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Oxygen enrichment combustion to reduce fossil energy consumption and emissions in hot rolling steel production

The reheating furnace operation in the hot mill is natural gas- and electricity-intensive. Oxygen enrichment combustion for reheating furnaces has been proposed to curb and replace natural gas use. In this study, heat transfer in steel slabs in the combustion environment of a push-type reheating furnace was simulated using a computational fluid dynamics (CFD) model. Two oxygen enrichment methods that optimized for performance were selected— a medium oxygen enrichment (MOE) case and an oxy-fuel (OF) case. A life cycle analysis (LCA) characterized the energy and emission profiles of an integrated iron and steel manufacturing process using the two oxygen enrichment cases for the hot mill. These conditions were evaluated for energy use and carbon intensity and compared with a baseline case. Results show that with oxygen enrichment, natural gas consumption can decrease by 19.6%–26.8%, total energy consumption (natural gas and electricity) can decrease by 15.1%–20.7% in the hot mill. Emissions of greenhouse gases can decrease by 11.1%–15.2% in the two optimized cases with 14%–27% reductions in regulated criteria pollutants (nitrogen oxides, carbon monoxide, particulate matter, volatile organic compounds, black carbon, organic carbon, and volatile organic carbons). There is a tradeoff between reducing natural gas consumption and increasing electricity demand from a life cycle perspective. Although the OF case resulted in higher energy- and emissions-related benefits, the MOE case showed the more desirable heat flux uniformity, which is key to maintaining product quality. The analysis suggests that oxygen enrichment in the reheating furnace process can have a significant impact on hot mill environmental performance and become a contributing factor in transitioning to low-carbon steel manufacturing.

36 MATERIALS SCIENCE↗

High-efficiency, air-stable manganese–iron oxide nanoparticle-pigmented solar selective absorber coatings toward concentrating solar power systems operating at 750 °C

Solar selective absorber coating with long-term thermal stability at high temperatures ≥750 °C in air is an important component to reduce the levelized cost of energy (LCOE) of concentrating solar power (CSP) systems toward 50% power efficiency and dispatchable solar electricity. Conventionally, solar spectral selectivity requires multilayer-interference coatings implemented by stringently controlled vacuum deposition, and these coatings degrade significantly at >700 °C in air. Herein, we established a quantitative design approach and demonstrated a proof-of-concept air-stable, manganese–iron oxide nanoparticle (NP)-pigmented solar selective coatings with a high solar absorptance of ~93%, a relatively low thermal emittance of ~52%, and an optical-to-thermal energy conversion efficiency >89% under 1,000× solar concentration at 750 °C toward Generation 3 CSP systems. These coatings demonstrate spectral selectivity using cost-effective spray coating approach, a notable improvement over conventional vacuum-deposited, multilayer solar selective coatings for low-cost, high-efficiency solar thermal receivers. In contrast to the thermal degradation of spectrally non-selective benchmark Pyromark 2500 coatings at 750 °C in air, the solar absorptance of the MnFe 2 O 4 -pigmented coatings on stainless steel 310 (SS 310) substrates is increased to ~92.9% and the optical-to-thermal energy conversion efficiency is improved to 89.7% after serving at 750 °C in air for 700 h. X-ray diffraction results reveal that this improvement is due to the transformation of MnFe 2 O 4 NPs into more thermodynamically stable, non-stoichiometric manganese-rich manganese ferrite and iron-rich manganese–iron oxide phases after 500 h aging at 750 °C. For >1,000 h-endurance testing at 750 °C in air and the subsequent 19 day-night thermal cycling between 750 °C (12 h/cycle) and 25 °C (12 h/cycle) on SS 310 substrates, the thermal degradation is mainly due to the CrO x microflake formation from SS 310 substrates rather than the coatings, which can be suppressed by preoxidizing the surface of SS 310. With lower emittance matrix material and further optimization of pigment NP stoichiometry, concentration, and coating thickness, it is promising to achieve an optimized thermal efficiency ≥92.5% with long-term thermal stability at 750 °C for Generation 3 CSP systems.

