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NASA NTRS1993

Stormtime transport of ring current and radiation belt ions

This is an investigation of stormtime particle transport that leads to formation of the ring current. Our method is to trace the guiding-center motion of representative ions (having selected first adiabatic invariants mu) in response to model substorm-associated impulses in the convection electric field. We compare our simulation results qualitatively with existing analytically tractable idealizations of particle transport (direct convective access and radial diffusion) in order to assess the limits of validity of these approximations. For mu approximately less than 10 MeV/G (E approximately less than 10 keV at L equivalent to 3) the ion drift period on the final (ring-current) drift shell of interest (L equivalent to 3) exceeds the duration of the main phase of our model storm, and we find that the transport of ions to this drift shell is appropriately idealized as direct convective access, typically from open drift paths. Ion transport to a final closed drift path from an open (plasma-sheet) drift trajectory is possible for those portions of that drift path that lie outside the mean stormtime separatrix between closed and open drift trajectories, For mu approximately 10-25 MeV/G (110 keV approximately less than E approximately less than 280 keV at L equivalent to 3) the drift period at L equivalent to 3 is comparable to the postulated 3-hr duration of the storm, and the mode of transport is transitional between direct convective access and transport that resembles radial diffusion. (This particle population is transitional between the ring current and radiation belt). For mu approximately greater than 25 MeV/G (radiation-belt ions having E approximately greater than 280 keV at L equivalent to 3) the ion drift period is considerably shorter than the main phase of a typical storm, and ions gain access to the ring-current region essentially via radial diffusion. By computing the mean and mean-square cumulative changes in 1/L among (in this case) 12 representative ions equally spaced in drift time around the steady-state drift shell of interest (L equivalent to 3), we have estimated (from both our forward and our time-reversed simulations) the time-integrated radial-diffusion coefficients D(sup sim)(sub LL) for particles having selected values of mu approximately greater than 15 MeV/G. The results agree surprisingly well with the predictions (D(sup ql)(sub LL)) of quasilinear radial diffusion theory, despite the rather brief duration (approximately 3 hrs) of our model storm and despite the extreme variability (with frequency) of the spectral-density function that characterizes the applied electric field during our model storm. As expected, the values of D(sup sim)(sub LL) deduced (respectively) from our forward and time-reversed simulations agree even better with each other and with D(sup sim)(sub LL) when the impulse amplitudes which characterize the individual substorms of our model storm are systematically reduced.

Chen, Margaret W.↗

NASA NTRS1975

Calculations of the cosmic ray modulation in interplanetary space taking into account the possible dependence of the transport travel for the scattering of the particles and of the velocity of the solar winds on the angles they make with the helioequator plane: The case of isotropic diffusion

The modulation of galactic cosmic rays is studied by the magnetic heterogeneities stream on the assumption that the diffusion coefficient is reduced whereas the solar wind velocity is increased with the growth of the angle between the sun's rotation axis and the direction of solar plasma motion. The stationary plane problem of isotropic diffusion is solved as it applies to two cases: (1) with due account of particle retardation by the antiphermium mechanism; and (2) without an account of the above mechanism. This problem is solved by the grid method in the polar coordinate system. The results of the calculations are followed by a discussion of the method of solution and of the errors.

Dorman, L. I.↗

NASA NTRS1976

Pioneer 10 ultraviolet photometer observations of Jupiter - The helium to hydrogen ratio

Pioneer 10 UV photometric observations of solar He I 584-A emissions diffusely reflected from the atmosphere of Jupiter are discussed which establish the expected presence of He in the planet. The intensity and profile of the solar He line are remeasured and found to be more intense than originally supposed, implying a lower value for the diffuse 584-A reflectivity of Jupiter and less He than previously estimated. Other measurements of the solar He line are reviewed, resonance scattering by He is analyzed, and radiative-transfer calculations for Jovian model atmospheres are improved by including the anisotropic phase function for helium resonance scattering. The assumption of coherent scattering in the formation of the Jovian airglow line is shown to be an accurate approximation, and present estimates of the atmospheric temperature and eddy diffusion coefficient are examined. An atmospheric He/H abundance ratio greater than zero but less than approximately 28% is determined by assuming an isothermal atmosphere with a temperature of 150 K and the range of eddy-diffusion values given by Pioneer 10 Ly-alpha observations. The effect of higher temperatures on the He/H abundance is briefly evaluated.

