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DOE OSTI2024

Measurement bias in self-heating x-ray free electron laser experiments from diffraction studies of phase transformation in titanium

X-ray self-heating is a common by-product of X-ray Free Electron Laser (XFEL) techniques that can affect targets, optics, and other irradiated materials. Diagnosis of heating and induced changes in samples may be performed using the x-ray beam itself as a probe. However, the relationship between conditions created by and inferred from x-ray irradiation is unclear and may be highly dependent on the material system under consideration. Here, we report on a simple case study of a titanium foil irradiated, heated, and probed by a MHz XFEL pulse train at 18.1 keV delivered by the European XFEL using measured x-ray diffraction to determine temperature and finite element analysis to interpret the experimental data. We find a complex relationship between apparent temperatures and sample temperature distributions that must be accounted for to adequately interpret the data, including beam averaging effects, multivalued temperatures due to sample phase transitions, and jumps and gaps in the observable temperature near phase transformations. The results have implications for studies employing x-ray probing of systems with large temperature gradients, particularly where these gradients are produced by the beam itself. Finally, this study shows the potential complexity of studying nonlinear sample behavior, such as phase transformations, where biasing effects of temperature gradients can become paramount, precluding clear observation of true transformation conditions.

Crystallography↗

DOE OSTI2024

Current potential patches

A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element basis, called current potential patches. Current potential patches leverage the relationship between distributions of magnetic dipoles and current potentials to explore limits of the access properties of stellarator coil sets. An example calculation is shown using the Helically Symmetric Experiment (HSX) equilibrium, demonstrating the method's use in coil design and understanding the limits of the access properties of coil sets. Current potential patches have additional desirable properties such as of promoting sparse current sheet solutions and identifying crucial locations of shaping current placement. A result is found for the HSX equilibrium that shaping currents covering only 22% of the winding surface are sufficient to produce the equilibrium to a good accuracy, provided a toroidal field is generated by an exterior coil set.

Elder, Todd↗

DOE OSTI2026

Pattern-enhanced Resonant Soft X-ray Scattering for Operando monitoring of electrochemical solid-liquid interfaces

Unveiling interfaces at sub-nanometer scales is essential for advancing the understanding of complex chemical transformations. However, characterizing solid-liquid interfaces with high dimensional sensitivity and temporal resolution remains challenging, due to their dynamic nature and inaccessibility by conventional probes. Here we present an approach, Pattern-enhanced Resonant Soft X-ray Scattering, to overcome the challenges. Rooted in a “sample-as-optics” philosophy, this technique utilizes precisely engineered line-grating nanopatterns to modulate near-field X-ray illumination, coherently enhancing scattering signals from the line-gratings. We implement the method using Ni line-grating nanopatterns in electrochemical water oxidation. The periodic nanostructures serve as diffractive optical elements to reveal the Ni oxidation gradients and structural dynamics at the electrode-electrolyte interfaces. Finite-element simulations corroborate the observed trends by modeling variations in compositions and structures during electrocatalysis. Through integrating advanced sample design with coherent wave nature of soft X-rays, our approach opens accessible pathways to operando exploring chemical evolution and sub-nanometer dimensional variations simultaneously in electrochemical systems. This non-destructive method is efficient and element-specific, making it valuable for probing chemical and dimensional dynamics with appropriate modeling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A practical approach to calculating magnetic Johnson noise for precision measurements

Magnetic Johnson noise is an important consideration for many applications involving precision magnetometry, and its significance will only increase in the future with improvements in measurement sensitivity. The fluctuation–dissipation theorem can be utilized to derive analytic expressions for magnetic Johnson noise in certain situations, but when used in conjunction with finite element analysis tools, the combined approach is particularly powerful as it provides a practical means to calculate the magnetic Johnson noise arising from conductors of arbitrary geometry and permeability. In this paper, we demonstrate this method to be one of the most comprehensive approaches presently available to calculate thermal magnetic noise. In particular, its applicability is shown to not be limited to cases where the noise is evaluated at a point in space but also can be expanded to include cases where the magnetic field detector has a more general shape, such as a finite-size loop, a gradiometer, or a detector that consists of a polarized atomic species trapped in a volume. Furthermore, some physics insights gained through studies made using this method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Orbit-averaging and deposition accuracy for runaway electron beams in hybrid kinetic-MHD simulations of the runaway plateau

