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Hale & Paris (T-2) have evaluated the 15 N system to provide nuclear cross section and covariance information for nuclear data uncertainty quantification. This memo gives a brief discussion of the R-matrix method used to generate this nuclear scattering and reaction data in the ENDF-6 format.
For the long-term safety assessment of direct disposal of spent nuclear fuel in deep geologic repositories, knowledge on the radionuclide release rate from the UO 2 matrix is essential. This work provides a conceptual model to explain the results of leaching experiments involving used nuclear fuel or simulant materials in confirmed reducing conditions. Key elements of this model are: direct effect of radiation from radiolytic species (including defects and excited states) in the solid and in the first water layers in contact with its surface; and excess H 2 may be produced due to processes occurring at the surface of the spent fuel and in confined water volumes, which may also play a role in keeping the spent fuel surface in a reduced state. The implication is that the fractional radionuclide release rate used in most long-term safety assessments (10 -7 year -1 ) is over estimated because it assumes that there is net UO 2 oxidation caused by radiolysis, in contrast with the alternative conceptual model presented here. Furthermore, conventional water radiolysis models and radiation chemical yields published in the literature are not directly applicable to a heterogeneous system such as the spent fuel–water interface. Suggestions are provided for future work to develop more reliable models for the long-term safety assessment of spent nuclear fuel disposal.
Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.
This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Finally, additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.
Light–matter interaction at the nanoscale in magnetic alloys and heterostructures is a topic of intense research in view of potential applications in high-density magnetic recording. While the element-specific dynamics of electron spins is directly accessible to resonant x-ray pulses with femtosecond time structure, the possible element-specific atomic motion remains largely unexplored. We use ultrafast electron diffraction (UED) to probe the temporal evolution of lattice Bragg peaks of FePt nanoparticles embedded in a carbon matrix following excitation by an optical femtosecond laser pulse. The diffraction interference between Fe and Pt sublattices enables us to demonstrate that the Fe mean square vibration amplitudes are significantly larger that those of Pt as expected from their different atomic mass. Both are found to increase as energy is transferred from the laser-excited electrons to the lattice. Contrary to this intuitive behavior, we observe a laser-induced lattice expansion that is larger for Pt than for Fe atoms during the first picosecond after laser excitation. This effect points to the strain-wave driven lattice expansion with the longitudinal acoustic Pt motion dominating that of Fe.
Abstract Elastomeric polymer materials hold a special place in today’s industrial sectors with respect to structural application needs. Low quality materials are detrimental to industries like aerospace, and automotive engineering. Assessment of the durability of elastomers for structural applications has been of much interest among the literary circles for decades and new materials keep outperforming the existing ones. Polymeric adhesives are one of the most abundantly used materials in these industries. All polymeric materials get damaged when in contact with aggressive environments in presence of high temperature and oxygen. Commonly referred to as thermo-oxidation, this environment exposes the material to heat and oxidation reactions in presence of oxygen. Resultantly, during service life, the damage to the polymer matrix is primarily caused by two factors: mechanical damage and environmental aging. Environmental aging is an irreversible phenomenon caused by changes in the molecular structure while mechanical damage maintains the shape of the polymer matrix, and the deterioration is mostly due to polymer chain mobility. Environmental aging can be caused by a single environmental agent or by a synergized impact of several environmental elements. Increasing temperature is found to be proportional to decreasing tensile strength and toughness of material. The rate and extent of degradation can be accessed by scrutinizing the changes in constitutive behavior of material through mechanical and chemical properties. Accelerated thermal aging is among the most common modes of process related degradation, leading generally to chain scission, and crosslinking phenomena and reduced resistance to fracture stress, and strain. In this experimental study, our goal is to separate the environmental degradation from mechanical damage. A silicone-based adhesive was aged in thermo-oxidative at (0%RH) aging environment. The damage and decay mechanisms have been used to draw a distinction between environmental degradation and mechanical damage. Material characterization included uniaxial tensile test (failure and cyclic) and scanning electron microscopy (SEM) tests on as-received and aged samples. Aging was conducted at three different temperatures (60°C, 80°C and 95°C) and six different exposure durations (1, 3, 10, 30, 90 and 200 days). This work confirms that environmental damage is superposed on top of the mechanical damage, and thus, they are separable. The total mechanical and environmental damage is a synergized effect of all exposure conditions and parameters involved i.e., aging time, temperature, and oxygen. The chemistry and mechanics of the polymer degradation were found to be in good agreement with each other.
