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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

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

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 OSTI2021

Magnetic-Confinement Fusion—Plasma Theory: Tokamak Magnetohydrodynamic Equilibrium and Stability

Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.

Dispersive pellet injection↗
DOE OSTI2021

Current-conserving relativistic linear response for collisional plasmas

Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Multiscale modeling of microwave-heated multiphase systems

Modeling of microwave heating of multiphase systems requires resolving the electromagnetic field from the single particle to the entire cavity. We introduce a multiscale methodology for computationally affordable simulations of microwave heating of multiphase systems consisting of one phase dispersed in a continuum phase. The methodology homogenizes the original multiphase system, by taking advantage of the large separation of length scales, to calculate the effective permittivity, effective thermal conductivity, and volumetric power absorbed in each phase. The methodology is rigorously assessed against particle-resolved detailed numerical simulations of model systems. We demonstrate a significant reduction in computational cost while retaining the accuracy of detailed simulations. Lastly, the present methodology enables high throughput exploration of novel multiphase system designs utilizing microwave heating.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2022

SPACE: 3D parallel solvers for Vlasov-Maxwell and Vlasov-Poisson equations for relativistic plasmas with atomic transformations

A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-order Particle-in-Cell (PIC) algorithm, SPACE includes efficient novel algorithms to resolve atomic physics processes such as multi-level ionization of plasma atoms, recombination, and electron attachment to dopants in dense neutral gases. SPACE also contains a highly adaptive particle-based method, called Adaptive Particle-in-Cloud (AP-Cloud), for solving the Vlasov-Poisson problems. It eliminates the traditional Cartesian mesh of PIC and replaces it with an adaptive octree data structure. The code's algorithms, structure, capabilities, parallelization strategy, and performance have been discussed. Additionally, typical examples of SPACE applications to accelerator science and engineering problems are described.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Nyström type exponential integrators for strongly magnetized charged particle dynamics

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized due numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior. A promising approach to solve these problems is by a class of methods known as exponential integrators that can solve linear problems exactly and are A-stable. This work extends the standard exponential integration framework to derive Nyström-type exponential integrators that integrates the Newtonian equations of motion as a second-order differential equation directly. In particular, we derive second-order and third-order Nyström-type exponential integrators for strongly magnetized particle pushing problems. Numerical experiments show that the Nyström-type exponential integrators exhibit significant improvement in computation speed over the standard exponential integrators.

general physics↗
DOE OSTI2020

Platform development for dE/dx measurements on short-pulse laser facilities

We illustrate generating benchmark data on charged-particle stopping power in dense plasma is a challenge, motivating new experimental platforms for facilities such as short-pulse lasers. We report on several experiments that aimed to develop a platform for high-precision stopping power measurements at OMEGA EP, specifically developing target-normal sheath acceleration (TNSA) sources, proton isochoric heating, and radiatively heated foams. Integrated experiments were performed to measure stopping power, but several phenomena have been identified that would need to be mitigated for a stopping-power measurement, including irreproducibility of the TNSA sources, spurious electromagnetic fields around proton-heated targets, and cross-talk between the source and subject targets. This work provides a basis for potential future work towards mitigating these problems and performing stopping-power measurements, and is also valuable data for general understanding of TNSA and proton isochoric heating experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Plasmonic hybrid core-shell (HyCoS) AgPt NP template hybridized with GQDs for SERS enhancement of 4-MBA and BT

Surface-enhanced Raman spectroscopy (SERS) is an attractive vibrational spectroscopic technique that can enable a non-destructive and ultra-sensitive detection down to the single-molecule level. Herein, a novel hybrid SERS platform is developed based on hybrid core-shell (HyCoS) AgPt nanoparticles (NPs) and graphene quantum dots (GQDs) for the enhancement of Raman vibration of 4-mercaptobenzoic acid (4-MBA) and benzenethiol (BT). The unique design of HyCoS AgPt NPs induces strong electromagnetic mechanism (EM) enhancement through the amplification of electromagnetic fields by the excitation of high-density surface plasmons and hot spots. Superior localized surface plasmon resonance (LSPR) is generated by the AgPt core-shell and background Ag NP coupling, which is systematically investigated by the optical properties and FDTD simulations. The background Ag NPs can further increase the coverage of metallic NPs, leading to higher-density hot spots and enhanced SERS response. At the same time, GQDs can provide plentiful accessible edges for the charge transfer to the HOMO and LUMO of 4-MBA and BT based on the chemical mechanism (CM) enhancement. The mixing approach of GQDs and target molecules on the HyCoS AgPt NPs can significantly amplify the Raman signals via the strong adsorption of probe molecules by the π – π interaction. The enhancement factors of proposed SERS platform can reach ~107 and ~105 for the 4-MBA and BT respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fast nonlinear iterative solver for an implicit, energy-conserving, asymptotic-preserving charged-particle orbit integrator

