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DOE OSTI2025

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗

DOE OSTI2026

Robustness of pairwise kinematic Sunyaev–Zel’dovich effect to optical-cluster-selection bias

The pairwise kinematic Sunyaev–Zel’dovich (kSZ) effect measures both the pairwise motion between galaxy groups and clusters and the amount of gas within them, providing a tracer for cosmic growth. To interpret the cosmological information in the kSZ measurements, it is crucial to understand the optical-cluster-selection bias on the kSZ observables. Line-of-sight structures that contribute to both the optical observable (e.g., richness) and the cosmological signal can induce a correlation between these two quantities at a fixed cluster mass. The selection bias arising from this correlation is a key systematic effect for cosmological analyses. For cosmological observables such as cluster abundance and weak lensing, controlling this selection bias may help explain the tension between the DES-Y1 results and the Planck constraints. In order to test for a kSZ effect equivalent of such a bias, we adopted an alternative mock richness based on galaxy counts within cylindrical volumes along the line of sight. We applied the cylindrical count method to hydrodynamical simulations across a wide range of galaxy-selection criteria, assigning richness consistent with DES-Y1 to the mock clusters. When comparing optically selected clusters to mass-selected halos, we find no significant bias on pairwise kSZ signals, pairwise velocities, or optical depth within our uncertainty limits of approximately 16, 10, and 8%, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Biconjugate Impedance Matching Control of the HERO WEC: Preprint

Effective control strategies are essential for maximizing the power output of wave energy converters (WECs). In this study, we explore the methodology of port-based modelling which can be used for bi-conjugate impedance matching, a type of reactive control that involves maximizing power transfer by setting the load (PTO) impedance to be the complex conjugate of the source impedance (WEC). Despite its foundational role in electrical engineering, this method has seen limited application in wave energy and has not yet been demonstrated in wave-powered desalination systems. We represent our complex multidisciplinary system as an equivalent circuit to explore frequency-based relations. The HERO WEC, a small-scale, modular point absorber (PA) designed for reverse osmosis desalination is used as a case study to demonstrate port-based modelling for control applications. Improving the performance of wave-powered water desalination systems could play a critical role in addressing freshwater scarcity for coastal communities, especially those in remote or disaster-prone regions.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

CANA v1.0.0: efficient quantification of canalization in automata networks

The biomolecular networks underpinning cell function exhibit canalization, or the buffering of fluctuations required to function in a noisy environment. We present a new major release of $\tt{CANA}$, v1.0.0, an open-source Python package for understanding canalization in automata network models, discrete dynamical systems in which activation of biomolecular entities (e.g. transcription of genes) is modeled as the activity of coupled automata. One understudied putative mechanism for canalization is the functional equivalence of biomolecular regulators (e.g. among the transcription factors for a gene). We study this mechanism using the theory of symmetry in discrete functions. We present a new exact method, $\tt{schematodes}$, for finding maximal symmetry groups among the inputs to discrete functions, and integrate it into $\tt{CANA}$. The $\tt{schematodes}$ method substantially outperforms the inexact method of previous $\tt{CANA}$ versions both in speed and accuracy. We apply $\tt{CANA}$ v1.0.0 to study symmetry in 74 experimentally supported automata network models from the Cell Collective (CC) repository. The symmetry distribution is significantly different in the CC than in random automata with the same in-degree (connectivity) and bias (average output) (Kolmogorov–Smirnov test, P ≪ .001). Its spread is much wider than in a null model (IQR 0.31 versus IQR 0.20 with equal medians), demonstrating that the CC is enriched in functions with extreme symmetry or asymmetry.

