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DOE OSTI2022

On the Statistics of Elsasser Increments in Solar Wind and Magnetohydrodynamic Turbulence

In this Letter we investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous reduced MHD turbulence on a 2048 3 rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power laws of the form α l ∝ l –μ , where l is the scale size, with μ between 0.17 and 0.25 for observations and 0.43 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results point to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative approach to investigate high-order statistics in solar wind observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Stochastic tensor contraction for quantum chemistry

Many computational methods in ab initio quantum chemistry are formulated in terms of high-order tensor contractions, whose cost determines the size of system that can be studied. We introduce stochastic tensor contraction to perform such operations with greatly reduced cost, and present its application to the gold-standard quantum chemistry method, coupled cluster theory with up to perturbative triples. For total energy errors more stringent than chemical accuracy, we reduce the computational scaling to that of mean-field theory, while starting to approach the mean-field absolute cost, thereby challenging the existing cost-to-accuracy landscape. Benchmarks against state-of-the-art local correlation approximations further show that we achieve an order-of-magnitude improvement in both total computation time and error, with significantly reduced sensitivity to system dimensionality and electron delocalization. We conclude that stochastic tensor contraction is a powerful computational primitive to accelerate a wide range of quantum chemistry.

Chemical Physics (physics.chem-ph)↗

DOE OSTI2026

Disentangling High Harmonic Generation from Surface and Bulk States of a Topological Insulator

The discovery of topological phases has introduced a new dimension to materials science. Three-dimensional (3D) topological insulators (TIs) are a remarkable class of matter that is insulating in the bulk while hosting conductive topological surface states (TSSs) with unique charge and spin properties. High-order harmonic generation (HHG) has emerged as a powerful tool to probe condensed matter systems by providing insights into their electronic structure and dynamic behavior. Here, we investigate HHG in the prototype 3D-TI Bi$_2$Se$_3$. We demonstrate that the contributions of bulk and surface states to the harmonic emission can be controlled by tuning the thickness of thin film samples. An ultrathin (6 nm) film substantially enhances HHG from the surface states, while the bulk states dominate HHG in a thicker (50 nm) film. By applying a quasi-static terahertz perturbing field, we disentangle the bulk and surface responses and reveal the significant impact of the surface states' shift vector and Berry curvature on HHG. Our study provides effective methods for isolating the optical responses of TSSs from those of the bulk, which opens the door to resolving an ongoing debate regarding whether it is possible to reliably extract topological signatures in HHG.

Atomic Physics (physics.atom-ph)↗

DOE OSTI2023

Attosecond light-field control of high-density plasmas (Final Scientific/Technical Report)

Sub-optical-cycle dynamics of dense electron bunches in relativistic-intensity laser—solid interactions (relativistic plasma mirrors) lead to the emission of high-order harmonics and attosecond light pulses. The aim of this project was to advance our understanding of the fundamental principles underlying high-energy-density physics behind this phenomenon. We achieved this goal by conducting experiments and a comprehensive theoretical analysis of harmonics driven by specially tailored light waveforms providing precise control over the sub-laser-cycle trajectories of the emitting electron bunches. The multi-color laser waveforms, generated in our experiments in a cascaded plasma mirror configuration, allowed us to manipulate (enhance and suppress) harmonic generation in relativistic laser-solid interactions by adjusting the relative phase between the colors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics

Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A tunable dielectric resonator for axion searches at 11 GHz

In the context of axion search with haloscopes, tunable cavity resonators with high quality factor and high effective volume at frequencies above about 8 GHz are central for probing the axion-photon coupling with the required sensitivity to reach the QCD axion models. Higher order modes in dielectrically-loaded cavities allow for higher effective volumes and larger quality factors compared to basic cylindrical cavities, but a proper cavity frequency tuning mechanism to probe broad axion mass ranges is yet not available. In this work, we report about the design and construction of a tunable prototype of a single-shell dielectric resonator with its axion-sensitive pseudo-TM$_{030}$ high-order mode at about 11 GHz frequency. A clamshell tuning method previously tested for empty cylindrical resonators has been perfected for this geometry through simulations and in situ tests conducted at cryogenic temperature. Tuning is accomplished in a range of about 2 $\%$ the central frequency, without significantly impacting the quality factor of about 175000. The experimental results presented in this work demonstrate the tunability of this type of resonator, definitely confirming its applicability to high frequency axion searches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract A new adaptive clipping‐and‐redistribution method is presented which provides bounds‐preservation for multidimensional interpolation in the context of high‐order finite‐volume discretizations with adaptive mesh refinement (AMR). The underlying finite‐volume method (FVM) for the computational fluid dynamics applications is fourth‐order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High‐order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high‐order interpolation method. First, the method needs to be bound‐preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth‐order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock‐induced ‐ combustion and a ‐air flame in a practical bluff‐body combustor. Results show the method prevents new extrema near discontinuities while maintaining high‐order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗

DOE OSTI2025

Coupling Approaches with Non-matching Grids for Classical Linear Elasticity and Bond-based Peridynamic Models in 1D

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. Further, the effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Feature extraction for subtle anomaly detection using semi-supervised learning

