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NASA NTRS1992

Physics of pitch angle scattering and velocity diffusion. I - Theory

A general theory for the pitch angle scattering and velocity diffusion of particles in the field of a spectrum of waves in a magnetized plasma is presented. The test particle theory is used to analyze the particle motion. The form of diffusion surfaces is examined, and analytical expressions are given for the resonance width and bounce frequency. The resonance widths are found to vary strongly as a function of harmonic number. The resulting diffusion can be quite asymmetric with respect to pitch angle of 90 deg. The conditions for the onset of pitch angle scattering and energy diffusion are explained in detail. Some of the known shortcomings of the standard quasi-linear theory are also addressed, and ways to overcome them are shown. In particular, the often stated quasi-linear gap at 90 deg is found to exist only under very special cases. For instance, oblique wave propagation can easily remove the gap. The conditions for the existence of the gap are described in great detail. A new diffusion equation which takes into account the finite resonance widths is also discussed. The differences between this new theory and the standard resonance broadening theory is explained.

Karimabadi, H.↗

NASA NTRS1992

Effect of the geomagnetic field on the diffusion of meteor trains

A solution to the problem of the diffusion of a meteor train in the geomagnetic field from an initial line density may be written in closed form in terms of effective diffusion coefficients depending on direction, enabling detailed calculations across the entire range of angle of train to field and relevant heights. While the effective diffusion coefficient in the plane of train and field then remains close to the zero field ambipolar value right up to 90 deg, the effective coefficient in the direction of the normal to plane of train and field drops steadily to its theta = 0 value at theta = 90 deg. At 95 km this corresponds to a change of almost 5 km, in 'diffusion height', that is, the height of an underdense meteor calculated on the basis of the exponential decay of its radar echo. We have estimated the consequent changes in the expected distribution of diffusion heights for various orientations of radar antenna and find the dependence on azimuth is very marked. The effect of the field is relatively minor for a south pointing beam but very strong if the beam is pointing north.

Jones, William↗

NASA NTRS1991

Requirements of a solar diffuser and measurements of some candidate materials

If the solar spectral irradiance and the orientation and directional reflectance of a solar diffuser are known, then the spectral radiance of the diffuser is readily calculated and it can be used for the accurate absolute calibration of a satellite sensor. However, the solar diffuser is exposed during in-flight satellite sensor calibration to high-energy ultraviolet irradiance, particle impacts and atomic oxygen effects. This paper describes desirable solar diffuser characteristics and the results of proton and UV irradiation on the directional-hemispheric spectral reflectance, the bidirectional spectral reflectance factor and the polarization properties of candidate diffuser materials.

Guzman, Carmen T.↗

NASA NTRS1992

Anomalous plasma diffusion and the magnetopause boundary layer

An overview of the current state of anomalous diffusion research at the magnetopause and its role in the formation of the magnetopause boundary layer is presented. Plasma wave measurements in the boundary layer indicate that most of the relevant unstable wave modes contribute negligibly to the diffusion process at the magnetopause under magnetically undisturbed northward IMF conditions. The most promising instability is the lower hybrid drift instability, which may yield diffusion coefficients of the right order if the highest measured wave intensities are assumed. It is concluded that global stationary diffusion due to wave-particle interactions does not take place at the magnetopause. Microscopic wave-particle interaction and anomalous diffusion may contribute to locally break the MD frozen-in conditions and help in transporting large amounts of magnetosheath plasma across the magnetospheric boundary.

Treumann, Rudolf A.↗

NASA NTRS1993

An almost 'perfectly' diffuse, 'perfect' reflector for far-infrared reflectance calibration

Specular and diffuse reflectance measurements made near normal incidence of two very rough, solid aluminum surfaces are presented for the wavelength range from 2.2 to 512 microns. The diffuse measurements made at nonspecular angles by two different detectors indicate that between 33 and 201 microns the reflectance of one surface is nearly Lambertian (isotropic) with a bidirectional reflectance distribution function (BRDF) value within 32 percent of the theoretical value of (1/pi)/sr for a perfectly diffuse, perfect reflector. Photometric reflectance spectra at the specular angle show that between 6.9 and 100 microns the specular BRDF of these surfaces is within 5 percent of the theoretical value of (1/pi)/sr. At longer wavelengths of 235, 320, and 512 microns the specular reflectance rapidly departs from that of a perfectly diffuse, perfect reflector. The two samples studied have rms surface roughnesses of 44 and 60 microns. A durable metal surface with these near perfect reflectance characteristics can be advantageously used in the FIR as a black-body source, the interior surface of an integrating sphere, and most especially as an absolute calibration standard. BRDF measurements at 40 deg incidence, though still highly diffuse, show a significant departure from Lambertian reflectance.

