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NASA NTRS1994

The cosmological dependence of cluster density profiles

We use N-body simulations to study the shape of mean cluster density and velocity profiles in the nonlinear regime formed via gravitational instability. The dependence of the final structure on both cosmology and initial density field is examined, using a grid of cosmologies and scale-free initial power spectra P(k) varies as k(exp n). Einstein-de Sitter, open (Omega(sub 0) = 0.2 and 0.1) and flat, low density (Omega(sub 0) = 0.2 lambda(sub 0) = 0.8) models are examined, with initial spectral indices n = -2, -1 and 0. For each model, we stack clusters in an appropriately scaled manner to define an average density profile in the nonlinear regime. The profiles are well fit by a power law rho(r) varies as r(exp -alpha) for radii whereat the local density contrast is between 100 and 3000. This covers 99% of the cluster volume. We find a clear trend toward steeper slopes (larger alphas) with both increasing n and decreasing Omega(sub 0). The Omega(sub 0) dependence is partially masked by the n dependence; there is degeneracy in the values of alpha between the Einstein-de Sitter and flat, low-density cosmologies. However, the profile slopes in the open models are consistently higher than the Omega = 1 values for the range of n examined. Cluster density profiles are thus potentially useful cosmological diagnostics. We find no evidence for a constant density core in any of the models, although the density profiles do tend to flatten at small radii. Much of the flattening is due to the force softening required by the simulations. An attempt is made to recover the unsoftened profiles assuming angular momentum invariance. The recovered profiles in Einstein-de Sitter cosmologies are consistent with a pure power law up to the highest density contrasts (10(exp 6)) accessible with our resolution. The low-density models show significant deviation from a power law above density contrasts approximately 10(exp 5). We interpret this curvature as reflecting the non-scale-invariant nature of the background cosmology in these models. These results are at the limit of our resolution and so should be tested in the future using simulations with larger numbers of particles. Such simulations will also provide insight on the broader problem of understanding, in a statistical sense, the full phase space structure of collapsed, cosmological halos.

Crone, Mary M.↗
NASA NTRS2012

Joining and Assembly of Bulk Metallic Glass Composites Through Capacitive Discharge

