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NASA NTRS1978

Two-stream theory of spectral reflectance of snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption within the snowcover due to the randomly distributed ice grains are characterized by the single scattering albedo and anisotropic phase function. Geometric optics calculations are used to relate the scattering and absorption parameters to grain size and density of snow. Analytical expressions for the intensity within the snowpack and the asymptotic flux extinction coefficient are also obtained. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance and asymptotic flux extinction coefficient. The theory also may be used to explain the observed effect of aging on the snow reflectance.

Choudhury, B. J.↗

NASA NTRS1979

Two-stream theory of reflectance of snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption parameters of the radiative transfer equation - the single scattering albedo, the optical depth, and the integrated phase function are obtained from the grain size and density of snow. Analytical expressions for the intensity within the snowpack, the reflectance, and the asymptotic flux extinction coefficient, are given. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance, and the asymptotic flux extinction coefficient. The theory may also be used to explain the observed effect of aging on the snow reflectance.

Choudhury, B. J.↗

NASA NTRS1980

Shield topology in lightning transient control

A formalism in which the interaction of a system with an electromagnetic source is described by sets of scattering, penetrations, and propagation functions is reviewed and interpreted in the context of the lightning interaction problem. In this formalism, the system is decomposed into simple volumes separated by closed shield surfaces. These surfaces are nested and interconnected to produce higher levels of shielding and subvolumes within a given level. The interaction analysis uses scattering theory to define current and charge densities on the shield surface in conjunction with the diffusion, apertures, and transmission line analysis to define penetration through shield imperfections and propagation within the protected volume.

Vance, E. F.↗

NASA NTRS1986

Time-dependent coronal shock acceleration of energetic solar flare particles

A global time-dependent model is presented for the coronal and interplanetary shock acceleration and propagation of energetic solar flare particles. The calculations are carried out to help prove that coronal shock acceleration of solar flare particles is responsible for energetic solar flare event data gathered in interplanetary space. The model is based on the theory of diffusive shock acceleration, and requires particle speeds to be much greater than bulk velocities. Also, sufficient scattering must occur upstream and downstream of the shock for the particle scattering mean free path to be smaller than the characteristic scale lengths, which causes the same particles to encounter the shock repeatedly. A spherically symmetric shock wave is assumed, which leads to the same emission configuration for impulsively and monoenergetically emitted particles. Consideration is given to acceleration by compression at the shock front, adiabatic deceleration in the divergent downstream flow, the temporal evolution of the shock and the three-dimensional geometry of the corona. The model is used to generate normalized proton omnidirectional distributions at 1 AU and at the shock front. The spectral exhibit trends similar to those in observational data, especially proton acceleration times and the proton distribution profiles at 1 AU.

Lee, M. A.↗

NASA NTRS1986

Multiple scattering of laser beams in dense hydrosols

The multiple scattering of laser beams is usually described within the framework of small-angle scattering theory. The validity of this approximation as well as improvements due to the incorporation of diffusion theory in the calculations were studied.

Zardecki, A.↗

NASA NTRS1991

Comptonization of gamma rays by cold electrons

An analytic method is developed for calculating the emergent spectrum of gamma-rays and X-rays scattered in a homogeneous medium with low-temperature electrons. The Klein-Nishina corrections of the scattering cross section and absorption processes are taken in account. The wavelength relaxation and the spatial diffusion problems are solved separately, and the emergent spectrum is calculated by convolving the evolution function of the spectrum in an infinite medium with the photon luminosity resulting from the spatial diffusion in a finite sphere. The analytic results are compared with that of Monte Carlo calculations and it is concluded that the analytic result is quite accurate.

Xu, Yueming↗

NASA NTRS1992

Modeling surface solar irradiance for satellite applications on a global scale

An early version of a physical model was modified and expanded to derive surface solar irradiance from satellite observations. The model is based on radiative transfer theory, and can produce both direct and diffuse spectral components in the 0.2-4.0-micron interval. Attention is given to the absorption and scattering processes in the atmosphere and the interaction of radiation with the surface. The bidirectional nature of the exiting radiation at the top of the atmosphere is also accounted for. In this paper the emphasis will be on describing the current status of the model and its implementation on a global scale with the International Satellite Cloud Climatology Project C1 data.

