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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Optimized manufacturing process for multilayer two-dimensional focusing mirrors in laboratory X-ray applications

Recent advances in laboratory X-ray applications require high-performance optical components that achieve exceptional imaging resolution and beam uniformity within compact experimental setups. Montel mirrors have become a preferred solution due to their unique dual-reflection focusing mechanism and a space-efficient design. Here, in this study, we present an effective manufacturing process for producing Montel mirrors tailored to focus laboratory X-ray beams. The mirrors were fabricated from single-crystal silicon substrates, chosen for their high mechanical stability and compatibility with precision polishing techniques. Our approach begins with the integration of a deterministic chemo-mechanical polishing (CMP)-based pre-shaping step followed by ion beam figuring (IBF), significantly improving manufacturing efficiency. Subsequently, our custom-developed advanced metrology and IBF techniques were employed for fabricating an off-axis, elliptical cylinder Montel mirror system with a 6-mrad total slope, with stringent optical specifications. While post-IBF processes, including multilayer coating, dicing, and gluing, introduced minor surface errors, yet their impact on performance remained negligible. The Montel mirrors manufactured with the optimized process exhibited significantly improved beam uniformity and a reduced focal spot size. These findings validate our approach as a viable solution for high-precision Montel mirror fabrication and facilitate further advancements in laboratory X-ray applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Parametric study and speciation analysis of rare earth precipitation using oxalic acid in a chloride solution system

Oxalic acid precipitation is a common step in the purification of rare earth elements (REE) from a concentrated pregnant leach solution (PLS). However, the presence of contaminants such as Al, Fe, and Ca in given amounts decreases the REE precipitation efficiency and product purity while also increasing the amount of oxalic acid needed to maximize recovery. As such, a statistically designed test program was performed to identify the optimal conditions necessary for a relatively low REE content PLS containing elevated concentrations of contaminant ions. The performance objective was maximization of REE precipitation efficiency while minimizing the oxalic acid dosage. A central composite design was utilized to quantify performance impacts and identify the ultimate set of parameter values for oxalic acid dosage, Fe(III) contamination concentration, solution pH, and reaction temperature. The resultant model suggested that oxalic acid dosage and reaction pH are the most significant factors for the REE precipitation efficiency, followed by the interaction of oxalic dosage and Fe concentration. Test results indicate that increasing the oxalic acid concentration from 0 g/L to 80 g/L improved the REE precipitation efficiency from approximately 4.2% to 95.0%. Furthermore, raising the solution pH from 0.5 to 2.5 considerably enhanced the precipitation efficiency from 0.0% to 98.9%. A solution temperature elevation decreased REE recovery, which indicated an exothermic reaction between REEs and oxalate anions. Finally, a high level of Fe contamination adversely impacted REE precipitation efficiency. Here, to further the understanding of the REE-oxalate system, a fundamental solution chemistry study was performed using the equilibrium constants of the reactions. The study resulted in the development of oxalate speciation diagrams and provided an analysis of the REE precipitation characteristics at various oxalate anion concentrations and Fe(III) contamination levels using MINTEQ software. The dominant Fe(III) species in the solution system were found to be Fe-(C 2 O 4 ) 3 3- , Fe-(C 2 O 4 ) 2- , and Fe-(C 2 O 4 ) + , which consume the majority of the oxalate anions. The simulated model was found to be in agreement with the experimental findings and helped to explain the adverse impact of increased iron concentrations on REE precipitation efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Climate Vulnerability Assessment and Resilience Planning for Idaho National Laboratory