Bulk metallic glasses (BMGs), a class of amorphous metals defined as having a thickness greater than 1 mm, are being broadly investigated by NASA for use in spacecraft hardware. Their unique properties, attained from their non-crystalline structure, motivate several game-changing aerospace applications. BMGs have low melting temperatures so they can be cheaply and repeatedly cast into complex net shapes, such as mirrors or electronic casings. They are extremely strong and wear-resistant, which motivates their use in gears and bearings. Amorphous metal coatings are hard, corrosion-resistant, and have high reflectivity. BMG composites, reinforced with soft second phases, can be fabricated into energy-absorbing cellular panels for orbital debris shielding. One limitation of BMG materials is their inability to be welded, bonded, brazed, or fastened in a convenient method to form larger structures. Cellular structures (which can be classified as trusses, foams, honeycombs, egg boxes, etc.) are useful for many NASA, commercial, and military aerospace applications, including low-density paneling and shields. Although conventional cellular structures exhibit high specific strength, their porous structures make them challenging to fabricate. In particular, metal cellular structures are extremely difficult to fabricate due to their high processing temperatures. Aluminum honeycomb sandwich panels, for example, are used widely as spacecraft shields due to their low density and ease of fabrication, but suffer from low strength. A desirable metal cellular structure is one with high strength, combined with low density and simple fabrication. The thermoplastic joining process described here allows for the fabrication of monolithic BMG truss-like structures that are 90% porous and have no heat-affected zone, weld, bond, or braze. This is accomplished by welding the nodes of stacked BMG composite panels using a localized capacitor discharge, forming a single monolithic structure. This removes many complicated and costly fabrication steps. Moreover, the cellular structures detailed in this work are among the highest- strength and most energy-absorbent materials known. This implies that a fabricated structure made from these materials would have unequaled mechanical properties compared to other metal foams or trusses. The process works by taking advantage of the electrical properties of the matrix material in the metal-matrix composite, which in this case is a metallic glass. Due to the random nanoscale arrangement of atoms (without any grain boundaries), the matrix glass exhibits a near-constant electrical resistivity as a function of temperature. By placing the composite panels between two copper electrode plates and discharging a capacitor, the entire matrix of the panel can be heated to approximately 700 C in 10 milliseconds, which is above the alloy s solidus but below the liquidus. By designing the geometry of the panels into the shape of an egg box, the electrical discharge localizes only in the tips of each pyramidal cell. By applying a forging load during discharge, the nodes of the panels can be fused together into a single piece, which then dissipates heat through radiation back into a glassy state. This means that two panels can be metallurgically fused into one panel with no heat-affected zone, creating a seamless connection between panels. During the process, the soft metal particles (dendrites) that are uniformly distributed in the glassy matrix to increase the toughness are completely unaffected by the thermoplastic joining. The novelty is that a truss (or foam-like) structure can be formed with excellent energy- absorbing capabilities without the need for machining. The technique allows for large-scale fabrication of panels, well-suited for spacecraft shields or military vehicle door panels. Crystalline metal cellular structures cannot be fabricated using the thermoplastic joining technique described here. If metal panels were te assembled into a cellular structure, they would either have to be welded, brazed, bonded, or fastened together, creating a weak spot in the structure at each connection. Welded parts require a welding material to be added to the joint and exhibit a soft and weak heat-affected zone. Brazing and bonding do not form a metallurgical joint and thus exhibit low strengths, especially when the panels are pulled apart and fasteners require high-stress-concentration holes to be drilled. No equivalent rapid heating method exists for assembling metal panels together into cellular structures, and thus, those parts must be foamed, machined, or investment cast if they are to form a monolithic structure. If the crystalline panels were to be joined using capacitive discharge, as with a spot welder, their bond would be very weak, and the panels would have to be extremely thin. In contrast, the strength of joined BMG parts has been demonstrated to have strength comparable to the parent material. This technique opens up the possibility of using large-scale BMG hardware in spacecraft, military, or commercial applications.

Hofmann, Douglas C.↗
DOE OSTI2025

Molecular fluctuations inhibit intermittency in compressible turbulence

In the standard picture of fully developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients. Microscopically, however, constituent fluid molecules are in constant thermal (Brownian) motion, but the role of molecular fluctuations in large-scale turbulence is largely unknown, and with rare exceptions, it has historically been considered irrelevant at scales larger than the molecular mean free path. Recent theoretical and computational investigations have shown that molecular fluctuations can impact energy cascade at Kolmogorov length scales. Here, we show that molecular fluctuations not only modify energy spectrum at wavelengths larger than the Kolmogorov length in compressible turbulence, but also significantly inhibit spatio-temporal intermittency across the entire dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly Gaussian statistics in the dissipation range. These results demonstrate that the compressible Navier–Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range. Our findings have significant consequences for turbulence modelling in applications such as astrophysics, reactive flows and hypersonic aerodynamics, where dissipation-range turbulence is approximated by closure models.

compressible turbulence↗
DOE OSTI2021

Theoretical study of intrinsic defects in cubic silicon carbide 3C-SiC

Using the local moment counter charge (LMCC) method to accurately represent the asymptotic electrostatic boundary conditions within density functional theory supercell calculations, we present a comprehensive analysis of the atomic structure and energy levels of point defects in cubic silicon carbide (3C-SiC). Finding that the classical long-range dielectric screening outside the supercell induced by a charged defect is a significant contributor to the total energy. we describe and validate a modified Jost screening model to evaluate this polarization energy. This leads to bulk-converged defect levels in finite size supercells. With the LMCC boundary conditions and a standard Perdew-Burke-Ernzerhof (PBE) exchange correlation functional, the computed defect level spectrum exhibits no band gap problem: the range of defect levels spans ~2.4 eV, an effective defect band gap that agrees with the experimental band gap. Comparing with previous literature, our LMCC-PBE defect results are in consistent agreement with the hybrid-exchange functional results of Oda et al. [J. Chem. Phys. 139, 124707 (2013)] rather than their PBE results. The difference with their PBE results is attributed to their use of a conventional jellium approximation rather than the more rigorous LMCC approach for handling charged supercell boundary conditions. The difference between standard dft and hybrid functional results for defect levels lies not in a band gap problem but rather in solving a boundary condition problem. The LMCC-PBE entirely mitigates the effect of the band gap problem on defect levels. The more computationally economical PBE enables a systematic exploration of 3C-SiC defects, where, most notably, we find that the silicon vacancy undergoes Jahn-Teller-induced distortions from the previously assumed T d symmetry, and that the divacancy, like the silicon vacancy, exhibits a site-shift bistability in p -type conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1994