Boolean networks↗

DOE OSTI2025

Orthogonality broadcasting and quantum position verification

The no-cloning theorem leads to information-theoretic security in various quantum cryptographic protocols. However, this security typically derives from a possibly weaker property that classical information encoded in certain quantum states cannot be broadcast. To formally capture this property, we introduce the study of ‘orthogonality broadcasting.’ When attempting to broadcast the orthogonality of two different qubit bases, we establish that the power of classical and quantum communication is equivalent. However, quantum communication is shown to be strictly more powerful for broadcasting orthogonality in higher dimensions. We then relate orthogonality broadcasting to quantum position verification and provide a new method for establishing error bounds in the no pre-shared entanglement model that can address protocols previous methods could not. Our key technical contribution is an uncertainty relation that uses the geometric relation of the states that undergo broadcasting rather than the non-commutative aspect of the final measurements.

quantum cryptography↗

DOE OSTI2025

Measuring the thermal conductivity of hydrogels with a bidirectional 3w method

Hydrogels are soft, water-absorbing polymer materials with diverse applications in biomedicine and agriculture. Recently, hydrogels have been proposed to encapsulate water-soluble phase change materials which store energy in their latent heat of solidification. In these applications, the thermal conductivity of these materials affects their performance. Few methods exist for measuring the thermal conductivity of small quantities of hydrogels. Here, we describe an implementation of the bidirectional 3w technique to measure the thermal conductivity of hydrogels with particular attention to their moisture content. Our implementation of the technique can probe sample volumes as little as ~20 mL and yields the thermal conductivity without requiring fitting of additional thermal parameters. We numerically simulate 3w sensor designs with frequency-domain 3-D models to quantify and reduce errors introduced by the choice of substrate and insulation layer thickness. Frequencies in the ~1−20 Hz range yield less error for the materials considered here. We verify our setup with measurements on water and report values for polyacrylamide and poly(2-acrylamido-2-methylpropane sulfonic acid) (PAMPS) hydrogels. Our swollen hydrogels exhibited thermal conductivities nearly equivalent to water, 0.6 W m-1 K-1, and we estimate thermal conductivities of 0.43 and 0.42 W m-1 K-1 for neat polyacrylamide and PAMPS, respectively. Finally, we estimate an error of ±7%, consistent with other 3ω methods, with the largest error coming from the sensor calibration. We find our implementation of the bidirectional 3w method gives reasonable results and can be employed for prototyping soft materials relevant for thermal storage.

3-omega, thermal conductivity, hydrogel, moisture ↗

DOE OSTI2025

The R -Process Alliance: Exploring the cosmic scatter among ten r -process sites with stellar abundances

Context. The astrophysical origin of the rapid neutron-capture process (r-process), responsible for producing roughly half of the elements heavier than iron, remains uncertain. Detailed chemical signatures from the oldest, most metal-poor stars, which act as fossil records of the earliest nucleosynthesis events, can be used to identify the dominant r-process sites. Aims. We present a homogeneous chemical abundance analysis of ten r-process element-enhanced stars. These old and metal-poor stars are strongly enriched in r-process elements with minimal contamination from other nucleosynthetic sources. By focusing on this chemically pure sample, we aim to investigate intrinsic variations in the r-process abundance patterns and explore their implications for the nature and potential diversity of r-process sites. Methods. We performed a detailed chemical abundance analysis of high-resolution, high-signal-to-noise spectra. For each star, we inspected over 1400 individual absorption lines using a combination of equivalent width measurements and spectral synthesis. The analysis was conducted under the assumption of 1D local thermodynamic equilibrium and employing the MOOG radiative transfer code. Results. We derived abundances for 54 chemical species, including 29 neutron-capture (n-capture) elements, covering the full mass range of the r-process abundance pattern. A kinematic analysis reveals that stars likely originated from ten kinematically distinct systems. Based on this assumption, we used the sample to probe the maximum variation expected from ten independent r-process nucleosynthesis events and computed the intrinsic dispersion of each element relative to Zr and Eu for the light and heavy r-process elements, respectively. This exercise resulted in a remarkably low cosmic scatter across the ten r-process sites enriching these stars; for the rare earth and third peak elements, for example, we find σ [La/Eu] = 0.08 and σ [Os/Eu] = 0.11 dex, while the scatter between light and heavy elements, σ [Zr/Eu] , is slightly higher at 0.18 dex. Conclusions. The elemental abundance patterns across the ten independent r-process sites show remarkably small cosmic dispersions. This minimal dispersion suggests a high degree of uniformity in r-process yields across diverse astrophysical environments.

