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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Abstract Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract : Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

Robinson, Alex W.↗
DOE OSTI2020

A new soil mixing layer model for simulating conservative solute loss from initially saturated soil to surface runoff

Surface water pollution due to solute loss from soil to surface runoff is a serious threat to the environment, and it is of great significance to predict the solute loss. While soil mixing layer theory has been widely used to predict the solute loss, it has been observed that the conventional soil mixing layer models with constant mixing layer depth underestimate solute concentration in surface runoff, and thus underestimate the solute loss after surface runoff starts. This study introduced a new soil mixing layer model with a new concept that the mixing layer depth increases downward with time after surface runoff occurs. This new concept was implemented by adding a mixing front between the soil mixing layer and its underlying soil layer, which is conceptually similar to the wetting front of soil infiltration given by the Green-Ampt equation. This is equivalent to treating the soil mixing layer as a deforming control volume. A mechanistic explanation for the new model was presented. This study also developed a closed form solution of the new model. The new model was evaluated by simulating five laboratory experiments conducted by two groups of researchers. The first two experiments have ponding water, and consider different drainage and runoff conditions at both early and late runoff times. The other three experiments do not have ponding water, and consider different infiltration conditions at the bottom of soil boxes. Simulation results of the five experiments show that the new model resolves the underestimation problem of conventional soil mixing layer models. The new model is subject to a total of six limits such as that the new model only considers conservative solute. Three limits are related to the assumptions used to derive the closed form solution, and they may be alleviated in a future research as briefly discussed at the end of the paper.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Analytical Identification Method of Generalized Short‐Circuit Ratio Using Phasor Measurement Units

This paper introduces a novel analytical approach for the identification of the admittance matrix and the generalized short-circuit ratio (gSCR) in power systems integrated with renewable energy sources. The proposed method leverages voltage and current measurements from phasor measurement units (PMUs) to construct a least squares objective function, which is then solved using matrix calculus and partial derivatives. Unlike conventional optimization algorithms, this approach provides an analytical solution that substantially reduces data requirements, enabling the efficient and accurate identification of the gSCR with smaller datasets. Additionally, its fixed computational complexity allows for real-time updates as new data are collected, ensuring continuous refinement of the system of equations and enabling rapid, precise gSCR calculations. The method also exhibits strong robustness against measurement noise, making it well-suited for practical applications in dynamic power systems. The combination of reduced data requirements, real-time adaptability, noise robustness and fixed computational load establishes this method as a highly efficient and reliable tool for real-time power system stability analysis. Case studies on an EPRI 36-bus system demonstrate the method's effectiveness, highlighting its accuracy in closely matching true gSCR values, even under diverse disturbances and noisy conditions.

Han, Zelei [Hohai University, Nanjing (China)] (OR↗
DOE OSTI2023

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

Here, in this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open-source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT . This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open-source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Unitary Qubit Lattice Algorithms for Plasma Physics

This final technical report summarizes research conducted under DOE Award DE-SC0021653 to develop unitary Quantum Lattice Algorithms for modeling electromagnetic wave propagation and scattering in complex media, including plasmas. The project developed and validated quantum-inspired formulations of Maxwell's equations that preserve unitary evolution and can be evaluated on classical high-performance computing systems while providing a foundation for future quantum-computing implementations. Major accomplishments include the development of two- and three-dimensional algorithms for electromagnetic scattering; scalable, distributed-memory implementations demonstrated on the Perlmutter supercomputer; formulations for nonlinear lossless fluid dynamics and cold, lossless, inhomogeneous magnetized plasmas; and an explicit quantum algorithm for a time-discretized Lorenz model. Simulations reproduced a range of characteristic wave phenomena, including transient effects that are not readily apparent in conventional frequency-domain studies, demonstrating the effectiveness of the proposed approach for modeling complex electromagnetic and plasma systems. The work establishes a unified theoretical and computational framework for quantum and quantum-inspired simulation and provides a foundation for future implementation on fault-tolerant quantum systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗
DOE OSTI2021

Distinguishing bulk and surface recombination in CdTe thin films and solar cells using time-resolved terahertz and photoluminescence spectroscopies

