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NASA NTRS1992

Design and analysis of soft X-ray imaging microscopes

The spherical Schwarzschild microscope for soft X-ray applications in microscopy and projection lithography consists of two concentric spherical mirrors configured such that the third-order spherical aberration and coma are zero. Since multilayers are used on the mirror substrates for X-ray applications, it is desirable to have only two reflecting surfaces in a microscope. To reduce microscope aberrations and increase the field of view, generalized mirror surface profiles are here considered. Based on incoherent and sine wave modulation transfer function calculations, the object plane resolution of a microscope has been analyzed as a function of the object height and numerical aperture (NA) of the primary for several spherical Schwarzschild, conic, and aspherical Head reflecting two-mirror microscope configurations. The Head microscope with a NA of 0.4 achieves diffraction limited performance for objects with a diameter of 40 microns. Thus, it seems possible to record images with a feature size less than 100 A with a 40x microscope when using 40 A radiation.

Shealy, David L.↗

NASA NTRS1995

Turbulance boundary conditions for shear flow analysis, using the DTNS flow solver

The effects of different turbulence boundary conditions were examined for two classical flows: a turbulent plane free shear layer and a flat plate turbulent boundary layer with zero pressure gradient. The flow solver used was DTNS, an incompressible Reynolds averaged Navier-Stokes solver with k-epsilon turbulence modeling, developed at the U.S. Navy David Taylor Research Center. Six different combinations of turbulence boundary conditions at the inflow boundary were investigated: In case 1, 'exact' k and epsilon profiles were used; in case 2, the 'exact' k profile was used, and epsilon was extrapolated upstream; in case 3, both k and epsilon were extrapolated; in case 4, the turbulence intensity (I) was 1 percent, and the turbulent viscosity (mu(sub t)) was equal to the laminar viscosity; in case 5, the 'exact' k profile was used and mu(sub t) was equal to the laminar viscosity; in case 6, the I was 1 percent, and epsilon was extrapolated. Comparisons were made with experimental data, direct numerical simulation results, or theoretical predictions as applicable. Results obtained with DTNS showed that turbulence boundary conditions can have significant impacts on the solutions, especially for the free shear layer.

Mizukami, M.↗

NASA NTRS1995

What is the source of observed annual variations in plasmaspheric density?

Plasmaspheric densities have been observed previously to be higher in December than in June, with the ratio varying between 1.5 and 3.0 and with larger variations at lower L shells. In order to search for the cause of the observed annual variations, we have modeled plasmaspheric density, using a time-dependent hydrodynamic model. On an L = 2 field line with geomagnetic longitude equal to 300 deg, the modeled plasmaspheric densities were a factor of 1.5 times higher in December than in June. The modeled December to June density ratio was found to increase slightly with L shell, in contrast to observations; this discrepancy may be due to the fact that outer plasmaspheric flux tubes are never completely full. In addition, for an L = 2 field line with geomagnetic longitude equal to 120 deg, the modeled plasmaspheric density was higher in June than in December by a factor of about 1.2. Various numerical tests were also performed in order to examine the sensitivity of plasmaspheric density to various parameters. In particular, a large vertical neutral wind was applied in order to raise the O(+) profile which had the effect of raising plasmaspheric density by a factor of 6. This in conjunction with a theoretical analysis suggests that plasmaspheric density levels are very sensitive to O(+) levels in the upper ionosphere. We conclude that annual variations in plasmaspheric density are due to similar variations in ionospheric O(+).

Guiter, S. M.↗

NASA NTRS1958

Elliptic Functions and Integrals with Real Modulus in Fluid Mechanics

Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.