We develop a new procedure that combines the kinetic orbit runaway electron code (KORC) and the NIMROD extended-magnetohydrodynamic code to simulate runaway electrons (REs) in the post-disruption plateau. KORC integrates guiding-center orbits, with a barycentric-based binary search strategy providing initial guesses for the Newton–Raphson logical-to-physical coordinate inversion, ensuring reliable particle-to-mesh mapping in NIMROD, whose fields remain static for the present study. Samples are drawn in accord with experimental parallel current profiles of RE beams during the plateau phase. Deposition in NIMROD is verified through comparison with a Python-based finite-element code that ensures periodicity in the poloidal direction and continuity at the magnetic axis. Accurate representation of near-axis fields requires finer mesh resolution to prevent under- and overshoots in current density from orbit inaccuracies. Yet, at a fixed particle count, increasing mesh resolution amplifies statistical noise in the deposited fields. An orbit-averaging method accumulates partial current deposits over multiple kinetic steps and reduces the statistical noise with little added computational cost. By coupling kinetic routines from KORC directly into the NIMROD codebase, these developments lay essential groundwork for future self-consistent KORC–NIMROD coupling.

Algorithms and data structure↗

DOE OSTI2026

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID↗

DOE OSTI2025

Hydrogen charging and desorption from microstructural viewpoint: A method for deconvoluting hydrogen desorption spectra and unveiling the hydrogen-microstructure interaction

Understanding the interaction of hydrogen with microstructural features in metallic materials is crucial for designing hydrogen-resistant alloys. Although thermal desorption spectroscopy (TDS) is widely used for investigating the hydrogen binding behavior of various microstructural features, its application to face-centered cubic (fcc) metals and alloys that exhibit low hydrogen diffusivity is limited due to the lumped TDS desorption signals. This paper shows that, by coupling a Sofronis–McMeeking type hydrogen transport model with a microstructure-informed finite-element model, TDS data can be deconvoluted to reveal the underlying adsorption–diffusion–desorption processes, hydrogen diffusivity, and trap-binding energies. In conclusion, the austenitic steel SS316L in solution-annealed condition is used as a demonstration material, and we focused on investigating the interaction of deuterium (hydrogen isotope) with grain boundaries, which is difficult to investigate from experiments alone but critical for design of alloys for hydrogen infrastructure.

Finite element simulation, Polycrystalline Microst↗

DOE OSTI2026

A Unified Design Theory for Multi-Port Polyphase Transformers Enabling Scalable Power-Multiplexed EV Fleet Charging Systems

This paper presents a unified analytical design theory for multi-port polyphase transformers, targeting scalable and isolated high-power Electric Vehicle (EV) fleet charging systems with power multiplexing capability. As fleet electrification accelerates, conventional one-to-one charger architectures face significant challenges in infrastructure cost, peak power demand, and low utilization of installed power electronics. Power-multiplexed charging architectures, which dynamically distribute power from a shared pool of converter modules across multiple vehicles, have emerged as a promising solution. However, such architectures require scalable, isolated multi-port power interfaces capable of routing energy among multiple inputs and outputs, whose design remains complex and dependent on iterative modeling. To address this gap, the proposed theory provides closed-form expressions for self-inductance, leakage inductance, and mutual coupling terms for arbitrary multi-phase, multi-port transformer structures. The formulation enables direct synthesis of isolated multi-input and multi-output resonant converter systems without reliance on geometry-specific finite-element analysis or extensive parameter extraction. This capability is particularly critical for power-multiplexed systems, where modular converter structures must interface with multiple vehicles while maintaining galvanic isolation and flexible power allocation. The effectiveness of the proposed framework is demonstrated through the design of a 360 kW multi-phase system operating over a 700–900 VDC input and 400–1250 VDC output range. PLECS simulation results confirm accurate prediction of system behavior and validate the applicability of the approach to multi-port, power-multiplexed charging scenarios. The proposed method significantly reduces design complexity while enabling scalable, cost-effective, and fully utilized EV fleet charging infrastructure.