Smith, Sheldon M.↗

NASA NTRS1950

The Effect of the Inlet Mach Number and Inlet-boundary-layer Thickness on the Performance of a 23 Degree Conical-diffuser-tail-pipe Combination

An investigation was conducted to determine the effect of the inlet Mach number and entrance-boundary-layer thickness on the performance of a 23 degree 21-inch conical-diffuser - tail-pipe combination with a 2:1 area ratio. The air flows used in this investigation covered an inlet Mach number range from 0.17 to 0.89 and corresponding Reynolds numbers of 1,700,000 to 7,070,000. Results are reported for two inlet-boundary-layer thicknesses. Over the entire range of flows, the mean value of the inlet displacement thickness is about 0.034 inch for the thinner inlet boundary layer and about 0.170 inch for the case of the thicker inlet boundary layer. The performance of the diffuser - tail-pipe combination is presented together with examples of longitudinal static-pressure distribution and the results of boundary-layer pressure surveys made at six points along the diffuser wall. The results indicated a progressive diminution of the static-pressure recovery and a steady increase in the total-pressure losses as the inlet Mach number was increased for both inlet-boundary-layer thicknesses. The ratio of actual static-pressure rise to that theoretically possible was much less and the total-pressure losses were greater for the case of the thicker inlet boundary layer throughout the speed range investigated. With the thinner inlet boundary layer, flow separation occurred at the diffuser exit at all inlet Mach numbers.Unseparated flow alternating with separated flow was observed near the inlet at the higher velocities. For the case of the thicker inlet boundary layer, the origin of the separated region occurred in the vicinity of the inlet-duct-diffuser junction section at all Mach numbers.

Persh, Jerome↗

NASA NTRS1993

Chemical zoning and diffusion of Ca, Al, Mn, and Cr in olivine of springwater pallasite

The pallasites, consisting mainly of Fe-Ni metal and olivine, are thought to represent the interior of a planetary body which slowly cooled from high temperature. Although the olivines are nearly homogeneous, ion microprobe studies revealed variations of Ca, Ti, Co, Cr, and Ni near grain edges. These variations were thought to represent diffusion in response to falling temperature of the parent body. Pallasite cooling rates have been estimated based on kamacite taenite textures but results differ by x100. In principle elemental profiles in olivine can allow estimates of cooling rate if diffusion coefficients are known; in addition, given a cooling rate, diffusion coefficients could be derived. Data are presented which show that apparent diffusion profiles can be measured for Al, Ca, Cr, and Mn which qualitatively agree with expected diffusion rates and have the potential of providing independent estimates of pallasite cooling rates.

Zhou, Y.↗

NASA NTRS1993

Diffusion on Cu surfaces

Understanding surface diffusion is essential in understanding surface phenomena, such as crystal growth, thin film growth, corrosion, physisorption, and chemisorption. Because of its importance, various experimental and theoretical efforts have been directed to understand this phenomena. The Field Ion Microscope (FIM) has been the major experimental tool for studying surface diffusion. FIM have been employed by various research groups to study surface diffusion of adatoms. Because of limitations of the FIM, such studies are only limited to a few surfaces: nickel, platinum, aluminum, iridium, tungsten, and rhodium. From the theoretical standpoint, various atomistic simulations are performed to study surface diffusion. In most of these calculations the Embedded Atom Method (EAM) along with the molecular static (MS) simulation are utilized. The EAM is a semi-empirical approach for modeling the interatomic interactions. The MS simulation is a technique for minimizing the total energy of a system of particles with respect to the positions of its particles. One of the objectives of this work is to develop the EAM functions for Cu and use them in conjunction with the molecular static (MS) simulation to study diffusion of a Cu atom on a perfect as well as stepped Cu(100) surfaces. This will provide a test of the validity of the EAM functions on Cu(100) surface and near the stepped environments. In particular, we construct a terrace-ledge-kink (TLK) model and calculate the migration energies of an atom on a terrace, near a ledge site, near a kink site, and going over a descending step. We have also calculated formation energies of an atom on the bare surface, a vacancy in the surface, a stepped surface, and a stepped-kink surface. Our results are compared with the available experimental and theoretical results.