Legendre, Robert↗

NASA NTRS2008

Polarization/Spatial Combining of Laser-Diode Pump Beams

A breadboard version of an optical beam combiner is depicted which make it possible to use the outputs of any or all of four multimode laser diodes to pump a non-planar ring oscillator (NPRO) laser. The output of each laser diode has a single-mode profile in the meridional plane containing an axis denoted the 'fast' axis and a narrower multimode profile in the orthogonal meridional plane, which contains an axis denoted the 'slow' axis and a narrower multimode profile in the orthogonal meridional plane, which contains an axis denoted the 'slow' axis. One of the purposes served by the beam-combining optics is to reduce the fast-axis numerical aperture (NA) of the laser-diode output to match the NA of the optical fiber. Along the slow axis, the unmodified laser-diode NA is already well matched to the fiber optic NA, so no further slow-axis beam shaping is needed. In this beam combiner, the laser-diode outputs are collimated by aspherical lenses, then half-wave plates and polarizing beam splitters are used to combine the four collimated beams into two beams. Spatial combination of the two beams and coupling into the optical fiber is effected by use of anamorphic prisms, mirrors, and a focusing lens. The anamorphic prisms are critical elements in the NA-matching scheme, in that they reduce the fast-axis beam width to 1/6 of its original values. Inasmuch as no slow-axis beam shaping is needed, the collimating and focusing lenses are matched for 1:1 iumaging. Because these lenses are well corrected for infinite conjugates the combiner offers diffraction-limited performance along both the fast and slow axes.

Gelsinger, Paul↗

NASA NTRS2019

Three CA-Related Covariance Issues and Their Solutions

This presentation addresses three issues that arise in the use of DoD-produced satellite state estimate covariances in the conjunction assessment process: the realism of the provided covariances, how to address correlated error between two satellites' covariance matrices, and how to proceed when a furnished covariance is non-positive-definite. To address the first, DoD has implemented a set of two "consider parameters" with which to alter/expand the covariance to account for atmospheric density forecast error and satellite frontal area uncertainty, the two largest sources of unmodeled position prediction error for LEO orbits; these values are governed by a satellite's orbital parameters and ballistic coefficient histories, as well as the current and predicted space weather situation. This approach substantially improves the realism of the covariance by accounting for expected prediction errors that are not part of the fit process that generates the covariance. The second issue of covariance correlation is a complicated one, but the main shared error sourceâ€”global atmospheric density error that is common to both satellites can be characterized and, through sensitivity vectors, quantified at the conjunction's time of closest approach and removed from the joint covariance, which is used in the CA probability of collision (Pc) calculation. Finally, while according to the orbit determination theory a non-positive-definite (NPD) covariance is not possible, numerical truncation and covariance interpolation can conspire to produce NPD results, which render the covariance unusable for certain CA risk assessment calculations, such as Monte Carlo Pc determination. Three similar techniques are profiled and the simplest of them recommended as a reasonable remediation technique when NPD covariances are encountered by CA practitioners.

Dynamic Consider Parameter↗

DOE OSTI2022

Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series

Abstract. Improving the quantification of soil thermal and physical properties is key to achieving a better understanding and prediction of soil hydro-biogeochemical processes and their responses to changes in atmospheric forcing. Obtaining such information at numerous locations and/or over time with conventional soil sampling is challenging. The increasing availability of low-cost, vertically resolved temperature sensor arrays offers promise for improving the estimation of soil thermal properties from temperature time series, and the possible indirect estimation of physical properties. Still, the reliability and limitations of such an approach need to be assessed. In the present study, we develop a parameter estimation approach based on a combination of thermal modeling, sliding time windows, Bayesian inference, and Markov chain Monte Carlo simulation to estimate thermal diffusivity and its uncertainty over time, at numerous locations and at an unprecedented vertical spatial resolution (i.e., down to 5 to 10 cm vertical resolution) from soil temperature time series. We provide the necessary framework to assess under which environmental conditions (soil temperature gradient, fluctuations, and trend), temperature sensor characteristics (bias and level of noise), and deployment geometries (sensor number and position) soil thermal diffusivity can be reliably inferred. We validate the method with synthetic experiments and field studies. The synthetic experiments show that in the presence of median diurnal fluctuations ≥ 1.5 ∘C at 5 cm below the ground surface, temperature gradients > 2 ∘C m−1, and a sliding time window of at least 4 d the proposed method provides reliable depth-resolved thermal diffusivity estimates with percentage errors ≤ 10 % and posterior relative standard deviations ≤ 5 % up to 1 m depth. Reliable thermal diffusivity under such environmental conditions also requires temperature sensors to be spaced precisely (with accuracy to a few millimeters), with a level of noise ≤ 0.02 ∘C, and with a bias defined by a standard deviation ≤ 0.01 ∘C. Finally, the application of the developed approach to field data indicates significant repeatability in results and similarity with independent measurements, as well as promise in using a sliding time window to estimate temporal changes in soil thermal diffusivity, as needed to potentially capture changes in bulk density or water content.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1993

