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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Conceptual Design of the Reactor Cavity Cooling System for the Horizontal Compact High Temperature Gas Reactor (HC-HTGR)

Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe, low-cost HTGR. Argonne National Laboratory (Argonne) is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept. This report documents the design study to derive a conceptual design study of the RCCS for the HC-HTGR. It includes the identification of the functions and requirements of the HC-HTGR RCCS, design analyses including high-level design consideration and the calculations for optimizing design space of the system with supporting component-level analysis to inform the material selection and performance of the water panel, the description of the conceptual design of the HC-HTGR RCCS derived based on the analyses results, and performance evaluation of the conceptual RCCS for the HC-HTGR. A detailed concept of the RCCS has been identified and high-level system requirements has been developed for the HC-HTGR. Design space focusing on the natural circulation loop portion of the RCCS has been investigated to optimize the system performance. The initial baseline dimensions were firstly derived based on the scoping calculations. A component level design analysis was conducted for the water panel to inform the material selection and to assess its conduction performance. A preliminary system-level performance analysis was performed for the 1/8th of the compartment of the initial baseline design of the RCCS using RELAP5-3D. To improve the system thermal performance, the RCCS design has been updated by exploring various design options by design parametric analyses. Based on the results, the conceptual design of the RCCS for the HC-HTGR has been derived, which satisfies the target performance of ~1 MWt at the elevated vessel wall temperature conditions. Transient simulations were conducted for the conceptual RCCS design for the HC-HTGR under various operation modes and heat load conditions using RELAP5-3D. The system dynamics in different operating states was investigated and the system performance under transients of interest was evaluated. The results demonstrated the overall system feasibility that the RCCS design maintains structures temperatures lower than maximum allowable temperature with sufficient system inventory without any active heat removal in the design process with certain transients addressed. The HC-HTGR RCCS will have additional design updates of subsystems or optimization of the system components during the preliminary and final design phases. Since the entire plant has not been integrated yet, this delivered conceptual design is subject to changes for integration, that require additional conceptual design activities and Quality and Assurance implementation (Q&A). The performance assessment of the RCCS for the HC-HTGR will be then revisited and optimized to finalize the system design, and the RCCS integrated primary system analysis will be utilized to simulate selective accident scenarios of interest where efforts are currently undergoing in the project.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Pressure Drop in Seven-Pin Wire-Wrapped Rod Bundle for the Sodium Cartridge Loop in Versatile Test Reactor

This work studies the hydrodynamics of the seven pin wire-wrapped rod bundle in the sodium cartridge loop for the Versatile Test Reactor (VTR) through scaled water experiments and computational fluid dynamics (CFD) simulations. Here, the scaling analysis is first performed to demonstrate the hydrodynamic similarity between water and sodium flows at the same Reynolds number Re. A separate-effects test facility is designed and constructed based on the scaling analysis. Detailed experimental data on the pressure drop covering a wide range of Re values (1165 to 27 689) are obtained, which are used to evaluate existing correlations for friction factor and to benchmark CFD simulations. The experimentally determined friction factors f Exp agree well with the Upgraded Cheng and Todreas Detailed Correlation and Pacio-Chen-Todreas Detailed Model within ±7% but are significantly underpredicted by Rehme's correlation by 25%. Various CFD near-wall treatment methods are tested using ANSYS Fluent and evaluated by experimental data. It is found that when the recommended wall y + values are met, most of the near-wall treatment methods can give accurate friction factor predictions. The resolved near-wall method (y + ~ 1) with the Shear Stress Transport k - ω turbulence model and the scalable wall functions (y + > 12) with the realizable k - ε turbulence model can predict f Exp within ±5% The standard wall functions (y + > 30) and nonequilibrium wall functions (y + > 30) with the realizable k - ε model can predict f Exp within ±10%.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Scalable Federated Learning for Scientific Foundation Models on Leadership-Class Systems