Karimi, Majid↗

NASA NTRS1993

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

Shen, F.↗

NASA NTRS1994

The Flux-integral Method for Multidimensional Convection and Diffusion

The flux-integral method is a procedure for constructing an explicit, single-step, forward-in-time, conservative, control volume update of the unsteady, multidimensional convection-diffusion equation. The convective plus diffusive flux at each face of a control-volume cell is estimated by integrating the transported variable and its face-normal derivative over the volume swept out by the convecting velocity field. This yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudoflux-difference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation assumed, given cell-average data. Cellwise constant behavior results in a (very artificially diffusive) first-order convection scheme. Second-order convection-diffusion schemes correspond to cellwise linear (or bilinear) subcell interpolation. Cellwise quadratic subcell interpolants generate a highly accurate convection-diffusion scheme with excellent phase accuracy. Under constant-coefficient conditions, this is a uniformly third-order polynomial interpolation algorithm (UTOPIA).

Leonard, B. P.↗

NASA NTRS1994

Loss of solar He and Ne from IDPS in subducting sediment: Diffusion and the effect of phase changes

The results of the diffusion experiment for solar He and Ne in IDP's in a magnetic separate from Pacific Ocean sediment suggest that solar He and Ne would be easily released from IDP grains and hence lost from subducting slabs at shallow depths. However, since the diffusion experiments was conducted under high vacuum, there may be a possibility that magnetite grains, which are supposedly the main constituent of the magnetic fraction, might be partly reduced to form a metal phase due to low oxygen fugacity in the experimental condition. If this is the case, such a phase change might affect the gas release and hence the results of the diffusion coefficients. In order to examine whether or not such a phase change really occurred in the condition of the diffusion experiment, I conducted a heating experiment for a magnetic separate from Pacific Ocean sediment. In the same condition as in the diffusion experiment, and the run products were examined with an x ray diffraction method. Three samples were prepared: they were wrapped with platinum foil, put in a vacuum line, and heated in a molybdenum crucible for two hours at 500 C, 800 C,and 950 C, respectively. After cooling the furnace, the samples were taken out from the crucible and analyzed with an x ray diffraction method.

Hiyagon, H.↗

NASA NTRS1994

Diffused ionized gas in the spiral galaxy M31

We present a study of diffuse ionized gas (DIG, or WIM for warm ionized medium) in the nearby spiral M31, based on charge coupled device (CCD) imagery in H alpha and (S II) emission lines. We find that the DIG in M31 contributes 40% of the observed total H alpha luminosity, and at least 20% of the total after correction for extinction. This fraction is constant across the disk of M31. The total H alpha luminosity of M31, corrected for extinction, is about 4.1 x 10(exp 40) ergs/s. This implies a low star formation rate of about 0.35 M solar mass/yr, in agreement with earlier estimates. DIG is concentrated near regions of star formation. The average emission measure (EM) perpendicular to the disk ranges from about 6 pc cm(exp-6) in weaker spiral arms to 15 pc cm(exp-6) in the main spiral arms, with (rare) peak values reaching 50 pc cm(exp-6). Overall, the EM in the main arms is substantially higher than that of DIG in the solar neighborhood, implying higher power requirements per unit area in these regions of M31. However, the strong concentration of DIG near regions of star formation keeps the total area covered by DIG in M31 relatively small, which makes it possible to sustain this gas in spite of the low star formation rate. We argue that the DIG extent in vertical direction in M31 may well be lower than in our Galaxy, because of its low star formation rate. A simple parameterization of the electron distribution then shows that the DIG in the spiral arms may contribute between 15% and 40% of the total atomic gas column. The average electron densities implied by the high EMs reached in some regions seem to indicate a higher thermal pressure in the DIG than in the diffuse H I gas in M31. This pressure in-equilibrium can be avoided if part of the diffuse emissions due to a denser component, as proposed most recently by Miller & Cox, because this would reduce the EM and implied pressures for the actual widespread DIG. Column densities of the ionized gas might then be lower as well. We also show, however, that it is not possible to attribute all of the diffuse emission to a relatively dense component, such as earlier proposed extended low-density H II regions. The DIG in M31 shows an overall (S II)/H alpha intensity ratio of 0.5, significantly higher than in discrete H II regions, and similar to that in other galaxies. This number does not vary with radius in M31. There is a suggestion that (S II)/H alpha intensity may be higher at the lowest detectable emission measures, up to 0.7 or even 1. The discrete source population in M31 also shows a trend toward increasing (S II)/H alpha flux ratios as the sources become more diffuse. Few sources (apart from supernova remnants), however, reach the value of 0.5 found in the DIG as a whole. The distinct spectral signature of the DIG in M31, and its energy requirements favor photoionization of the gas, although it is likely that shock ionization occurs in selected regions.