Idaho National Laboratory’s (INL’s) mission is to discover, demonstrate, and secure innovative nuclear energy solutions, other clean energy options, and critical infrastructure. This INL’s Climate Vulnerability Assessment and Resilience Plan (VARP) was developed to enable and sustain that mission while ensuring the viability of operations considering expected climate change impacts. The VARP was developed according to the narrative requirements from the “Vulnerability Assessment and Resilience Planning Guidance, Version 1.2” document issued in February 2022. A prescribed process was used to identify mission-critical systems and components, determine historical and expected climate impacts, and develop resilient solutions. Experts from across INL, including operations staff, researchers, and climate scientists supplied input to the process. Analyses of climate modeling sources revealed that under scenarios of higher and lower greenhouse gas emissions (Representative Concentration Pathway (RCP) 4.5 and RCP 8.5), INL anticipates an increase in climate hazards, including drought, heat waves, wildfire, and precipitation. Increased frequency and duration of climatic hazards forecasts high impacts on certain mission-critical asset and infrastructure types. Utilizing the VARP Risk Assessment Tool, projected high climate hazard impacts across multiple asset and infrastructure types at the INL include energy generation and distribution systems, Site buildings, specialized or mission-critical equipment, and transportation and fleet infrastructure. Some of these mission-critical asset and infrastructure types maintain high adaptive capacity to climatic changes; however, others may need additional adaptive capacity to withstand increased frequency and duration of climate hazards. INL identified close to 300 resilient solutions that were consolidated into 11 solution categories to be tracked in the Department of Energy Sustainability Dashboard. The identified solutions are a starting point for future project development and analysis. These data are intended to inform decision makers on climate issues and potential solutions across INL and associated communities. The VARP is not intended to be a budget tool or project decision document on its own, but rather one of many tools used by decision makers to establish resilient priorities. This initial document provides the framework and foundation to resilient solutions. In the coming years, each solution needs to be fully developed, costed, and prioritized based on mission-critical risk and funding priorities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

An evolutionarily conserved tryptophan cage promotes folding of the extended RNA recognition motif in the hnRNPR ‐like protein family

Abstract The heterogeneous nuclear ribonucleoprotein (hnRNP) R‐like family is a class of RNA binding proteins in the hnRNP superfamily with diverse functions in RNA processing. Here, we present the 1.90 Å X‐ray crystal structure and solution NMR studies of the first RNA recognition motif (RRM) of human hnRNPR. We find that this domain adopts an extended RRM (eRRM1) featuring a canonical RRM with a structured N‐terminal extension (N ext ) motif that docks against the RRM and extends the β‐sheet surface. The adjoining loop is structured and forms a tryptophan cage motif to position the N ext motif for docking to the RRM. Combining mutagenesis, solution NMR spectroscopy, and thermal denaturation studies, we evaluate the importance of residues in the N ext –RRM interface and adjoining loop on eRRM folding and conformational dynamics. We find that these sites are essential for protein solubility, conformational ordering, and thermal stability. Consistent with their importance, mutations in the N ext –RRM interface and loop are associated with several cancers in a survey of somatic mutations in cancer studies. Sequence and structure comparison of the human hnRNPR eRRM1 to experimentally verified and predicted hnRNPR‐like proteins reveals conserved features in the eRRM.

Biochemistry & Molecular Biology↗
DOE OSTI2022

Optimizing power system restoration with damaged communications

Utility procedures for power system blackstart and restoration typically assume that energization decisions can be reliably communicated across the grid. In reality, the communications and control network would likely also be affected in power outages, such as those caused by extreme weather events or cyber-attacks. This paper studies the effect of damage to the power system communications and control infrastructure on restoration operations following a blackout. We model the communications infrastructure as a graph, overlaying the power grid, and imposing the requirement that every energized element in the power grid be observable from a control center. We expand on a specialized branch-and-bound algorithm from the literature to optimize the restoration process and devise an initialization heuristic and a rounding heuristic to improve solution speed. We perform numerical experiments on synthetic systems for Illinois and Texas with outages based on a solar flare or hurricane. We compare the results of our specialized branch-and-bound algorithm to the results from (i) the initialization heuristic alone, (ii) a variation of this heuristic that we use as a baseline, and (iii) the restoration optimization for the power system without communications constraints. Here, we find that damage to the communications infrastructure significantly increases the time required to re-energize the grid. Moreover, by simultaneously optimizing communications repairs and grid energization decisions, we are able to re-energize the grid significantly faster than if communications repairs and energization decisions were made independently or with partial coordination, motivating improvements to current industry practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Real-time biomass feedstock particle quality detection using image analysis and machine vision