DEAL.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. In this paper, we outline its primary design considerations and its sophisticated features such as distributed meshes, h p -adaptivity, support for complex geometries, and matrix-free algorithms. But DEAL.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.
Waste-to-energy (WTE) facilities incinerate ~35 million tons of municipal solid waste annually in the United States. The incineration process reduces the mass and the volume of the waste fraction by over 75 and 95%, respectively. The fraction left after incineration remains as ash residues and is referred to as WTE ash, compromising of bottom and fly ash. In the United States, ~10 million tons of WTE ashes are generated annually and predominantly landfilled because of the lack of secondary end-use pathways. This incurs a significant financial burden (landfilling costs) on U.S. WTE facilities and also results in the loss of materials to the landfill. The primary objective of this research is to understand better the elemental and mineralogical composition of WTE ashes from diverse origins and find composition dependent upcycling pathways for diverting these ashes from landfills. This primary objective was addressed through three research tasks –(Task I) An AI-led Multi-Modal Approach for Compositional Analysis, (Task II) Developing a Dissolution-Based Test for Real Time Analysis, and (Task III) Establishing composition-dependent end uses. The chemical composition of WTE ash is dependent on two factors, i.e., the input waste composition and the operational parameters of a WTE facility (combustion conditions). Amongst these two factors, the input waste composition will likely show spatial and temporal variation. As a result, the chemical composition of WTE ash will also fluctuate. To understand the spatial and temporal variation in WTE ash composition, in Task I, we collected 128 ash samples (62 bottom ash and 66 fly ash samples) from 11 WTE facilities located in 11 U.S. states and characterized them via X-ray Fluorescence, powder X-ray Diffraction, and Raman Spectroscopy. The findings from this extensive characterization work indicated that the key elements in WTE fly ashes are Ca, Cl (greater than 10 wt. %), Si, S, K, Zn ( between 1 and 10 wt. %), Mg, Al, P, Ti, Fe, Cu, Br, and Pb (between 0.1 and 1 wt. %). Similarly, the key elements in WTE bottom ash fraction finer than 45μm are Ca (greater than 10 wt. %), Mg, Al, Si, S, Cl, K, Ti, Fe, Zn (between 1 and 10 wt. %), P, V, Cr, Mn, Cu, Br, and Pb (between 0.1 and 1 wt. %). Here, we note that the dominant fraction of WTE bottom ash is the coarse fraction. The coarse WTE bottom ash fraction (rich in silicon) was not characterized in this study because of excessive grinding requirements and their unsuitability as a supplementary cementitious material due to their coarse nature. The elements in WTE bottom ashes are present as calcite, anhydrite, vaterite, hydroxyapatite, quartz, bassanite, gehlenite, akermanite, hydrocalumite, and portlandite. Similarly, the mineralogical species present in WTE fly ashes are calcium chloride hydroxide, halite, calcite, anhydrite, sylvite, hydrocalumite, vaterite, hannebachite, quartz, and bassanite. Temporal variation in ash composition may also result in significant fluctuations in chemical compositions. Therefore, a WTE facility may need to monitor the ash composition (elemental and mineralogical composition) in real time. In Task I, we evaluated the possibility of using a portable X-ray fluorescence (XRF) spectrometer to monitor the elemental composition in real-time. Specifically, we collected XRF data on identical specimens via a portable XRF spectrometer (low-end) and a lab-based benchtop XRF spectrometer (high-end). The collected data was used to train an A.I. algorithm (portable XRF data as an input and benchtop XRF data as an output) to predict accurate elemental composition using portable XRF data. Finally, we developed a 2-minute photobleaching protocol to monitor the mineralogical characteristics of WTE ashes via Raman spectroscopy. Overall, the activities in Task I improved our understanding of ash composition and developed techniques to monitor elemental and mineralogical composition in near real-time. Based on the findings of Task I, we find that WTE ashes exhibit wide variability in mineralogy. For ICP-based elemental analysis, all the mineralogical species in WTE ashes must be brought into solution. This is traditionally accomplished with acid digestion using a combination of multiple acids. However, acid digestion with multiple acids is time-consuming and often fails to ensure complete digestion of the ash matrix. To address this limitation, in Task II, we developed an alkali-fusion-based digestion protocol using a combination of lithium tetraborate, lithium metaborate, and their combinations as possible alkali fluxes for digesting WTE ashes entirely and rapidly. The validity of the developed method was evaluated on two standard ash specimens, i.e., SRM 1633c coal fly ash and BCR-176R incineration fly ash specimen. The findings suggest that the developed protocol can ensure complete digestion of elements such as Al, Ba, Ca, Cr, Cu, Mg, Mn, P, Sr, V, Zn, Be, K, and rare earth elements. The recent changes in the energy market towards renewables and increased metal recycling have resulted in reduced supplies of supplementary cementitious materials (coal fly ash and slag). Therefore, in Task III, we evaluated the possibility of employing WTE ashes as SCMs. As the chemical composition of WTE ashes varies temporally (on an hourly basis), there was also a need to develop tests that can evaluate the suitability of material to act as supplementary cementitious material rapidly, i.e., in a few minutes. Therefore, in Task II, we also developed a rapid test to assess the suitability of a material to act as an SCM in 5 minutes. This represents a significant advance over the state-of-the-art R 3 test, which takes ~144 hours. This test was initially validated on amorphous aluminosilicates, such as calcined clays, and could be extended to evaluate other industrial by-products, such as WTE ashes. In Task III, we evaluated the possibility of employing WTE ashes for two applications, i.e., as an SCM and a lime substitute for clay stabilization. The findings from Task I indicated that WTE ashes are enriched in chlorine and, therefore, cannot be used directly as an SCM due to corrosion-related risks and altered hydration kinetics. Accordingly, we developed an ash treatment protocol to reduce the solubility of chlorine-containing species in WTE ashes. The developed treatment protocol also immobilized lead in certain mineral forms. As a result of the treatment, WTE ashes can be used as SCMs without any corrosion or heavy metal leaching concerns. The second application examined in this study was clay stabilization. WTE ashes are calcium-rich and can be an adequate lime replacement for clay stabilization. Our findings reveal that the sum of the concentrations of Ca(OH) 2 and CaClOH controls the clay stabilization capability of WTE ashes. In summary, in this work, we evaluated the elemental and mineralogical characteristics of U.S. WTE ashes from diverse origins and developed tests to evaluate the chemical characteristics of these ashes in real time through a portable XRF and a benchtop Raman spectrometer. Based on the chemical characteristics of these ashes, we developed an ash treatment process to enable the use of WTE ashes as an SCM and also evaluated the possibility of employing these ashes for clay stabilization. Overall, the findings from this work enables the diversion of WTE ashes from landfills for multiple end-uses, i.e., as an SCM or a lime substitute for clay stabilization.
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.
When solving the first-order form of the linear Boltzmann equation, a common misconception is that the matrix-free computational method of “sweeping the mesh”, used in conjunction with the Discrete Ordinates method, is too complex or does not scale well enough to be implemented in modern high performance computing codes. This has led to considerable efforts in the development of matrix-based methods that are computationally expensive and is partly driven by the requirements placed on modern spatial discretizations. In particular, modern transport codes are required to support higher order elements, a concept that invariably adds a lot of complexity to sweeps because of the introduction of cyclic dependencies with curved mesh cells. In this article we will present a comprehensive implementation of sweeping, to a piecewise-linear DFEM spatial discretization with particular focus on handling cyclic dependencies and possible extensions to higher order spatial discretizations. We find that these methods are implemented in a new C++ simulation framework called Chi-Tech (). We present some typical simulation results with some performance aspects that one can expect during real world simulations, we also present a scaling study to >100k processes where Chi-Tech maintains greater than 80% efficiency solving a total of 87.7 trillion angular flux unknowns for a 116 group simulation.
Acidic hydraulic fracturing fluid chemically and physically alters shale rock fabric during injection and shut-in, creating a “reaction-altered zone” along the fracture faces. To better characterize the variable thickness and composition of this reaction-altered zone under advective flow, we take a coupled experimental and modeling approach. A fluidic cell, with six fiducial markers, is first fabricated to keep the rock sample in place during the core floods and to allow image alignment of acquired images. Then, we conduct a series of reactive core floods in a clay-rich siliceous Wolfcamp shale sample with 10 wt % carbonate, using a synthetic fracturing fluid under no confining stress and at room temperature. High-resolution computed tomography (CT) scans are periodically conducted to observe the spatial alteration of the fracture network. We then perform scanning electron microscopy (SEM-EDS) on the two orthogonal surfaces (fracture surface and freshly cut profile face) to generate high-resolution elemental maps that show the change in mineralogy, both with distance along a given flow path along a fracture surface and with depth from the fracture surface into the shale matrix. These results are contrasted against a two-dimensional (2D) advection-diffusion reaction model developed previously for batch reactions between shale and synthetic fracturing fluids. The model simulates the geochemical interaction occurring at the fracture/matrix interface and penetrating into the shale matrix during the reactive core flood. Both model and experimental results show that the acidic brine is neutralized during the core flood, corresponding to an increase in fracture aperture as a function of fluid volume injected with the greatest change near the inlet. SEM-EDS scans reveal significant dissolution of carbonates on the fracture surface without pyrite oxidation. The reactive transport model indicates that carbonate depletion into the shale interior should be observable, yet SEM-EDS shows no discernible loss of carbonate in the orthogonal profile face. The combination of these observations suggests an additional fracture evolution mechanism in the reactive system, i.e., fines migration. We show that fines migration enhances the access of fracturing fluid to the matrix resulting in a more pronounced fracture widening. Finally, we conclude that coupled mineral dissolution and fines migration govern fracture aperture growth during acidized brine injection. In this work, we effectively show the underlying risk of relying solely on models that do not include an important (transport) process that can alter the system significantly and propose a combined chemomechanical mechanism for fracture evolution appropriate for this shale mineralogy.
