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DOE OSTI2022

Data-driven surrogate modeling of hPIC ion energy-angle distributions for high-dimensional sensitivity analysis of plasma parameters' uncertainty

In this work, we present a data-driven strategy for effective construction of a surrogate model in high-dimensional parameter space for the ion energy-angle distribution (IEAD) output of hPIC simulations of plasma-surface interactions. The methodology is based on a bin-by-bin least-squares fitting of the IEAD in the parameter space. The fitting is performed in a transformed coordinate system to normalize the IEAD, and it employs sparse grids for sampling the parameter space to overcome sampling challenges in high dimensions. The surrogate model is significantly cheaper computationally than direct hPIC simulations yet maintains high fidelity to them, providing a fast emulator for hPIC simulations. Sensitivity analysis based on the surrogate model is utilized to characterize the dependence of the ion impact angle and energy moments on the physical parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Magnetothermal properties of Ho 1-x Dy x Al 2 (x = 0, 0.05, 0.10, 0.15, 0.25 and 0.50) compounds

Magnetic and magnetocaloric properties of H o 1 - x D y x A l 2 compounds with x = 0 , 0.05 , 0.10 , 0.15 , 0.25 and 0.50 , modelled using a Hamiltonian that includes the exchange interactions between Ho-Dy, Ho-Ho and Dy-Dy ions in addition to the crystalline electric field and the Zeeman effects, have been compared with those determined experimentally. In order to reproduce experimentally observed global ferromagnetic ordering temperatures and spin reorientation transition temperatures as x Dy varies, the exchange interactions between Ho-Dy and Ho-Ho were set as free parameters and adjusted to match the experimental results. We demonstrate that heat capacity of polycrystalline materials in non-zero magnetic fields can be satisfactory reproduced by using the average of multiple magnetic field directions with respect to the crystallographic coordinate system, while reasonably good agreement between experimentally determined and theoretically predicted magnetocaloric effects can be achieved considering an average of only three field directions.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Austenitic parent grain reconstruction in martensitic steel using deep learning

In this work we develop a deep convolutional architecture to estimate the prior austenite structure from observed martensite electron backscatter diffraction micrographs. A novel data augmentation strategy randomizes the global reference coordinate system which makes it possible to train our model from only four micrographs. The model is much faster than algorithmic approaches and generalizes well when applied to micrographs of a different material. Empirical evidence suggests the efficacy of the model depends on the scale of the microstructure and receptive field of the vision model. Furthermore, this work demonstrates that modern computer vision approaches are well suited for capturing complex spatial-orientation patterns present in orientation imaging micrographs.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Process planning for hybrid manufacturing using additive friction stir deposition

Additive friction stir deposition (AFSD) provides a solid-state approach to metal deposition that does not rely on local melting and solidification, but rather on kinetic energy and plastic flow. Here, in this study, AFSD is combined with structured light scanning, turning, and milling to produce metal components while considering the unique requirements imposed by the hybrid manufacturing process sequences. Two demonstrations are presented which include: 1) a cylindrical build plate selection to enable coordinate system transfer between deposition and turning of a hollow cone; and 2) intermittent deposition-machining operations with structured light scanning to fabricate a two-sided hexagon-cylinder geometry.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Modeling magnetic fields with helical solutions to Laplace’s equation

The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via linear, multidimensional curve-fitting. A judicious choice of functional forms, a small number of free parameters and sparse input data can lead to highly accurate, fine-grained modeling of solenoidal magnetic fields, including helical features arising from the winding of the solenoid, with overall field accuracy at better than one part per million.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

First 3D vector tracking of helium recoils for fast neutron measurements at Super$\mathrm{KEKB}$