The Local Supercluster as a test of cosmological models

The Local Supercluster kinematic properties (the Local Group infall toward the Virgo Cluster and galaxy density distribution about the Virgo Cluster) in various cosmological models are examined utilizing large-scale N-body (PM) simulations 500(exp 3) cells, 250(exp 3) particles, and box size of 400 h(exp -1) Mpc) and are compared to observations. Five models are investigated: (1) the standard, Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with omega = 1, h = 0.5, and sigma(sub 8) = 1.05; (2) the standard Hot Dark Matter (HDM) model with omega = 1, h = 0.75, and sigma(sub 8) = 1; (3) the tilted CDM model with omega = 1, h = 0.5, n = 0.7, and sigma(sub 8) = 0.5; (4) a CDM + lambda model with omega = 0.3, lambda = 0.7, h = 2/3, and sigma(sub 8) = 2/3; (5) the PBI model with omega = 0.2, h = 0.8, x = 0.1, m = -0.5, and sigma(sub 8) = 0.9. Comparison of the five models with the presently available observational measurements v(sub LG) = 85 - 305 km/s (with mean of 250 km/s), delta(n(sub g))/(n(sub g)-bar) = 1.40 + or - 0.35) suggests that an open universe with omega approximately 0.5 (with or without lambda) and sigma(sub 8) approximately 0.8 is preferred, with omega = 0.3-1.0 (with or without lambda) and sigma(sub 8) = 0.7-1.0 being the acceptable range. At variance with some previous claims based on either direct N-body or spherical nonlinear approaches, we find that a flat model with sigma(sub 8) approximately 0.7-1.0 seems to be reasonably consistent with observations. However, if one favors the low limit of v(sub LG) = 85 km/s, then an omega approximately 0.2-0.3 universe seems to provide a better fit, and flat (omega = 1) models are ruled out at approximately 95% confidence level. On the other hand, if the high limit of v(sub LG) = 350 km/s is closer to the truth, then it appears that omega approximately 0.7-0.8 is more consistent. This test is insensitive to the shape of the power spectrum, but rather sensitive to the normalization of the perturbation amplitude on the relevant scale (e.g., sigma(sub 8)) and omega. We find that neither linear nor nonlinear relations (with spherical symmetry) are good approximations for the relation between radial peculiar velocity and density perturbation, i.e., nonspherical effects and gravitational tidal field are important. The derived omega using either of the two relations is underestimated. In some cases, this error is as large as a factor of 2-4.

Cen, Renyue↗
NASA NTRS2007

On the Nature of the Variability Power Decay towards Soft Spectral States in X-Ray Binaries. Case Study in Cyg X-1

