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Results for “Radiation Scattering Equations”

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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Comparison of results obtained by solving the radiative transfer equation with an iterative method and a spherical harmonics method

Fluxes and intensities of light scattered by a model atmosphere are computed by a spherical harmonics approximation and by an iterative method of solving the radiative transfer equation and are compared. The large differences in the net fluxes and intensities reported by Dave and Armstrong (1974) for the two methods are reduced here by making a few changes in the iterative routine. Decreasing the polar angle increment from 2 to 1 deg in the iterative method of computing the source function does not improve the results as suggested by Dave and Armstrong.

Bahethi, O. P.↗
NASA NTRS1982

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Sharma, A.↗
NASA NTRS1980

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗
DOE OSTI2025

Dependent scattering and fractal microstructure determine the transparency of aerogel monoliths

This study reveals how dependent scattering and microstructure significantly affect electromagnetic wave propagation through aerogel monoliths, contributing to their transparency. Light scattering by particle ensembles is considered “dependent” when the scattering properties rely not only on particle size and optical constants but also on their spatial distribution, typically occurring when the average interparticle distance is small in comparison with the wavelength of incident radiation. Addressing dependent scattering requires solving Maxwell’s equations for complex heterogeneous structures, which is computationally demanding and usually limited to sample thicknesses on the same scale as the wavelength. This study combines computer-generated ambigel microstructures of fractal aggregates of polydisperse nanoparticles and the radiative transfer with reciprocal transaction method to predict the transmittance of thick ambigel slabs. Transmittance measurements of ambiently dried aerogel monoliths (ambigels) with porosities from about 50% to 90% closely matched the predicted values for their digital twins. However, ignoring dependent scattering or particle aggregation led to inaccurate predictions. This study validated the computational framework, and its findings offer insights for designing photonic metamaterials and analyzing their interactions with electromagnetic waves.

Yalcin, Refet A. (ORCID:0000000339973494)↗
NASA NTRS1986

The temperature structure in accretion flows onto massive protostars

Radiation transfer problems involved in the infall of dust and gas during star formation are studied. Dust properties are discussed, and modifications of spherical radiative transfer equations are presented that permit forward scattering by dust to be treated for the small size of the star relative to the inner radius of the shell. A procedure for deriving the stellar radiation field incident on the inner edge of the shell is developed. The temperature correction procedure of Cassinelli and Hartmann (1975) for extended stellar atmospheres is modified so that the multitemperature nature of the grains in the cloud may be derived. Temperature distributions for three schematic models in which the density is prespecified are discussed. Radiative acceleration of grains is addressed, showing that the proper mean opacity differs by a large factor from the Rosseland mean opacity that is commonly used. Emergent fluxes for the models are given.

Wolfire, Mark G.↗
NASA NTRS1981

Comparison of sigma(o) obtained from the conventional definition with sigma(o) appearing in the radar equation for randomly rough surfaces

A comparison is made of the radar cross section of rough surface calculated in one case from the conventional definition and obtained in the second case directly from the radar equation. The validity of the conventional definition representing the cross section appearing in the radar equation is determined. The analysis is executed in the special case of perfectly conducting, randomly corrugated surfaces in the physical optics limit. The radar equation is obtained by solving for the radiation scattered from an arbitrary source back to a colocated antenna. The signal out of the receiving antenna is computed from this solution and the result put into a form recognizeable as the radar equation. The conventional definition is obtained by solving a similar problem but for backscatter from an incident planewave. It is shown that these tow forms for sigma are the same if the observer is far enough from the surface.

Levine, D. M.↗
NASA NTRS1981

Bidirectional reflectance spectroscopy. I - Theory

An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Hapke, B.↗
NASA NTRS2020

Electromagnetic scattering by discrete random media illuminated by a Gaussian beam I: Derivation of the radiative transfer equation

In this paper we present the vector radiative transfer theory for a discrete random medium illuminated by a Gaussian beam. The analysis is based on a plane wave spectrum representation for a Gaussian beam and uses an approach developed previously for a discrete random medium illuminated by a plane electromagnetic wave. Specifically, we establish an integral representation for the coherent field, define an approximate coherent field that satisfies the differential equation fulfilled by the coherent field corresponding to a plane electromagnetic wave and matches the Gaussian beam at the interface of the particulate medium, and finally, derive the vector radiative transfer equation. For weakly focused Gaussian beams, the resulting equation is the traditional radiative transfer equation

Gaussian beam↗
NASA NTRS2020

Electromagnetic Scattering by Discrete Random Media Illuminated by a Gaussian Beam II: Solution of the Radiative Transfer Equation

In this paper, we present numerical methods for solving the phenomenological scalar radiative transfer equation for a discrete random medium illuminated by a Gaussian beam. These rely on the Fourier transform method for the horizontal variables and the discrete ordinate method with matrix exponential for solving the underlying one-dimensional radiative transfer equation in the wavenumber domain. The problem of a Gaussian beam at oblique and normal incidence, as well as, the searchlight problem are treated. A complete description of the methods and the numerical algorithms is provided.

Gaussian beam↗
NASA NTRS1986

Radiative transfer in a sphere illuminated by a parallel beam - An integral equation approach

The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. The analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the interconnection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems as provided.

