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DOE OSTI2025

Carbon in GaN as a nonradiative recombination center

Trap-assisted nonradiative recombination has been shown to limit the efficiency of optoelectronic devices. While substitutional carbon (⁠C N ) has been suggested to be a nonradiative recombination center in GaN devices, a complete recombination cycle including the two charge-state transition levels has not been previously described. In this work, we investigate the trap-assisted recombination process due to C N in GaN, including multiphonon emission, radiative recombination, trap-assisted Auger–Meitner (TAAM) recombination as well as thermal emission of holes. Our study shows the key role of TAAM processes at the high carrier densities relevant for devices. We also reveal the carrier-density regimes where thermal emission and radiative recombination are expected to play an observable role. Our results highlight that carbon concentrations exceeding ~10 17 cm −3 can have a noticeable impact on device efficiency, not just in GaN active layers but also in InGaN and AlGaN. Furthermore, our comprehensive formalism not only offers detailed results for carbon but also provides a general framework for assessing the multiple processes that participate in trap-assisted recombination in semiconductors.

36 MATERIALS SCIENCE↗

DOE OSTI2026

String-Breaking Dynamics in Quantum Adiabatic and Diabatic Processes

Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking : the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.

Ising model↗

DOE OSTI2024

Energy conversion and transport in molecular-scale junctions

Molecular-scale junctions (MSJs) have been considered the ideal testbed for probing physical and chemical processes at the molecular scale. Due to nanometric confinement, charge and energy transport in MSJs are governed by quantum mechanically dictated energy profiles, which can be tuned chemically or physically with atomic precision, offering rich possibilities beyond conventional semiconductor devices. While charge transport in MSJs has been extensively studied over the past two decades, understanding energy conversion and transport in MSJs has only become experimentally attainable in recent years. As demonstrated recently, by tuning the quantum interplay between the electrodes, the molecular core, and the contact interfaces, energy processes can be manipulated to achieve desired functionalities, opening new avenues for molecular electronics, energy harvesting, and sensing applications. This Review provides a comprehensive overview and critical analysis of various forms of energy conversion and transport processes in MSJs and their associated applications. We elaborate on energy-related processes mediated by the interaction between the core molecular structure in MSJs and different external stimuli, such as light, heat, electric field, magnetic field, force, and other environmental cues. Key topics covered include photovoltaics, electroluminescence, thermoelectricity, heat conduction, catalysis, spin-mediated phenomena, and vibrational effects. Furthermore, the review concludes with a discussion of existing challenges and future opportunities, aiming to facilitate in-depth future investigation of promising experimental platforms, molecular design principles, control strategies, and new application scenarios.

Charge transport↗

DOE OSTI2026

Influence of Powder Characteristics and Processing Methods on Creep Performance of Powder Metallurgy Hot Isostatic Pressed SS316