Here recently, an asymptotic-preserving (AP) particle orbit integrator has been proposed with remarkable properties including exact energy conservation, the ability to capture of all first-order drifts (including the ∇B-drift), the ability to capture trapped-passing boundaries with parallel velocity extremely close to the critical velocity, and the ability to transition from strongly to weakly magnetized spatial regions. The new AP orbit integrator is implicit, employing a Crank-Nicolson (CN) temporal discretization to ensure exact energy conservation. This, in turn, requires a local nonlinear iteration involving particle velocities and positions, and the local electromagnetic fields, to obtain the new-time solution. Ref. [1] did not attempt to provide an efficient solver for this system, and employed a brute-force GMRES-driven Jacobian-free Newton-Krylov (JFNK) solver to invert the particle orbit equations at every timestep for expediency. While JFNK is robust and reliable, it is also expensive and very intrusive for practical implementations of the method (it requires having the JFNK machinery available and solving a 6 x 6 Jacobian system iteratively once per iteration per particle).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An explicit, energy-conserving particle-in-cell scheme

We present an explicit temporal discretization of particle-in-cell schemes for the non-relativistic Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple, second-order explicit scheme that conserves energy exactly in the Eulerian context. We show that direct translation to particle-in-cell does not result in strict conservation, but derive a simple correction based on an analytically solvable optimization problem that recovers conservation. While this optimization problem is not guaranteed to have a real solution for every particle, we provide a correction that makes imaginary values extremely rare and still admits $\mathcal{O}$(10 –12 ) fractional errors in energy for practical simulation parameters. We present the scheme in both electrostatic – where we use the Ampère formulation – and electromagnetic contexts. With an electromagnetic field solve, the field update is most naturally linearly implicit, but the more computationally intensive particle update remains fully explicit. Here, we also show how the scheme can be extended to use the fully explicit leapfrog and pseudospectral analytic time-domain (PSATD) field solvers. The scheme is tested on standard kinetic plasma problems, confirming its conservation properties.

Energy conservation↗
DOE OSTI2025

Accelerating high-order continuum kinetic plasma simulations using multiple GPUs

Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.

Continuum kinetics↗
DOE OSTI2021

Potential environmental effects of deepwater floating offshore wind energy facilities

Over the last few decades, the offshore wind energy industry has expanded its scope from turbines mounted on fixed platforms driven into the seafloor and standing in less than 50 meters of water, to floating turbines moored in 120 meters of water, to prospecting the development of floating turbines moored in ~1000 meters of water. Since there are few prototype turbines and mooring systems of these deepwater, floating offshore wind energy facilities (OWFs) currently deployed, their effects on the marine environment are largely unknown. Using the available scientific literature concerning appropriate analogs, this study provides the first synthesis of the potential environmental effects of deepwater, floating OWFs during operation, as well as potential mitigation measures to some of the risks. Potential effects we identify and evaluate include changes to atmospheric and oceanic dynamics, electromagnetic fields, habitat alterations, noise, structural impediments, and changes to water quality that could affect a variety of marine species across trophic levels. Our synthesis suggests that many of these potential effects could be mitigated to pose a low risk to the marine environment if developers adopt appropriate mitigation strategies and best-practice protocols. This review takes the necessary first steps in summarizing the available information on the potential environmental effects of deepwater, floating OWFs and can serve as a valuable reference document for marine scientists and engineers, the energy industry, permitting agencies and regulators of the energy industry, project developers, and concerned stakeholders such as coastal residents, conservationists, and fisheries.