Federated learning (FL) at leadership-class HPC systems remains largely unexplored, despite growing interest in deploying federated workflows on modern HPC systems. This paper provides the first system-level empirical characterization of federated fine-tuning of pretrained foundation models on an exascale supercomputer under a multi-node deployment. Using up to 96 concurrent FL clients deployed across Frontier nodes, we study the impact of client scale, model size, data heterogeneity, partial participation, and differential privacy on runtime, communication overhead, and convergence stability. Our results show that pretrained transformer models remain robust to heterogeneity, client dropout, and privacy noise, while system efficiency degrades rapidly with scale as synchronizat and orchestration dominate runtime. We further demonstrate that system-aware execution strategies, including intra-node aggregation and early aggregation, significantly reduce wall-clock time without degrading model quality. These findings establish a practical performance baseline and inform the design of communication-efficient FL systems on leadership-class HPC platforms.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗
DOE OSTI2023

Thorium and Rare Earth Monoxides and Related Phases

Thorium was a part of energy infrastructure in the 19th century due to the refractory and electronic properties of its dioxide. It will be a part of future energy infrastructure as the most abundant energy reserve based on nuclear fission. This paper discusses the solid-state chemistry of the monoxides and related rocksalt phases of thorium and the rare earths, both at atmospheric and at high pressure. The existence of solid thorium monoxide was first suggested more than 100 years ago; however, it was never obtained in bulk and has been studied mostly theoretically. Monoxides of lanthanides from Eu to Ho are ferromagnetic semiconductors sought for spintronics and were studied in thin films. La to Sm metallic monoxides were synthesized in bulk at pressures below 5 GPa. Recently, ThO formation in thin films has been reported and the stability of bulk ThO at high pressure was theoretically predicted based on first principles computations at 0 K. New ab initio computations were performed accounting for temperature effects up to 1000 K using lattice dynamics in the quasi-harmonic approximation. New computational results confirm the stabilization of pure ThO above 30 GPa and suggest the possibility of high-pressure synthesis of (Th,Nd)O at 1000 K and 5 GPa.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Lithium–Divertor Interactions and Helium/Hydrogen Trapping in Lithiated Metals (Final Technical Report)

The goal of this project was to develop a fundamental understanding of helium and hydrogen behavior in lithium, both in bulk and at interfaces with tungsten, in order to inform the design of lithium based plasma facing components for fusion devices. Over the course of the award, the project produced the first comprehensive, peer reviewed dataset describing helium energetics, migration behaviors, and defect interactions in lithium. The research demonstrated that helium behaves in ways not previously observed in any other body centered cubic (BCC) metal: its interstitial configurations are more stable than substitutional ones, and its migration barriers are extraordinarily low, in some cases more than an order of magnitude below those in tungsten or iron. These discoveries reveal that helium in lithium diffuses so rapidly that its transport may be dominated by translational motion rather than the vibrationally activated mechanisms that underpin conventional solid state diffusion. This work lays a scientific foundation for understanding gas retention, bubble formation, and wall evolution in lithium based fusion environments and provides new computational tools, most notably a newly developed Li–He interatomic potential, for advancing future modeling efforts.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Scaling the memory wall using mixed-precision - HPG-MxP on an exascale-class machine

Mixed-precision algorithms have been proposed as a way for scientific computing to benefit from some of the gains seen for AI on recent high performance computing (HPC) platforms. A few applications dominated by dense matrix operations have seen substantial speedups by utilizing low precision formats such as FP16. However, a majority of scientific simulation applications are memory bandwidth limited. Beyond preliminary studies, the practical gain from using mixed-precision algorithms on a given high-performance computing (HPC) system is largely unclear. The High Performance GMRES Mixed Precision (HPG-MxP) benchmark has been proposed to measure the useful performance of a HPC system on sparse matrix-based mixed-precision applications. In this work, we present an implementation of the HPG-MxP benchmark for an exascale system and describe our algorithm enhancements. We show for the first time a speedup of 1.6x using a combination of double- and single-precision keeping the same residual level on modern GPU-based supercomputers.