Walterbos, Rene A. M.↗

NASA NTRS1994

Statistical analysis of diffuse ion events upstream of the Earth's bow shock

A statistical study of diffuse energetic ion events and their related waves upstream of the Earth's bow shock was performed using data from the Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) satellite over two 5-month periods in 1984 and 1985. The data set was used to test the assumption in the self-consistent model of the upstream wave and particle populations by Lee (1982) that the particle acceleration through hydromagnetic waves and the wave generation are directly coupled. The comparison between the observed wave power and the wave power predicted on the observed energetic particle energy density and solar wind parameters results in a high correlation coefficient of about 0.89. The intensity of diffuse ions falls off approximately exponentially with the distance upstream from the bow shock parallel to the magnetic field with e-folding distances which vary from approximately 3.3 R(sub E) to approximately 11.7 R(sub E) over the energy range from 10 keV/e to 67.3 keV/e for both protons and alpha particles. After normalizing the upstream particle densities to zero bow shock distance by using these exponential variations, a good correlation (0.7) of the density of the diffuse ions with the solar wind density was found. This supports the suggestion that the solar wind is the source of the diffuse ions. Furthermore, the spectral slope of the diffuse ions correlates well with the solar wind velocity component in the direction of the interplanetary magnetic field (0.68 and 0.66 for protons and alpha particles) which concurs with the notion that the solar wind plays an important role in the acceleration of the upstream particles.

Trattner, K. J.↗

NASA NTRS1995

Stellar models with microscopic diffusion and rotational mixing. 1: Application to the Sun

The Yale stellar evolution code has been modified to include the combined effects of diffusion and rotational mixing on H-1, H-4, and the trace elements He, Li-6, Li-7, and Be-9. The interaction between rotational mixing and diffusion is studied by calculating a number of calibrated solar models. The rotational mixing inhibits the diffusion in the outer parts of the models, leading to a decrease in the envelope diffusion by 25%-50%. Conversely, diffusion leads to gradients in mean molecular weight which can inhibit the rotational mixing. The degree to which gradients in mean molecular weight inhibit the rotational mixing is somewhat uncertain. A comparison with the observed solar oblateness suggests that gradients in the mean molecular weight play a smaller role in inhibiting the rotational mixing than previously believed. This is reinforced by the fact that the model with the standard value for the inhibiting effect of mean molecular weight on the rotational mixing depletes no Li on the main sequence. This is clear in contrast to the observations. A reduction in the inhibiting effect of mean molecular weight gradients by a factor of 10 loads to noticeable main-sequence Li depletion.

Chaboyer, Brian↗

NASA NTRS1995

Diffusion at the magnetopause: Hybrid simulations

Electromagnetic wave generation and resulting cross-field diffusion of plasma are considered at a tangential discontinuity, which characterizes the magnetopause for northward interplanetary magnetic field. Two-dimensional hybrid (particle ions, massless fluid electrons) simulations, in which the tangential discontinuity is generated self-consistently via a stream-stream interaction, are used to show that wave growth occurs when the ambient magnetic field is predominantly perpendicular to the direction of the density gradient. Low-frequency (much less than ion gyrofrequency) waves, with amplitudes delta B/B less than or equal to 0.2 and anticorrelated density fluctuations delta n/n less than or equal to 0.6, are generated at the discontinuity, resulting in cross-field diffusion that is comparable to the Bohm rate. Both the fluctuation level and the lack of ion heating in the calculations are consistent with observations at the magnetopause. The magnitude of the diffusion is considered in the presence of numerical effects and in the context of the inferred diffusion rate at the magnetopause. The relation of the low-frequency waves and their consequences to faster growing, short-wavelength waves due to the lower hybrid drift instability is also addressed. The overall conclusion of this initial study is that diffusion due to low frequency waves is not likely to be a major effect at the magnetopause.