Shia, R.-L.↗
NASA NTRS1978

Some aspects of the interaction of radiation with the thermal and mass budgets of cloud droplets

It is shown that the effects of radiative heating or cooling can have a substantial influence on the mass budget of a cloud droplet and thus on the microphysical properties of a cloud as a whole. The radiative transfer equation, including all orders of multiple scattering, is solved for spectral windows of earth's atmosphere by adopting the Eddington approximation and assuming that the cloud is isothermal and illuminated by fluxes from both the ground and the sky. The results obtained for the 8-12-micron window indicate that radiative cooling can increase a droplet's growth rate and may also make the droplet cooler than the surrounding gas while water vapor is diffusing in, which would cause diffusiophoreisis and thermophoreisis to combine and increase the efficiency with which droplets would scavenge aerosols.

Barkstrom, B. R.↗
DOE OSTI2025

Microscopic calculations with noniterative finite amplitude methods and the application to neutron radiative captures and inelastic scatterings

We derive the fully self-consistent quasiparticle random-phase approximation (QRPA) equations with noniterative finite amplitude methods and calculate the transition strengths of giant resonances. Then, we apply the QRPA results to both neutron radiative capture calculations based on the statistical Hauser-Feshbach theory and inelastic scattering calculations based on distorted-wave Born approximation (DWBA). We compare the calculated results with available experimental data and demonstrate how our approach can reproduce giant resonances and various nuclear reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1996

A Model of Radiative and Conductive Energy Transfer in Planetary Regoliths

The thermal regime in planetary regoliths involves three processes: propagation of visible radiation, propagation of thermal radiation, and thermal conduction. The equations of radiative transfer and heat conduction are formulated for particulate media composed of anisotropically scattering particles. Although the equations are time dependent, only steady state problems are considered in this paper. Using the two-stream approximation, solutions are obtained for two cases: a layer of powder heated from below and an infinitely thick regolith illuminated by visible radiation. Radiative conductivity, subsurface temperature gradients, and the solid state greenhouse effect all appear intrinsically in the solutions without ad hoc additions. Although the equations are nonlinear, approximate analytic solutions that are accurate to a few percent are obtained. Analytic expressions are given for the temperature distribution, the optical and thermal radiance distributions, the hemispherical albedo, the hemispherical emissivity, and the directional emissivity. Additional applications of the new model to three problems of interest in planetary regoliths are presented by Hapke.

Hapke, Bruce↗
NASA NTRS1990

Two-dimensional convection and radiation with scattering from a Poiseuille flow

Two-dimensional combined convection and radiation heat transfer from a gray scattering fluid in a reflecting channel is considered. The model, represented by a set of simultaneous nonlinear integro-partial differential equations, is solved numerically. The effects of aspect ratio, conduction-radiation parameter, scattering albedo, and wall emissivity, are systematically investigated. It is found that these parameters have a significant influence on the temperature field and alter the radiative and convective fluxes at the hot and cold walls. In particular, when radiation effects are considerable, the heat-transfer characteristics of the fluid at the hot and cold walls are very different.

Kassemi, M.↗
NASA NTRS1992

Time-dependent models of magnetized pair plasmas

Attention is given to a numerical code developed to study the time evolution of electron-positron plasmas. The code solves in a self-consistent manner kinetic equations describing the effects of Compton scattering, two-photon pair production, pair annihilation, cooling of pairs via Coulomb scattering, e-e bremsstrahlung, and synchrotron radiation. The kinetic equations are derived under the approximation of homogeneous and isotropic particle distributions on the basis of a study by Coppi and Blandford (1993). Both stationary and time-varying output radiation spectra are computed. Good qualitative agreement with previous calculations is found, except where the differences are attributable to the improved treatment of the microphysics.

Coppi, Paolo S.↗
NASA NTRS1984

The zonal distribution of hydrogen in the Jovian atmosphere

The Lyman-alpha intensities measured by Voyagers 1 and 2 and by the IUE are used as the bases of deductions for the distribution of atomic hydrogen in the Jovian atmosphere, under the assumption that the sources of the dayside Lyman alpha include resonance scattering of solar Lyman alpha, resonance scattering of the interplanetary Lyman-alpha radiation, and direct excitation by charged particles. The daytime equation of radiative transfer is solved to determine the longitudinal distribution of freely scattering atomic hydrogen that would account for the observed flux. This solution indicates that if the hydrogen bulge is due to localized heating and a consequent increase in scale height, the perturbed region temperature must be about 100 K warmer than that in the normal region. The H distribution derived from the dayside solution is used with the nightside flux to estimate the longitude variation of particle precipitation on the nightside.

Killen, R. M.↗
NASA NTRS1986

Three-Dimensional Radiative-Transfer Equation

Progress made toward interpretation of radiometric observations. Paper discusses equation of radiative transfer in three-dimensional, inhomogeneous, scattering medium illuminated from above and bounded below by laterallyinhomogeneous, reflective plane. Representation of radiation field with full three-dimensional variability derived by use of spatial Fourier transform and matrix-operator techniques developed previously for one-dimensional version of problem. Equations useful for radiometric measurements from aircraft and spacecraft. Although derivations and resulting equations complicated, use of Fourier-transform, matrix-operator approach to solve practical problems simpler than direct solution of complete three-dimensional, linear wave equations.

Martonchik, J. V.↗