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Goddard's Astrophysics Science Divsion Annual Report 2014

The Astrophysics Science Division (ASD, Code 660) is one of the world's largest and most diverse astronomical organizations. Space flight missions are conceived, built and launched to observe the entire range of the electromagnetic spectrum, from gamma rays to centimeter waves. In addition, experiments are flown to gather data on high-energy cosmic rays, and plans are being made to detect gravitational radiation from space-borne missions. To enable these missions, we have vigorous programs of instrument and detector development. Division scientists also carry out preparatory theoretical work and subsequent data analysis and modeling. In addition to space flight missions, we have a vibrant suborbital program with numerous sounding rocket and balloon payloads in development or operation. The ASD is organized into five labs: the Astroparticle Physics Lab, the X-ray Astrophysics Lab, the Gravitational Astrophysics Lab, the Observational Cosmology Lab, and the Exoplanets and Stellar Astrophysics Lab. The High Energy Astrophysics Science Archive Research Center (HEASARC) is an Office at the Division level. Approximately 400 scientists and engineers work in ASD. Of these, 80 are civil servant scientists, while the rest are resident university-based scientists, contractors, postdoctoral fellows, graduate students, and administrative staff. We currently operate the Swift Explorer mission and the Fermi Gamma-ray Space Telescope. In addition, we provide data archiving and operational support for the XMM mission (jointly with ESA) and the Suzaku mission (with JAXA). We are also a partner with Caltech on the NuSTAR mission. The Hubble Space Telescope Project is headquartered at Goddard, and ASD provides Project Scientists to oversee operations at the Space Telescope Science Institute. Projects in development include the Neutron Interior Composition Explorer (NICER) mission, an X-ray timing experiment for the International Space Station; the Transiting Exoplanet Sky Survey (TESS) Explorer mission, in collaboration with MIT (Ricker, PI); the Soft X-ray Spectrometer (SXS) for the Astro-H mission in collaboration with JAXA, and the James Webb Space Telescope (JWST). The Wide-Field Infrared Survey Telescope (WFIRST), the highest ranked mission in the 2010 decadal survey, is in a pre-phase A study, and we are supplying study scientists for that mission.

Caltech on the NuSTAR mission↗

Summary of Pressure Gain Combustion Research at NASA

NASA has undertaken a systematic exploration of many different facets of pressure gain combustion over the last 25 years in an effort to exploit the inherent thermodynamic advantage of pressure gain combustion over the constant pressure combustion process used in most aerospace propulsion systems. Applications as varied as small-scale UAV's, rotorcraft, subsonic transports, hypersonics and launch vehicles have been considered. In addition to studying pressure gain combustor concepts such as wave rotors, pulse detonation engines, pulsejets, and rotating detonation engines, NASA has studied inlets, nozzles, ejectors and turbines which must also process unsteady flow in an integrated propulsion system. Other design considerations such as acoustic signature, combustor material life and heat transfer that are unique to pressure gain combustors have also been addressed in NASA research projects. In addition to a wide range of experimental studies, a number of computer codes, from 0-D up through 3-D, have been developed or modified to specifically address the analysis of unsteady flow fields. Loss models have also been developed and incorporated into these codes that improve the accuracy of performance predictions and decrease computational time. These codes have been validated numerous times across a broad range of operating conditions, and it has been found that once validated for one particular pressure gain combustion configuration, these codes are readily adaptable to the others. All in all, the documentation of this work has encompassed approximately 170 NASA technical reports, conference papers and journal articles to date. These publications are very briefly summarized herein, providing a single point of reference for all of NASA's pressure gain combustion research efforts. This documentation does not include the significant contributions made by NASA research staff to the programs of other agencies, universities, industrial partners and professional society committees through serving as technical advisors, technical reviewers and research consultants.

Perkins, H. Douglas↗

Interpretation of Vector Electric Field Measurements of Bursty Langmuir Waves in the Cusp

An analysis of auroral Langmuir waves in the cusp observed by two high-frequency electric field instruments on the TRICE high-flyer sounding rocket shows many examples of Langmuir wave bursts modulated at approximately 10 kHz. Previous studies have explained these and similar observations as the result of beating between waves with very close frequencies near the Langmuir cutoff, resulting from either wave-wave interactions or independent linear excitations. The unique three-dimensional (3-D) data set provided by the NASA Goddard Space Flight Center TAEFWD instrument shows that up to 25% of waveforms selected from the most intense bursts exhibit anisotropic modulations, i.e., the beat nulls and peaks are not aligned in time across the three perpendicular electric field components. Modulations of this type arise when superposed wave normal modes possess differing polarizations, and simulations using wave modes calculated with the J-WHAMP numerical dispersion code show (1) that waves with differing polarizations can exist in conditions like those observed by TRICE-High and (2) that superpositions of such waves can produce anisotropic modulation. Fourier analysis of the 3-D waveform data suggests that both linear and elliptically polarized waves are present near the Langmuir cutoff at these times. These observations illustrate how 3-D measurements can give valuable insight into the nature of wave interactions in the auroral plasma environment.

