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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.

Bailo, Rafael (ORCID:0000000180183799)↗
DOE OSTI2024

Characterization of latent image of electron beam resist via critical-dimension resonant soft X-ray scattering

Metrology plays a crucial role in semiconductor manufacturing by providing accurate and precise measurement and characterization of critical parameters. With the development of high-resolution extreme ultraviolet lithography (EUVL) processes, critical dimensions are shrinking to sub-10 nm. Resist materials encounter the challenge of providing heightened sensitivity and a handle on exacerbating stochastic variations. A comprehensive understanding of the chemical profile of the latent image is pivotal for mitigating stochastic effects and optimizing pattern quality. However, the subtle differences in chemistry between the exposed and unexposed regions of the resists make it extremely challenging to characterize the latent images with sub-nanometer precision. Here, we develop the metrology with critical-dimension resonant soft X-ray scattering (CD-RSoXS) to probe the chemical profiles of latent images stored in resist after exposure. The combination of absorption spectroscopy and enhanced scattering contrast makes it possible to characterize the subtle structural and chemical variations in the latent image. Moreover, the results of the measurements are compared with the simulations with a finite element method–based Maxwell solver to extract a detailed profile of the latent and developed images. We demonstrate that the CD-RSoXS technique can provide valuable insights into the high spatial resolution and local chemical sensitivity simultaneously, which is crucial to understanding the resolution limits and stochastic effects in EUVL processes.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Viscoelastic necking dynamics between attractive microgels

Hypothesis: Microgels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer–solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. Here we hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales. Experiments: We simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics. Findings: We evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.

42 ENGINEERING↗
DOE OSTI2024

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

We utilize a Fourier transformation-based representation of Maxwell’s equations to develop physics-constrained neural networks for electrodynamics without gauge ambiguity, which we label the Fourier–Helmholtz–Maxwell neural operator method. In this approach, both of Gauss’s laws and Faraday’s law are built in as hard constraints, as well as the longitudinal component of Ampère–Maxwell in Fourier space, assuming the continuity equation. An encoder–decoder network acts as a solution operator for the transverse components of the Fourier transformed vector potential, $\hat{A}_⟂(k,t)$, whose two degrees of freedom are used to predict the electromagnetic fields. This method was tested on two electron beam simulations. Among the models investigated, it was found that a U-Net architecture exhibited the best performance as it trained quicker, was more accurate and generalized better than the other architectures examined. We demonstrate that our approach is useful for solving Maxwell’s equations for the electromagnetic fields generated by intense relativistic charged particle beams and that it generalizes well to unseen test data, while being orders of magnitude quicker than conventional simulations. We show that the model can be re-trained to make highly accurate predictions in as few as 20 epochs on a previously unseen data set.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Scattering of radio frequency waves by randomly modulated density interfaces in the edge of fusion plasmas

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radio frequency (RF) electromagnetic waves that propagate through this region. It is important to know, whether used for diagnostics or for heating and current drive, the spectral properties of these scattered RF waves. The spectral changes influences the interpretation of the diagnostic-data obtained and the current and heating profiles. A full-wave, 3D electromagnetic code ScaRF (see Papadopoulos et al. 2019) has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma, anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can be for the study of scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U, DIII-D. For the case of medium-sized tokamaks, there's experimental evidence that drift waves and rippling modes are present in the edge region (see Ritz et al. 1984). Hence, we study the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes (see Papadopoulos et al. 2019). The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion (see Xiu & Karniadakis 2002) method in conjunction with the Smolyak sparse grid integration (see Papadopoulos et al. 2018) (PCE-SG). The PCE-SG method is proven accurate and much more efficient (roughly 2-orders of magnitude shorter execution time) compared to alternative methods such as the Monte Carlo (MC) approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Design of a Nanophotonic Hybrid Coupler

This project aims to design and simulate a nanophotonic hybrid coupler for detecting vacuum ultraviolet (VUV) light with higher efficiency. VUV light is of significant interest because of its applications ranging from high energy physics to space science and electronic industry. However, current VUV photodetectors have very low efficiencies because most materials absorb in the VUV region (100-200 nm). To address this challenge, I have designed a plasmonic-dielectric coupler with wavelength shifting properties, enabling high Purcell enhancement and far-field confinement. The coupler consists of a cylindrical cSi resonator on top of a thin ZnO layer, and Ag and SiO2 are used as substrates. Simulations are done using the finite-difference time domain method to solve Maxwell’s equations, and specifically with Meep and Lumerical. The effectiveness of the coupler is characterized by the Purcell factor and far-field radiation. The Purcell factor reaches a maximum near 390 nm and is in the o rder of 10^4. Furthermore, the coupler also allows partial control of the directionality of the far-field radiation. With the presence of the resonator, the radiation is directed towards the coupled metalens. Overall, our design combines the advantages of plasmonic and dielectric couplers, along with the intrinsic wavelength shifting properties of materials to enhance VUV detection significantly, and such a device can be used in, for example, the DUNE project.