Pinker, R. T.↗

NASA NTRS1992

X-ray scattering and fluorescence in the wind of a massive X-ray binary

Spectral data from the binary X-ray pulsar 4 U 0900 - 40 obtained with the Ginga satellite and covering a range of orbital phases are presented and interpreted using simulated spectra created with a Monte Carlo scattering code. It is found that scattering and fluorescence in a simple spherically symmetric distribution of matter surrounding the companion star can reproduce the eclipse spectrum, as well as the 'soft X-ray-excess' observed during egress and other orbital phases. Reasonably secure values are found for a number of the parameters that characterize the density profile of the stellar wind and atmosphere of the companion star. The Fe abundance is within a factor of about 1.3 of that in the solar neighborhood. It is shown that ionization zones are not critical to understanding the orbital-phase-resolved spectra in this source. It is also found that the contribution by scattering from interstellar dust grains to the observed spectra during eclipse is negligible, while that from diffuse emission from the 'Galactic ridge' is significant.

Lewis, W.↗

NASA NTRS1994

Microwave signatures and surface properties of Ovda Regio and surroundings, Venus

Magellan observations of horizontally and vertically polarized emissivity and radar specific cross sections are jointly modeled to separate dielectric constants from textural effect for lobate plains, fractured plains, fracture belts, festoon flows, and tessera in Ovda Regio and surroundings. The model assumes surface emission and scattering dominate and that signatures are controlled by a combination of quasi-specular and diffuse-scale mechanisms. Textural parameters are found to correlate with geology whereas dielectric constants are found to depend on elevation. A gradual increase in dielectric constant from rock-like values (4 to 5) to a value of approximately 50 is evident over the interval from 6054 to 6056 km, where elevations are derived from Magellan altimetry observations. Stereo radargrammetric analyses demonstrate that a return to rock-like values occurs over approximately 0.5 km above the terrain with highest dielectric constants. The abrupt return to rock-like values occurs independently of geology and reinforces the hypothesis of elevation control on dielectric constant values. Variations in dielectric constant with elevation are modeled using an 1000-ppm concentration of a ferroelectric mineral with a Curie temperature of 707 K. The model reproduces the abrupt change at highest elevations, as the Curie temperature is reached, and the gradual change as lower elevations are encountered. To our knowledge no other model explains the trends with such simplicity.

Arvidson, R. E.↗

NASA NTRS1997

Simulation of Ultra-Small Electronic Devices: The Classical-Quantum Transition Region

Concern is increasing about how quantum effects will impact electronic device operation as down-scaling continues along the SIA Roadmap through 2010. This document describes part of a new semiconductor device modeling (SDM) program at NAS to investigate these concerns by utilizing advanced NAS and third-party numerical computation software to rapidly implement and investigate electronic device models including quantum effects. This SDM project will investigate quantum effects in devices in the classical-quantum transition region, especially sub-0.1 mm MOSFETs. Specific tasks planned for this project include the use of quantum corrections to the classical drift-diffusion and hydrodynamic models of electron transport, arid the use of nominally quantum models including significant scattering.

Biegel, Bryan A.↗

NASA NTRS1972

Monte Carlo analysis of lobular gas-surface scattering in tubes applied to thermal transpiration

A model of rarefied gas flow in tubes was developed which combines a lobular distribution with diffuse reflection at the wall. The model with Monte Carlo techniques was used to explain previously observed deviations in the free molecular thermal transpiration ratio which suggest molecules can have a greater tube transmission probability in a hot-to-cold direction than in a cold-to-hot direction. The model yields correct magnitudes of transmission probability ratios for helium in Pyrex tubing (1.09 to 1.14), and some effects of wall-temperature distribution, tube surface roughness, tube dimensions, gas temperature, and gas molecular mass.

Smith, J. D.↗

NASA NTRS1973

Reflectance and unsteady temperature distribution of diffuse reflectors

The applicability of a previously derived solution of the Kubelka-Munk differential equations for the reflectance of an absorbing and scattering material for the case of a zero absorption coefficient to the description of the reflectance of a weakly absorbing, highly scattering material is examined. A solution for the transient heating of a one-dimensional volume reflector is obtained, and the error incurred in the use of the zero absorption coefficient solution is assessed for early times appropriate to the entry heat protection system application. It is found that the small difference in reflectance causes a significant difference in internal temperature.

