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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2016

Expansion of Tabulated Scattering Matrices in Generalized Spherical Functions

An efficient way to solve the vector radiative transfer equation for plane-parallel turbid media is to Fourier-decompose it in azimuth. This methodology is typically based on the analytical computation of the Fourier components of the phase matrix and is predicated on the knowledge of the coefficients appearing in the expansion of the normalized scattering matrix in generalized spherical functions. Quite often the expansion coefficients have to be determined from tabulated values of the scattering matrix obtained from measurements or calculated by solving the Maxwell equations. In such cases one needs an efficient and accurate computer procedure converting a tabulated scattering matrix into the corresponding set of expansion coefficients. This short communication summarizes the theoretical basis of this procedure and serves as the user guide to a simple public-domain FORTRAN program.

scattering matrix↗
NASA NTRS1994

The effects of gravity darkening on the ultraviolet continuum polarization produced by circumstellar disks

We investigate the effects of gravity darkening on the UV continuum polarization produced by an axisymmetric disk that surrounds a rapidly rotating star. Although the model is a single scattering approximation, we do include the effects of attenuation (electron scattering plus hydrogen bound-free absorption) by the disk, using an approach similar to that of Sobolev (1963). Because of the gravity darkening of the star and the attenuation within the disk, the radiation field is not axially symmetric about the radius vector. This implies that the polarization source functions are no longer provided by the finite disk depolarization factors of Cassinelli, Nordsieck, & Murison (1987), which are functions of the intensity moments in a spherically symmetric atmosphere. We reformulate the polarization source functions using generalized intensity moment tensors (J, H(sub i), K(sub ij)) that are valid for an arbitrary radiation field and envelope geometry. We find that the polarization source functions are simplest when using intensity moments in the observer's reference frame. On the other hand, the intensity moments are most easily evaluated in the stellar reference frame. Using the rotation transformation properties of the generalized intensity moments, we relate the observer's moments to those evaluated in the stellar reference frame. Our procedure for determining the polarization source functions thus merely involves choosing a set of Euler angles for the coordinate rotations, and then evaluating the associated rotation matrix. The geometrical complications of polarization transfer are thus reduced to obtaining a coordinate rotation matrix.

Bjorkman, J. E.↗
NASA NTRS1991

Statistics of primordial density perturbations from discrete seed masses

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.

Scherrer, Robert J.↗
NASA NTRS1973

Double scattering corrections for the theory of the sun's aureole

Double scattering corrections for aureole radiances are calculated by adding the effects of two successive single scatterings. Atmospheric absorption, polarization, and variation of refractive index with altitude are ignored. Corrections due to spherical atmosphere were taken into account by the use of a generalized Chapman function. Realistic scattering phase functions based upon the Lorenz-Mie theory and model altitude-size distribution are used. The model distribution is assumed to be representable in terms of two separable particulate components. It was found that for a moderately clear day, tau (0) is approximately equal to 0.5, and for forward scattering angles, the radiance, B sub 2, due to double scattering is less than 6 percent of that due to single scattering.

Deepak, A.↗
NASA NTRS1991

In-flight performance of the Faint Object Camera of the Hubble Space Telescope

An overview of the Faint Object Camera and its performance to date is presented. In particular, the detector's efficiency, the spatial uniformity of response, distortion characteristics, detector and sky background, detector linearity, spectrography, and operation are discussed. The effect of the severe spherical aberration of the telescope's primary mirror on the camera's point spread function is reviewed, as well as the impact it has on the camera's general performance. The scientific implications of the performance and the spherical aberration are outlined, with emphasis on possible remedies for spherical aberration, hardware remedies, and stellar population studies.

Greenfield, P.↗
NASA NTRS1981

Characteristics of reflected and diffuse ions upstream from the earth's bow shock

The distinction between two types of upstream ion populations is made on the basis of pronounced differences in their distribution functions. The reflected ions represent a fast beam with temperatures typically one-million to five-million K and speeds up to five times the solar wind speed. An important feature of the reflected ion distributions is their strong temperature anisotropy, with perpendicular temperature exceeding parallel temperature by a factor of two or three. In contrast, the diffuse ions occupy a much larger region of phase space, both in energy and angle; their distribution function generally has the form of a circular ridge in two dimensions and a spherical shell in three dimensions. Accordingly, their temperature is much larger (not less than about 10-million K) and their bulk speed is typically smaller than the solar wind speed.

Paschmann, G.↗
NASA NTRS1992

The wind geometry of the Wolf-Rayet star HD 191765

A time-dependent spectropolarimetric data set of HD 191765 in the wavelength range 3159-7593 A is presented. At all epochs the present observations display a large and strongly wavelength-dependent continuum polarization and reduced levels of polarization across the emission lines. The data imply a significant intrinsic continuum polarization which requires a general deviation of the electron distribution from spherical symmetry. The global shape is quite stable as a function of time; small fluctuations may arise from localized density/temperature changes. The line polarizations are consistent with an axisymmetric wind geometry and ionization stratification. A qualitative model for polarization in a Wolf-Rayet atmosphere is developed. It is argued that the blueward rise of the continuum polarization in HD 191765 can be explained if the density in the wind is high, resulting in a competition of thermal and electron-scattering continuum opacity in the vertical.