Carlson, R. W.↗

NASA NTRS1961

Effect of Static Strains on Diffusion

A theory is developed that gives the diffusion coefficient in strained systems as an exponential function of the strain. This theory starts with the statistical theory of the atomic jump frequency as developed by Vineyard. The parameter determining the effect of strain on diffusion is related to the changes in the inter-atomic forces with strain. Comparison of the theory with published experimental results for the effect of pressure on diffusion shows that the experiments agree with the form of the theoretical equation in all cases within experimental error.

Girifalco, L. A.↗

NASA NTRS1974

Analytic approximations in the study of the solar modulation of electrons

Numerical solutions to the transport equation of galactic cosmic rays in the interplanetary medium have been used to investigate the applicability of commonly used approximate analytic solutions for electrons (10 MeV to 10 GeV). We find that for a given cosmic-ray diffusion coefficient the force-field approximation is in reasonable agreement with the numerical solution at energies above 200 MeV, but deviates significantly at lower energies, depending on the shape of the interstellar electron spectrum. The diffusion-convection approximation agrees generally with the numerical solution within a factor of 2 over the entire energy range.

Cummings, A. C.↗

NASA NTRS1981

Diffusion tube

The diffusion tube was designed to operate below about 0.25 percent of water supersaturation. It is simply a long tube lined on the inside with a damp chamois cloth, and heated isothermally to a few degrees centigrade above the incoming air. The diffusion coefficient for water vapor is slightly larger than that for heat, making it possible to supersaturate the airflow. This is the same principle by which transient supersaturations may occur in parallel plate cloud chambers. Only the diffusion of vapor and heat from the walls into the moving air are considered.

Leaitch, R.↗

NASA NTRS1993

Effects of thermal-solutal convection on temperature and solutal fields under various gravitational orientations

Semiconductor crystals such as Hg(1-x)CD(x)Te grown by unidirectional solidification Bridgmann method have shown compositional segregations in both the axial and radial directions. Due to the wide separation between the liquidus and the solidus of its pseudobinary phase diagram, there is a diffusion layer of higher HgTe content built up in the melt near the melt-solid interface which gives a solute concentration gradient in the axial direction. The value of effective diffusion coefficient calculated from fitting of the data to 1D model varies with Hg(1-x)Cd(x)Te growth conditions. This indicates that the growth condition of the Hg(1-x)Cd(x)Te is not purely diffusion controlled. Because of the higher thermal conductivity in the melt than that in the crystal in the growth system, there is a thermal leakage through the fused silica crucible wall near the melt-solid interface. This gives a thermal gradient in the radial direction. Hart, and Thorpe, Hutt and Soulsby have shown that under such conditon a fluid will become convectively unstable as a result of different diffusitivities of temperature and solute. It is quite important to understand the effects of this thermosolute convection on the compositonal segregation in both axial and radial directions in the unidirectionally solidified crystals under various gravitational directions. To reach this goal, we start with a simplified problem to study the effects of thermal-solutal convection on the temperature and solutal fields under various gravitional orientations. We begin by reviewing model governing equations.

Wang, Jai-Ching↗

NASA NTRS1993

Diffusion length damage coefficient and annealing studies in proton-irradiated InP

We report on the measurement of the diffusion length damage coefficient (K(sub L)) and the annealing characteristics of the minority carrier diffusion length (L(sub n)) in Czochralski-grown zinc-doped indium phosphide (InP), with a carrier concentration of 1 x 10(exp l8) cm(exp -3). In measuring K(sub L) irradiations were made with 0.5 MeV protons with fluences ranging from 1 x 10(exp 11) to 3 x 10(exp 13) cm(exp -2). Pre- and post-irradiation electron-beam induced current (EBIC) measurements allowed for the extraction of L(sub n) from which K(sub L) was determined. In studying the annealing characteristics of L(sub n) irradiations were made with 2 MeV protons with fluence of 5 x 10(exp 13) cm(exp -2). Post-irradiation studies of L(sub n) with time at room temperature, and with minority carrier photoinjection and forward-bias injection were carried out. The results showed that recovery under Air Mass Zero (AMO) photoinjection was complete. L(sub n) was also found to recover under forward-bias injection, where recovery was found to depend on the value of the injection current. However, no recovery of L(sub n) after proton irradiation was observed with time at room temperature, in contrast to the behavior of 1 MeV electron-irradiated InP solar cells reported previously.