14 SOLAR ENERGY↗

Machine Learning Calibration of Groundwater Table Depth in ELM: Impact on Land Surface Hydrology and Land‐Atmosphere Fluxes

Accurate representation of groundwater table depth (GWTD) is crucial for simulating hydrological cycling in Earth system models (ESM). Nevertheless, there is a notable gap in the literature regarding the validation of GWTD simulations in ESMs and their subsequent impact on downstream hydrological components. This study explores the calibration of parameterization of global GWTD using machine learning within the Energy Exascale Earth System Model (E3SM) Land Model (ELM). Despite achieving significant gains in simulating GWTD through calibration, offline ELM simulations unexpectedly show that these improvements do not translate to substantial enhancements in model performance for other key hydrological variables, including soil moisture (SM), runoff, groundwater contribution to runoff or base flow index (BFI), and evapotranspiration and its partitioning. The performance in SM and runoff was even degraded in some regions, while BFI was mostly overestimated. Although there is significant improvement in GWTD within the critical range of 1–5 m, where groundwater traditionally influences land surface energy fluxes, these improvements occurred mostly in humid areas where the impact of GWTD on surface processes is minimal. Although the impacts of model calibration are generally small in offline ELM simulations, coupled land-atmosphere simulations exhibit much stronger responses to GWTD calibration, highlighting the role of land-atmosphere feedbacks in Earth system modeling. These findings underscore the need for integrated calibration strategies that simultaneously optimize multiple hydrological variables. However, if a single-variable approach is necessary, it is crucial to establish clear priorities for calibration, identifying the most critical variables that have the greatest impact on overall model performance.

Fang, Yilin [Pacific Northwest National Laboratory↗

Physics of Edge-Core Coupling by Inward Turbulence Propagation

The dynamics of edge-core coupling is critically important to the optimization of magnetically confined fusion plasmas. Since early proposals, there has been persistent speculation that inward propagation of turbulence from the boundary is a possible means to energize the edge-core coupling region. However, the detailed mechanism of this process has remained a mystery until recent experiments observed that regular, intense gradient relaxation events generated blob-void pairs very close to the last closed flux surface. Blobs ($\tilde{n}$ >0) propagate outward and detach from the bulk plasma, while voids ($\tilde{n}$ <0) propagate inward, and so stir the core plasma. Here, in this work, we demonstrate that this heretofore ignored process of void emission can drive a broad turbulent layer of width ∼100 𝜌 𝑠 , for typical parameters. The mechanism is the Cherenkov emission of drift waves from inward-propagating voids. The model shows promise to resolve several questions surrounding the shortfall problem and the strong turbulence in the edge-core coupling region.

drift waves↗

Comparison of Machine Learning-Based Predictive Models of the Nutrient Loads Delivered from the Mississippi/Atchafalaya River Basin to the Gulf of Mexico

Predicting nutrient loads is essential to understanding and managing one of the environmental issues faced by the northern Gulf of Mexico hypoxic zone, which poses a severe threat to the Gulf’s healthy ecosystem and economy. The development of hypoxia in the Gulf of Mexico is strongly associated with the eutrophication process initiated by excessive nutrient loads. Due to the complexities in the excessive nutrient loads to the Gulf of Mexico, it is challenging to understand and predict the underlying temporal variation of nutrient loads. The study was aimed at identifying an optimal predictive machine learning model to capture and predict nonlinear behavior of the nutrient loads delivered from the Mississippi/Atchafalaya River Basin (MARB) to the Gulf of Mexico. For this purpose, monthly nutrient loads (N and P) in tons were collected from US Geological Survey (USGS) monitoring station 07373420 from 1980 to 2020. Machine learning models—including autoregressive integrated moving average (ARIMA), gaussian process regression (GPR), single-layer multilayer perceptron (MLP), and a long short-term memory (LSTM) with the single hidden layer—were developed to predict the monthly nutrient loads, and model performances were evaluated by standard assessment metrics—Root Mean Square Error (RMSE) and Correlation Coefficient (R). The residuals of predictive models were examined by the Durbin–Watson statistic. The results showed that MLP and LSTM persistently achieved better accuracy in predicting monthly TN and TP loads compared to GPR and ARIMA. In addition, GPR models achieved slightly better test RMSE score than ARIMA models while their correlation coefficients are much lower than ARIMA models. Moreover, MLP performed slightly better than LSTM in predicting monthly TP loads while LSTM slightly outperformed for TN loads. Furthermore, it was found that the optimizer and number of inputs didn’t show effects on the LSTM performance while they exhibited impacts on MLP outcomes. This study explores the capability of machine learning models to accurately predict nonlinearly fluctuating nutrient loads delivered to the Gulf of Mexico. Further efforts focus on improving the accuracy of forecasting using hybrid models which combine several machine learning models with superior predictive performance for nutrient fluxes throughout the MARB.