Asa, Erdem [ORNL] (ORCID:0000000190884812)↗

DOE OSTI2025

Automated Redox Titrations via Interdigitated Electrode Arrays: Application to the Mediated Electron Transfer Interrogation of Charge and Rate on Electrodeposited Polymers

Mediated electron transfer (MET) plays a crucial role in energy storage and conversion technologies such as redox targeting flow batteries (RTFBs), yet its experimental investigation often requires labor-intensive and low-throughput setups. To address this, we developed a microfabricated interdigitated electrode array (IDA) platform that enables automated, high-throughput electrochemical redox titration measurement to be performed to study the MET process. Our redox titration method enables simultaneous measurement of the charge capacity and rate of MET processes on a material or surface. Automated redox titration (ART) facilitates systematic investigation of the MET process across a broad parameter space, exemplified through the study of polypyrrole (PPy) and a pyrene-4,5,9,10-tetrone azo group-based polymer (PTAP), both redox-active polymers relevant to various energy storage applications. Using PPy as a model material, 500 redox titration measurements were conducted within 50 h, varying the electrode gap widths, polymer charging potentials, voltammetric scan rates, and electrolyte concentrations. Finite-element simulations confirmed the electrochemical responses and elucidated the kinetics of the MET reactions. Our automated methodology was further tested with PTAP, revealing a surprising charging potential dependence on the rate of MET. The automation, flexibility, and scalability of our redox titration platform pave the way not only for advanced studies of MET processes relevant to RTFBs, but also with implications in the understanding of next-generation energy storage materials, molecular electrocatalysis, and biosensing.

electrochemical analysis↗

DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Benchmarking of massively parallel phase-field codes for directional solidification

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A three-dimensional laser ray-tracing methodology for radiation-hydrodynamics simulations

We report on a methodology for performing laser ray-tracing in three spatial dimensions for radiation-hydrodynamics simulation codes. Our method, which is an extension of that developed in Haines et al., Comput. Fluids 201, 104478 (2020), utilizes an automatically generated separate mesh for the laser ray-tracing from the radiation-hydrodynamics mesh. This enables the laser mesh to be tailored to minimize ray noise with significantly fewer rays than would be required when the ray-tracing is performed on the radiation-hydrodynamics mesh, primarily by allowing the use of high-aspect-ratio cells that are not suitable for hydrodynamics solvers. For a planar target, we show that our method provides a ≈ 100× reduction in computational expense to achieve a fixed level of ray noise relative to ray-tracing directly on the radiation-hydrodynamics mesh. The relatively low ray requirement also enables efficient computation of cross-beam energy transfer. Each cell in the logically cubic laser mesh is a non-convex dodecahedron with triangular sides, and numerical integration of the ray trajectories and inverse bremsstrahlung is performed by mapping each cell to the unit cube. We will describe our methodology in detail as well as its implementation in the xRAGE radiation-hydrodynamics code, discuss performance, and present the results from applying the methodology to test problems with analytic solutions for laser ray-tracing through a quadratic density gradient with an analytic solution as well as for a laser-driven heat front. In 3D radiation-hydrodynamics simulations of laser-driven experiments performed on the National Ignition Facility, laser ray-tracing with our methodology uses less than 1% of total computational time while introducing acceptably low levels of ray noise.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