Zhou, Jiayang↗
DOE OSTI2024

Production of Readily Compressible Dies for the Enhanced Sintering of Solids (PRESS) Preliminary Investigations

Non-oxide ceramics, which consist of predominantly carbides, borides, and nitrides, are of great interest to modern engineering because of their resistance to extreme conditions. Properties of such materials include high temperature resistance, high hardness, chemical resistance, and high fracture toughness. However, the main method for manufacturing parts of these materials is by machining cylindrical billets to the desired geometry. Not only does this produce waste, but the cost of machining is high since the part materials are of such high hardness. This method is used because these non-oxide ceramics must be sintered to high density using simultaneous heat and pressure within a hot-pressing unit. These units are inherently restricted to cylindrical geometries. A proposed way to expand the capabilities of a hot-press is by using intermediate compressible dies. This method consists of surrounding a ceramic part green body with a material that will shrink at the same rate as the part and survive the hot-pressing conditions. At the end, the compressible die material would be removed leaving a nearly net shaped hot-pressed part. In this study, graphite powder was investigated as the compressible die material with its shrinkage rate being controlled by particle size mixing. Both ceramic materials and graphite were then cast into parts and compressible dies respectively to show the feasibility of the compressible die hot-pressing method.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine learning of consistent thermodynamic models using automatic differentiation

In this study, we propose a data-driven method to describe consistent equations of state (EOS) for arbitrary systems. Complex EOS are traditionally obtained by fitting suitable analytical expressions to thermophysical data. A key aspect of EOS is that the relationships between state variables are given by derivatives of the system free energy. In this work, we model the free energy with an artificial neural network and utilize automatic differentiation to directly learn the derivatives of the free energy. We demonstrate this approach on two different systems, the analytic van der Waals EOS and published data for the Lennard-Jones fluid, and we show that it is advantageous over direct learning of thermodynamic properties (i.e., not as derivatives of the free energy but as independent properties), in terms of both accuracy and the exact preservation of the Maxwell relations. Furthermore, the method implicitly provides the free energy of a system without explicit integration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Scattering of radiofrequency waves by randomly modulated density interfaces in the edge of fusion plasmas

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radiofrequency (RF) electromagnetic waves that propagate through this region. It is important to know the spectral properties of these scattered RF waves, whether used for diagnostics or for heating and current drive. The spectral changes influence the interpretation of the obtained diagnostic data, and the current and heating profiles. A full-wave, three-dimensional (3-D) electromagnetic code ScaRF has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method used for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma by the anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can also be used for the study of the scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U and DIII-D. For the case of medium-sized tokamaks, there is experimental evidence that drift waves and rippling modes are present in the edge region. Hence, we have studied the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes. The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion method in conjunction with the Smolyak sparse-grid integration, which is known as the PCE-SG method. The PCE-SG method is proven to be accurate and more efficient compared with alternative methods such as the Monte Carlo (MC) approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Application of mesh refinement to relativistic magnetic reconnection

During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the inherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse–fine interface. We have used the ultrahigh-order pseudo-spectral analytical time-domain Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (or “Yee”) method. Absorbing layers are introduced at the coarse–fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse–fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high-resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Probing two-path electron quantum interference in strong-field ionization with time-correlation filtering

We report attosecond dynamics in strong-field tunnel ionization are encoded in intricate holographic patterns in the photoelectron momentum distributions. These patterns show the interference between two or more superposed quantum electron trajectories, which are defined by their ionization times and subsequent evolution in the laser field. We determine the ionization time separation between interfering pairs of electron orbits by performing a differential Fourier analysis on the measured momentum spectrum. We identify electron holograms formed by trajectory pairs whose ionization times are separated by less than a single quarter cycle, between a quarter cycle and half cycle, between a half cycle and three fourths of a cycle, and a full cycle apart. We compare our experimental results to the predictions of the Coulomb quantum orbit strong-field approximation (CQSFA) with significant success. We also time-filter the CQSFA trajectory calculations to demonstrate the validity of the technique on spectra with known time correlations. As a general analysis technique, the filter can be applied to all energy- and angularly resolved data sets to recover time correlations between interfering electron pathways, providing an important tool to analyze any strong-field ionization spectra. Moreover, it is independent of theory and can be applied directly to experiments, without the need of a direct comparison with orbit-based theoretical methods.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

A Refinement-by-Superposition -Method for (curl)- and (div)-Conforming Discretizations

Here, we present refinement-by-superposition (RBS) hp-refinement infrastructure for computational electromagnetics (CEMs), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on explicit constraint equations, the multilevel strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease, and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H (curl)- and H (div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. As an additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

42 ENGINEERING↗