Hakimzadeh, Roshanak↗

NASA NTRS1977

Two-dimensional hygrothermal diffusions into a finite width composite laminate

Two dimensional hygroscopic diffusion into composite laminates with free edges was obtained through the use of a second order finite difference scheme. A computer program was developed for the transient nonlinear coupled hygrothermal diffusion into finite width laminates with varying surface conditions along two edges. The formulation permits the diffusion coefficient to be a function of temperature, moisture concentration, and fiber orientation. The moisture distributions thus obtained are necessary for analysis of the moisture induced interlaminar stresses in the vicinity of free edges. It is shown that large diffusion times tend to eliminate the significance of stacking sequence, but gradients within and between layers are significant for all diffusion times.

Farley, G. L.↗

NASA NTRS1991

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Treumann, R. A.↗

NASA NTRS1992

Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

Earl, James A.↗

NASA NTRS2001

Modelling of Trapped Radiation Near Jupiter

Energetic (62 to approx. 130 MeV) proton fluxes measured with the Galileo Probe inside Jupiter's main ring (radii 122,500 to 128,940 km) show a modest increase as Jupiter is approached. Solutions of a reduced (1-d) equatorial diffusion equation with-constant losses described by a lifetime tau match those data for tau greater than or equal to 10(exp 9) s for diffusion coefficient D(sub LL) = 10(exp -9) L(exp 4)/s, 10(exp -9) L(exp -3)/s, or 10(exp -10) L(exp 4)/s (this particle population may be undergoing nearly loss-free inward radial diffusion). Tau would increase as Jupiter is approached if its value were determined by pitch angle scattering due to EM wave-particle interactions. if the absolute amplitudes of the waves' magnetic fluctuations did not vary with radial distance. Exploration of numerical solutions of the diffusive transport equation for Jupiter's magnetospheric ions at die planetary ring and closer to Jupiter has been done. Explicit range-energy relationships for energy loss in ring matter (SiO2), modeled as a continuous disk, are incorporated. A spatial resolution of approx. 1000 km in the radial direction is used in the vicinity of the main ring; off-equatorial ion fluxes have been included (assuming the atmosphere is a perfect absorber). For protons the maximum effect of energy loss in the microscopic size range of ring particles is expected at energies approx. 0.1 Mev. Presumably there could be sufficiently large, unobserved bodies within the ring that would have to be modeled as discrete objects, as planetary satellites would be. Within limitations of the model and computational resources it's planned to characterize solutions for transport of magnetospheric ions past the planetary ring; the procedures that are used are fairly well known and may be applied generally to the simpler magnetospheric models.

Mihalov, John D.↗

NASA NTRS1978

Numerical simulation of warm fog and its application to warm fog prediction and modification

The considered theoretical model describes the evolution of potential temperature, water vapor content, liquid water content, and horizontal and vertical winds as determined by the processes of vertical turbulent transfer and horizontal advection for momentum, energy, and moisture, as well as radiation cooling, growth of water droplets based on microphysical processes, and drop sedimentation. The mathematical model is two-dimensional in the X-Z plane. The diffusivity coefficient is the same for liquid water droplets as for vapor. The fundamental equations governing the macrophysical processes of the evolution of wind components, water vapor content, liquid water content, and potential temperature under the influences of vertical turbulent diffusion transfer, turbulent momentum transfer, and turbulent energy transfer are expressed by three sets of conservation equations.