Dombrowski, M. P.↗

Imposing strong correlated energy spread on relativistic bunches with transverse deflecting cavities

We demonstrate a novel scheme for imposing or removing large energy chirp on relativistic electron bunches. This method relies on the transverse-to-longitudinal mixing accomplished with a set of transverse deflecting cavities. The working principles of the new concept are explained using the first-order matrix formalism in the approximation of the linear single-particle dynamics. The scheme demonstrates versatility regarding the average beam energy and, hence, positioning along the accelerator beam line. The performance of the scheme is numerically investigated with the elegant particle-tracking code. It is shown that the associated nonlinear effects causing emittance deterioration for the extreme quantities of the total energy spread can be effectively compensated by optimization of the Twiss parameters while relying on the eigenemittance analysis. The impact of the longitudinal space charge effects on the beam dynamics in the proposed scheme is also investigated.

43 PARTICLE ACCELERATORS↗

Full 3D Kinetic Modeling and Quantification of Positive Streamer Evolution in an Azimuthally Swept Pin-to-Plane Wedge Geometry

Cathode-directed streamer evolution in near atmospheric air is modeled in 3D pin-to-plane geometries using a 3D kinetic Particle-In-Cell (PIC) code that simulates particle-particle collisions via the Direct Simulation Monte Carlo (DSMC) method. Due to the computational challenges associated with a complete 360° volumetric domain, a practical alternative was achieved using a wedge domain and a range of azimuthal angles was explored (5°, 15°, 30°, and 45°) to study possible effects on the streamer growth and propagation due to the finite wedge angle. A DC voltage of 6 kV is administered to a hemispherical anode of radius 100 μm, with a planar cathode held at ground potential, generating an over-volted state with an electric field of 4 MV/m across a 1500 μm gap. The domain is seeded with an initial ion and electron density of 10 18 m -3 at 1 eV temperature confined to a spherical region of radius 100 μm centered at the tip of the anode. The air chemistry model [1] includes standard Townsend breakdown mechanisms (electron-neutral elastic, excitation, ionization, attachment, and detachment collision chemistry and secondary electron emission) as well as streamer mechanisms (photoionization and ion-neutral collisions) via tracking excited state neutrals which can then either quench via collisions or spontaneously emit a photon based on specific Einstein-A coefficients [2, 3]. In this work, positive streamer dynamics are formally quantified for each wedge angle in terms of electron velocity and density as temporal functions of coordinates r, Φ, and z. Applying a random plasma seed for each simulation, particles of interest are tracked with near femtosecond temporal resolution out to 1.4 ns and spatially binned. This process is repeated six times and results are averaged. Prior 2D studies have shown that the reduced electric field, E/n, can significantly impact streamer evolution [4]. We extend the analysis to 3D wedge geometries, to limit computational costs, and examine the wedge angle’s effect on streamer branching, propagation, and velocity. Results indicate that the smallest wedge angle that produced an acceptably converged solution is 30°. The potential effects that a mesh, when under-resolved with respect to the Debye length, can impart on streamer dynamics and numerical heating were not investigated, and we explicitly state here that the smallest cell size was approximately 10 times the minimum λ D in the streamer channel at late times. This constraint on cell size was the result of computational limitations on total mesh count.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

An investigation of dynamic-analysis methods for variable-geometry structures

Selected space structure configurations were reviewed in order to define dynamic analysis problems associated with variable geometry. The dynamics of a beam being constructed from a flexible base and the relocation of the completed beam by rotating the remote manipulator system about the shoulder joint were selected. Equations of motion were formulated in physical coordinates for both of these problems, and FORTRAN programs were developed to generate solutions by numerically integrating the equations. These solutions served as a standard of comparison to gauge the accuracy of approximate solution techniques that were developed and studied. Good control was achieved in both problems. Unstable control system coupling with the system flexibility did not occur. An approximate method was developed for each problem to enable the analyst to investigate variable geometry effects during a short time span using standard fixed geometry programs such as NASTRAN. The average angle and average length techniques are discussed.