The demand for automated and effective monitoring techniques has soared with the increased digitization of industrial monitoring systems. State-of-the-art machine learning methods are effectively detecting abrupt changes in system states. However, these methods lack comparable maturity in detecting subtle changes that may be signs of incipient faults. This manuscript argues that the current anomaly detection methods can be enhanced by exploring weak patterns to enable subtle variation detection. Specifically, the concept of semi-supervised learning is employed, with labels representing knowledge about some anomalous conditions of a system. The basic idea is to extract a candidate set of weak patterns discarded by state-of-the-art baselining algorithms. With few labeled anomalous data, the algorithm selects the weak patterns and allows for their possible fusion using the highest sensitivity to the labeled anomalies. Here, the method’s applicability is demonstrated using a representative pressurized water reactor (PWR) model simulated by Dymola.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Mesh refinement for anisotropic diffusion in magnetized plasmas

Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. Here, this work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗

DOE OSTI2023

Towards critical and supercritical electromagnetic fields

Abstract The availability of ever stronger, laser-generated electromagnetic fields underpins continuing progress in the study and application of nonlinear phenomena in basic physical systems, ranging from molecules and atoms to relativistic plasmas and quantum electrodynamics. This raises the question: how far will we be able to go with future lasers? One exciting prospect is the attainment of field strengths approaching the Schwinger critical field ${E}_{\mathrm{cr}}$ in the laboratory frame, such that the field invariant ${E}^2-{c}^2{B}^2>{E}_{\mathrm{cr}}^2$ is reached. The feasibility of doing so has been questioned, on the basis that cascade generation of dense electron–positron plasma would inevitably lead to absorption or screening of the incident light. Here we discuss the potential for future lasers to overcome such obstacles, by combining the concept of multiple colliding laser pulses with that of frequency upshifting via a tailored laser–plasma interaction. This compresses the electromagnetic field energy into a region of nanometre size and attosecond duration, which increases the field magnitude at fixed power but also suppresses pair cascades. Our results indicate that laser facilities with peak power of tens of PW could be capable of reaching ${E}_{\mathrm{cr}}$ . Such a scenario opens up prospects for the experimental investigation of phenomena previously considered to occur only in the most extreme environments in the universe.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Wavelength scaling and multicolor operation of a plasma-driven attosecond x-ray source via harmonic generation

The generation of high-power coherent soft x-ray pulses of sub-100 as duration and 10 nm wavelength using beams from a GeV energy plasma wakefield accelerator has been recently investigated in Emma []. As a future upgrade to this concept, this contribution investigates scaling to shorter x-ray wavelengths by cascading undulators tuned to higher harmonics of the fundamental. We present two simulation studies for plasma-driven attosecond harmonic generation schemes with final photon wavelengths of 2 and 0.40 nm. We demonstrate in these schemes that using undulators with retuned fundamental frequencies can produce GW-scale pulses of sub-nm radiation with tens of attosecond-scale pulse lengths, an order of magnitude shorter than current state-of-the-art attosecond x-ray free electron lasers (XFELs). This multipulse multicolor operation will be broadly applicable to attosecond pump-probe experiments. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Uncovering extreme nonlinear dynamics in solids through time-domain field analysis

Time-domain analysis of harmonic fields with sub-cycle resolution is now experimentally viable due to the emergence of sensitive, on-chip techniques for petahertz-scale optical-field sampling. We demonstrate how such a time-domain, field-resolved analysis uncovers the extreme nonlinear electron dynamics responsible for high-harmonic generation within solids. Time-dependent density functional theory was used to simulate harmonic generation from a solid-state band-gap system driven by near- to mid-infrared waveforms. Particular attention was paid to regimes where both intraband and interband emission mechanisms play a critical role in shaping the nonlinear response. We show that a time-domain analysis of the harmonic radiation fields identifies the interplay between intra- and interband dynamical processes underlying the nonlinear light generation. With further analysis, we show that changes to the dominant emission regime can occur after only slight changes to the peak driving intensity and central driving wavelength. Furthermore, time-domain analysis of harmonic fields also reveals, for the first time, the possibility of rapid changes in the dominant emission mechanism within the temporal window of the driving pulse envelope. Finally, we examine the experimental viability of performing time-domain analysis of harmonic fields with sub-cycle resolution using realistic parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Light-Matter Interaction near the Schwinger Limit Using Tightly Focused Doppler-Boosted Lasers

Strong-field quantum electrodynamics (SF QED) is a burgeoning research topic dealing with electromagnetic fields comparable to the Schwinger field (≈1.32×10 18 V/m). While most past and proposed experiments rely on reaching this field in the rest frame of relativistic particles, the Schwinger limit could also be approached in the laboratory frame by focusing to its diffraction limit the light reflected by a plasma mirror irradiated by a multipetawatt laser. Here, we explore the interaction between such intense light and matter with particle-in-cell simulations. We find that the collision with a relativistic electron beam would enable the study of the nonperturbative regime of SF QED, while the interaction with a solid target leads to a profusion of SF QED effects that retroact on the interaction. In both cases, relativistic attosecond pair jets with high densities are formed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

High-Performance Electron Sources: Numerical Methods and Beam Dynamics at the Precision Frontier

Electron sources have a wide range of applications and there are many stakeholders that express continuing need for improvements and performance enhancements. Whether we consider ultra-cold, high-brightness, high-charge or high-average current source needs, there are some common themes from the point of view of the beam dynamics involved. These are the following ones: ability to model accurately the emission processes, including the presence of often complicated cathode and other boundary surfaces with a wide range of spatial scales; ability to deal accurately and efficiently with a large number of particles interacting pair-wise, including the stochastic part of these interactions with a wide range of spatial scales; and ability to propagate the particle distributions in time, including collisions with a wide range of temporal scales. These tasks require high precision and accuracy since the goal is usually generation, transport and preservation of very high-quality beams. This grant addressed one of the rem

43 PARTICLE ACCELERATORS↗