Kashi, Aditya [ORNL] (ORCID:0000000325893792)↗
DOE OSTI2022

Application of reference-free natural background–oriented schlieren photography for visualizing leakage sites in building walls

Air leakage in buildings can cause health and comfort concerns for occupants and can contribute to mold growth on building materials, or in extreme conditions, rot of building materials. Unwanted air leakage through the building envelope also contributes to approximately 4 quadrillion Btu (1172 TWh) of energy consumption per year in the building sector in the United States. Locating and sealing leakage sites can improve the energy efficiency, comfort, air quality, and moisture durability of the building stock. Typical methods of finding leakage sites, such as infrared imaging and smoke tracing, rely on concurrent blower door operation, which can also measure the total leakage rate of the building. Smoke tracing can be disruptive to occupants, and infrared imaging and smoke tracing cannot measure the contribution of individual leaks to prioritize sealing efforts. Here, an optical fluid flow imaging technique, reference-free natural background–oriented schlieren imaging, was adapted to visualize air exfiltration. This is the first step in developing a method to noninvasively locate and measure exfiltration or infiltration sites so that sealing efforts can be prioritized. Experimental results of this technique are presented, demonstrating the method's applicability to visualizing exfiltration through three common building claddings in an outdoor environment. Key variables impacting the performance of this technique when applied to building leakage are also discussed.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Effects of turbulence-radiation coupling in pressurized oxy-combustion

Concerns over climate change have led to numerous efforts in developing low-carbon energy technologies. Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emission in power generation. Due to the strong impact of pressure on thermal radiation, heat transfer in POC differs significantly from the situation of conventional atmospheric pressure combustion. Thus thermal radiation in POC needs to be investigated to aid new combustor development. The present computational work is a step in this direction, initiating a systematic analysis of thermal radiation and heat transfer in a pilot-scale POC combustor, which has been developed at Washington University in St. Louis (WUSTL). In a POC process, pulverized coal is burned under elevated pressure and O2-CO2 environment. While most previous computational works on flame radiation focused on atmospheric pressure condition, this work considered a pressurized flame. Specifically, a 15-bar POC combustor of power 50 kW is modeled employing the Ansys FLUENT commercial platform, using both Reynolds-averaged Navier-Stokes (RANS) modeling and large-eddy simulation (LES). A recently published and validated global radiation model is used to predict the radiative property of the flue gas. The discrete ordinates (DO) radiation model is chosen to solve the radiative transport equation. Incident radiation on the walls of the combustor is identified and investigated. It is revealed that for this pilot-scale, pressurized combustor, thermal radiation exhibits similar patterns in the RANS and LES models. However, the magnitudes of radiation are different in both models, presumably because interactions between radiation and turbulence are embedded in the LES model but not in the RANS model. This difference thereby underlines the major goal of this research: investigating the impact of such turbulence-to-radiation coupling on thermal radiation in a pilot-scale POC setting. Most previous studies on turbulence-to-radiation interactions focused on bench-scale, atmospheric pressure flames. This work is the first effort to extend this study to a pilot-scale, pressurized flame.

Li, Lei↗
DOE OSTI2021

Acute Stent-Induced Endothelial Denudation: Biomechanical Predictors of Vascular Injury

Recent concern for local drug delivery and withdrawal of the first Food and Drug Administration-approved bioresorbable scaffold emphasizes the need to optimize the relationships between stent design and drug release with imposed arterial injury and observed pharmacodynamics. In this study, we examine the hypothesis that vascular injury is predictable from stent design and that the expanding force of stent deployment results in increased circumferential stress in the arterial tissue, which may explain acute injury poststent deployment. Using both numerical simulations and ex vivo experiments on three different stent designs (slotted tube, corrugated ring, and delta wing), arterial injury due to device deployment was examined. Furthermore, using numerical simulations, the consequence of changing stent strut radial thickness on arterial wall shear stress and arterial circumferential stress distributions was examined. Regions with predicted arterial circumferential stress exceeding a threshold of 49.5 kPa compared favorably with observed ex vivo endothelial denudation for the three considered stent designs. In addition, increasing strut thickness was predicted to result in more areas of denudation and larger areas exposed to low wall shear stress. We conclude that the acute arterial injury, observed immediately following stent expansion, is caused by high circumferential hoop stresses in the interstrut region, and denuded area profiles are dependent on unit cell geometric features. Such findings when coupled with where drugs move might explain the drug–device interactions.