The U.S. nuclear energy expansion goals are driving the demand for manufacturing routes that can rapidly produce large, complex, near net shape components. Powder metallurgy hot isostatic pressing (PM HIP) is an advanced manufacturing technique that can be economically scaled-up, while alleviating the supply chain challenges that forging and casting face in terms of cost and lead time constraints. This makes PM-HIP a viable technology to aid and accelerate large-scale part manufacturing for nuclear applications. However, large-scale qualification and deployment of this technology require a thorough understanding of the influence of powder feedstock quality, powder handling history, hot isostatic pressing (HIP) parameters, and subsequent heat treatment on microstructural evolution and elevated temperature mechanical performance. The present work focusses on 316 austenitic stainless steel (SS316) which is most commonly used in high temperature environments for nuclear applications Results from this study show that PM HIPed SS316 meets ASME tensile requirements at room temperature and at elevated temperature. However, creep performance of PM-HIPed SS316 remains inferior to its wrought counterpart, demonstrating that tensile performance alone is not a reliable metric for long duration high temperature integrity. Further, this report delineates powder derived microstructural features that govern creep damage, with key evidences pointing to “microstructural inheritance” from gas atomized powder feedstocks. Commercial SS316 powders of varying chemical compositions and recycling histories were studies, and the results showed large differences in elemental segregation, oxide surface layers and secondary phase distributions. Multi-scale characterization revealed segregation of chromium, molybdenum, manganese and silicon at the boundaries and the precipitation of manganese-, silicon-, and molybdenum-oxides. During HIP consolidation, these surface oxides transform into decorated prior particle boundaries (PPBs) and grain boundary inclusions that persist through conventional post-HIP solution annealing treatment. The retained oxides in post-HIP microstructures were found to influence grain growth, precipitation behavior, and ultimately creep cavitation and fracture. Such post-HIP heat treatments are therefore limited by a complex trade-off between grain growth, and oxide coarsening which aggravate creep damage by acting as nucleation sites for cavities. The objective of this work is to establish an integrated processing–structure–property framework for PM-HIP 316 stainless steel by investigating the influence of powder feedstock characteristics in pre- and post-HIP processing as well as to understand the significance of post-HIP heat treatment on microstructural evolution and creep properties. The results from this report emphasize the significance of powder feedstock integrity in improving creep performance of PM-HIPed SS316, by highlight the effect of rapid solidification, elemental segregation, oxide formation and powder recycling on microstructural defect inheritance following HIP consolidation. Rather than considering HIP processing, solution annealing, and mechanical performance independently, this report treats powder production, HIP consolidation, post-HIP thermal processing, and creep deformation as interconnected stages within a continuous metallurgical process. The resulting framework will provide a scientific basis for developing feedstock engineering strategies capable of improving long-term reliability of PM-HIP stainless steels and accelerating their qualification for advanced nuclear applications.

Ajjarapu, Pavan [Oak Ridge National Laboratory (OR↗

DOE OSTI2025

Keldysh tuning of photoluminescence in a lead halide perovskite crystal

In 1964, Keldysh laid the groundwork for strong-field physics in atomic, molecular, and solid-state systems by delineating a ubiquitous transition from multiphoton absorption to quantum electron tunneling under intense AC driving forces. While both processes in semiconductors can generate carriers and result in photon emission through electron-hole recombination, the low quantum yields in most materials have hindered direct observation of the Keldysh crossover. Leveraging the large quantum yields of photoluminescence in lead halide perovskites, we show that we can not only induce bright light emission from extreme sub-bandgap light excitation but also distinguish between photon-induced and electric-field-induced processes. Our results are rationalized by the Landau-Dykhne formalism, providing insights into the non-equilibrium dynamics of strong-field light-matter interactions. These findings open new avenues for light upconversion and sub-bandgap photon detection, highlighting the potential of lead halide perovskites in advanced optoelectronic applications.

FOS: Physical sciences↗

DOE OSTI2025

Establishing model credibility for process-microstructure-property relationships in additive manufacturing using exascale computing

Additive Manufacturing (AM) of alloys holds significant promise as a disruptive technology in various industries, yet its adoption is often hindered by challenges in achieving consistent part quality. These issues are primarily due to the complex process-microstructure-property (PSP) relationships inherent to AM. Computational models can greatly aid in understanding these relationships, but their widespread impact and adoption has been limited by a lack of validated, open-source, and computationally efficient PSP modeling frameworks and hardware limitations. Here, this study leverages the ExaAM software suite and data from the AMBench-2018 series of laser powder bed fusion (LPBF) benchmark experiments to perform a comprehensive model assessment, including verification, validation, sensitivity analysis, and uncertainty quantification. The RADICAL-EnTK workflow manager was used to perform an ensemble of heat transport, solidification, and mechanical response simulations on the exascale computer Frontier, considering uncertainties in critical model inputs such as laser spot size and nucleation parameters, and consisting of 125 explicit grain structure simulations and 7875 crystal plasticity simulations. For a selected location within the Inconel 625 AMBench-2018 test artifact, sensitivity analysis and uncertainty quantification were performed using the predicted distributions of grain structure and mechanical properties. Qualitative agreement was found between the predicted grain size and texture and the observed AMBench-2018 microstructure, the mean predicted yield stress was within 5% of the experimental measurement mean, and the mean predicted engineering stress at 5% strain was within 10% of the experimental measurement mean. The insights gained from development and validation of the ExaAM PSP modeling framework will help guide future directions for enhancing the credibility and reliability of PSP models in AM, thereby accelerating the adoption of AM technologies in various industries.