Careful regulation of monovalent metal ions (M + ) is necessary to maintain a functional cellular system. Of these ions, appropriate sodium (Na + ) and potassium (K + ) concentrations are particularly integral for electrochemical signaling, as well as the secondary transport of nutrients and waste. Dysregulation of M + homeostasis can disrupt these mechanisms, potentially influencing the metabolism of downstream biomolecules such as lipids. Thus, the relationship between M + abundances and related biomolecular distributions must be elucidated to better understand the physiology of healthy and disordered tissues. Traditional techniques for imaging biological metal distributions include SIMS, LA-ICP-MS, and XRF; however, these capabilities are limited to elemental analysis or the analysis of molecular fragments and must be paired with other modalities to visualize distributions of more complex biomolecules within the same or similar samples. Conversely, matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI IMS) is a powerful tool often used for mapping such biomolecular distributions, but current methods are unable to detect metals within tissue. This study illustrates a novel methodology that adds metal detection to the MALDI IMS repertoire through which the simultaneous detection of M + metals and lipids is achievable. Using a robotic sprayer for homogeneous application, on-tissue deposition of the chelator deferiprone (DEF) enables subsequent detection of the ionizable metal-chelator complex by MALDI without hindering lipid detection. Our work provides proof-of-concept data for the simultaneous detection of K + , Na + , and intact lipids using MALDI IMS.
Abstract The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a ∼ 20% excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code,mnms, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).
Particular combinations of solute atoms segregated to the interface of the Al and θ ' - Al 2 Cu in Al-Cu alloys can help stabilize θ ' precipitates at high temperatures. Stabilization of such precipitates is determined by a combination of thermodynamics (including driving forces for coarsening and transformation and solute segregation tendencies) and kinetic effects (including solute diffusion and interfacial mobility in the presence of interfacial solute segregation). For some alloys such as recent Al-Cu-based alloys, multiple solutes segregate in significant quantities to interfaces, and solute-solute interactions at the interface are important, with multiple types of solutes competing for similar interfacial sites. To treat this situation, we develop and apply a statistical mechanics approach to calculate the temperature-dependent equilibrium solute atoms distribution near the coherent and semicoherent interfaces between the Al matrix and the θ ' - Al 2 Cu precipitates. The developed approach is applied to the investigation of Si, Mn, and Zr segregation at the interface, as particular combinations of these elements affect the thermal stability of the θ ' precipitates. We demonstrate that because Si and Mn atoms segregate on the same semicoherent interface, the presence of Si reduces the concentration of Mn solutes at the interface. Si atoms preferably occupy the first layer of the interface and compete with Mn atoms for one type of particular sites in the layer. Mn atoms preferably occupy the second layer of the semicoherent interface, and the Mn-Mn interaction plays an important role in their distribution. Zr atoms mostly segregate on one of the two nonequivalent sites of the second layer of the coherent interface. Due to symmetry properties of the coherent interface, the calculations show that the segregation Zr of atoms to this interface will likely lead to the formation of L 1 2 ordered Al 3 Zr layer.
The Multiphysics Object-Oriented Simulation Environment (MOOSE) framework is a foundational capability used by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work transcribed in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities outlined in this report include a factor of 10^4 improvement in dependency resolution speed, sorting of user objects, ability to compute residuals and Jacobians together, transfer fixes, support for the mortar method in finite volume discretizations, addition of generalized advection schemes for fluid simulations, 10^2 speedup in some Griffin simulations due to a new matrix-only solve type, and much more.
Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.
Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.
Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.