54 ENVIRONMENTAL SCIENCES↗

Pathway Evolution Through a Bottlenecking-Debottlenecking Strategy and Machine Learning-Aided Flux Balancing

The evolution of pathway enzymes enhances the biosynthesis of high-value chemicals, crucial for pharmaceutical, and agrochemical applications. However, unpredictable evolutionary landscapes of pathway genes often hinder successful evolution. Here, the presence of complex epistasis is identifued within the representative naringenin biosynthetic pathway enzymes, hampering straightforward directed evolution. Subsequently, a biofoundry-assisted strategy is developed for pathway bottlenecking and debottlenecking, enabling the parallel evolution of all pathway enzymes along a predictable evolutionary trajectory in six weeks. This study then utilizes a machine learning model, ProEnsemble, to further balance the pathway by optimizing the transcription of individual genes. The broad applicability of this strategy is demonstrated by constructing an Escherichia coli chassis with evolved and balanced pathway genes, resulting in 3.65 g L -1 naringenin. The optimized naringenin chassis also demonstrates enhanced production of other flavonoids. This approach can be readily adapted for any given number of enzymes in the specific metabolic pathway, paving the way for automated chassis construction in contemporary biofoundries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Status report on HFIR irradiation of optimized alumina forming alloys

Properties of FeCrAl alloys under neutron irradiation are of interest because of these materials’ potential application as accident-tolerant fuel cladding in nuclear systems. In parallel, alumina-forming austenitic (AFA) alloys are of interest for use as structural materials in advanced nuclear systems for their potential higher resistance to embrittlement and high-temperature steam oxidation resistance. An irradiation campaign for fiscal year 2024 has been developed under the Advanced Fuels Campaign to perform irradiation testing of various FeCrAl and AFA alloys in Oak Ridge National Laboratory’s High Flux Isotope Reactor (HFIR). The goals of this irradiation campaign are to (1) study the impact of minor alloying elements on the neutron-irradiated mechanical properties of FeCrAl alloys and (2) collect neutron-irradiated mechanical properties on AFA alloys for comparison with those of FeCrAl alloys. This campaign will include both tensile and fracture toughness specimens tested following HFIR irradiation at temperatures representative of normal operating conditions in light-water reactors. The pre-irradiation characterization to date, the irradiation plan for the FeCrAl and AFA specimens, and the subsequent post-irradiation experimental test plan are presented in this report, along with the status of HFIR builds and scheduled insertion dates.

36 MATERIALS SCIENCE↗

Light‐driven Transformation of Carbon Monoxide into Hydrocarbons using CdS@ZnS : VFe Protein Biohybrids

Enzymatic Fisher-Tropsch (FT) process catalyzed by vanadium (V)-nitrogenase can convert carbon monoxide (CO) to longer-chain hydrocarbons (>C2) under ambient conditions, although this process requires high-cost reducing agent(s) and/or the ATP-dependent reductase as electron and energy sources. Using visible light-activated CdS@ZnS (CZS) core-shell quantum dots (QDs) as alternative reducing equivalent for the catalytic component (VFe protein) of V-nitrogenase, we first report a CZS : VFe biohybrid system that enables effective photo-enzymatic C−C coupling reactions, hydrogenating CO into hydrocarbon fuels (up to C4) that can be hardly achieved with conventional inorganic photocatalysts. Surface ligand engineering optimizes molecular and opto-electronic coupling between QDs and the VFe protein, realizing high efficiency (internal quantum yield >56 %), ATP-independent, photon-to-fuel production, achieving an electron turnover number of >900, that is 72 % compared to the natural ATP-coupled transformation of CO into hydrocarbons by V-nitrogenase. The selectivity of products can be controlled by irradiation conditions, with higher photon flux favoring (longer-chain) hydrocarbon generation. The CZS : VFe biohybrids not only can find applications in industrial CO removal for high-value-added chemical production by using the cheap, renewable solar energy, but also will inspire related research interests in understanding the molecular and electronic processes in photo-biocatalytic systems.