Abstract A common and costly challenge in the nascent biorefinery industry is the consistent handling and conveyance of biomass feedstock materials, which can vary widely in their chemical, physical, and mechanical properties. Solutions to cope with varying feedstock qualities will be required, including advanced process controls to adjust equipment and reject feedstocks that do not meet a quality standard. In this work, we present and evaluate methods to autonomously assess corn stover feedstock quality in real time and provide data to process controls with low-cost camera hardware. We explore the use of neural networks to classify feedstocks based on actual processing behavior and pixel matrix feature parameterization to further assess particle attributes that may explain the variable processing behavior. We used the pretrained ResNet neural network coupled with a gated recurrent unit (GRU) time-series classifier trained on our image data, resulting in binary classification of feedstock anomalies with favorable performance. The textural aspects of the image data were statistically analyzed to determine if the textural features were predictive of operational disruptions. The significant textural features were angular second moment, prominence, mean height of surface profile, mean resultant vector, shade, skewness, variation of the polar facet orientation, and direction of azimuthal facets. Expansion of these models is recommended across a wider variety of labeled feedstock images of different qualities and species to develop a more robust tool that may be deployed using low-cost cameras within biorefineries.

09 BIOMASS FUELS↗
DOE OSTI2024

Off-axis and nonplanar slicing

Traditionally, slicing processes have assumed a horizontal plane that moves up the Z axis to produce layers. However, through relatively straightforward modifications, this process can be extended to allow planar slicing at any angle and along any axis in a process referred to as off-axis slicing. Additionally, more advanced pathing solutions are moving away from planar approaches entirely by printing directly on non-flat surfaces. Both of these alternative approaches to slicing, as well as some common issues associated with them, are discussed in this chapter to provide a foundation for more advanced pathing solutions.

Borish, Michael↗
DOE OSTI2022

Partitioning behavior and mechanisms of rare earth elements during precipitation in acid mine drainage

Rare earth elements (REEs) are frequently found concentrated in acid mine drainage (AMD). The recovery of REEs from AMD has been successfully achieved using selective chemical precipitation. However, a portion of the REEs is often lost to the precipitates of the dominant metal contaminant ions. To better understand the REE partitioning behavior and mechanisms during the precipitation process, a systematic study was performed on both natural and synthetic AMD solutions. Precipitation test results show that REE removal was noticeably elevated at pH 4.0 after adding H 2 O 2 to convert ferrous to ferric ions, causing nearly complete precipitation of iron. Solution equilibrium calculations suggested that the REE removal increase was realized through adsorption onto the surfaces of the ferric precipitates. The presence of aluminum species in the solutions reduced the adsorption of REEs on the ferric precipitates. Based on electro-kinetic test results, it was concluded that aluminum species neutralize the negative surface charge of the ferric precipitates and compete with REEs for the adsorption active sites. The presence of ferrous ions in the solutions reduced REE adsorption on the aluminum precipitates at lower pH values (e.g., 5.0) due to competitive adsorption. However, at higher pH values (e.g., 6.0), REE removal to the precipitate product increased due to the precipitation of ferrous ions. Additionally, to the electro-kinetic tests and solution equilibrium calculations, mineralogy characterization, specific surface area measurement, particle size analysis, and morphology analysis were also conducted to investigate and identify the partitioning mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Regression models using shapes of functions as predictors

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the $\mathbb L^2$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. In this paper, we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Electro-osmo-dialysis through nanoporous layers physically conjugated to micro-perforated ion-exchange membranes: Highly selective accumulation of trace coions