Winske, D.↗

NASA NTRS1995

The galactic distribution of aliphatic hydrocarbons in the diffuse interstellar medium

The infrared absorption feature near 2950(exp -1) (3.4 micron), characteristic of dust in the diffuse interstellar medium (ISM), is attributed to C-H stretching vibrations of aliphatic hydrocarbons. We show here that the strength of the band does not scale linearly with visual extinction everywhere, but instead increases more rapidly for objects near the center of the Galaxy, a behavior that parallels that of the Si-O stretching band due to silicate materials in the diffuse ISM. This implies that the grains responsible for the diffuse medium aliphatic C-H and silicate Si-O stretching bands are different from those responsible for much of the observed visual extinction. It also suggests that the distribution of the carbonaceous component of the diffuse ISM is not uniform throughout the Galaxy, but instead may increase in density toward the center of the Galaxy. The similar behavior of the C-H and Si-O stretching bands suggests that these two components may be coupled, perhaps in the form of silicate-core, organic-mantle grains. Several possible models of the distribution of this material are presented and it is demonstrated that the inner parts of the Galaxy has a carrier density that is 5 to 35 times higher than in the local ISM. Depending on the model used, the density of aliphatic material in the local ISM is found to be about 1 to 2 -CH3 groups m(exp -3) and about 2 to 5 -CH2- groups m(exp -3). These densities are consistent with the strengths of the 2955 and 2925 cm(exp -1) (3.4 micron) band being described by the relations A(sub nu)/tau(sub 2955 cm(exp -1)) = 270 +/- 40 and A(sub nu)/tau(sub 2925 cm(exp -1)) = 250 +/- 40 in the local diffuse ISM.

Sandford, Scott A.↗

NASA NTRS1995

Low-energy ion acceleration at quasi-perpendicular shocks: Transverse diffusion

The problem of ion injection and acceleration at quasi perpendicular shocks has been the subject of some debate over the past two decades. It is widely known that these shocks efficiently accelerate particles that are well in the high-energy tail of the distribution. However, the issue of injection, or the acceleration of low-energy ions, has yet to reach a consensus. The fundamental issue is whether there is enough diffusion normal to the magnetic field for the particles to remain near the shock. Since transverse diffusion is a physical process that is not well understood in space plasmas, this is an important, and difficult issue to address. In this report, we will investigate the ion injection problem by performing test particle orbit integrations using synthesized turbulent fields. These fields are fully three-dimensional so that transverse diffusion is possible (cross-field diffusion is not possible in geometries where the electromagnetic fields are less than three dimensional). The synthesized fields are produced by superimposing a three-dimensional wave field on a background field. For completeness, we will compare the results from this model with the more well-established theories, such as the diffusive approximation and scatter-free shock drift acceleration. We will also compare these results with other numerical simulation techniques such as the well known hybrid simulation, and other test-particle calculations in which the shock fields are specified to have less than three dimensions. We will also discuss some recent relevant observations and how these compare with our results.

Giacalone, J.↗

NASA NTRS1997

Diffusion Flame Extinction in a Low Strain Flow

Diffusion flames are of great interest in fire safety and many industrial processes. Many parameters significantly affect the flame structure, shape and stability, of particular importance are the constraints imposed by geometrical boundaries. Physical boundaries determine the characteristics of the flow, affect heat, fuel, and oxidizer transport from and towards the flame and can act as heat sinks or heat sources. As a result, the existence of a flame, its shape and nature are intimately related to the geometrical characteristics of the environment that surrounds it. The counter-flow configuration provides a constant strain flow, therefore, is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in micro-gravity conditions have begun to explore the low strain regimes. The main objective of these on-going studies is to determine the effect of radiative heat losses and variable strain on the structure and radiation-induced extinction of diffusion flames. For these programs, size, geometry, and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. Whether is the burning of condensed or gaseous fuels, for most real situations the boundaries impose a significant effect on the nature of the flame. There is, therefore, a need to better understand the effect that geometrical constraints (i.e. flow nonperpendicular to a fuel surface, heat losses to the boundaries, etc.) might have on the final characteristics of a diffusion flame. Preliminary experiments have shown that, in the absence of gravity, and depending on the distance from the flame to the boundary, three characteristically different regimes can be observed. Close to the boundary, the flame is parabolic, very thin and blue, almost soot-less. Diffusion is the main mechanism controlling fuel transport to the reaction zone, conduction towards the inlets is the main source of heat losses. As the distance increases the flame becomes linear and thickens, remaining blue at the oxidizer side and turning yellow at the fuel side. Here, convection brings fuel and oxidizer together and the reaction occurs in the viscous layer formed between the fuel and oxidizer streams. This region corresponds to the characteristic counter-flow flame where conduction and convection become negligible forms of heat losses and radiation becomes dominant. The flame in the third (mixed) region, between the two others, results from the combination of the scenarios presented above.

Sutula, Jason↗