A characteristic feature of the Fourier Power Density Spectrum (PDS) observed from black hole X-ray binaries in low/hard and intermediate spectral states is a broad band-limited noise, characterized by a constant below some frequency (a "break" frequency) and a power law above this frequency. It has been shown that the variability of this type can be produced by the inward diffusion of the local driving perturbations in a bounded configuration (accretion disk or corona). In the framework of this model, the perturbation diffusion time to is related to the phenomenological break frequency, while the PDS power-law slope above the "break" is determined by the viscosity distribution over the configuration. The perturbation diffusion scenario explains the decay of the power of X-ray variability observed in a number of compact sources (containing black hole and neutron star) during an evolution of theses sources from low/hard to high/soft states. We compare the model predictions with the subset of data from Cyg X-1 collected by the Rossi X-ray Time Explorer (RXTE). Our extensive analysis of the Cyg X-1 PDSs demonstrates that the observed integrated power P(sub x), decreases approximately as a square root of the characteristic frequency of the driving oscillations v(sub dr). The RXTE observations of Cyg X-1 allow us to infer P(sub dr), and t(sub o) as a function of v(sub dr). We also apply the basic parameters of observed PDSs, power-law index and low frequency quasiperiodic oscillations. to infer Reynolds (Re) number from the observations using the method developed in our previous paper. Our analysis shows that Re-number increases from values about 10 in low/hard state to that about 70 during the high/soft state. Subject headings: accretion, accretion disks-black hole physics-stars:individual (Cyg X-1) :radiation mechanisms: nonthermal-physical data and processes

Titarchuk, Lev↗
NASA NTRS1994

The cosmic X-ray background-IRAS galaxy correlation and the local X-ray volume emissivity

We have cross-correlated the galaxies from the IRAS 2 Jy redshift survey sample and the 0.7 Jy projected sample with the all-sky cosmic X-ray background (CXB) map obtained from the High Energy Astronomy Observatory (HEAO) 1 A-2 experiment. We have detected a significant correlation signal between surface density of IRAS galaxies and the X-ray background intensity, with W(sub xg) = (mean value of ((delta I)(delta N)))/(mean value of I)(mean value of N)) of several times 10(exp -3). While this correlation signal has a significant implication for the contribution of the local universe to the hard (E greater than 2 keV) X-ray background, its interpretation is model-dependent. We have developed a formulation to model the cross-correlation between CXB surface brightness and galaxy counts. This includes the effects of source clustering and the X-ray-far-infrared luminosity correlation. Using an X-ray flux-limited sample of active galactic nuclei (AGNs), which has IRAS 60 micrometer measurements, we have estimated the contribution of the AGN component to the observed CXB-IRAS galaxy count correlations in order to see whether there is an excess component, i.e., contribution from low X-ray luminosity sources. We have applied both the analytical approach and Monte Carlo simulations for the estimations. Our estimate of the local X-ray volume emissivity in the 2-10 keV band is rho(sub x) approximately = (4.3 +/- 1.2) x 10(exp 38) h(sub 50) ergs/s/cu Mpc, consistent with the value expected from the luminosity function of AGNs alone. This sets a limit to the local volume emissivity from lower luminosity sources (e.g., star-forming galaxies, low-ionization nuclear emission-line regions (LINERs)) to rho(sub x) less than or approximately = 2 x 10(exp 38) h(sub 50) ergs/s/cu Mpc.

Miyaji, Takamitsu↗
DOE OSTI2021

Fourier-like Thermal Relaxation of Nanoscale Explosive Hot Spots

Hot spots are local regions of high temperature that are widely considered to govern explosive initiation. Hot spot dynamics rests on a delicate balance between heat generation due to chemical reactions and heat loss through thermal conduction, making accurate determinations of the conductivity under extreme conditions a key component of predictive explosive models. We develop here an approach to directly determine the thermal transport properties of explosive hot spots with realistic initial structures through a combination of molecular dynamics (MD) and diffusive heat equation (HEq) modeling. Effective thermal conductivity values are determined by fitting HEq models to MD predictions of long timescale hot spot relaxation. The approach is applied to model hot spots in the molecular crystalline explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) for a range of shock strengths and two limiting cases for impact orientation. Isotropic and anisotropic HEq models yield similar results, despite TATB exhibiting some of the largest and most anisotropic thermal conductivity values for explosive near normal conditions. The conductivity is found to be a strong function of density, which parametrically captures dependence on temperature, pressure, and material state. The associated root-mean-square errors of the fitted HEq models are approximately 5% of MD predicted final equilibrium temperatures. Here, the conductivity values determined here for TATB hot spots are considerably larger than those used in a prior hot spot criticality study, which may significantly impact predictions for critical hot spot sizes. The approach provides a convenient foundation for determining the effective thermal conductivity for hot spot problems in other explosives and directly yields information on reasonable approximations that might be taken in higher-level models for those materials.