Astronomy and AstroPhysics↗

DOE OSTI2025

Oblique diffraction geometry for the observation of several non-coplanar Bragg reflections under identical illumination

A method to determine the strain tensor and local lattice rotation with dark-field X-ray microscopy is presented. Using a set of at least three non-coplanar symmetry-equivalent Bragg reflections, the illuminated volume of the sample can be kept constant for all reflections, facilitating easy registration of the measured lattice variations. This requires an oblique diffraction geometry,i.e.the diffraction plane is neither horizontal nor vertical. We derive a closed analytical expression that allows determination of the strain and lattice rotation from the deviation of experimental observables (e.g.goniometer angles) from their nominal values for an unstrained lattice.

Chemistry↗

DOE OSTI2024

Cellulose Nanofibrils Dewatered with Poly(Lactic Acid) for Improved Bio-Polymer Nanocomposite Processing

Cellulose nanofibrils (CNFs) have theoretically ideal properties for bio-based composite applications; however, the incorporation of these materials into polymers is made challenging by the strong binding of water to CNFs and the irreversible agglomeration of CNFs during drying. Previous methods used “contact dewatering”, wherein the addition of wood flour (WF) to CNFs facilitated the mechanical removal of water from the system via cold pressing, which showed potential in producing dried CNF fibrils attached to wood fibers for biocomposite applications. In this work, the viability of contact dewatering with poly(lactic) acid (PLA) powder for PLA/CNF composites was evaluated. The energy efficiency of dewatering, preservation of nanoscale CNF morphology, and mechanical properties were examined by mixing wet CNFs with pulverized PLA at various loading levels, pressing water out of the system, and compression molding and shear mixing composites for testing. The most impressive results from this dewatering method were the preservation of micron-to-nanoscale fibers with high aspect ratios in PLA-CNF composites; increased strength and modulus of 1.7% and 4.2%, respectively, compared to neat PLA; equivalent or better properties than spray-dried nanocellulose at similar loading levels; and an 11-194x reduction in drying energy compared to spray-drying CNFs.

Chemistry↗

DOE OSTI2026

Flux Cube Reconstruction from Slitless Spectroscopy

Slitless spectroscopy enables efficient, large-area surveys without target preselection, yet it faces challenges from source blending, higher noise, and lost spatial–spectral information. We present an advanced, nonparametric, data-driven algorithm that leverages multiple dispersion angles to reconstruct three-dimensional flux distributions, providing low-resolution integral field unit capabilities from slitless data. By treating each pixel as an independent element, our method naturally handles source confusion without requiring prior assumptions regarding redshifts, templates, or model libraries. We validate the algorithm using simulated Roman Space Telescope wide-field slitless spectroscopy images that are equivalent to what is expected from the High-Latitude Time-Domain Survey. First, we demonstrate that a host-galaxy model reconstructed from multiple dispersion angles can be used to accurately subtract host light from a transient, recovering a Type Ia supernova spectrum with minimal bias. Second, we showcase a high-fidelity flux-cube reconstruction of a complex galaxy, successfully measuring the redshift and recovering continuum, emission, and absorption features. This approach highlights the potential of multi-dispersion-angle slitless data to provide spatially resolved spectral information in a nonparametric way, which is traditionally accessible only with integral field spectroscopy, opening a new window into large, unbiased, and spatially resolved studies of galaxy evolution.

Griggio, M. [Space Telescope Science Institute, Ba↗

DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗

DOE OSTI2025

Fiber-optic bolometer with low detection limit fabricated using thermal release tape and precise laser heating

Fiber-optic bolometers (FOBs) based on a fiber-tipped silicon Fabry–Perot (FP) interferometric temperature sensor and a gold disk absorber have been shown to be an attractive alternative to conventional resistive bolometers for plasma radiation measurement in fusion devices. Either a high-finesse FP or a low-finesse FP can be used, each with trade-offs between noise performance and fabrication complexity. In this paper, we present an FOB design that overcomes these limitations by combining a low-finesse long silicon FP cavity with a large gold disk absorber to achieve enhanced sensitivity and noise performance without increasing the fabrication complexity and the time constant. We also demonstrated a fabrication method for the sensor head facilitated by thermal release tape and precise laser heating. Our FOB demonstrates a temperature resolution of 0.08 mK, a cooling time constant of 230 ms, and a noise equivalent power density of 0.015 W m −2 . This represents an eightfold improvement over previous high-finesse FOBs and 26-fold improvement over previous low-finesse FOBs with similar demodulation bandwidths and similar cooling time constants.

