processes with atmospheric plasma oxidation. This manufacturing approach was estimated to reduce the cost of carbon fiber material systems by greater than 10% and can be used with textile carbon systems or traditional carbon fiber precursors. The pultrusion cost model was also used to assess the opportunity for using pultruded fiberglass in wind blades, studying conventional E-glass fiber reinforcement. When using pultruded fiberglass as the spar cap material for two design classifications, the blade weight was reduced by 6% and 9% compared to infused fiberglass. However, due to the relatively large share of the pultrusion manufacturing cost compared to fiber cost, the spar cap material cost increased by 12% and 7%. When considering the system benefits of reduced blade mass and potentially lower blade manufacturing costs for pultruded composites, there may be opportunity for pultruded E-glass in wind blade spar caps, but further studies are needed. There is a clearer outcome for using pultruded fiberglass in the edgewise reinforcement where it resulted in a blade mass reduction of 2% and associated reinforcement material cost reduction of 1% compared to infused E-glass. The use of higher performing glass fibers, such as S-glass and H-glass systems, will produce greater mass savings but a study is needed to assess the cost implications for these more expensive systems. The most likely opportunity for these high-performance glass fibers is in the edgewise reinforcement, where the increased strength will reduce the damage accumulation of this fatigue-driven component. The blade design assessments in this project characterize the controlling material properties for the primary structural components in the flapwise and edgewise directions for modern wind blades. The observed trends with low and high wind speed turbine classifications for carbon and glass fiber reinforced polymer systems help to identify where cost reductions are needed, and where improvements in mechanical properties would help to reduce the material demands.

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Freeplay is a common type of piecewise-smooth nonlinearity in dynamical systems, and it can cause discontinuity-induced bifurcations and other behaviors that may bring about undesirable and potentially damaging responses. Prior research has focused on piecewise-smooth systems with two or three distinct regions, but less attention is devoted to systems with more regions (i.e., multi-segmented systems). In this work, numerical analysis is performed on a dynamical system with multi-segmented freeplay, in which there are four stiffness transitions and five distinct regions in the phase space. The effects of the multi-segmented parameters are studied through bifurcation diagram evolution along with induced multi-stable behavior and different bifurcations. These phenomena are interrogated through various tools, such as harmonic balance, basins of attraction, phase planes, and Poincaré section analysis. Results show that among the three multi-segmented parameters, the asymmetry has the strongest effect on the response of the system.

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Strongly charged polyelectrolytes (PEs) demonstrate complex solution behavior as a function of chain length, concentrations, and ionic strength. The viscosity behavior is important to understand and is a core quantity for many applications, but aspects remain a challenge. Molecular dynamics simulations using implicit solvent coarse-grained (CG) models successfully reproduce structure, but are often inappropriate for calculating viscosities. To address the need for CG models which reproduce viscoelastic properties of one of the most studied PEs, sodium polystyrene sulfonate (NaPSS), we report our recent efforts in using Bayesian optimization to develop CG models of NaPSS which capture both polymer structure and dynamics in aqueous solutions with explicit solvent. We demonstrate that our explicit solvent CG NaPSS model with the ML-BOP water model [Chan et al. Nat Commun 10, 379 (2019)] quantitatively reproduces NaPSS chain statistics and solution structure. The new explicit solvent CG model is benchmarked against diffusivities from atomistic simulations and experimental specific viscosities for short chains. We also show that our Bayesian-optimized CG model is transferable to larger chain lengths across a range of concentrations. Overall, this work provides a machine-learned model to probe the structural, dynamic, and rheological properties of polyelectrolytes such as NaPSS and aids in the design of novel, strongly charged polymers with tunable structural and viscoelastic properties

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent -β. The static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension df. In three dimensions, df≈2.0 for 2.5≤β≤3.8, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find 1.0df1.34 for 2.1≤β≤2.9. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long-wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings.

Numerical simulations are used to study the dynamics of a developing suspension Poiseuille flow with monodispersed and bidispersed neutrally buoyant particles in a planar channel, and machine learning is applied to learn the evolving stresses of the developing suspension. The particle stresses and pressure develop on a slower time scale than the volume fraction, indicating that once the particles reach a steady volume fraction profile, they rearrange to minimize the contact pressure on each particle. We consider the timescale for stress development and how the stress development connects to particle migration. For developing monodisperse suspensions, we present a new physics-informed Galerkin neural network that allows for learning the particle stresses when direct measurements are not possible. We show that when a training set of stress measurements is available, the MOR-physics operator learning method can also capture the particle stresses accurately.