36 MATERIALS SCIENCE↗
NASA NTRS2020

Formation and Topology of Foreshock Bubbles

We use global and local hybrid (kinetic ions and fluid electrons) simulations to investigate the conditions under which foreshock bubbles (FBs) form and how their topology changes with solar wind conditions. FBs form as a result of the interaction between solar wind discontinuities and backstreaming ion beams in the foreshock. They consist of an outer shock and its associated sheath plasma and a low density high temperature core with low magnetic field strength. The structure of FBs is determined by the angle between the interplanetary magnetic field and the normal to the solar wind discontinuity. We show that interaction of rotational discontinuities with the foreshock during small angles between the interplanetary magnetic field and discontinuity normal results in the formation of a nearly spherical bubble with a radius that scales with the width of the foreshock. As this angle increases, FBs become more elongated and eventually become nearly planar structures with dimensions that scale with the length of the foreshock. Despite this transformation, the signatures of FBs in spacecraft time series data remain the same in agreement with the observations. Global simulation results show that FBs form when the solar wind flow speed corresponds to high or intermediate Alfvén Mach numbers (approximately >7 MA). In general, this is tied to the relative speed between the solar wind and ion beams and drop in density of the back streaming ions.

Nick Omidi↗
NASA NTRS1992

Lunar Observer Laser Altimeter observations for lunar base site selection

One of the critical datasets for optimal selection of future lunar landing sites is local- to regional-scale topography. Lunar base site selection will require such data for both engineering and scientific operations purposes. The Lunar Geoscience Orbiter or Lunar Observer is the ideal precursory science mission from which to obtain this required information. We suggest that a simple laser altimeter instrument could be employed to measure local-scale slopes, heights, and depths of lunar surface features important to lunar base planning and design. For this reason, we have designed and are currently constructing a breadboard of a Lunar Observer Laser Altimeter (LOLA) instrument capable of acquiring contiguous-footprint topographic profiles with both 30-m and 300-m along-track resolution. This instrument meets all the severe weight, power, size, and data rate limitations imposed by Observer-class spacecraft. In addition, LOLA would be capable of measuring the within-footprint vertical roughness of the lunar surface, and the 1.06-micron relative surface reflectivity at normal incidence. We have used airborne laser altimeter data for a few representative lunar analog landforms to simulate and analyze LOLA performance in a 100-km lunar orbit. We demonstrate that this system in its highest resolution mode (30-m diameter footprints) would quantify the topography of all but the very smallest lunar landforms. At its global mapping resolution (300-m diameter footprints), LOLA would establish the topographic context for lunar landing site selection by providing the basis for constructing a 1-2 km spatial resolution global, geodetic topographic grid that would contain a high density of observations (e.g., approximately 1000 observations per each 1 deg by 1 deg cell at the lunar equator). The high spatial and vertical resolution measurements made with a LOLA-class instrument on a precursory Lunar Observer would be highly synergistic with high-resolution imaging datasets, and will allow for direct quantification of critical slopes, heights, and depths of features visible in images of potential lunar base sites.

Garvin, James B.↗
DOE OSTI2025

Assessment of integral models for non-Boussinesq lazy plumes using numerical simulations

Integral modelling of turbulent buoyant plumes is crucial for rapid predictions of plume characteristics. While the governing equations are typically derived using self-similarity and a Boussinesq approximation, these assumptions may not hold for plumes originating from finite-area sources with large density ratios. Here, this work evaluates the accuracy of integral-scale models for non-Boussinesq lazy plumes using high-fidelity numerical simulations of turbulent helium plumes. We analyse the plume kinematics by computing vertical fluxes, plume radius and radial profiles, establishing some disparities between common practice and physical accuracy. We identify how the definition of the plume radius changes the perception of the plume structure when the flow is not self-similar and derive a relationship between the flux-based and threshold-based definitions without requiring self-similarity. We then examine the plume dynamics by evaluating the source terms from the governing plume equations. Our results support neglecting diffusive and viscous effects but emphasise the importance of the mean pressure gradient, even in the self-similar regime. Two coefficients need to be modelled: the well-known entrainment coefficient and the lesser-known momentum correction coefficient, which is a correction required for the momentum equation to account for self-similar and slender approximations. The momentum correction coefficient is found to be approximately constant and slightly greater than the assumed value of 1. The standard entrainment coefficient models perform well up to a local Richardson number three times the asymptotic value but overpredict entrainment for larger Richardson numbers. We propose a correction using the known finite limit of entrainment at infinite Richardson number.