Fabry–Perot interferometer↗

DOE OSTI2026

From Rules to Reasoning: A Survey of Large Language Model-Based Approaches to Scientific Hypothesis and Idea Generation

Scientific hypothesis generation represents a fundamental challenge in contemporary research due to exponentially expanding literature volumes and increasing disciplinary specialization. Large language models (LLMs) have emerged as transformative tools for automated scientific discovery, moving beyond traditional rule-based and literature-mining approaches. Four paradigmatic approaches define current LLM-driven hypothesis generation: direct prompting and fine-tuning methods, knowledge-enhanced frameworks integrating retrieval-augmented generation (RAG), multi-agent collaborative systems simulating research teams, and reasoning-focused approaches implementing cognitive architectures. Domain-specific applications demonstrate statistical equivalence to human expert performance in social psychology, experimental validation in biomedical research, and near-expert quality in astronomy. Evaluation methodologies encompass human expert assessment, LLM-as-judge frameworks, and comprehensive benchmarking systems. Technical challenges include hallucination management, knowledge integration limitations, and balancing novelty with feasibility. Future directions emphasize hybrid neural-symbolic architectures and sophisticated human-AI collaboration models for responsible scientific discovery acceleration.

AI-driven discovery↗

DOE OSTI2025

2025 Review and Revision of Federal Guidance Report 15

Federal Guidance Report No. 15 (FGR 15), External Exposure to Radionuclides in Air, Water and Soil, published in 2019 and referred to below as FGR 2019, provides age-specific effective dose rate coefficients for reference persons externally exposed to each of 1252 radionuclides homogenously distributed in environmental media. Soon after completion of FGR 2019, the International Commission on Radiological Protection (ICRP) published a similar report (ICRP Publication 144, 2020) addressing the same radionuclides and many of the external exposure scenarios addressed in FGR 2019. In 2023 Argonne National Laboratory (ANL) published a review of dose coefficients in FGR 2019, concluding that “The external effective dose from beta radiation is not appropriately accounted for in FGR 15 for both low- and high-energy beta emitters in air, in soil, and on soil surfaces.” That conclusion was based largely on comparisons of dose coefficients in FGR 2019 with values in ICRP Publication 144 but also on consideration of some unexpected patterns of equivalent dose rate coefficients across tissues and of effective dose rate coefficients across different soil depths, for a selected set of low-energy beta emitters. In response to the ANL report, the Center for Radiation Protection Knowledge (CRPK) at Oak Ridge National Laboratory (ORNL) performed an extensive reexamination of the methods and published values of FGR 2019. CRPK found that coding errors had resulted in inaccurate estimates, primarily overestimates, in many of the dose coefficients tabulated in FGR 2019 but that many of the differences between results in FGR 2019 and ICRP Publication 144 could be traced to differences in methodology. CRPK has corrected all errors in FGR 2019 associated with the coding errors and has taken the opportunity to improve a major portion of the remaining dose coefficients in FGR 2019, primarily through additional Monte Carlo calculations resulting in improved statistics for tissue equivalent dose rate coefficients for exposure to monoenergetic sources. This has eliminated the need for extrapolation of results from high and medium energies to low energies, as was done in FGR 2019. In addition, inconsistencies in the methodology identified in the review, such as computational representation of the adult female, were eliminated. The revised effective dose rate coefficients are consistent with values in ICRP Publication 144 except for differences in values clearly arising from differences in methodology; and differences in values for a relatively small set of very low-energy radionuclides with highly uncertain dose coefficients regardless of methodology.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Tailored Solvent Treatment for Optimized Production of Upcycled Anodes from End-Of-Life Li-Ion Batteries