This study explores theoretically and numerically the phenomenon of counter-flow accumulation of trace coions during electro-osmo-dialysis through composite membranes containing nanoporous and perforated ion-exchange layers. The combination of charged nanopores and perforations allows electroosmosis, and ion concentration polarization appears near the ion-exchange layer. Accumulation of trace coions occurs because their advective and electromigration flow velocity components have opposite signs and are locally compensating in depletion regions where electric fields are high. This local compensation of flow components can give rise to high accumulation factors (>1000 in some cases) for trace coions at some distance from the interface between the nanoporous and ion-exchange layers. Moreover, the extent of this accumulation depends on the trace-coion diffusion coefficient. The resulting selectivity between different coions might serve as a basis for environmentally friendly separation of ionic species such as synthetic peptides or rare-earth elements. For example, a periodic process might include accumulation followed by species release into smaller volumes of solution. For both rare-earth ions and peptide-like species, the accumulation selectivity between ions with small differences in mobilities depends on system parameters such as nanoporous-layer thickness, distance between the perforations, and the zeta potential of the nanopore surface. Here, the use of optimal values of these membrane parameters may enable tuning of the electro-osmo-dialysis system for separation of specific ions. Modelling reveals that despite inhomogeneous patterns of fluid and ion flows close to the nanoporous/perforated ion-exchange interface, at relatively short distances from this interface (less than half the distance between the perforations) all the flows become practically one-dimensional (1D). Similarly, the concentration profiles of trace coions also become 1D. The flow one-dimensionality at short distances from the current-polarized interface enables a simple 1D approximation that is useful for an approximate analysis of trends in this multi-parameter system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Energy and exergy analysis of multi-stage vacuum membrane distillation integrated with mechanical vapor compression

Membrane distillation (MD) is a promising candidate for desalinating hypersaline brine, but its poor energy efficiency has remained a major barrier for widespread application. One possible solution to this issue is to recover the latent heat in the process. In this work, a multi-stage vacuum MD (MSVMD) was integrated with a mechanical vapor compressor (MVC) to enhance the latent heat recovery, and the energetic and exergetic performance of this integrated process was examined. A comprehensive energy and exergy analysis is provided to compare MSVMD and MSVMD-MVC processes for desalination of hypersaline brine. This analysis was conducted by examining the effect of the compression ratio on the energetic and exergetic performance, and the findings are reported in terms of specific thermal energy consumption (STEC), specific electricity consumption (SEC), and exergetic efficiency. The energy analysis shows that thermal energy consumption can be reduced as the compression ratio increases, due to the enhancement of latent heat recovery. The MSVMD-MVC process can be operated in a steady-state condition, without the need for thermal heat input; with STEC and SEC of 0 and 49 kWh/m 3 at the feed temperature of 50 °C and MVC compression ratio of 2.14. Moreover, exergy analysis demonstrates the efficacy of the eNRTL model in exergy calculation. Exergy destruction can be greatly reduced by increasing the compression ratio to an optimal value. For high salinity brine (124 g/L), MSVMD-MVC achieved a higher exergetic efficiency of 6.85%, compared to 2.42% in MSVMD. Furthermore, the result suggests that the application of MVC can intensify the energy efficiency and exergetic efficiency of the MSVMD system, although this process cannot outperform the current desalination technologies from the standard primary energy point of view.

42 ENGINEERING↗
DOE OSTI2022

Advancing Chemical Separations: Unraveling the Structure and Dynamics of Phase Splitting in Liquid–Liquid Extraction

Liquid-liquid extraction (LLE), the go-to process for a variety of chemical separations, is limited by spontaneous organic phase splitting upon sufficient solute loading, called third phase formation. In this study we explore the applicability of critical phenomena theory to gain insight into this deleterious phase behavior with the goal of improving separations efficiency and minimizing waste. Here, a series of samples representative of rare earth purification were constructed to include each of one light and one heavy lanthanide (cerium and lutetium) paired with one of two common malonamide extractants (DMDOHEMA and DMDBTDMA). The resulting postextraction organic phases are chemically complex and often form rich hierarchical structures whose statics and dynamics near the critical point were probed herein with small-angle X-ray scattering and high-speed X-ray photon correlation spectroscopy. Despite their different extraction behaviors, all samples show remarkably similar critical behavior with exponents well described by classical critical point theory consistent with the 3D Ising model, where the critical behavior is characterized by fluctuations with a single diverging length scale. This unexpected result indicates a significant reduction in relevant chemical parameters at the critical point, indicating that the underlying behavior of phase transitions in LLE rely on far fewer variables than are generally assumed. The obtained scalar order parameter is attributed to the extractant fraction of the extractant/diluent mixture, revealing that other solution components and their respective concentrations simply shift the critical temperature but do not affect the nature of the critical fluctuations. These findings point to an opportunity to drastically simplify studies of liquid-liquid phase separation and phase diagram development in general while providing insights into LLE process improvement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Self-Aligned Fluorinated-Organic Ligand for Boosting the Performance of Perovskite Solar Cells