Meehan, Michael Alexander [Sandia National Laborat↗
NASA NTRS2010

EPR Imaging at a Few Megahertz Using SQUID Detectors

An apparatus being developed for electron paramagnetic resonance (EPR) imaging operates in the resonance-frequency range of about 1 to 2 MHz well below the microwave frequencies used in conventional EPR. Until now, in order to obtain sufficient signal-to-noise radios (SNRs) in conventional EPR, it has been necessary to place both detectors and objects to be imaged inside resonant microwave cavities. EPR imaging has much in common with magnetic resonance imaging (MRI), which is described briefly in the immediately preceding article. In EPR imaging as in MRI, one applies a magnetic pulse to make magnetic moments (in this case, of electrons) precess in an applied magnetic field having a known gradient. The magnetic moments precess at a resonance frequency proportional to the strength of the local magnetic field. One detects the decaying resonance-frequency magnetic- field component associated with the precession. Position is encoded by use of the known relationship between the resonance frequency and the position dependence of the magnetic field. EPR imaging has recently been recognized as an important tool for non-invasive, in vivo imaging of free radicals and reduction/oxidization metabolism. However, for in vivo EPR imaging of humans and large animals, the conventional approach is not suitable because (1) it is difficult to design and construct resonant cavities large enough and having the required shapes; (2) motion, including respiration and heartbeat, can alter the resonance frequency; and (3) most microwave energy is absorbed in the first few centimeters of tissue depth, thereby potentially endangering the subject and making it impossible to obtain adequate signal strength for imaging at greater depth. To obtain greater penetration depth, prevent injury to the subject, and avoid the difficulties associated with resonant cavities, it is necessary to use lower resonance frequencies. An additional advantage of using lower resonance frequencies is that one can use weaker applied magnetic fields: For example, for a resonance frequency of 1.4 MHz, one needs a magnetic flux density of 0.5 Gauss approximately the flux density of the natural magnetic field of the Earth.

Hahn, Inseob↗
DOE OSTI2021

Foundations of variational discrete action theory

Variational wave functions and Green's functions are two important paradigms for solving quantum Hamiltonians, each having their own advantages. Here we detail the variational discrete action theory (VDAT), which exploits the advantages of both paradigms in order to approximately solve the ground state of quantum Hamiltonians. VDAT consists of two central components: the sequential product density matrix (SPD) ansatz and a discrete action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer $\mathscr{N}$, recovering many well-known variational wave functions, in addition to the exact solution for $\mathscr{N}$ = ∞. The discrete action describes all dynamical information of an effective integer time evolution with respect to the SPD. We generalize the path integral to our integer time formalism, which converts a dynamic correlation function in integer time to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism to integer time, which results in analogous but distinct mathematical structures, yielding integer time versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We prove that the SPD can be exactly evaluated in the multiband Anderson impurity model (AIM) by summing a finite number of diagrams. For the multiband Hubbard model, we prove that the self-consistent canonical discrete action approximation (SCDA), which is the integer time analog of the dynamical mean-field theory, exactly evaluates the SPD for d = ∞. VDAT within the SCDA provides an efficient yet reliable method for capturing the local physics of quantum lattice models, which will have broad applications for strongly correlated electron materials. More generally, VDAT should find applications in various many-body problems in physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2012