Radiative properties of a plasma moving across a magnetic field. I - Theoretical analysis. II - Numerical results

The early-time evolution of plasmas moving across a background magnetic field is addressed with a 2D model in which a plasma cloud is assumed to have formed instantaneously with a velocity across a uniform background magnetic field and with a Gaussian density profile in the two dimensions perpendicular to the direction of motion. This model treats both the dynamics associated with the formation of a polarization field and the generation and propagation of electromagnetic waves. In general, the results indicate that, to zeroth order, the plasma cloud behaves like a large dipole antenna oriented in the direction of the polarization field which oscillates at frequencies defined by the normal mode of the system. Radiation damping is shown to play an important role in defining the plasma cloud evolution, causing a rapid decay of the polarizaiton field and a loss of plasma kinetic energy and momentum on time scales comprable to several ion gyroperiods. Scaling laws are derived for the plasma momentum and energy loss rates, and predictions for the braking time, the amplitude and spectrum of the radiation field, and the total radiated power are presented for conditions relevant to the recent Combined Release and Radiation Effects Satellite experiments.

Roussel-Dupre, Robert↗

NASA NTRS2013

Integrating Wind Profiling Radars and Radiosonde Observations with Model Point Data to Develop a Decision Support Tool to Assess Upper-Level Winds for Space Launch

On the day of launch, the 45th Weather Squadron (45 WS) Launch Weather Officers (LWOs) monitor the upper-level winds for their launch customers. During launch operations, the payload/launch team sometimes asks the LWOs if they expect the upper-level winds to change during the countdown. The LWOs used numerical weather prediction model point forecasts to provide the information, but did not have the capability to quickly retrieve or adequately display the upper-level observations and compare them directly in the same display to the model point forecasts to help them determine which model performed the best. The LWOs requested the Applied Meteorology Unit (AMU) develop a graphical user interface (GUI) that will plot upper-level wind speed and direction observations from the Cape Canaveral Air Force Station (CCAFS) Automated Meteorological Profiling System (AMPS) rawinsondes with point forecast wind profiles from the National Centers for Environmental Prediction (NCEP) North American Mesoscale (NAM), Rapid Refresh (RAP) and Global Forecast System (GFS) models to assess the performance of these models. The AMU suggested adding observations from the NASA 50 MHz wind profiler and one of the US Air Force 915 MHz wind profilers, both located near the Kennedy Space Center (KSC) Shuttle Landing Facility, to supplement the AMPS observations with more frequent upper-level profiles. Figure 1 shows a map of KSC/CCAFS with the locations of the observation sites and the model point forecasts.

Bauman, William H., III↗

DOE OSTI2023

A semi-analytic study of self-interacting dark-matter haloes with baryons

ABSTRACT We combine the isothermal Jeans model and the model of adiabatic halo contraction into a semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. The model agrees well with cosmological SIDM simulations over the entire core-forming stage up to the onset of gravothermal core-collapse. Using this model, we show that the halo response to baryons is more diverse in SIDM than in CDM and depends sensitively on galaxy size, a desirable feature in the context of the structural diversity of bright dwarfs. The fast speed of the method facilitates analyses that would be challenging for numerical simulations – notably, we quantify the SIDM halo response as functions of the baryonic properties, on a fine mesh grid spanned by the baryon-to-total-mass ratio, Mb/Mvir, and galaxy compactness, r1/2/Rvir; we show with high statistical precision that for typical Milky-Way-like systems, the SIDM profiles are similar to their CDM counterparts; and we delineate the regime of core-collapse in the Mb/Mvir − r1/2/Rvir space, for a given cross section and concentration. Finally, we compare the isothermal Jeans model with the more sophisticated gravothermal fluid model, and show that the former yields faster core formation and agrees better with cosmological simulations. We attribute the difference to whether the target CDM halo is used as a boundary condition or as the initial condition for the gravothermal evolution, and thus comment on possible improvements of the fluid model. We have made our model publicly available at https://github.com/JiangFangzhou/SIDM.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1978