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The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. This means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

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There is an increasing aspiration to utilize machine learning (ML) for various tasks of relevance to national security. ML models have thus far been mostly applied to tasks and domains that, while impactful, have sufficient volume of data. For predictive tasks of national security relevance, ML models of great capacity (ability to approximate nonlinear trends in input-output maps) are often needed to capture the complex underlying physics. However, scientific problems of relevance to national security are often accompanied by various sources of sparse and/or incomplete data, including experiments and simulations, across different regimes of operation, of varying degrees of fidelity, and include noise with different characteristics and/or intensity. State-of-the-art ML models, despite exhibiting superior performance on the task and domain they were trained on, may suffer detrimental loss in performance in such sparse data environments. This report summarizes the results of the Laboratory Directed Research and Development project entitled Trust-Enhancing Probabilistic Transfer Learning for Sparse and Noisy Data Environments. The objective of the project was to develop a new transfer learning (TL) framework that aims to adaptively blend the data across different sources in tackling one task of interest, resulting in enhanced trustworthiness of ML models for mission- and safety-critical systems. The proposed framework determines when it is worth applying TL and how much knowledge is to be transferred, despite uncontrollable uncertainties. The framework accomplishes this by leveraging concepts and techniques from the fields of Bayesian inverse modeling and uncertainty quantification, relying on strong mathematical foundations of probability and measure theories to devise new uncertainty-aware TL workflows.

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A digital twin has intelligent modules that continuously monitor the condition of the individual components and the whole of a system. Digital twins can provide nuclear power plants (NPP) operators an unprecedented level of monitoring, control, supervision, and security by contributing a greater volume of data for more comprehensive data analysis and increased accuracy of insights and predictions for decision making throughout the entire NPP lifecycle. NPP operators and managers have historically relied on limited, second hand or incomplete data. With proper implementation, digital twins can provide a central hub of all intel that allows for a multidisciplinary view of an NPP. This equips operators and managers with the ability to have more information, context, and intel that can be used for greater granularity during planning and decision making. Digital twins can be used in many activities as the technology has many different concepts surrounding it. From the various definitions of a digital twin within the industry, digital twins can be differentiated by levels of integration/automation. The three main models include digital model, digital shadow, and digital twin. Digital twins offer many potential advancements to the nuclear industry that could reduce costs, improve designs, provide safer operation, and improve their overall security.

A new approach to analytically derive constitutive stress-strain relationships from modeling the work hardening behavior of alloys was developed for assessing the strength and ductility of the Ti-6Al-4V alloy. This new approach is now successfully applied for assessing the quasi-static stress-strain behavior of an additively manufactured 304L sample. A predictive capability of this modelling approach may then be extended to model material stress-strain behavior at higher strain rates of loading.

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Plasma distribution in 3D space is heavily influenced by complex surfaces and the coupling interactions between plasma properties and interfacing material properties. For example, guided streamers that transition to surface ionization waves (SIWs) and propagate over structured dielectrics experience field enhancements that can lead to localized increases in ionization rates and complex 3D configurations that are difficult to analyze. Investigating these configurations requires techniques than can provide a more complete 3D picture. To help address this capability gap, a tomographic optical emission spectroscopy (tomo-OES) diagnostic system has been developed at Sandia National Laboratories that can resolve SIWs. The system includes four intensified cameras that measure the angular projections of the plasma light emission through bandpass filters. A dot calibration target co-registers each angular projection to the same voxel grid and an algebraic reconstruction technique (ART) recovers the light intensity at each voxel. An atmospheric pressure plasma jet (APPJ), provided by Peter Bruggeman, has been investigated and representative results are shown in Figure 1. Here, a bandpass filter was used to isolate emission from the N₂ second positive system (SPS) at 337.1 nm to capture the transition of the streamer to SIW on a planar dielectric surface (relative permittivity 3.3) located 3 mm below the APPJ [3]. The surface wave velocity was 3.5x10⁴ (m/s), consistent with measurements made by Steven Shannon. Characterization of this APPJ will support the group effort of standing up a reproducible APPJ across institutions for applications such as liquid treatment, catalysis, and plasma aided combustion. Future work will investigate non-planar surfaces and eventually develop tomographic laser-induced fluorescence (tomo-LIF) approaches.

Poster communicating our work in SHASTA project for the upcoming GSA conference.

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In the dynamic landscape of Operational Technology (OT), and specifically the emerging landscape for Advanced Reactors, the establishment of trust between digital assets emerges as a challenge for cybersecurity modernization. This report reviews existing approaches to authentication in Enterprise environments, and proposed methods for authentication in OT, and analyzes each for its applicability to future Advanced Reactor digital networks. Principles of authentication ranging from underlying cryptographic mechanisms to trust authorities are evaluated through the lens of OT. These facets emphasize the importance of mutual authentication in real-time environments, enabling a paradigm shift from the current approach of strong boundaries to a more malleable network that allows for flexible operation. This work finds that there is a need for evaluation and decision making by industry stakeholders, but current technologies and approaches can be adapted to fit needs and risk tolerances.