Additive manufacturing↗

DOE OSTI2025

Development of a high fidelity CFD model for solvent evaporation and transport in porous structure during battery electrode drying

An efficient battery manufacturing process is the key to the mass production of Electric Vehicles (EV), in which drying is one of the most energy-intensive steps significantly influencing the battery cell performance. An accurate 3D CFD model for drying is essential for predicting the drying mechanism and optimizing its parameters. By optimizing the drying process, it is possible to reduce energy consumption and cost during battery manufacturing, minimize binder loading and maximize active material loading to achieve superior electrochemical performances and facilitate wider and faster public adoption of EV. This project aims to optimize the drying process during electrode manufacturing by leveraging high-fidelity, porous electrode simulations for solvent evaporation. By optimizing this process, we seek to reduce energy consumption during battery manufacturing, while minimizing binder loading and maximizing active material loading, with the overall goal of enhancing electrical vehicle performance.

Horner, Jeffrey Scott [Sandia National Laboratorie↗

DOE OSTI2026

NanoPSD: A software for automatic detection of Nano-Particle Shape Distribution in electron microscopy images

Accurate quantification of the size and morphology of nanoparticles from electron microscopy (EM) images is essential to understand growth mechanisms, surface reactivity, and functional behavior in nanoscale materials. Manual analysis remains slow, subjective, and difficult to reproduce in large datasets. We introduce NanoPSD (Nano-Particle Shape Distribution), an open-source and fully automated framework for quantitative particle detection and morphology analysis from EM images. NanoPSD integrates adaptive contrast enhancement, polarity-agnostic scale-bar detection, Optical Character Recognition (OCR)-based calibration, and classical segmentation via Otsu thresholding with morphological refinement. Particle contours are used to extract geometric descriptors, including equivalent circular diameter, aspect ratio, circularity, and solidity, enabling automated classification into spherical, rod-like, and aggregate morphologies. The framework supports both single-image and batch processing, generating publication-quality visualizations, LaTeX-ready tables, and structured comma-separated values (CSV) datasets. As a demonstration, we applied NanoPSD to plasma-synthesized nanoparticle samples diagnosed via transmission electron microscopy (TEM). The code produced statistically robust size and morphology distributions spanning a few to tens of nanometers with minimal user supervision. The pipeline demonstrates high reproducibility and scalability, processing large image collections with consistent calibration and output formatting. Its modular design enables seamless integration of future deep-learning-based segmentation models, providing a pathway toward intelligent, data-driven electron microscopy analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Time-Resolved Stochastic Dynamics of Quantum Thermal Machines

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. Here, in this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as enginelike, coolinglike, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.