An infrared radiation routine for use in numerical atmospheric models

Previous methods for calculating radiative fluxes due to water vapor and CO2 absorption bands are extended to take into consideration the entire water vapor and CO2 bands, including e-type absorption in the window region and the overlapping of different absorptions. Cooling rate profiles in the water vapor bands for a tropical atmosphere were computed by a detailed line-by-line method and by a far-wing approximation method, and the error of both methods is less than 0.2 C/day. Cooling rate profiles in the 15 micron band including overlapping of CO2 absorption with water vapor were calculated by a method in which flux transmittance is computed by means of a linear expansion and the multiplication rule, and maximum errors of 0.3 C/day were found in comparison with the exact line-by-line method.

Chow, M.-D.↗

DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Poor confinement in stellarators at high energy

High-energy particle resonances can modify particle distributions and even cause significant particle loss. Resonances can be present in any toroidal confinement device and can easily be found numerically. Many stellarators have weak magnetic shear so that large islands and large chaotic regions can be produced by resonant perturbations with small amplitudes. Additionally, while the choice of the field line helicity profile in the plasma can limit the presence of resonances at low particle energy, the resonance location is energy-dependent, and they can move into the plasma at higher energy. If resonances match the toroidal variation of the equilibrium, they can produce wide islands in the phase space of orbits even in the absence of perturbations due to instabilities. These islands increase in size with particle energy and can seriously affect the confinement of high-energy ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Nonlocal elastic metasurfaces: Enabling broadband wave control via intentional nonlocality

While elastic metasurfaces offer a remarkable and very effective approach to the subwavelength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. In applications to electromagnetic and photonic metamaterials, some success in extending the operating dynamic range was obtained by using nonlocality. However, while electronic properties in natural materials can show significant nonlocal effects, even at the macroscales, in mechanics, nonlocality is a higher-order effect that becomes appreciable only at the microscales. This study introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements, whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase-gradient profiles that are functions of the wavenumber of the incident wave. The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semianalytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin-plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Density wavenumber spectrum measurements, synthetic diagnostic development, and tests of quasilinear turbulence modeling in the core of electron-heated DIII-D H-mode plasmas

Abstract Measurements of the turbulent density wavenumber spectrum, δ n ˆ e ( k ⊥ ) , using the Doppler Back-Scattering (DBS) diagnostic are reported from DIII-D H-mode plasmas with electron cyclotron heating as the only auxiliary heating method. These electron-heated plasmas have low collisionality, ν e ∗ < 1 , T e / T i > 1 , and zero injected torque—a regime expected to be relevant for future fusion devices. We probe density fluctuations in the core ( ρ ≈ 0.7) over a broad wavenumber range, 0.5 ⩽ k ⊥ ⩽ 16 cm −1 ( 0.1 ⩽ k ⊥ ρ s ⩽ 5 ), to characterize plasma instabilities and compare with theoretical predictions. We present a novel synthetic DBS diagnostic to relate the back-scattered power spectrum, P s ( k ⊥ ) —which is directly measured by DBS—to the underlying electron density fluctuation spectrum, δ n ˆ e ( k ⊥ ) . The synthetic DBS P s ( k ⊥ ) spectrum is calculated by combining the SCOTTY beam-tracing code with a model δ n ˆ e ( k ⊥ ) predicted either analytically or numerically. In this work we use the quasi-linear code Trapped Gyro-Landau Fluid (TGLF) to approximate the δ n ˆ e ( k ⊥ ) spectrum. We find that TGLF, using the experimental profiles, is capable of closely reproducing the DBS measurements. Both the DBS measurements and the TGLF-DBS synthetic diagnostic show a wavenumber spectrum with variable decay. The measurements show weak decay ( k −0.6 ) for k < 3.5 cm −1 , with k −2.6 at intermediate- k ( 3.5 ⩽ k ⩽ 8.5 cm −1 ), and rapid decay ( k −9.4 ) for k > 8.5 cm −1 . Scans of physics parameters using TGLF suggest that the normalized ∇ T e scale-length, R / L T e , is an important factor for distinguishing microturbulence regimes in these plasmas. A combination of DBS observations and TGLF simulations indicate that fluctuations remain peaked at ITG-scales (low k ) while R / L T e -driven TEM/ETG-type modes (intermediate/high k ) are marginally sub-dominant.