Austin, F.↗

A higher order theory of laminated composite cylindrical shells

A new higher order theory has been proposed for the analysis of composite cylindrical shells. The formulation allows for arbitrary variation of inplane displacements. Governing equations are presented in the form of a hierarchy of sets of partial differential equations. Each set describes the shell behavior to a certain degree of approximation. The natural frequencies of simply-supported isotropic and laminated shells and stresses in a ring loaded composite shell have been determined to various orders of approximation and compared with three dimensional solutions. These numerical studies indicate the improvements achievable in estimating the natural frequencies and the interlaminar shear stresses in laminated composite cylinders.

Krishna Murthy, A. V.↗

Vibration analysis of quasi-symmetric structures

A computational technique is developed to reduce the size of the dynamical model of a large complex quasi-symmetric structure prior to free vibration analysis. The structure is discretized using a two-field mixed FEM model; the response vectors are decomposed into symmetric and antisymmetric components; the eigenvectors of the quasi-symmetric structure are approximated by a linear combination of a few preselected sets of symmetric and antisymmetric modes generated by the reduced-size model; global approximation vectors are selected and generated; and the resulting eigenvalue problem is significantly reduced via a classical Bubnov-Galerkin procedure. Numerical results for a shallow laminated anisotropic panel of quadrilateral planform are presented in extensive tables and graphs, demonstrating the effectiveness of the method.

Noor, Ahmed K.↗

Asymptotic boundary conditions for dissipative waves: General theory

An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Hagstrom, Thomas↗

Asymptotic boundary conditions for dissipative waves - General theory

An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Hagstrom, Thomas↗

Partitioning of unstructured problems for parallel processing

Many large-scale computational problems are based on unstructured computational domains. Primary examples are unstructured grid calculations based on finite volume methods in computational fluid dynamics, or structural analysis problems based on finite element approximations. The question of how to distribute such unstructured computational domains over a large number of processors in a MIMD machine with distributed memory is addressed. A graph theoretical framework for these problems is established. Based on this framework three decomposition algorithms are introduced. In particular a new decomposition algorithm is discussed, which is based on the computation of an eigenvector of the Laplacian matrix associated with the graph. Numerical comparisons on large-scale two- and three-dimensional problems demonstrate the superiority of the new spectral bisection algorithm.

Simon, H. D.↗

Current issues concerning the representativeness and utility of cloud drift winds in mesoscale meteorology

High-resolution cloud motion wind (CMW) data sets obtained from geostationary satellites for approximately the past decade have been used for the purpose of estimating mesoscale wind fields in various research studies. Yet there remains much controversy surrounding the proper interpretation and use of the resultant wind vector and kinematic fields. This paper is concerned with: (1) how representative are cloud draft winds of actual ambient air motions; and (2) what is the degree of practical usefulness of CMW fields for both mesoscale analysis and as input to numerical weather prediction models.

Koch, Steven E.↗

A numerical investigation of film cooling as an alternate thermal protection system for spacecraft during atmospheric reentry

Research was undertaken to determine the mass required to protect a surface during atmospheric reentry by injecting a cold gas tangentially along the surface. A consideration of this problem revealed that the boundary layer equations could be employed to approximate the most important flow configurations which occur in film cooling. However, even with this simplification, the equations to be solved are complex, nonlinear, coupled partial differential equations. Due to the relative weakness of classical methods of boundary layer analysis, finite difference methods were chosen as the best approach to the formidable problem under consideration. Instead of blindly adopting a proposed technique and trying to force it to the problem, a more systematic study was deemed to be not only desirable but necessary. A relatively basic study of the application of finite difference methods was undertaken with the objective of developing an algorithm capable of obtaining accurate solutions to film cooling problems.

Clausing, A. M.↗

Decoupled direct method for sensitivity analysis in combustion kinetics

An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.

Radhakrishnan, Krishnan↗

Method for Approximating the Vacuum Motions of Spinning Symmetrical Bodies with Nonconstant Spin Rates

The analysis includes non-constant spin rates and inertias and considers the effects of time-varying thrust misalignments, mass unbalance, and jet damping. The method was developed for bodies having small trans verse angular velocities. Results are presented in the form of equations for space-referenced Euler angles, flight-path angles, body-referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. Also, equations for maximum wobble have been derived for certain input conditions. Comparisons with numerical solutions are included for two sample problems.

Martz, C. William↗

An analytic approach to quasinormal modes for coupled linear systems

Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schrödinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter ε and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when ε is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will [1] to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