Here we present results from the first deployment of novel, high definition, compact gas Time Projection Chambers (TPCs) with pixel chip readout as part of the BEAST II beam background measurement project at SuperKEKB. The TPCs provide detailed 3D imaging of ionization from neutron-induced nuclear recoils in a helium and carbon dioxide target gas mixture at standard temperature and pressure. We present the TPC performance and the neutron backgrounds observed during the initial stage of collider commissioning. We find excellent electron background rejection, leading to background-free nuclear recoil measurements above 50 keV ee , despite the extreme high-background environment. We measure an angular resolution better than 20° for recoil tracks longer than 1.7 mm, corresponding to an average ionization energy of approximately 100 keV ee . We also obtain the full 3D vector direction of helium recoils by utilizing charge profile measurements along the recoil axis, with a correct head/tail assignment efficiency of approximately 80%. With this performance, we present comparisons between measured and simulated event rates, recoil energy spectra, and directional distributions originating from beam–gas and Touschek beam losses at SuperKEKB. We utilize head/tail recognition to distinguish neutron components traveling with positive radial velocity in the Belle II coordinate system from those traveling in the opposite direction. Finally, we present a novel method of discriminating beam–gas interactions from Touschek beam losses that can eliminate the need for dedicated accelerator runs for background measurements. This method is still statistics-limited. However, future studies should be able to verify this method, which in turn could lead to neutron background analysis runs symbiotic with normal Belle II operation. The capabilities demonstrated here also suggest that high definition recoil imaging in gas TPCs is applicable to low energy, low-background experiments, such as directional dark matter searches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

A streamline coordinate analysis of a turbulent boundary layer subject to pressure gradients and curvature on the windward side of a bump

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

42 ENGINEERING↗

DOE OSTI2026

Analytic Nuclear Gradients Including Oriented External Electric Fields in a Molecule-Fixed Frame

Electric-field-assisted chemistry has attracted much attention in recent years, particularly in the context of oriented external electric fields for controlling molecular structure and reactivity. Such fields have been explored in a wide range of applications, including switching materials, nanoparticles, controllable catalysts, medicines, and clinical therapies. However, the determination of fixed fields in the laboratory frame becomes ineffective for flexible molecules, as conformational changes can significantly alter the relative orientation between the applied field and molecular structure. In this work, we propose two molecular reference frames─the principal axis frame and the local reference frame─to define oriented electric fields within the molecular framework. These coordinate systems powerfully eliminate ambiguities in the relative orientation between the applied field and the molecule. Analytic nuclear gradients in the presence of external electric fields are derived and implemented, with an initial application to field-dependent geometry optimizations of cis - and trans -formanilide. Analysis of the resulting field-induced equilibrium structures reveals distinct structural responses, validating the accuracy and robustness of the proposed formalism. The analytic gradient framework enables systematic investigations of molecular properties and reactivity under arbitrarily oriented electric fields, opening new opportunities for computational modeling and rational design in electric-field-controlled chemistry.

electric fields↗

DOE OSTI2024

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. Here we present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

1,3,5-triamino-2,4,6-trinitrobenzene↗

DOE OSTI2020

First Analysis of Earth's Stratospheric γ ‐Ray Emission in Geographical Coordinates With Fermi LAT

Abstract From low‐Earth orbit, the Earth is an extremely bright γ ‐ray source compared to distant astrophysical objects. The high‐energy γ ‐ray emission, from the Earth's upper atmosphere, is produced by the interactions between cosmic rays (CRs) and air molecules. As CRs are predominantly charged particles, the geomagnetic field acts as a spectrometer, forbidding CRs below a certain energy to arrive and interact with the atmosphere at a given geomagnetic location from a given direction. We use photon data between 0.2 and 20 GeV as observed by the Fermi Large Area Telescope (LAT) to create, for the first time, stratospheric γ ‐ray emission maps of the Earth in the geographical coordinate system, for different viewing directions from LAT altitude. These maps confirm a strong association between measured γ ‐ray fluxes and geomagnetic cutoffs for CRs. We also report the spectrum of the Earth's stratospheric γ ‐ray emission in cardinal directions and use the geomagnetic spectrometer effect to infer the atmosphere's yield function of γ rays per incoming CR proton as a function of CR rigidity at the altitude of the Fermi spacecraft. This work is relevant to the study of near‐Earth radiation exposure for astronauts and spacecraft, modeling the geomagnetic field, and CR‐air interactions.