Understanding the nature of recombination and its dependence on defects and interfaces is essential for engineering materials and contacts for higher open circuit voltage (V oc ) and power conversion efficiency in photovoltaic (PV) devices. Time-resolved photoluminescence (TRPL) has conventionally been used to evaluate recombination, but carrier redistribution often dominates the response at short times. In this work, we report on the quantification of carrier dynamics and recombination mechanisms by complementary use of both time-resolved terahertz spectroscopy (TRTS) and TRPL combined with numerical modeling of the continuity equations and Poisson’s equation. We have demonstrated this approach using CdTe thin films. A thin film stack with CdTe fabricated by vapor transport deposition and treated with CdCl 2 exhibited a bulk lifetime of 1.7 ± 0.1 ns, negligible CdTe/CdS interface recombination velocity, and back surface recombination velocity of 6.3 ± 1.3 x10 4 cm/s. In contrast, a film stack without CdCl 2 treatment had a bulk lifetime of only 68 ± 12 ps and a higher interface recombination velocity of 4 ± 2 x10 8 cm/s. By determining the locus and mechanisms of performance-limiting recombination, we can accelerate the development of thin-film PVs with higher V oc and efficiency. While the method has been demonstrated here using CdTe, it is also applicable to perovskites, Cu(InGa)Se 2 , Cu2ZnSn(S,Se) 4, and emerging technologies.

14 SOLAR ENERGY↗
DOE OSTI2022

Accurate relativistic observables from postprocessing light cone catalogs

We introduce and study a new scheme to construct relativistic observables from postprocessing light cone data. This construction is based on a novel approach, LC-metric, which takes general light cone or snapshot output generated by arbitrary N-body simulations or emulations and solves the linearized Einstein equations to determine the spacetime metric on the light cone. We find that this scheme is able to determine the metric to high precision, and subsequently generate accurate mock cosmological observations sensitive to effects such as post-Born lensing and nonlinear integrated Sachs-Wolfe contributions. By comparing to conventional methods in quantifying those general relativistic effects, we show that this scheme is able to accurately construct the lensing convergence signal. We also find that the accuracy of this method in quantifying the integrated Sachs-Wolfe effects in the highly nonlinear regime outperforms conventional methods by an order of magnitude. Furthermore, this scheme opens a new path for exploring and modeling higher-order and nonlinear general relativistic contributions to cosmological observables, including mock observations of gravitational lensing and the moving lens and Rees-Sciama effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Holotomography Phase-Retrieval

Holotomography is a non-destructive x-ray imaging technique which allows to visualize the interior morphology of object without damaging them. It is similar to x-ray computed tomography (CT), but unlike conventional CT, which is based on the attenuation of x-rays passing through the object, holotomography exploits the phase shift caused by the sample. This phase-contrast imaging allows to increase image contrast by recovering refractive index of materials and is proven to be more sensitive to density variations than conventional absorption-based X-ray imaging when applied to low-Z materials. In holotomography, the phase is retrieved by measuring the variations in intensity of the object at different sample to detector distances. Several algorithms exist to perform this task such as, contrast transfer function (CTF), transport of intensity equation (TIE), and a mixed approach which combine both TIE and CTF.

Forien, Jean-Baptiste↗
DOE OSTI2025

Chiral rank-$k$ truncations for the multigrid preconditioner of Wilson fermions in lattice QCD

We present a modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD. A larger number of test vectors than that used in conventional multigrid is generated by the smoother. This set of test vectors is then truncated by a singular value decomposition on the chiral components of the test vectors, which are subsequently used to form the prolongation and restriction matrices of the multigrid hierarchy. This modification is demonstrated to improve the convergence of linear equations on an anisotropic lattice with 𝑚𝜋 ≈ 280 MeV from the Hadron Spectrum Collaboration and an isotropic lattice with 𝑚𝜋 ≈ 220 MeV from the MILC Collaboration. The lattice volume dependence of the method is also examined.

Whyte, Travis [Jülich Supercomputing Center, Jülic↗
DOE OSTI2021

Large Eddy Simulation of Lean Mixed-Mode Combustion Assisted by Partial Fuel Stratification in a Spark-Ignition Engine