synthetic diagnostics↗

DOE OSTI2026

Planetary Boundary-Layer Height (PBLHT) Value-Added Product: Remote-Sensing Retrievals

The planetary boundary layer (PBL) is fundamental to numerous atmospheric processes, including aerosol mixing and transport, cloud evolution, and precipitation formation. A critical parameter in these studies is the PBL height (PBLHT). This vertical depth is essential for characterizing PBL structures in numerical simulations and serves as a primary metric for estimating flux exchanges between the Earth’s surface and the atmosphere. Radiosonde (SONDE) observations provide high-vertical-resolution measurements of temperature and moisture profiles and are widely used to estimate PBLHT (Liu and Liang 2010, Seidel et al. 2010). The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s PBLHT value-added product (VAP) for radiosonde measurements, known as PBLHTSONDE, applies three commonly used methods—the Heffter (1980) method, the Liu and Liang (2010) method, and the bulk Richardson number approach (Seibert et al. 2000)—to derive PBLHT. The PBLHTSONDE VAP operates routinely at ARM observatories and mobile facilities, with data available from the ARM Data Center shortly after sounding observations are collected (Sivaraman et al. 2013). However, radiosonde observations are limited by their low temporal resolution. Most stations launch soundings only twice daily, which constrains the ability to investigate and characterize the temporal evolution of the PBL using radiosonde data alone. The use of continuous remote-sensing observations provides high temporal resolution of PBLHT estimates. These observations include aerosol lidars (Dang et al. 2019, Su et al. 2020), Doppler lidar (DL; Tucker et al. 2009, Krishnamurthy et al. 2021), and water vapor and/or temperature lidars and radiometers (Turner et al. 2014). These observations provide valuable data on the PBL’s thermodynamic properties (e.g., water vapor and/or temperature lidars and radiometers), dynamic properties (e.g., DL), and distribution of tracer substances (e.g., aerosol lidars), all of which can be used to estimate PBLHT. ARM developed PBLHT estimates from the micropulse lidar (MPL; PBLHTMPL), Doppler lidar (PBLHTDL), and combined Raman lidar (RL)/atmospheric emitted radiance interferometer (AERI) thermodynamic profiles (PBLHTTHERMO). Each estimate captures different physical characteristics of the boundary layer—aerosol tracers, vertical velocity turbulence, and thermodynamic structure—and exhibits distinct strengths and limitations depending on the PBL regime and time of day. In addition, the ARM ceilometer (CEIL) provides three potential PBLHT candidates derived from the vendor's built-in algorithm. Building on these individual retrievals, ARM developed the PBLHTBEML VAP, which combines the four remote-sensing-based estimates with ancillary meteorological variables using the machine learning approach of Zhang et al. (2025) to produce a best-estimate PBLHT at 10-minute resolution.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

Remote sensing of atmospheric and surface temperatures with microwaves.

Solids, liquids, and gases emit at microwave wavelengths measurable amounts of black-body thermal radiation. Receiver sensitivities readily approach 0.01 K, and permit accurate measurements of land, sea, and atmospheric temperatures. Sea and land temperature measurements must be corrected for the effects of surface emissivity, but these effects can often be measured or estimated. Observations near the 5 mm wavelength 02 resonances can yield atmospheric temperature profiles with an approximate accuracy of 2 K for altitudes 0-80 km. Such measurements from balloons and aircraft suggest that the planned earth-orbital satellite experiments will yield data valuable for numerical weather prediction. Ground-based radio telescopes and planetary-probes have yielded similar information about the surfaces and atmospheres of other planets.

Staelin, D. H.↗

NASA NTRS1975

Numerical calculation of finite amplitude effects in unstable laminar boundary layers

A numerical study of one stage of the transition region from laminar to turbulent flow of the boundary layer over a flat plate is performed. Benney-Lin theory is applied to the laminar profile, which is closer to that of the experiment, i.e., the Blasius profile. Several laminar profiles are studied, all belonging to the Falkner-Skan family. The flow is found to depend principally upon the disturbance spanwise wavenumber, beta, whose variation results, in some instances, in a system of counter-rotating vortices, one on top of the other, for the mean secondary flow.

Antar, B. N.↗