Madlee, S.↗

DOE OSTI2021

Vertical Variations of Cloud Microphysical Relationships in Marine Stratocumulus Clouds Observed During the ACE‐ENA Campaign

Abstract This study examines the vertical variations of cloud microphysical relationships and their implications to cloud microphysical processes in marine stratocumulus clouds using in‐situ aircraft observations during the Aerosol and Cloud Experiments in Eastern North Atlantic (ACE‐ENA) field campaign. A new diagram with a coordinate system based on cloud droplet liquid water content (L c ) and phase relaxation time scale is proposed to investigate mixing mechanisms. This new diagram analysis shows that the inhomogeneous mixing trait is dominant near the cloud top, but homogeneous mixing trait is stronger at lower altitudes. The relevant scale parameters (i.e., transition length scale and transition scale number) also indicate a high likelihood of inhomogeneous mixing. The relationship between L c and standard deviation of droplet radius (σ R ) clearly shows the vertical transition: the correlation between L c and σ R is positive at lower cloud altitudes, but it becomes negative as altitude increases. Such a vertical transition is consistent with the vertical circulation mixing, modulating the cloud microphysical relationships to suggest homogeneous mixing at a significant depth from the cloud top.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Estimation of the Kelvin–Helmholtz Unstable Boundary

The Kelvin–Helmholtz (KH) instability is one of the most important mechanisms of the viscous-like interaction between the solar wind and the magnetosphere (MSP), which transport the mass, energy, momentum, and magnetic flux. Thus, it is important to examine whether the magnetopause boundary is KH unstable or not. Based on the KH onset conditions, this report proposes to use a matrix to identify the most KH unstable direction based on the in situ measurements of the density, velocity, and magnetic field in the MSP and magnetosheath. The range of the KH unstable direction can be easily estimated based on the eigenvalues of the matrix. The eigenvectors of the matrix provide a new boundary normal coordinate system, which could be useful for 2-D KH instability simulation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Optical analogues to the equatorial Kerr–Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

X-point effects on the ideal MHD modes in tokamaks in the description of dual-poloidal-region safety factor

The flux coordinates with dual-region safety factor (q) in the poloidal direction are developed in this work. The X-point effects on the ideal MHD modes in tokamaks are then analyzed using this coordinate system. Since the X-point effects mainly affect the edge region, the modes localized at the tokamak edge are particularly examined. Two types of modes are studied. The first is related to the conventional peeling or peeling-ballooning modes. The mode existence aligned with the local magnetic field in the poloidally core region as observed experimentally is confirmed. The X points are shown to contribute to a stabilizing effect for the conventionally treated modes with the surface-averaged q and with the tokamak edge portion truncated. The other is the axisymmetric modes localized in the vicinity of X points, which can affect the cross-field-line transport near the X points. The existence of axisymmetric modes points to the possibility of applying a toroidally axisymmetric resonant magnetic perturbation (RMP) in the X-point area for mitigating the edge localized modes, which can be an alternative to the current RMP design. The dual q description also has important implications for the existing non-axisymmetric RMP concept. It helps to understand why the RMP suppression of edge localized modes is difficult to achieve in the double-null tokamak configurations and points to the possibility of further improving the current RMP concept by considering the alignment to the local q.

Fourier analysis↗

DOE OSTI2025

A Grad-Shafranov model for compact quasisymmetric stellarators

A Grad-Shafranov equation (GSE) valid for compact quasisymmetric stellarators is derived by an asymptotic expansion around a vacuum field carried to first order. We obtain an equation for the existence of flux surfaces leading up to the GSE. The flux surface label must simultaneously satisfy the existence equation and the GSE, which generally leads to an overdetermined problem. We show how the overdetermined problem can be resolved within our model for a class of hybrid devices similar to that studied by Henneberg and Plunk [Phys. Rev. Res. 6, L022052 (2024)]. We are also able to solve the existence equation for flux surfaces analytically in the most general case by introducing a special coordinate system. This will enable us to carry out an optimization seeking to minimize the error in our GSE while obeying the flux surface existence equation, which will allow us to find solutions outside the class of hybrid devices. This will allow for a coarse-grained approximate search in the space of quasisymmetric equilibria that should be faster than a conventional stellarator optimization. Nevertheless, it would still be necessary to fine-tune the approximate solutions using conventional tools to obtain a more precise optimized equilibrium.