Partial fuel stratification (PFS) is a promising fuel injection strategy to improve the stability of lean combustion by applying a small amount of pilot injection right before spark timing. Mixed-mode combustion, which makes use of end-gas autoignition following conventional deflagration-based combustion, can be further utilized to speed up the overall combustion. In this study, PFS-assisted mixed-mode combustion in a lean-burn direct injection spark-ignition (DISI) engine is numerically investigated using multi-cycle large eddy simulation (LES). A previously developed hybrid G-equation/well-stirred reactor combustion model for the well-mixed operation is extended to the PFS-assisted operation. The experimental spray morphology is employed to derive spray model parameters for the pilot injection. The LES-based model is validated against experimental data and is further compared with the Reynolds-averaged Navier–Stokes (RANS)-based model. Overall, both RANS and LES predict the mean pressure and heat release rate traces well, while LES outperforms RANS in capturing the cycle-to-cycle variation (CCV) and the combustion phasing in the mass burned space. Liquid and vapor penetrations obtained from the simulations agree reasonably well with the experiment. Detailed flame structures predicted from the simulations reveal the transition from a sooting diffusion flame to a lean premixed flame, which is consistent with experimental findings. LES captures more wrinkled and stretched flames than RANS. Finally, the LES model is employed to investigate the impacts of fuel properties, including heat of vaporization (HoV) and laminar burning speed (SL). Combustion phasing is found more sensitive to SL than to HoV, with a larger fuel property sensitivity of the heat release rate from autoignition than that from deflagration. Moreover, the combustion phasing in the PFS-assisted operation is shown to be less sensitive to SL compared with the well-mixed operation.

fuel property sensitivity↗
DOE OSTI2023

COMPUTATIONAL MODELING OF IGNITION AND PREMIXED FLAME PROPAGATION INITIATED BY A PRE-CHAMBER TURBULENT JET

Addressing the pressing need for reduced carbon emissions, Turbulent Jet Ignition (TJI) emerges as a promising technology for ultra-lean combustion, offering enhanced thermal efficiencies and minimized cyclic variability in spark-ignited engines. To facilitate rapid testing and integration of this technology, a robust computational modeling framework is crucial. This study delves into the predictive capabilities of computational models for main-chamber ignition and premixed flame propagation using a single-cycle TJI rig measured by Biswas et al. (Applied Thermal Engineering, vol 106, 2016). Employing an open-source compressible flow simulation solver with Large Eddy Simulation (LES) for turbulence modeling, the investigation integrates the conventional Laminar Finite Rate Chemistry (LFRC) model alongside the transported Probability Density Method (PDF) for turbulence-chemistry interaction. A fully-consistent Eulerian Monte-Carlo Fields (EMCF) method is utilized to approximate the transported PDF, while Interaction by Exchange with Mean is employed to close micro-mixing terms in stochastic differential equations. A reduced chemical reaction mechanism with 21 species and 84 reactions (DRM-19) is used for solving chemical kinetics, and a double Gaussian energy deposition model is used to approximate the spark ignition in the pre-chamber. An unstructured O-grid mesh with 0.3 million cells in the prechamber and 1 million cells in the main chamber is employed. Results are divided into two phases: pre-chamber initialization and full TJI simulations. Validation of the predicted pre-chamber flame propagation and the lean ignition in the main-chamber is carried out by using available experimental data. Under quiescent conditions, both the LFRC and transported PDF methods largely underestimate the flame speed and subsequent pressure growth in the pre-chamber. A linear momentum forcing technique is applied to investigate the impact of initial turbulence in the pre-chamber, demonstrating a notable influence on flame propagation. Fine-tuning of the forcing coefficient reproduces the sudden pressure growth observed in the experiment. The experimentally validated pre-chamber simulation serves as the initial condition for the full TJI simulations. It is found that the LFRC model fails to predict lean-ignition in the main-chamber, resulting in a misfiring event. Incorporation of turbulence-chemistry interaction using the transported PDF method substantially improves the prediction of the ignition event in the main-chamber, achieving fair qualitative agreement and quantitative validation of combustion parameters within ±10% of the reported experimental data. The rich simulation results consisting of a full set of statistical description of the thermo-chemical states enable us to gain deep insights into the ignition mechanisms in the main chamber, which is limited when done experimentally. A novel dual ignition phenomenon is revealed in the TJI rig for the first time. Initially, a primary ignition kernel is formed at a downstream location which eventually detaches from the main jet. As the jet momentum decreases, a secondary ignition event follows, this time at a more upstream location which eventually combines with the primary ignition kernel to form a single connected flame front. Investigation of these ignition sequences in chemical composition space reveal distinct differences between the two. The primary ignition event in the main-chamber is followed by a large concentration of active radicals from the pre-chamber jet, accelerating the chain-branching steps, characterizing what has been referred to as flame ignition. In contrast, the secondary ignition occurs in the absence of active radicals in the pre-chamber jet, hence characterized as jet ignition. Further analysis of the effect of pre-chamber jet characteristics on lean ignition in the main-chamber is conducted by setting up cases with different initial pressure ratios (por) between the two chambers, a non-dimensional parameter, ranging from 1.2 to 3.2. As the initial pressure ratio increases, jet momentum increases, with dual ignition observed in cases above por= 2.2. Case with por= 3.2 lead to misfiring. The effect of ignition sequence on global combustion characteristics of TJI is analyzed. Dual ignition events lead to non-monotonicity in combustion characteristics such as global reaction progress variable, flame penetration, and global heat release rate. In dual ignition events, although the rate of fuel consumption and global heat release rate is initially lower, the secondary ignition leads to a sudden increase in flame surface area, resulting in a sudden jump and promoting the overall performance of the TJI system.