Surface passivation is evident to be one of the most efficient approaches to achieve high efficiency with superior stability of perovskite solar cells (PeSCs). However, most previous approaches to surface passivation involve adding an additional coating process either before or after perovskite film fabrication, thereby introducing an extra processing step and significantly increasing production costs. Here, a simple yet novel one-step interfacial passivation approach was implemented by utilizing the self-aligning properties of fluorinated organic ligands (F4TmI) within a perovskite precursor solution. The inherent propensity of the ligand to spontaneously anchor onto the surface of perovskite guides the crystallization process of perovskites, thus largely enhancing the device performance and humidity stability. The optimized F4TmI-based devices achieved an efficiency of 21.1%, surpassing that of the control (19.8%). Furthermore, the device stability significantly improved after the incorporation of F4TmI, maintaining 78.9 and 95.1% of its initial efficiency after aging at 60 °C and 60% relative humidity, respectively, for 330 h.

14 SOLAR ENERGY↗
DOE OSTI2020

Self-Assembly of Metallo-Supramolecules under Kinetic or Thermodynamic Control: Characterization of Positional Isomers Using Scanning Tunneling Spectroscopy

Coordination-driven self-assembly has been extensively employed to construct a variety of discrete structures as a bottom-up strategy. However, mechanistic understanding regarding whether self-assembly is under kinetic or thermodynamic control is less explored. To date, such mechanistic investigation has been limited to distinct, assembled structures. It still remains a formidable challenge to study the kinetic and thermodynamic behavior of self-assembly systems with multiple assembled isomers due to the lack of characterization methods. Herein, we use a stepwise strategy which combined self-recognition and self-assembly processes to construct giant metallo-supramolecules with 8 positional isomers in solution. With the help of ultrahigh-vacuum, low-temperature scanning tunneling microscopy and scanning tunneling spectroscopy, we were able to unambiguously differentiate 14 isomers on the substrate which correspond to 8 isomers in solution. Through measurement of 162 structures, the experimental probability of each isomer was obtained and compared with the theoretical probability. Finally, such a comparison along with density functional theory (DFT) calculation suggested that although both kinetic and thermodynamic control existed in this self-assembly, the increased experimental probabilities of isomers compared to theoretical probabilities should be attributed to thermodynamic control.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Mountainous Floodplain Connectivity in Response to Hydrological Transitions

In mountainous watersheds, floodplain sediments are typically characterized by gravel bed layers capped by an overlying soil unit that serves as a hotspot for biogeochemical reactivity. However, the influence of soil biogeochemistry on gravel bed underflow composition remains unclear, especially during hydrological transitions that alter the vertical connectivity between overlaying soils and the underlying gravel bed. This study investigates these dynamics by measuring hydraulic gradients and water compositions over three hydrological years in a typical mountainous, low-order stream floodplain in the Upper Colorado River Basin. Results indicate that the timing of hydrological conditions strongly influences the vertical exchanges that control water quality. Specifically, during flooding events such as beaver ponding, that induce downward flushing of the soil, anoxic conditions prevalent in the biogeochemically active soil are transferred downstream via gravel bed underflow. Conversely, snowmelt and drought conditions increase oxic conditions in the gravel bed due to diminished hydrological connectivity with the overlying soil. To compare water quality response to hydrological transitions across similar floodplain environments, we propose a conceptual model that quantifies the inundation-induced flushing of soil porewater to measure solute exchange efficiency with the gravel bed solute convergence efficiency (SCE). This model provides a framework for quantifying biogeochemical processes in hydrological underflow systems, which is critical for water and elemental budgets in these globally important mountainous ecosystems.