Conway, Claire↗
DOE OSTI2025

Long-Range Charge Transport Facilitated by Electron Delocalization in MoS 2 and Carbon Nanotube Heterostructures

Controlling charge transport at the interfaces of nanostructures is crucial for their successful use in optoelectronic and solar energy applications. Mixed-dimensional heterostructures based on single-walled carbon nanotubes (SWCNTs) and transition metal dichalcogenides (TMDCs) have demonstrated exceptionally long-lived charge-separated states. However, the factors that control the charge transport at these interfaces remain unclear. In this study, we directly image charge transport at the interfaces of single- and multilayered MoS 2 and (6,5) SWCNT heterostructures using transient absorption microscopy. We find that charge recombination becomes slower as the layer thickness of MoS 2 increases. This behavior can be explained by electron delocalization in multilayers and reduced orbital overlap with the SWCNTs, as suggested by nonadiabatic (NA) molecular dynamics (MD) simulations. Dipolar repulsion of interfacial excitons results in rapid density-dependent transport within the first 100 ps. Stronger repulsion and longer-range charge transport are observed in heterostructures with thicker MoS 2 layers, driven by electron delocalization and larger interfacial dipole moments. These findings are consistent with the results from NAMD simulations. Our results suggest that heterostructures with multilayer MoS 2 can facilitate long-lived charge separation and transport, which is promising for applications in photovoltaics and photocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Pith–specific lignification in Nicotiana attenuata as a defense against a stem–boring herbivore

Plants have developed tissue-specific defense strategies in response to various herbivores with different feeding habits. Although defense responses to leaf-chewing insects have been well studied, little is known about stem-specific responses, particularly in the pith, to stem-boring herbivores. To understand the stem-specific defense, we first conducted a comparative transcriptomic analysis of the wild tobacco Nicotiana attenuata before and after attack by the leaf-chewing herbivore Manduca sexta and the stem borer Trichobaris mucorea. When the stem-boring herbivore attacked, lignin-associated genes were upregulated specifically in the inner parenchymal cells of the stem, the pith; lignin also accumulated highly in the attacked pith. Silencing the lignin biosynthetic gene cinnamyl alcohol dehydrogenase enhanced the performance of the stem-boring herbivore but had no effect on the growth of the leaf-chewing herbivore. Two-dimensional nuclear magnetic resonance results revealed that lignified pith contains feruloyltyramine as an unusual lignin component in the cell wall, as a response against stem-boring herbivore attack. Pith-specific lignification induced by the stem-boring herbivore was modulated by both jasmonate and ethylene signaling. Furthermore, these results suggest that lignin provides a stem-specific inducible barrier, protecting plants against stem-boring insects.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Analysis of runaway electron driven whistler wave instability experiments

Data acquired on the DIII-D tokamak were analyzed. The data are from experiments that were conducted to study an instability that is driven unstable by intense populations of electrons with MeV energies that are known as runaway electrons. The instability is a type of plasma wave called a whistler wave that occurs at frequencies above the ion cyclotron frequency but well below the electron cyclotron frequency. The waves were measured by magnetic fluctuation coils that are embedded in the DIII-D vacuum vessel wall. After upgrades to this diagnostic were completed, new experiments were conducted on July 13, 2020 in order to measure the toroidal mode number of the whistler waves and to extend the frequency of the detected waves. Through the use of mixers, instability between 600-700 MHz was detected. (The initial experiments only measured up to 200 MHz.) Analysis of the data was led by Hari Choudhury, a PhD student at Columbia University. Mr. Choudhury has submitted two papers for publication that include contributions by UC Irvine (UCI) Professor Heidbrink and his graduated PhD student Genevieve DeGrandchamp: “Detailed Characterization of Runaway Electron Driven Whistler Waves in Low-Density DIII-D Discharges” and “First Demonstration of Resonant Pitch-Angle Scattering of Relativistic Electrons by Externally-Launched Helicon Waves.” The first paper, which has been submitted to Physics of Plasmas, has significant contributions to both the data and the interpretation by UCI scientists. In contrast, UCI contributions to the second paper, which has been submitted to Physical Review Letters, are relatively minor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Enhancing $\phi$-sensitivity of ignition delay times through dilution of fuel-air mixture