Chemistry↗

Determining topological order from infinite projected entangled pair states

In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

36 MATERIALS SCIENCE↗

Regal Beloit Final Technical Report

The original project proposal submitted from NovaTorque Inc (NovaTorque) in 2016 was to improve the existing motor with 95% efficiency by reducing the losses by 21% to achieve 96%. A few months after the proposal was submitted, NovaTorque lost funding and went out of business. The assets of NovaTorque were then acquired by Regal Beloit Corporation (“Regal Beloit” or “Regal”). When the NovaTorque proposal was selected, the project was transferred to Regal Beloit. Once we had production samples from the new Regal production line, they were tested at the Regal Beloit test lab in Wausau, WI. The original NovaTorque motor had an efficiency of 95%, but when the technology was transferred to Regal Beloit, there were multiple manufacturing improvements made, even though the basic electromagnetic design did not change. The test results in Wausau showed that the motors made at the Regal Beloit plant had an efficiency of 96%. Since the goal of the project was to reduce the losses by 21%, a new efficiency target of 96.8% became the project objective. In the first budget period, motors were tested to get the baseline performance. We then used FEA modeling with ANSYS Maxwell to model the existing motor to get correlation between the FEA simulations and the actual test results. Once the model was validated, we evaluated some changes that could be made to the stator to reduce the losses and improve efficiency without changing the rotor or stator housing, keeping the modifications easy to implement. The changes were primarily in the area of making the stator axially shorter and adding Soft Magnetic Composite (SMC) tooth tips. In the second budget period, we proceeded to design and build the new stator that was identified above and identified additional improvements in the process that included a stator machining modification and the use of rectangular wire. When we actually built the motor, the choice of rectangular wire turned out to be a problem. The wire was made by squishing round wire to get the rectangular shape, which caused work hardening, making the wire too stiff to make the desired coils. We shifted to annealed square wire which was better, but we still could not maintain the proper coil envelope. The result was that we had reduced cross section area for stator laminations. We also had to have a radial offset resulting in a radial misalignment between the stator and rotor because of the oversized coils. After the motor was completed, it was shipped to Texas A&M University for testing. With the loss of flux from these issues, the measured motor efficiency was only 96.3%. The primary focus of this motor was to make sure our FEA simulation model predicted the measured losses and overall efficiency, this we moved on to the FEA simulation. The FEA simulations of the motor “as built” with misalignments had good correlation with the test results, so the next step was to use that model to optimize the design of the motor for a final build. This time we considered changes to the stator and rotor and also minor changes to the housing diameter. In the third budget period, we did the detailed design and construction of the final prototypes. The final prototypes had a slight increase in the stator diameter to fit in a standard Regal Beloit housing. We shortened the stator and use more layers of wire in the coils. We also increased the cone angle of the rotor and stator from the original 110 degrees to 130 degrees to get some additional efficiency and optimized the stator cross section. The predicted efficiency from the FEA simulations was 96.9%. When completed, the motors were tested. We were a little short of reaching our target efficiency goal of 96.8%. We were only able to get to 96.7% efficiency. While it may be possible with additional iterations in designs and future builds to gain that additional 0.1%, we believe that we are close to the best we can achieve from a practical viewpoint, and additional iterations would be more work than the potential gains would be worth. No other motor in this class can even reach the 96% that we started with.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Review of SiC material development for nuclear fusion applications: Cross-cutting research and emerging opportunities

The SiC-based materials, particularly SiC-fiber-reinforced SiC matrix (SiC/SiC) composites, show strong potential for structural and functional applications in future fusion power plants because they can operate at high temperatures with a range of coolants and breeders, thereby enabling higher energy conversion efficiency. Here, this paper presents recent advancements in the development of SiC-based materials, focusing on processing techniques and material performance and resistance under fusion-relevant environments. The processing activities have emphasized near-net-shape fabrication and the joining of SiC subcomponents, with processing methods and material compositions informed by previous irradiation experiments on various grades of SiC. Research on irradiation effects has remained focused on degradation mechanisms and the microstructural optimization of SiC/SiC composites irradiated to high neutron damage levels. Analysis of irradiation defects in SiC has advanced via the application of cutting-edge characterization methods, among which Raman spectroscopy is becoming a common tool to assess atomic-scale chemical disorder. Fusion–fission crosscutting irradiation research has explored combined effects in SiC/SiC composites with application-relevant geometries, including bowing of SiC/SiC composite channels under neutron flux gradients, stress evolution in SiC/SiC composite tubes under through-thickness temperature gradients, and irradiation-enhanced corrosion in SiC. Finally, research opportunities for component testing and assessment under fusion-relevant conditions, in support of emerging concepts from the private fusion sector, are discussed.