Farr, Hayley K.↗
DOE OSTI2025

No evidence of a reduction in the dipole polarisability at shell closures

Photoabsorption reactions have a long and productive history as probes of the response of nuclei to electromagnetic fields. In recent years, there has been a suggestion that the dipole polarisability may be reduced at shell closures, potentially due to the reduced level density. In the current paper, more recent photoabsorption strengths are reanalysed including nuclei on closed proton shells to search for a similar reduction. The previously reported reduction is not reproduced. We conclude that the previously observed reduction may be due to incomplete evaluations of the photoabsorption due to missing cross section contributions and experimental artefacts. More experimental data are necessary to draw a firm conclusion about whether shell effects persist into high excitation energies, especially data which can obviate any systematic effects and look at relative photoabsorption strengths between nuclei.

Giant dipole response↗
DOE OSTI2023

Hot QCD phase diagram from holographic Einstein–Maxwell–Dilaton models

In this review, we provide an up-to-date account of quantitative holographic descriptions of the strongly coupled quark-gluon plasma (QGP) produced in heavy-ion collisions, based on the class of gauge-gravity Einstein-Maxwell-Dilaton (EMD) models. Holography is employed to tentatively map the QCD phase diagram at finite temperature onto a dual theory of charged, asymptotically AdS black holes in 5D. With a quantitative focus on the hot QCD phase diagram, the EMD models reviewed are adjusted to describe lattice results for the finite-temperature QCD equation of state, with 2+1 flavors and physical quark masses, at zero chemical potential and vanishing electromagnetic fields. The predictive power of EMD models is tested by quantitatively comparing their predictions for the hot QCD equation of state at nonzero baryon density and the corresponding state-of-the-art lattice QCD results. The shear and bulk viscosities predicted by these EMD models are also compared to the corresponding profiles favored by the latest phenomenological multistage models describing different heavy-ion data. We report preliminary results from a Bayesian analysis which provide systematic evidence that lattice results at finite temperature and zero baryon density strongly constrains the free parameters of EMD models. Remarkably, the set of parameters constrained by lattice results at zero chemical potential produces EMD models in quantitative agreement with lattice QCD results also at finite baryon density. We also review results for equilibrium and transport properties from magnetic EMD models, describing the QGP at finite temperatures and magnetic fields. Lastly, we provide a critical assessment of the main limitations and drawbacks of the holographic models reviewed in the present work, and point out some perspectives we believe are of fundamental importance for future developments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Deuterated polyethylene nanowire arrays for high-energy density physics

Abstract The interaction of intense, ultrashort laser pulses with ordered nanostructure arrays offers a path to the efficient creation of ultra-high-energy density (UHED) matter and the generation of high-energy particles with compact lasers. Irradiation of deuterated nanowires arrays results in a near-solid density environment with extremely high temperatures and large electromagnetic fields in which deuterons are accelerated to multi-megaelectronvolt energies, resulting in deuterium–deuterium (D–D) fusion. Here we focus on the method of fabrication and the characteristics of ordered arrays of deuterated polyethylene nanowires. The irradiation of these array targets with femtosecond pulses of relativistic intensity and joule-level energy creates a micro-scale fusion environment that produced $2\times {10}^6$ neutrons per joule, an increase of about 500 times with respect to flat solid CD 2 targets irradiated with the same laser pulses. Irradiation with 8 J laser pulses was measured to generate up to 1.2 × 10 7 D–D fusion neutrons per shot.

Optics↗
DOE OSTI2020

The geometric theory of charge conservation in particle-in-cell simulations

In recent years, several gauge-symmetric particle-in-cell (PIC) methods have been developed whose simulations of particles and electromagnetic fields exactly conserve charge. While it is rightly observed that these methods’ gauge symmetry gives rise to their charge conservation, this causal relationship has generally been asserted via ad hoc derivations of the associated conservation laws. In this work, we develop a comprehensive theoretical grounding for charge conservation in gauge-symmetric Lagrangian and Hamiltonian PIC algorithms. For Lagrangian variational PIC methods, we apply Noether’s second theorem to demonstrate that gauge symmetry gives rise to a local charge conservation law as an off-shell identity. For Hamiltonian splitting methods, we show that the momentum map establishes their charge conservation laws. We define a new class of algorithms – gauge-compatible splitting methods – that exactly preserve the momentum map associated with a Hamiltonian system’s gauge symmetry – even after time discretization. This class of algorithms affords splitting schemes a decided advantage over alternative Hamiltonian integrators. We apply this general technique to design a novel, explicit, symplectic, gauge-compatible splitting PIC method, whose momentum map yields an exact local charge conservation law. Finally, our study clarifies the appropriate initial conditions for such schemes and examines their symplectic reduction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