42 ENGINEERING↗
DOE OSTI2026

Low-stress creep behavior of multiple salt caverns under cyclic operations

Here, the use of multiple salt caverns for large-scale underground hydrogen storage offers a strategic solution to the growing demand for efficient and flexible energy storage, due to the inherent low permeability, high mechanical strength, and self-healing properties of the salt formation. Despite these advantages, the long-term geomechanical response of salt caverns under cyclic injection and withdrawal remains a significant challenge for ensuring operational stability. This mechanistic study highlights the critical role of low-stress creep, also known as pressure solution creep, in governing deformation of salt caverns during cyclic operations. Unlike conventional creep mechanisms that dominate under high-stress conditions, low-stress creep becomes particularly relevant under the moderate stress changes induced by repeated injection and withdrawal, which provides a previously underexplored control on cavern closure. Our three-dimensional computational model integrates the low-stress creep mechanism into the Munson–Dawson creep equation across a spectrum of operational scenarios including variations in cavern pressure cycles, injection-withdrawal frequencies, and caprock mechanical property. The low-stress creep components accelerate the cavern creep closure, which is amplified with shorter cycle frequency and larger pressure difference. Sensitivity analyses capture the complex interactions between multiple caverns and surround formations at the field scale that allows for a quantitative assessment of deformation patterns and closure rates over time and thereby informs the design and operation of sustainable underground hydrogen storage system.

Cyclic operation↗
DOE OSTI2021

Taylor dispersion in osmotically driven laminar flows in phloem

Sucrose is among the main products of photosynthesis that are deemed necessary for plant growth and survival. It is produced in the mesophyll cells of leaves and translocated to different parts of the plant through the phloem. Progress in understanding this transport process remains fraught with experimental difficulties, thereby prompting interest in theoretical approaches and laboratory studies. The Münch pressure and mass flow model is one of the accepted hypotheses describing the physics of sucrose transport in the phloem. It is based on osmosis creating an energy potential difference between the source and the sink. The flow responding to this energy potential is assumed laminar and described by the Hagen–Poiseuille equation. This study revisits such osmotically driven flows in tubes with membrane walls by including the effects of Taylor dispersion on mass transport. This effect has been overlooked in phloem flow studies. Taylor dispersion can increase the effective transport of solutes by increasing the apparent diffusion coefficient. It is shown that, in addition to the conventional diffusive correction derived for impermeable tube walls, a new adjustment to the mean advective terms arises because of osmotic effects. Because the molecular Schmidt number is very large for sucrose in water, the sucrose front speed and travel times have a direct dependence on the Péclet number for different ranges of the Münch number. Fially, this study establishes upper limits on expected Taylor dispersion enhancement of sucrose transport.

42 ENGINEERING↗
DOE OSTI2025

Collision-Energy Dependence in Heavy-Ion Collisions from Nonlinear QCD Evolution

We explore the effects of including the energy dependence determined from evolution equations within the color glass condensate framework on observables in ultrarelativistic heavy-ion collisions. This amounts to integrating the JIMWLK evolution equations into the impact parameter-dependent glasma model, which is then coupled to viscous relativistic hydrodynamics. This methodology allows for a systematic representation of nuclei at specific Bjorken-x values, which are probed at different center-of-mass energies of the collision and rapidities of final state particles. Comparing the methodology to the conventional impact parameter-dependent glasma model, we find significant effects on multiplicity distributions and particle spectra, especially in smaller collision systems at the highest center-of-mass energies. Our results highlight the importance of incorporating nonlinear QCD evolution in the description of heavy-ion collisions at varying center-of-mass energies, as the precise extraction of transport coefficients will be affected. This Letter establishes a robust framework for understanding the quark gluon plasma and nuclear structure at high energy, integrating small-x physics into the initial conditions of heavy-ion collisions.

Mäntysaari, Heikki↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