Advanced manufacturing↗

Critical problems of energy frontier Muon Colliders: optics, magnets and radiation

This White Paper brings together our previous studies on a Muon Collider (MC) and presents a design concept of the 6 TeV MC optics, the superconducting (SC) magnets, and a preliminary analysis of the protection system to reduce magnet radiation loads as well as particle backgrounds in the detector. The SC magnets and detector protection considerations impose strict limitations on the lattice choice, hence the design of the collider optics, magnets and Machine Detector Interface (MDI) are closely intertwined. As a first approximation we use the Interaction Region (IR) design with beta-star=3 mm, whereas for the arcs we re-scale the arc cell design of the 3 TeV MC. Traditional cos-theta coil geometry and Nb3Sn superconductor were used to provide field maps for the analysis and optimization of the arc lattice and IR design, as well as for studies of beam dynamics and magnet protection against radiation. The stress management in the coil will be needed to avoid large degradation or even damage of the brittle SC coils. In the assumed IR designs, the dipoles close to the Interaction Point (IP) and tungsten masks in each IR (to protect magnets) help reducing background particle fluxes in the detector by a substantial factor. The tungsten nozzles in the 6 to 600 cm region from the IP, assisted by the detector solenoid field, trap most of the decay electrons created close to the IP as well as most of the incoherent electron-positron pairs generated in the IP. With sophisticated tungsten, iron, concrete and borated polyethylene shielding in the MDI region, the total reduction of background loads by more than three orders of magnitude can be achieved.

43 PARTICLE ACCELERATORS↗

Recrystallization, cracking, and erosion of dispersoid-strengthened tungsten materials during exposure to divertor plasmas

In this study, we investigated the effects of combined intense particle and heat flux exposure on advanced tungsten plasma-facing materials within the DIII-D fusion facility. Our test matrix included two types of dispersoid-strengthened tungsten (containing either 100 nm diameter TiO 2 or Ni particles), along with high-purity polycrystalline tungsten as a reference. This experiment relied on a sample geometry angled at 15° relative to the divertor surface, thereby allowing the surfaces to intercept steady-state perpendicular heat fluxes (q ⟂ ) ranging from 10.1 to 19.6 MW/m 2 . During each shot, the samples were exposed to 42 Hz edge-localized modes (ELMs), allowing us to test the material response to transient heating. We correlated the exposure conditions with extensive post-test surface composition analysis and microscopy to determine how the plasma modified each surface. The angled specimens closest to the strike point received the highest combined heat and particle flux and melted midway through the experiment. EBSD analysis revealed they were completely recrystallized throughout, with an average grain size >100 µm. On the other hand, the specimens that received a lower steady state heat flux survived with more superficial surface damage. Whereas the high-purity polycrystalline tungsten exhibited a higher surface roughness, the dispersoid-strengthened material exhibited more extensive shallow inter-granular cracking. In addition, the surface was depleted of dispersoids following plasma exposure, possibly because of evaporation and/or sputtering. The results described here provide insights into the performance of these materials in a fusion environment which can guide further optimization for use in long-pulse devices.

Kolasinski, Robert D. [Sandia National Laboratorie↗

Feasibility Assessment of a Natural-Circulation Salt Irradiation Loop in the Advanced Test Reactor

Molten-salt reactors will likely require some level of irradiation testing as part of their licensing basis. An ideal experiment would consider the integrated effect of neutron flux and fission product generation in addition to circulating flow conditions. The feasibility of a natural-circulation irradiation salt loop in the Advanced Test Reactor (ATR) is assessed here. The flow is induced by the innovative combination of gas gaps and fin gaps along the capsule wall to fine-tune radial heat conductance, and therefore drive an axial temperature gradient across the experiment height. Following multiple design optimizations, a promising configuration has been identified. The 45-kW experiment would generate a 0.15 m/s flow velocity with 6 kg of fuel-bearing salt. This demonstrates the possibility of generating appreciable flow rates within manageable experimental conditions (e.g., total size and heat generation). An initial assessment of species mass tracking inside the experiment was also performed to gain an understanding of radionuclide behavior within the system. Results showed that significant quantities of Xe can be extracted in the off-gas (1.7 kCi) for an 8% bubble removal efficiency rate. Here, these results highlight the potential value of such experiments. Further work will involve detailed engineering drawings and analyses of the loop, as well as more computationally expensive modeling of species mass tracking.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Magneto-optical study of Nb thin films for superconducting qubits