Schulte-Ladbeck, R. F.↗
NASA NTRS1972

General theory of spherically symmetric boundary-value problems of the linear transport theory.

A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.

Kanal, M.↗
NASA NTRS1977

Corrections for atmospheric refractivity in satellite laser ranging

The effects of departures from the spherical symmetry assumption are investigated by describing the refractivity profile on the earth's surface as a generalized function of the surface coordinates. Aspects of satellite ranging geometry are considered and the representation of the true group refractivity of the atmosphere at any point on the earth's surface is discussed. Surface meteorological data obtained from a few east coast weather stations are analyzed to obtain typical values of the higher order bias terms.

Iyer, R. S.↗
NASA NTRS1972

Spherical balloon response to three-dimensional time-dependent flows

The concept of the Lagrangian displacement of a balloon is introduced. It is shown that the general balloon response problem is extremely complicated because the wind-forcing functions in the balloon equations of motion are functions of the wind velocity vector and its Eulerian first derivatives evaluated at the location of the balloon. The linear perturbation equations for a spherical balloon are derived by perturbing the components of velocity of the balloon about a terminal velocity state which is in equilibrium with a space-time invariant mean horizontal flow. The atmospheric flow is also perturbed such that the resulting equations can be used to analyze the responses of spherical balloons to three-dimensional time-dependent flows. The wind field is represented in terms of a four-fold Fourier integral that involves three orthogonal wave numbers and a frequency, while the balloon components of velocity are represented as Fourier integrals involving a frequency which, in turn, is a function of the wind field wave numbers and frequency and the unperturbed flow components of velocity.

Fichtl, G. H.↗
NASA NTRS1979

Particle dynamics associated with the space environment

A major factor in dust dynamics in a microgravity environment is the absence of settling; hence, Spacelab air will contain larger particles than a comparable laboratory on earth. In addition, the presence of low level acceleration fluctuations (thruster firings, crew motions, etc.) could inhibit dust removal by surface scavenging. Because of the presence of larger particles, aerosol dynamics at larger Reynolds numbers must be considered. An accurate drag coefficient for spherical particles was developed for the higher Reynolds number phenomena. A general graphic correlation for the drag coefficient as a function of Reynolds and Knudsen numbers was developed based on currently available drag data for spheres. The general equations that govern dust dynamics were reviewed.

Sandborn, V. A.↗
NASA NTRS1989

Droplet model for autocorrelation functions in an Ising ferromagnet

The autocorrelation function of Ising spins in an ordered phase is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation which describes fluctuations in the radius of a single droplet is studied in detail. A general description of the transformation to a Fokker-Planck equations and the ways in which a spectral analysis of that equation can be used to compute the autocorrelation function is given. It is shown that the eigenvalues of the Fokker-Planck operator form (1) a continuous spectrum of relaxation rates starting from zero for d = 2, (2) a continuous spectrum with a finite gap for d = 3, and (3) a discrete spectrum for d greater than 4, where d is the spatial dimensionality. Detailed solutions for various cases are presented.

Tang, Chao↗
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 NTRS2011

Implicit Priors in Galaxy Cluster Mass and Scaling Relation Determinations

Deriving the total masses of galaxy clusters from observations of the intracluster medium (ICM) generally requires some prior information, in addition to the assumptions of hydrostatic equilibrium and spherical symmetry. Often, this information takes the form of particular parametrized functions used to describe the cluster gas density and temperature profiles. In this paper, we investigate the implicit priors on hydrostatic masses that result from this fully parametric approach, and the implications of such priors for scaling relations formed from those masses. We show that the application of such fully parametric models of the ICM naturally imposes a prior on the slopes of the derived scaling relations, favoring the self-similar model, and argue that this prior may be influential in practice. In contrast, this bias does not exist for techniques which adopt an explicit prior on the form of the mass profile but describe the ICM non-parametrically. Constraints on the slope of the cluster mass-temperature relation in the literature show a separation based the approach employed, with the results from fully parametric ICM modeling clustering nearer the self-similar value. Given that a primary goal of scaling relation analyses is to test the self-similar model, the application of methods subject to strong, implicit priors should be avoided. Alternative methods and best practices are discussed.

Mantz, A.↗
NASA NTRS1986

Hollow cathode plasma coupling study, 1986

The electron collection and emission characteristics of a simple hollow cathode contactor, an extended anode hollow cathode contactor supplied by JSC, and a ring cusp magnetic field contactor are presented and the effects of discharge power and argon or xenon expellant flowrate on these characteristics are examined. All of the contactors are shown to exhibit good electron emission performance over a wide range of discharge power and expellant type and flowrate. Good electron performance is shown to be more difficult to achieve. Results suggest that the extended anode and ring cusp contactors should perform satisfactorily to electron emission currents beyond 1000 mA and electron collection currents beyond 500 mA. All contactors performed better on xenon than argon. A general theory of plasma contactor operation in both the electron collection and electron emission modes, which describes the current-limiting effects of space-charge phenomena is given. This current-limiting and collecting phenomenon is shown to be a function of driving potential differences and emitting and collecting surface radius ratio for the case of a spherical geometry. Discharge power did not appear to influence the electron collection current substantially in the experiments so it is suggested in light of the model that the contactors are generally not limited by their ion production capabilities under conditions at which they were tested.

Wilbur, Paul J.↗