Nikulsin, N. (ORCID:0000000318611777)↗

DOE OSTI2025

Reference Correlations for the Density and Viscosity of Molten Alkali and Alkaline Earth Fluoride Salts

While there is a significant body of literature pertaining to thermophysical property measurements of molten salts, there is often a wide degree of variability among independent measurements of the same compounds. As such, the scientific community benefits greatly from an unbiased, independent assessment of duplicate datasets, so that reference correlations which describe these thermophysical properties as functions of temperature can be determined and then commonly used by researchers, scientists, and engineers. With regard to molten fluoride compounds, a significant time has elapsed since density and viscosity reference correlations have been determined; Janz conducted the most recent effort, in 1988, to provide reference correlations for the densities and viscosities of molten fluoride compounds via the National Standard Reference Data System coordinated by the National Bureau of Standards. Since then, new data have been published for molten fluoride compounds, and a new precedent has surfaced for putting forth reference correlations that involve fitting to multiple primary datasets. In this work, reference correlations are put forth for molten alkali and alkaline earth fluoride compounds in an effort to provide updated, improved correlations for general use. For molten alkali fluoride densities, estimated uncertainties with a 95% confidence interval are summarized as follows: LiF (0.63%), NaF (0.48%), KF (0.76%), RbF (0.93%), and CsF (0.75%). For molten alkaline earth fluoride densities, an estimated uncertainty was not able to be quantified for BeF 2 because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkaline earth fluorides: MgF 2 (1.5%), CaF 2 (0.92%), SrF 2 (1.6%), and BaF 2 (0.23%). For molten alkali fluoride viscosities, uncertainty was not able to be quantified for RbF and CsF because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkali fluorides: LiF (4.4%), NaF (3.0%), and KF (4.0%). For molten alkaline earth fluoride viscosities, limited consistent data resulted in the recommendation of single datasets (from literature) that are deemed to be the most trustworthy based on the quality of the underlying experimental studies.

Birri, A. [Oak Ridge National Laboratory (ORNL), O↗

DOE OSTI2025

Extending the Mott–Gurney law to one-dimensional nonplanar diodes using point transformations

Recent studies have applied variational calculus, conformal mapping, and point transformations to generalize the one-dimensional (1D) space-charge limited current density (SCLCD) and electron emission mechanisms to nonplanar geometries; however, these assessments have focused on extending the Child–Langmuir law (CLL) for SCLCD in vacuum. Since the charge in the diode is independent of the coordinate system (i.e., covariant), we apply bijective point transformations to extend the Mott–Gurney law (MGL) for the SCLCD in a collisional or semiconductor gap to nonplanar 1D geometries. This yields a modified MGL that replaces the Cartesian gap distance with a canonical gap distance that may be written generally in terms of geometric scale factors that are known for multiple geometries. We tabulate results for common geometries. Such an approach may be applied to any current density, including non-space-charge limited gaps and SCLCD that may fall between the CLL and MGL.

Garner, Allen L. [Purdue Univ., West Lafayette, IN↗

DOE OSTI2026

Novel approach to general curvilinear coordinates for plasma fluid applications

In general geometry, plasma fluid equations include nonlinear geometric sources associated with fictitious forces, which pose significant challenges to computer simulations. We reformulate the plasma fluid hierarchy to rigorously preserve geometry and conservation properties critical to numerical simulations, while concealing the geometric sources. In their discrete form, the reformulated models conserve mass, angular momentum, and energy naturally, by simple analogy with the continuum equations. These conservation properties have minimal requirements in discrete space, namely, the anti-symmetry of the first derivative and the orthogonality of the scalar and cross products. By decoupling magnetic geometry, coordinate systems, and numerical discretization, this enables maximum flexibility while preserving physics fidelity. As a testbed, we apply the novel representation to the resistive magnetohydrodynamic system, which involves a complete set of curvilinear operations. We verify the correctness of the approach using steady state liquid metal flows and the classic Orszag–Tang vortex.

Halpern, Federico D. [General Atomics, San Diego, ↗