full counting statistics↗

DOE OSTI2026

Advancing technologies for lignin-based jet fuel production in aqueous phase

Integrating lignin into a cellulosic ethanol plant for the co-production of lignin-based jet fuel (LJF) in aqueous phase offers a significant opportunity to boost operational efficiency, economic viability, carbon conversion, and the overall sustainability of biofuel and chemical production. LJF is lignin-structure-based jet fuel blendstocks primarily composed of alkyl-substituted mono-, bi-, and tri-cyclohexanes. It exhibits high energy density, potential for low emissions, and favourable blend characteristics that comply with drop-in specifications. An overview of lignin feedstock, catalytic processes, LJF chemical compositions, fuel properties tests, and techno-economic analysis (TEA) and life cycle assessment (LCA) indicate that (1) the reactivity of lignin plays a crucial role in its structure transformation to LJF molecules; (2) catalytic processing of lignin to LJF can occur through a simultaneous depolymerization and hydrodeoxygenation process, bypassing the intermediate step of producing and upgrading lignin-derived oil; (3) LJF's uniqueness molecules making it more promising for high energy content and low emission jet fuel properties for next generation sustainable aviation fuel (SAF); and (4) TEA and LCA demonstrate that LJF is not only potentially cost-effective but also offers favourable carbon footprint compared to other SAFs. In conclusion, this review highlights the most recent advancements in LJF technology, along with the challenges and opportunities that lie ahead in fulfilling its potential.

09 BIOMASS FUELS↗

DOE OSTI2026

Sintering effects on NpO 2 grain size and morphology: The role of precursor Np phase

Neptunium dioxide (NpO 2 ) is a key phase in nuclear material processing as a target material for the production of plutonium-238 ( 238 Pu) and has been historically synthesized via the calcination of a Np oxalate precursor. Alternative synthesis methods for NpO 2 are now more prevalent, necessitating their study and comparison with the more common oxalate route. The purpose of this work was to investigate the microstructural properties of NpO 2 synthesized from a nitrate-based Np precursor phase via the assessment of NpO 2 particle size and morphology as a function of calcination temperature and time. Scanning electron microscopy (SEM) was used to probe the primary grain size and morphology of NpO 2 after calcination at temperatures ranging from 700 to 1100 °C and hold times ranging from 1 to 10 h. Post-image analysis using ImageJ software enabled the quantification of mean particle diameter. This analysis indicated that particle diameter increases with both increasing calcination temperature and hold time. Primary particles were shown to be clumped in irregular patterns into the overall rough, blocky aggregates, but this macroscopic morphology was not affected by calcination time or temperature. Although trends in primary grain size of NpO 2 were consistent with available literature from other Np precursor phases, the macroscopic morphology of the NpO 2 aggregates was quite different than reported for other precursors. Through comparison with historical literature on Np oxalate, this work emphasizes the importance of Np precursor on the physical properties of NpO 2 .

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2023

Formation and Shape Changing of Conductive Helical Ribbons via Deposition of Highly Stressed Films on Mechanically Responsive Substrates

Abstract This work demonstrates that the electrodeposition of highly stressed films on compliant ribbons is a robust process to obtain helical structures with excellent mechanical stability and potentially high thermal and electrical conductance. Electrodeposition on end‐tethered ribbons alters their axial and bending stiffness while imparting mechanical stress to drive the formation of a helix with a microscale diameter and pitch in a controlled and scalable manner. The process generates helices with diameters and pitches between 80 and 200 µm and lengths as large as several millimeters. The approach is amenable to parallel processing a large number of 3D structures on any substrate, including large‐area semiconductor wafers. This phenomenon is explained in terms of the change of stress gradients as material is added. Applications of the fabricated helices include antennas, metamaterials, and slow‐wave structures in frequency ranges not previously attainable.

Chemistry↗

DOE OSTI2025

Theoretical perspective on phase stability and polarization switching in ferroelectric hafnia

Fluorite-based ferroelectric materials are revolutionizing the application space of polar semiconductors. These materials leverage robust polarization of extremely thin films, compatibility with the silicon chip processing, and decades of manufacturing experience to enable a new generation of ferroelectric memory devices. As a new paradigm for ferroelectrics, understanding of phase transitions and the switching mechanism in fluorites is essential both for advancing applications and for fundamental science. In this article, we outline the recent progress that has been made to understand the relative phase stability, phase transition and order parameter coupling, ferroelectric switching through unique nucleation and growth processes, and how defects affect these phases and processes. The main challenges, opportunities, and next steps for leveraging these materials for next-generation devices are reviewed.