Weston, K. C.↗

NASA NTRS1987

Bidirectional reflectance spectroscopy

An analytical model is developed for the opposition effects (heiligenshein) in the case of light scattering from a semi-infinite, particulate medium with particles that are large relative to the wavelength. The effect is common for natural materials, and comprises a bright surge in light diffusively reflected from a surface at near zero phase. A generalized expression is devised for the extinction coefficient of a particulate medium. Models are developed for step function and hyperbolic tangent distributions of light scattered from a stratified medium and exhibiting the opposition effect. A maximum brightness amplitude increase of 0.753 is projected for the effect. Greater values must have other causes. To illustrate the theory it is fitted to observations of the Moon, an asteroid, and a satellite of Uranus; Europa is also discussed.

Hapke, Bruce↗

NASA NTRS1986

Bidirectional reflectance spectroscopy. IV - The extinction coefficient and the opposition effect

An analytical model is developed for the opposition effect (heiligenshein) in the case of light scattering from a semi-infinite, particulate medium with particles that are large relative to the wavelength. The effect is common for natural materials, and comprises a brightness surge in light diffusively reflected from a surface at near zero phase. A generalized expression is devised for the extinction coefficient of a particulate medium. Models are developed for step function and hyperbolic tangent distributions of light scattered from a stratified medium and exhibiting the opposition effect. A maximum brightness amplitude increase of 0.753 is projected for the effect. Greater values must have other causes.

Hapke, B.↗

NASA NTRS2011

Bursty Precipitation Driven by Chorus Waves

The electron precipitation bursts have been shown to be a major sink for the radiation belt relativistic electrons. As underlying mechanism of such bursts, we propose particle scattering into the loss cone due to nonlinear resonance interaction between electrons and chorus. Stochastic heating due to the coupling leads to diffusion in pitch angle, and the rate of diffusion would be sufficient to account for the emptying of the Earth's radiation belt over the time of the main phase of geomagnetic storms. The results obtained in the present paper account for a strong energy dependence in the electron precipitation event and the correlation between the energization and loss processes on macroscopic timescales, which is primarily attributed to the cooperative effects of the coupling. This mechanism of chorus scattering should produce pitch angle distributions that are energy-dependent and butterfly-shaped. The calculated timescales and the total energy input to the atmosphere from precipitating relativistic electrons are in reasonable agreement with experimental data.

Khazanov, G. V.↗

NASA NTRS1976

A nonlinear theory of cosmic-ray pitch-angle diffusion in homogeneous magnetostatic turbulence

A plasma strong turbulence, weak coupling, theory is applied to the problem of cosmic-ray pitch-angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's 'resonance broadening' theory and contains no ad hoc approximations. A detailed calculation is presented for a model of 'slab' turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch-angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 deg pitch angle in earlier work.

Goldstein, M. L.↗

NASA NTRS1990

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

Jones, Frank C.↗

NASA NTRS2012

Constraints on the Galactic Halo Dark Matter from Fermi-LAT Diffuse Measurements

We have performed an analysis of the diffuse gamma-ray emission with the Fermi Large Area Telescope (LAT) in the Milky Way halo region, searching for a signal from dark matter annihilation or decay. In the absence of a robust dark matter signal, constraints are presented. We consider both gamma rays produced directly in the dark matter annihilation/decay and produced by inverse Compton scattering of the e+/e− produced in the annihilation/decay. Conservative limits are derived requiring that the dark matter signal does not exceed the observed diffuse gamma-ray emission. A second set of more stringent limits is derived based on modeling the foreground astrophysical diffuse emission using the GALPROP code. Uncertainties in the height of the diffusive cosmic-ray halo, the distribution of the cosmic-ray sources in the Galaxy, the index of the injection cosmic-ray electron spectrum, and the column density of the interstellar gas are taken into account using a profile likelihood formalism, while the parameters governing the cosmic-ray propagation have been derived from fits to local cosmic-ray data. The resulting limits impact the range of particle masses over which dark matter thermal production in the early universe is possible, and challenge the interpretation of the PAMELA/Fermi-LAT cosmic ray anomalies as the annihilation of dark matter.

DIFFUSE MEASUREMENTS↗