58 GEOSCIENCES↗
DOE OSTI2021

Curium(iii) radiation-induced reaction kinetics in aqueous media

Insight into the effects of radiolytic processes on the actinides is critical for advancing our understanding of their solution chemistry because the behaviour of these elements cannot be easily separated from the influence of their inherent radiation field. However, minimal information exists on the radiation-induced redox behaviour of curium (Cm), a key trivalent transuranic element present in used nuclear fuel and frequently used as an alpha radiation source. Here we present a kinetic study on the aqueous redox reactions of Cm(III) with radicals generated through the radiolysis of aqueous media. In particular, we probe reaction kinetics in nitric acid solutions that are used as the aqueous phase component of used nuclear fuel reprocessing solvent systems. Second-order rate coefficients (k) were measured for the reaction of Cm(III) with the hydrated electron (e aq - , k = (1.25 ± 0.03) × 10 10 M -1 s -1 ), hydrogen atom (H˙, k = (5.16 ± 0.37) × 10 8 M -1 s -1 ), hydroxyl radical (˙OH, k = (1.69 ± 0.24) × 10 9 M -1 s -1 ), and nitrate radical (NO 3 ˙, k = (4.83 ± 0.09) × 10 7 M -1 s -1 ). Furthermore, the first-ever Cm(II) absorption spectrum (300–700 nm) is also reported. These kinetic data dispel the status quo notion of Cm(III) possessing little to no redox chemistry in aqueous solution, and suggest that the resulting Cm(II) and Cm(IV) transients could exist in irradiated aqueous solutions and be available to undergo subsequent redox chemistry with other solutes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2021

Pore-scale simulation of drying in porous media using a hybrid lattice Boltzmann: pore network model

In this work, a hybrid method coupling a pseudo-potential lattice Boltzmann model (LBM) and a pore network model (PNM) to simulate drying in porous media is proposed. Based on the watershed method, the porous medium is firstly decomposed into pore regions. According to the liquid–vapor phase distribution at a given time, the pore regions are further divided into four pore types, namely two-phase pores where a liquid–vapor interface exists, buffer pores next to the two-phase pores, single-liquid and single-vapor phase pores. The pseudo-potential LBM is used in the two-phase and buffer pores to simulate liquid drying and track the movement of the interfaces, while the single-phase PNM simulations are conducted in the buffer and single-phase pores to simulate vapor or liquid flow. LBM and PNM are coupled in the buffer pores through exchange of boundary information. The hybrid method is applied to simulate liquid drying in a porous medium. The whole-domain LBM simulation is considered as the reference solution to validate the hybrid method. Liquid saturation variation during the drying process and detailed phase and pressure distributions obtained by the two methods match quite well, demonstrating the accuracy of the hybrid method. For the specific case studied, the hybrid method saves more than 60% computational time compared to the whole-domain LBM simulation. In addition, the speedup of the hybrid method becomes more significant for a larger computational domain. In summary, the hybrid method developed in this work combines the accuracy of LBM and the efficiency of PNM to simulate drying in porous media at pore scale and can lead to significant reduction of computation time, thus allowing the pore-scale consideration of drying in larger porous systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Greedy permanent magnet optimization

Abstract A number of scientific fields rely on placing permanent magnets in order to produce a desired magnetic field. We have shown in recent work that the placement process can be formulated as sparse regression. However, binary, grid-aligned solutions are desired for realistic engineering designs. We now show that the binary permanent magnet problem can be formulated as a quadratic program with quadratic equality constraints, the binary, grid-aligned problem is equivalent to the quadratic knapsack problem with multiple knapsack constraints, and the single-orientation-only problem is equivalent to the unconstrained quadratic binary problem. We then provide a set of simple greedy algorithms for solving variants of permanent magnet optimization, and demonstrate their capabilities by designing magnets for stellarator plasmas. The algorithms can a-priori produce sparse, grid-aligned, binary solutions. Despite its simple design and greedy nature, we provide an algorithm that compares with or even outperforms the state-of-the-art algorithms while being substantially faster, more flexible, and easier to use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