Among the recognized sources of decoherence in superconducting qubits, the spatial inhomogeneity of the superconducting state and the possible presence of magnetic-flux vortices remain comparatively underexplored. Niobium is commonly used as a structural material in transmon qubits that host Josephson junctions, and excess dissipation anywhere in the transmon can become a bottleneck that limits overall quantum performance. The metal/substrate interfacial layer may simultaneously host pair-breaking loss channels (e.g., two-level systems, TLS) and control thermal transport, thereby affecting dissipation and temperature stability. Here, we use quantitative magneto-optical imaging of the magnetic-flux distribution to characterize the homogeneity of the superconducting state and the critical current density, $j_{c}$, in niobium films fabricated under different sputtering conditions. The imaging reveals distinct flux-penetration regimes, ranging from a nearly ideal Bean critical state to strongly nonuniform thermo-magnetic dendritic avalanches. By fitting the measured magnetic-induction profiles, we extract $j_{c}$ and correlate it with film physical properties and with measured qubit internal quality factors. Our results indicate that the Nb/Si interlayer can be a significant contributor to decoherence and should be considered an important factor that must be optimized.

Datta, Amlan [Ames Lab; Iowa State U.]↗

Magnetic flux distribution, quasiparticle spectroscopy, and quality factors in Nb films for superconducting qubits

Niobium is a practical material platform for superconducting microwave circuits; however, device-level performance can vary significantly depending on film growth and processing conditions. We compare three epitaxial Nb films grown on $c-$plane sapphire substrates under nominally identical conditions, except for the deposition temperature. To correlate internal quality factors, $Q_{\mathrm {i}}$, with material properties, we combine magneto-optical imaging of magnetic flux distribution with quasiparticle spectroscopy via measurements of the London penetration depth, $λ(T)$. In the low-$Q_{\mathrm i}$ film, there is a lesser ability to screen the magnetic field and an irregular temperature variation of $λ(T)$, implying the existence of localized in-gap states. High $Q_{\mathrm i}$ films show the opposite trend. We conclude that our measurements provide an efficient method for characterizing and optimizing superconducting films for quantum informatics applications.

Datta, Amlan [Ames Lab; Iowa State U.]↗

Spectral properties of three-dimensional Anderson model

The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its properties from the perspective of modern numerical approaches. Our main focus is on the quantitative comparison between the level sensitivity statistics and the level statistics. While the former studies the sensitivity of Hamiltonian eigenlevels upon inserting a magnetic flux, the latter studies the properties of unperturbed eigenlevels. We define two versions of dimensionless conductance, the first corresponding to the width of the level curvature distribution relative to the mean level spacing, and the second corresponding to the ratio of the Heisenberg time and the Thouless time obtained from the spectral form factor. We show that both conductances look remarkably similar around the localization transition, in particular, they predict a nearly identical critical point consistent with other well-established measures of the transition. We then study some further properties of those quantities: for level curvatures, we discuss particular similarities and differences between the width of the level curvature distribution and the characteristic energy studied by Edwards and Thouless (1972) in their pioneering work, in which the hopping at one lattice edge is changed from periodic to antiperiodic boundary conditions. In the context of the spectral form factor, we show that at the critical point it enters a broad time-independent regime, in which its value is consistent with the level compressibility obtained from the level variance. Finally, we test the scaling solution of the average level spacing ratio in the crossover regime using the cost function minimization approach introduced recently in Šuntajs et al. (2020). The latter approach seeks for the optimal scaling solution in the vicinity of the crossing point, while at the same time it allows for the crossing point to drift due to finite-size corrections. We find that the extracted transition point and the scaling coefficient agree with those from the literature to high numerical accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theory of the thermionic current beyond the traditional space charge limit enabled by trapped ions in the virtual cathode

We show that trapped ions in virtual cathode potential wells can raise the transmitted current of emitted electrons into a plasma much closer to the full emission than is predicted by cathode sheath theories without trapped ions. The transmitted current is controlled by the well barrier voltage, which must adjust to balance the creation of low-energy ions within the well, and their loss. Our model considers the case of a plasma-facing cathode where trapped ions are created passively via charge-exchange collisions and lost passively via thermal leakage over the well. We quantify these rates and estimate the current in terms of system parameters for thermionic emission into a plasma with several cathode geometries. A general prediction is that the current as a function of emitted flux does not saturate at the traditional space charge limit (the onset of a well) but can reach far higher values until the trapped ion balance breaks down, causing instability. The maximum stable current depends on parameters but in principle can be arbitrarily high if active techniques are used to manipulate the trapped ion balance. We conclude that major improvements in plasma technologies with hot cathodes might be achieved by optimizing the current enhancement enabled by trapped ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