The high $\phi$-sensitivity (η) of ignition delay time (τ IDT ) is one of the desirable fuel properties for the high-load extension of advanced compression ignition engine. Recent studies revealed the effectiveness of a high dilution rate (x D ) for enhancing η at the engine-relevant conditions. This study aims to quantify the effect of dilution on the η of isooctane using a combined experiment-simulation approach. The ignition delay of the isooctane/air mixture was measured with an Advanced Fuel Ignition Delay Analyzer (AFIDA) over the temperature range of 623 - 923 K at 10 bar pressure with global $\phi$ = 0.3 - 0.6, with and without 28.6% of additional N 2 dilution. For precise evaluation of experimental η, the facility effect of the AFIDA experiment was characterized with three-dimensional computational fluid dynamics (3-D CFD) simulation. The temperature in the combustion chamber from 3-D CFD indicated a substantial temporal dependency, varying up to ~52 K by charge-cooling of fuel injection and heat transfer from the wall. We introduced the dimensionless number θ(t) for characterizing the temporal profile of chamber temperature. Consideration of the facility effect using θ(t) resulted in better agreement between the experimental ..eta.. and zero-dimensional (0-D) kinetics simulation. The refined η were then further utilized to quantify the effectiveness of dilution to η The extent of η enhancement with dilution strategy was maximized at the low-temperature chemistry regime, increasing η by 77% with a 28.6% dilution rate. Further analysis on the dilution effect was carried out using 0-D kinetics simulation, revealing the critical dimensionless numbers relevant to the effectiveness of dilution to η enhancement. Here, this study is the first experiment-simulation combined research to quantify the effect of dilution on η, facilitating the kinetics model refinement for better reproduction of $\phi$-sensitivity.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Comparative transcriptomics uncovers poplar and fungal genetic determinants of ectomycorrhizal compatibility

Ectomycorrhizal symbiosis supports tree growth and is crucial for nutrient cycling and temperate and boreal ecosystems functioning. The establishment of functional ectomycorrhiza (ECM) first requires the association of compatible partners. However, host and fungal genetic determinants governing mycorrhizal compatibility are unknown. To identify such factors in poplar and its fungal associates, we mined existing and de novo tree and fungal transcriptional datasets. We identified co-expressed genes enabling ECM symbiosis at early and mature stages of the interaction. These sets of genes can be divided into general fungal-sensing and ECM-specific components. We highlight the importance of fungal modulation of plant JA-related defenses and the regulation of secretory pathways for ECM compatibility, including upregulation of key fungal small secreted proteins, the downregulation of plant secreted peroxidases, and the downregulation of plant cell wall remodeling proteins concomitantly with the upregulation of fungal glycosyl hydrolases acting on pectin. Not only gene regulation, but also its temporal scale and dynamics seem to play a crucial role for mycorrhizal compatibility. The expression profile of the host Common Symbiosis Pathway and nutrient transporters was also studied, revealing constitutive levels of expression and moderate upregulation in compatible ECM interactions. Overall, these results underscore the importance of novel biological functions during the establishment of ECM symbiosis, help us gain insights into the molecular events determining mycorrhiza compatibility, and serve as a data-rich transcriptomic resource to open new research questions in the field.

Marqués‐Gálvez, José Eduardo↗
DOE OSTI2020

Experimentally Validated Computational Modeling of Creep and Creep-Cracking for Nuclear Concrete Structures

In a Nuclear Power Plant, one of the most important components is the concrete nuclear reactor cavity, which serves both a structural and protective function as the biological radiation shield. Given that creep has been identified as a major knowledge gap in the assessment of nuclear structures (NUREG/CR-7153), this work helps to further the understanding of creep behavior of massive concrete containment structures for decades to enable safe and long-term operation of these facilities. This project has developed a robust, experimentally validated model to predict creep in nuclear concrete structures for up 60 years using short-term creep data thereby enabling a longer service life of critical facilities and early detection of structural failure. The work presented in this report is a pairing of computational and experimental methods. For the first time, the time temperature superposition (TTS) principle was successfully used to generate a uniaxial creep compliance master curve to predict mortar creep response for up to 22,500 days (nearly 60 years) at a reference temperature of 20°C. These data were used as input into finite element analysis (FEA) codes that use highly realistic random, 3D concrete microstructures from reconstructed coarse limestone aggregates. Finite element analysis performed provides the ability to quickly upscale mortar viscoelastic behavior to long-term concrete creep/relaxation data. A master creep compliance curve, constructed from the TTS principle, spanning 27 years, was used to validate two and a half decades of simulated concrete creep. Concurrently, three different simulated wall specimens were designed to mimic the behavior of post-tensioned concrete nuclear containment facility vessel walls over time as a result of concrete creep. The specimens were designed with different thicknesses, transverse and longitudinal reinforcement ratios, and level of post-tensioning stress. Each specimen contained various instrumentation to measure internal concrete temperature, concrete strain, and post-tensioning strain hourly for over 3 years. The concrete creep model developed in this project, based on the FEA concrete simulations, was applied to simulate the structural-scale experiments of prestressed concrete walls conducted in this project using the Grizzly code. These models can represent the effects of reinforcing and prestressing. Although there are some discrepancies with the experimental data, the model can predict the overall trends of the creep response in these experiments. One of these experimental models was also applied to an extended time to demonstrate how the findings from this study can be used to predict the behavior of actual structures of interest that have been in service for extended periods of time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