The International Database of Reference Gamma-Ray Spectra of Various Nuclear Matter is designed to hold curated gamma spectral data and will be hosted by the International Atomic Energy Agency on its public facing web site. Currently, the database to be hosted is given to the International Atomic Energy Agency by Sandia. This document describes the application used by Sandia to load spectral data into a database.

The ability to track the concentrations of specific molecules in the body in real time would significantly improve our ability to study, monitor, and respond to diseases. To achieve this, we require sensors that can withstand the complex environment inside the body. Electrochemical aptamer-based sensors are particularly promising for in vivo sensing, as they are among the only generalizable sensing technologies that can achieve real-time molecular monitoring directly in blood and the living body. In this project, we first focused on extending the application space of aptamer sensors to support minimally-invasive wearable measurements. To achieve this, we developed individually-addressable sensors with commercial off-the-shelf microneedles. We demonstrated sensor function in buffer, blood, and porcine skin (a common proxy for human skin). In addition to the applied sensing project, we also worked to improve fundamental understanding of the aptamer sensing platform and how it responds to biomolecular interferents. Specifically, we explored the interfacial dynamics of biofouling – a process impacting sensors placed in complex fluids, such as blood.

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We describe a direct magneto-optical approach to measuring the magnetic field driven by a narrow pulse width (<10 ns), 20 kA electrical current flow in the transmission line of a high energy pulsed power accelerator. The magnetic field and electrical current are among the most important operating parameters in a pulsed power accelerator and are critical to understanding the properties of the radiation output. However, accurately measuring these fields and electrical currents using conventional pulsed power diagnostics is difficult due to the strength of ionizing radiation and electromagnetic interference. Our approach uses a fiber coupled laser beam with a rare earth element sensing crystal sensor that is highly resistant to electromagnetic interference and does not require external calibration. Here, we focus on device theory, operating parameters, results from an experiment on a high energy pulsed power accelerator, and comparison to a conventional electrical current shunt sensor.

Nonlinear modeling and optimization is a valuable tool for aiding decisions by engineering practitioners, but programming an optimization problem based on a complex electrical, mechanical, or chemical process is a time-consuming and error-prone activity. Therefore, there is a need for model analysis and debugging tools that can detect and diagnose modeling errors. One such tool is the Dulmage–Mendelsohn decomposition, which identifies structurally under- and over-determined subsets in systems of equations and variables by partitioning the bipartite graph of the system. This work provides the necessary background to understand the Dulmage–Mendelsohn decomposition and its application to the analysis of nonlinear optimization problems, demonstrates its use in diagnosing a variety of modeling errors, and introduces software implementations for analyzing nonlinear optimization problems in the Pyomo and JuMP algebraic modeling languages.

In this paper, an approach for 3D plasma structure diagnostics using tomographic optical emission spectroscopy (Tomo-OES) of a nanosecond pulsed atmospheric pressure plasma jet (APPJ) is presented. In contrast to the well-known Abel inversion, Tomo-OES does not require cylindrical symmetry to recover 3D distributions of plasma light emission. Instead, many 2D angular projections are measured with intensified cameras and the multiplicative algebraic reconstruction technique is used to recover the 3D distribution of light emission. This approach solves the line-of-sight integration problem inherent to optical diagnostics, allowing recovery of localized OES information within the plasma that can be used to better infer plasma parameters within complex plasma structures. Here, Tomo-OES was applied to investigate an APPJ operated with helium in ambient air and impinging on planar and structured dielectric surfaces. Surface charging caused the guided streamer from the APPJ to transition to a surface ionization wave (SIW) that propagated along the surface. The SIW experienced variable geometrical and electrical material properties as it propagated, leading to 3D configurations that were non-symmetric and spatially complex. Light emission from He, N 2 + , and N2 were imaged at ten angular projections and the respective time-resolved 3D emission distributions in the plasma were then reconstructed. The spatial resolution of each tomographic reconstruction was 7.4 µm and the temporal resolution was 5 ns, sufficient to observe the guided streamer and the effects of the structured surface on the SIW. Emission from He showed the core of the jet and emission from N 2 + and N2 indicated effects of entrainment of ambient air. Penning ionization of N2 created a ring or outer layer of N 2 + that spatially converged to form the ‘plasma bullet’ or spatially diverged across a surface as part of a SIW. The SIW entered trenches of size 150 µm, leading to decreases in plasma light emission in regions above the trenches. The plasma light emission was higher in some regions with trenches, possibly due to effects of field enhancement.

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