Condensed Matter Physics↗

DOE OSTI2026

Characterization of ceramic fuel powder packing fractions to support INFLUX

Triply periodic minimal surface (TPMS)-based structures show marked potential in novel nuclear reactor fuel designs, as their high surface area-to-volume ratio increases the efficiency of heat transfer out of the fuel, enabling safer, more innovative reactor designs. This milestone report addresses the role of dUO 2 powder processing route on the fill behavior of TPMS-based cladding shells to understand and advance the feasibility of manufacturing TPMS-based nuclear fuel forms. dUO 2 powder was processed through either a dry granulation route, varying consolidation pressure, or through milling, varying milling time, milling method and milled size distribution. The lowest tapped bulk densities (TBD), but best powder flowabilities, were obtained when testing unprocessed dUO 2 powder which was prone to self-agglomeration and formed low-density spheroids. The highest TBD and lowest flowabilities were obtained when using powder produced by hammer-milling dUO 2 powder to pass through a 200-mesh sieve, which led to particles with angular morphologies. Powder produced by dry granulation exhibited TBD that varied according to the consolidation pressure used to form the initial pellets and exhibited improved flowabilities when compared to hammer-milled material. Because of the large span of granule sizes formed as well as the irregular shape associated with the granules, a packing fraction of 0.69 was achieved, exceeding the analytical solution for random close packing of mono-sized spheres. TPMS polymer shells were loaded with unprocessed, granulated, and hammer-milled dUO 2 powders, and their qualitative packing behaviors were analyzed using x-ray computed tomography (xCT). TBDs calculated after loading TPMS polymer shells were 10-20% lower when compared to tapped bulk density measurements taken in a glass graduated cylinder, indicating a non-trivial impact on the tapped bulk density of either the TPMS channel size, TPMS channel surface material, powder cohesiveness, or a combination of the two parameters. A metallic zircaloy-4 TPMS shell will be loaded with hammer-milled dUO 2 powder upon receipt of the shell from Oak Ridge National Laboratory (ORNL) and shipped to Idaho National Labs (INL) for subsequent hot isostatic pressing (HIP) densification experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

A physics informed bayesian optimization approach for material design: application to NiTi shape memory alloys

Abstract The design of materials and identification of optimal processing parameters constitute a complex and challenging task, necessitating efficient utilization of available data. Bayesian Optimization (BO) has gained popularity in materials design due to its ability to work with minimal data. However, many BO-based frameworks predominantly rely on statistical information, in the form of input-output data, and assume black-box objective functions. In practice, designers often possess knowledge of the underlying physical laws governing a material system, rendering the objective function not entirely black-box, as some information is partially observable. In this study, we propose a physics-informed BO approach that integrates physics-infused kernels to effectively leverage both statistical and physical information in the decision-making process. We demonstrate that this method significantly improves decision-making efficiency and enables more data-efficient BO. The applicability of this approach is showcased through the design of NiTi shape memory alloys, where the optimal processing parameters are identified to maximize the transformation temperature.

Chemistry↗

DOE OSTI2026

MARVEL Reactor Digital Engineering Developments

The MARVEL reactor project has served to introduce a new generation of engineers to the processes required to transform a reactor design from simply an idea on paper into what will be an approved, constructed, and operational nuclear power system. Much as there have been advances in materials, analysis, and evaluation methodologies over the 50 years since the last reactor was built at INL, so too has the technology for managing the engineering process itself advanced. Digital Engineering tools and methods provide improved coordination between previously siloed engineering disciplines, reduced burdens of non-value-added data transcription processes and bring forward insights and improvements that might otherwise fall later in the design stage, where changes are much more costly. While the tools and techniques to support the full digital engineering vision are not yet complete, the MARVEL design processes provide valuable demonstrations and validations of key aspects and illuminate further areas for implementation by subsequent projects.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2025

Biochemical properties of glycerol kinase from the hypersaline-adapted archaeon Haloferax volcanii