GRAIL Refinements to Lunar Seismic Structure

The present ]day internal structure of the Moon provides insight not only into its own formation and evolution, but also that of all rocky planetary bodies. The most direct way to probe a planet fs interior structure is through seismology. As part of the Apollo lunar missions, four seismometers were deployed on the nearside surface of the Moon between the years 1969 and 1972. These instruments operated continuously until 1977, forming the only substantial extraterrestrial seismic data set in existence. These data have been used to constrain various aspects of the seismic velocity and density structure of the Moon. Typical 1-D models recognize a 30-60 km thick crust overlying a nearly constant ]velocity mantle, and extend to a depth of approximately 1000 km, below which the lack of penetrating moonquake ray ]paths precludes the seismic determination of deeper structure. Previously, the lack of observed moonquakes from the far side of the Moon has been used to infer the presence of a highly attenuating (possibly molten) core. Indirect geophysical measurements such as moment of inertia, magnetic induction, lunar laser ranging, and elemental abundances of mare basalts also place varying constraints on core size and state. In combination with seismic studies, these indirect measurements have been used to arrive at a commonly accepted model of the Moon's deepest interior that includes a solid inner and fluid outer core, overlain by a partial melt boundary layer. We recently applied modern array seismology techniques to the Apollo data and revealed detailed core structure, including the first direct confirmation of the presence of a solid inner core. Our study focused on the identification of core ]reflected phases in deep moonquake seismograms. The resulting model of the Moon fs innermost structure was found to be consistent with the commonly accepted model. However, the modeled layer radii may vary by tens of kilometers, as is expected when accounting for uncertainties such as moonquake location, timing errors, and potential seismic heterogeneities. In addition, the modeled velocities may vary with a 1-to-1 trade ]off with the modeled reflector depth. The GRAIL (Gravity Recovery and Interior Laboratory) mission, launched in Sept. 2011, placed two nearly identical spacecraft in lunar orbit. The two satellites make extremely high-resolution measurements of the lunar gravity field, which can be used to constrain the interior structure of the Moon using a "crust to core" approach. GRAIL fs constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten) will complement seismic investigations in several ways. Here we present a progress report on our efforts to advance our knowledge of the Moon fs internal structure using joint gravity and seismic analyses. We will focus on methodology, including 1) refinements to the seismic core constraint accomplished through array processing of Apollo seismic data, made by applying a set of travel time corrections based on GRAIL structure estimates local to each Apollo seismic station; 2) modeling deep lunar structure through synthetic seismograms, to test whether the seismic core model can reproduce the core reflections observed in the Apollo seismograms; and 3) a joint seismic and gravity inversion in which we attempt to fit a family of seismic structure models with the gravity constraints from GRAIL, resulting in maps of seismic velocities and densities that vary from a nominal model both laterally and with depth.

Weber, Renee↗
DOE OSTI2022

Details of the neutral energy distribution and ionization source using spectrally resolved Balmer-alpha measurements on DIII-D

Spectrally resolved passive Balmer- α (D- α, H- α) measurements from the DIII-D 16 channel edge main-ion charge exchange recombination system confirm the presence of higher energy neutrals (“thermal” neutrals) in addition to the cold neutrals that recycle off the walls in the edge region of DIII-D plasmas. Charge exchange between thermal ions and edge neutrals transfers energy and momentum between the populations giving rise to thermal neutrals with energies approximating the ions in the pedestal region. Multiple charge exchange events in succession allow an electron to effectively take a random walk, transferring from ion to ion, providing a pathway of increasing energy and velocity, permitting a neutral to get deeper into the plasma before a final ionization event that contributes to the ion and electron particle fueling. Spectrally resolved measurements provide information about the density and velocity distribution of these neutrals, which has been historically valuable for validating Monte Carlo neutral models, which include the multi stage charge exchange dynamics. Here, in this study, a multi-channel set of such measurements is used to specifically isolate the details of the thermal neutrals that are responsible for fueling inside the pedestal top. Being able to separate the thermal from the cold emission overcomes several challenges associated with optical filter-based neutral density measurements. The neutral dynamics, deeper fueling by the thermal neutrals, and spectral measurement are modeled with the FIDASIM Monte Carlo collisional radiative code, which also produces synthetic spectra with a shape that is in close agreement with the measurements. By scaling the number of neutrals in the simulation to match the intensity of the thermal emission, we show it is possible to obtain local neutral densities and ionization source rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Statistical properties of filaments in the cosmic web