Recycling processes for lithium-ion batteries typically overlook graphite because of its lower market value relative to that of transition-metal-containing cathode materials. However, graphite recovered from cycled lithium-ion batteries holds additional engineered value associated with the solid-electrolyte interphase (SEI). The SEI contributes critical electronic passivation of the graphite surface but becomes highly resistive with extended cycling, yielding poor cell performance. In this work, we apply tailored solvent treatment to end-of-life (EOL) graphite anodes to selectively remove adverse SEI components while retaining beneficially passivating species. We evaluate a series of polar protic solvents to achieve targeted removal of SEI components and control selectivity through rational variation in solvent properties. The physiochemical properties of treatment solvents correlate with both the retained SEI composition and the corresponding electrochemical performance of solvent-treated “upcycled” graphite anodes. Within the initial set of solvents evaluated, top-performing candidates show capacity and Coulombic efficiency nearly equivalent to those of an analogous pristine anode, as well as promising electrochemical performance enhancement with regard to irreversible capacity-loss metrics. This study establishes critical design principles for an optimized anode upcycling method that enhances the value of recycled graphite by retaining and upgrading the SEI.

25 ENERGY STORAGE↗

DOE OSTI2025

Scaling up the transcorrelated density matrix renormalization group

Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their application to larger systems has been hampered by the computational cost. We develop improved techniques for the transcorrelated density-matrix renormalization group (DMRG), in which the ground state of the transcorrelated Hamiltonian is represented as a matrix product state (MPS), and demonstrate large-scale calculations of the ground-state energy of the two-dimensional Fermi-Hubbard model. Our developments stem from three technical inventions: (i) constructing matrix product operators (MPOs) of transcorrelated Hamiltonians with low bond dimension and high sparsity, (ii) exploiting the entanglement structure of the ground states to increase the accuracy of the MPS representation, and (iii) optimizing the nonlinear parameter of the Gutzwiller correlator to mitigate the nonvariational nature of the transcorrelated method. Here, we examine systems of size up to 12×12 lattice sites, four times larger than previous transcorrelated DMRG studies, and demonstrate that transcorrelated DMRG yields significant improvements over standard nontranscorrelated DMRG for equivalent computational effort. Transcorrelated DMRG reduces the error of the ground-state energy by 2.4×–14×, with the smallest improvement seen for a small system at half filling and the largest improvement in a dilute closed-shell system.

Density matrix renormalization group↗

DOE OSTI2026

Irradiation Testing of Additively Manufactured Materials for LWR Applications: Alloy 718 and 316L Stainless Steel

The objective of this NSUF Project is to assess the changes in irradiated additively manufactured (AM) material properties as compared to non-irradiated material. Type 316L stainless steel and Alloy 718 samples were produced using Direct Metal Laser Melting (DMLM) fabrication. Materials produced from this fabrication method have several potential applications within the nuclear industry as reactor internal repair parts, fuel debris resistant filters, or fuel spacers within existing light water reactors (LWRs). AM materials have been shown to achieve equivalent mechanical behavior in simulated reactor environments as compared to wrought materials, but have significantly more flexibility when it comes to unique design features. The increased component design flexibility makes these AM materials an attractive choice for both current LWR applications as well as for small modular reactor (SMR) designs. Prior to use of these materials in reactor fleet operation, the industry as a whole must evaluate the effects of irradiation on their material properties. Standard 0.4 inch thick Compact Tension specimens and SSJ3 type tensile bars were neutron irradiated at the Advanced Test Reactor to ~1 dpa for the purpose of performing a variety of mechanical tests in a range of simulated environments applicable to LWRs. For the ductile austenitic Type 316L stainless steel, the irradiated data will be used to confirm that the AM process produces materials with properties that are equivalent to wrought materials under testing conditions applicable to LWR operation. Transmission electron microscopy analysis was also performed in order to understand microstructural and microchemical changes induced in each material in response to neutron irradiation. If possible, data collected from these AM 316L samples will be used to remove fluence limits from specifications of ASME code cases for this alloy, which will give vendors much more flexibility in building future components.

36 - MATERIALS SCIENCE↗

DOE OSTI2024

Towards modelling AR Sco: generalized particle dynamics and strong radiation-reaction regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realized the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time-step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform E- and B-fields and a static dipole B-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time-steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand–Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytical Aristotelian Electrodynamics expectations.

79 ASTRONOMY AND ASTROPHYSICS↗