ABSTRACT Extremophilic microorganisms are promising candidates for industrial and analytical biocatalysis.Haloferax volcanii, a halophilic archaeon that prefers glycerol over glucose, channels this substrate into central metabolism through glycerol kinase (GK). Here, we report the biochemical properties ofH. volcaniiGK and its potential for biotechnological applications. An N-terminal His-tagged GK was functionalin vivoand yielded 3 mg/L culture—4.5 times more enzyme than a C-terminal StrepII-tagged version. Size exclusion chromatography revealed a glycerol-induced oligomeric shift from homodimer to a dimer-dominant state with detectable tetramer. The purified enzyme showed robust activity across broad pH and salinity ranges, with optimal activity at 100 mM NaCl and 50°C–60°C. It retained catalytic activity in 5%–10% dimethyl sulfoxide (DMSO) and crude glycerol containing methanol. His-GK was freeze-thaw stable and thermotolerant in 2 M NaCl buffers. In the absence of ligands, the enzyme’s melting temperature (T m ) was 80°C. Glycerol increased the T m to 85°C, and combinations with MgCl₂ (84°C) or ATP (88°C) provided further stabilization. The highest T m (89°C) occurred with all three ligands, suggesting a cumulative stabilizing effect. Kinetic analyses revealed positive cooperativity for glycerol, ATP, and Mg² + ; Mn² + and Co² + also supported the activity.H. volcaniiGK is the first known GK to exhibit positive cooperativity with glycerol and ATP. Its high stability and substrate flexibility support its use in biodiesel waste valorization,in vitrobiocatalysis, and biosensor development—applications demanding robust, specific, and stable enzymes. IMPORTANCE This study reveals thatH. volcaniiGK exhibits positive cooperativity for glycerol, ATP, and Mg² + , a kinetic feature not previously reported for glycerol kinases. This behavior enables steep, switch-like responses to small substrate changes, offering unique advantages for biosensor design. Importantly,H. volcaniiGK also maintains high activity under extreme salinity, temperature, broad pH, and solvent conditions that typically limit enzyme use in industrial and environmental applications. These traits make this GK an ideal candidate for enzyme-based biosensors, which often suffer from poor tolerance to pH, solvent, and thermal stress. Its robustness supports its use in cross-linked enzyme crystals, an immobilization method that enhances enzyme stability and reusability under harsh conditions. Moreover, GKs are already employed in Mg² + detection kits; however,H. volcaniiGK’s ability to tolerate and respond to diverse divalent cations (e.g., Co² + , Mn² + ) broadens their potential for pollutant detection and environmental monitoring. These features collectively positionH. volcaniiGK as a valuable biocatalyst for biosensing,in vitrodiagnostics, and biotechnological applications requiring both precision and durability.

Biotechnology & Applied Microbiology↗

DOE OSTI2026

First Wall Design of a Tokamak Pilot Plant Using a Monte Carlo Model for 3-D Heat Flux Deposition

We present a method for calculating the heat fluxes deposited on nonaxisymmetric tokamak first wall components, allowing for a first-of-its-kind model for power handling in the tokamak far scrape-off layer (SOL). The DIV3D Monte Carlo model features strict global power conservation and can calculate the finite cross-field plasma transport into magnetically-shadowed regions, which is significant when dealing with meter-scale shadows introduced by components such as poloidal limiters or antennas. As a case study, we apply the DIV3D model to inform the distribution of first wall poloidal limiters in an ARC-class reactor device. We demonstrate that discrete protection limiters can efficiently reduce peak heat fluxes on recessed breeder wall components in the presence of significant far-SOL plasma fluxes. By varying the toroidal periodicity and radial standoff depth of the limiters, we demonstrate one of the tradeoffs that must be considered in first wall design: more limiters provide greater protection, but at the cost of reduced breeding performance. We also present the impact that radial misalignments between limiters would have on first wall power loading.

Monte Carlo methods↗