ABSTRACT In the context of the cosmological and constrained Exploring the Local Universe with the reConstructed Initial Density field (ELUCID) simulation, this study explores the statistical characteristics of filaments within the cosmic web, focussing on aspects such as the distribution of filament lengths and their radial density profiles. Using the classification of the cosmic web environment through the Hessian matrix of the density field, our primary focus is on how cosmic structures react to the two variables $R_{\rm s}$ and $\lambda _{\rm th}$. The findings show that the volume fractions of knots, filaments, sheets, and voids are highly influenced by the threshold parameter $\lambda _{\rm th}$, with only a slight influence from the smoothing length $R_{\rm s}$. The central axis of the cylindrical filament is pinpointed using the medial-axis thinning algorithm of the COsmic Web Skeleton (COWS) method. It is observed that median filament lengths tend to increase as the smoothing lengths increase. Analysis of filament length functions at different values of $R_{\rm s}$ indicates a reduction in shorter filaments and an increase in longer filaments as $R_{\rm s}$ increases, peaking around $2.5R_{\rm s}$. The study also shows that the radial density profiles of filaments are markedly affected by the parameters $R_{\rm s}$ and $\lambda _{\rm th}$, showing a valley at approximately $2R_{\rm s}$, with increases in the threshold leading to higher amplitudes of the density profile. Moreover, shorter filaments tend to have denser profiles than their longer counterparts.

Zhang, Youcai (ORCID:0000000319674091)↗
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

DROP DURABILITY ASSESSMENT OF ELECTRONIC ASSEMBLIES UNDER OFF-AXIS LOADING WITH SKEWED FIXTURES

This thesis studies drop durability of electronic assemblies when the acceleration vector is oriented at 45° to the out-of-plane direction of the circuit card. The off-axis drop tests are accomplished with a skewed fixture and are conducted as a proxy for multiaxial drop testing. Advanced shock testing and vibration test methods have been developed over the last few decades to better represent real-world field environments during ground-based laboratory testing. However, many of these test methods require expensive and specialized equipment not available in most laboratories. An alternative approach for approximating simultaneous loading along multiple axes on conventional equipment utilizes skewed fixtures which have seen use in off-axis random vibration and drop impact testing. These methods generally rely on the conversion of a uniaxial input load from the test equipment (using a uniaxial drop tower or shaker) into a multiaxial load when resolved in the reference frame of the test article (mounted on a skewed fixture). Skewed fixture design is presented and recommendations for conducting skewed angle drop testing are introduced based on local measurements along the skewed face of the fixture to accurately monitor the impact event. Characterization tests were performed with a skewed fixture, at simultaneous acceleration loads from 500 to 3,000 g in two (in-plane and out-of-plane) directions, while meeting standard time domain tolerances. Upon experimental characterization, drop shock durability tests were conducted on a printed circuit assembly (PCA). Mean drops-to-failure were measured and quantified with Weibull statistics. Dominant solder joint failure modes were identified via failure analysis. Prior work on inclined angle impact testing is limited, and the majority of solder joint interconnect level fatigue studies are conducted considering perpendicular loading normal the circuit card. Low-cycle fatigue curves are generated based on plastic strain and plastic work density within the solder joint. A multiscale nonlinear finite element model is used to relate board-level flexure to solder joint interconnect level plastic strain. A high strain rate solder constitutive model allows for accurate modeling of solder plasticity resulting from high-impact drop shock. Fatigue parameters are computed from the Coffin-Manson relation and Palmgren-Miner damage accumulation. This work serves to apply established low-cycle fatigue methods for conventional drop shock loading (impact normal to circuit card) to non-perpendicular loading with a skewed fixture.

Hower, Jonathan [Kansas City National Security Cam↗