I.1 Heavy-Duty Diesel Combustion (Sandia National Laboratories)

Regulatory drivers and market demands for lower pollutant emissions, lower carbon dioxide emissions, and lower fuel consumption motivate the development of cleaner and more fuel-efficient engine operating strategies. Most current production heavy-duty diesel engines use a combination of both in-cylinder and exhaust emissions-control strategies to achieve these goals. The emissions and efficiency performance of in-cylinder strategies depend strongly on flow and mixing processes that can be influenced by using multiple fuel injections. Past work performed under this project showed that adding a second injection can reduce soot to levels below what would have been produced by an unchanged first injection, thereby increasing load while decreasing soot and potentially reducing brake specific fuel consumption. Information characterizing the important in-cylinder processes with multiple injections has been gleaned from ensemble-averaged planar laser-induced incandescence (PLII) imaging visualizing the soot cloud and planar induced fluorescence (PLIF) of OH characterizing the soot oxidation regions. PLII showed a consistent disruption of the first injection soot cloud by the second injection. In conjunction with OH-PLIF, differences in soot oxidation patterns for multiple injections compared to single injections were observed. This understanding was further enhanced in FY20, when high-speed imaging resolving the above-mentioned effects in a single cycle were combined with direct numerical simulations investigating the multiple-injection ignition process on the microscopic level of turbulence and chemistry interaction. In FY21, these findings in conjunction with findings from other researchers published in the scientific literature were composed into a preliminary multiple-injection conceptual model of fuel-mixing, injection and ignition processes. Remaining key research questions were also highlighted. In addition, wall heat flux was investigated experimentally and with numerical simulations to understand the potential of multiple injections to reduce the engine heat losses and further enhance the efficiency.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Progress in the development and understanding of a high poloidal-beta tokamak operating scenario for an attractive fusion pilot plant

Abstract The high poloidal-beta ( $$\beta _{\textrm{P}}$$ β P ) regime was first proposed as a high bootstrap current scenario for a steady-state fusion pilot plant (FPP) in the 1990s (Kikuchi in Nucl Fusion 30:265, 1990). Since then, there have been many theoretical, modeling, and experimental research activities on this topic. A joint DIII-D/EAST research team began exploring the high- $$\beta _{\textrm{P}}$$ β P regime in 2013, focusing on addressing the needs of attractive FPP design by taking advantage of the extensive diagnostic set and sophisticated plasma control system on DIII-D and the well-developed integrated modeling capability at General Atomics. The ultimate goal is to demonstrate such a scenario on EAST with truly long pulse and metal wall compatibility. This paper summarizes the highlights of the research results on DIII-D by the joint team in the past decade. Experimental evidence and modeling analysis show the high- $$\beta _{\textrm{P}}$$ β P scenario has great advantages in addressing key needs for an attractive FPP design, such as high-energy confinement quality at low rotation, excellent core-edge integration, high line-averaged density above the Greenwald limit, low disruption risk, and high bootstrap current fraction for steady-state operation. This provides a relatively safe and economical option to base an FPP design on that will lead to commercial fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Numerical solution of large scale Hartree–Fock–Bogoliubov equations

The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size N b . We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most $\mathcal{O}$(N b 2 ) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with N b up to 2.88 × 10 6 , and the wall clock time is less than 100 s using 17 280 CPU cores. Finally, this enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

97 MATHEMATICS AND COMPUTING↗