Hung, R. J.↗

NASA NTRS1998

Directional Solidification and Characterization of Hg(0.89) Mn(0.11)Te

Two boules of Hg(0.89)Mn(0.11)Te(MMT) were solidified using the vertical Bridgman-Stockbarger method. Translation rates of 0.09 and 0. 18 microns/s were used. The influence of growth rate on axial compositional homogeneity in the MMT boules was evaluated experimentally by conducting precision density measurements on radial slices taken from each boule. In addition, Plane Front Solidification theory and segregation coefficient (k) data for the Hg(1-x)Mn(x)Te system were used to fit theoretical composition profiles to the measured MMT axial composition profiles. The strong correlation between the measured and calculated MMT axial composition profiles indicates diffusion dominated axial solute redistribution in the boules under the applied growth conditions. The analysis of the MMT axial composition profiles by Plane Front Solidification theory allowed the calculation of the effective diffusion coefficient (D(eff) = 3.5 x l0(exp -5) sq cm/s). The k-values for the Hg(1-x)Mn(x)Te system and the D(sub eff) - value were then used to verify that both boules were solidified under conditions which did not exceed the Constitutional Supercooling Criteria under ideal conditions. Finally, a preliminary examination of the radial compositional variation in each MMT was made using Fourier Transform Infra-Red Spectroscopy (FTIR). The radial homogeneity in the MMT boules was found to be comparable for both translation rates.

Price, M. W.↗

NASA NTRS1978

Prediction of moisture and temperature changes in composites during atmospheric exposure

The effects of variations in diffusion coefficients, surface properties of the composite, panel tilt, ground reflection, and geographical location on the moisture concentration profiles and average moisture content of composite laminates were studied analytically. A heat balance which included heat input due to direct and sky diffuse solar radiation, ground reflection, and heat loss due to reradiation and convection was used to determine the temperature of composites during atmospheric exposure. The equilibrium moisture content was assumed proportional to the relative humidity of the air in the boundary layer of the composite. Condensation on the surface was neglected. Histograms of composite temperatures were determined and compared with those for the ambient environment.

Tompkins, S. S.↗

NASA NTRS1990

Validation of parameterization scheme for eddy diffusion from satellite data

The eddy diffusion coefficient K(yy) has been calculated usign LIMS for the months of December 1978 and January and February 1979. Two methods have been used. The first implements the suggestion made by Tung (1987) to parameterize the eddy transport as a diffusive process along isentropes. The second method integrates the equation relating the parcel displacements to the eddy velocity fields. The latter method uses a filtering on both space and time domains to isolate transients and is referred to as the 'spectral method'. Results from the first method are shown to be reliable only for quiescent periods, breaking down when the meridional gradient of potential vorticity is negligible. Results from the two methods are in agreement only for very disturbed conditions, when transience is readily isolated. It is concluded that the parameterizations suggested for eddy transport and calculated in this paper may be meaningful for quiet periods, but are not reliable for unsteady and very large amplitude disturbances.

Sassi, F.↗

NASA NTRS1972

A study of the properties of beryllium doped silicon with particular emphasis on diffusion mechanisms: Profiles of depth dependent conductivity as determined by electrical surface probes

Very large diffusion coefficients were encountered and required the determination of impurity profiles for samples approximately 1 cm thick. Since conductivity values are readily converted into concentrations of electrically active impurities, the major problem became that of accurately determining the conductivity profiles of beryllium diffused silicon samples. Four-point probe measurements on samples having depth conductivities are interpreted in terms of conductivity profiles, based on an exact solution of the problem of exponentially depth dependent conductivity. Applications include surface conductivity determination where the form of the conductivity profile is known, and conductivity profile determination from probe measurements taken as the sample surface is progressively lapped away. The application is limited to samples having conductivity monotonically decreasing with depth from the probed surface.

Franks, R. K.↗

NASA NTRS1981

On the transport and propagation of relativistic electrons in galaxies

Analytic solutions to the time-dependent equation describing the transport of relativistic electrons that are being convected and diffused, and may be either gaining or losing energy, are described. The calculations yield a body of solutions from which specific ones can be chosen for the modelling of synchrotron radiation in the Galaxy and in other galaxies. The solutions allow for (1) spatially varying convection velocity; (2) an energy and spatially dependent diffusion coefficient; (3) adiabatic acceleration effects; (4) a term describing spatially dependent synchrotron loss and/or Fermi acceleration; (5) an injection source for the electrons that may be impulsive, steady-state, or variable-injection; (6) a spatial injection or spatially more diffuse source; (7) arbitrary energy dependence of the injection source; and (8) spatial and energy boundaries where the spatial or energy form of the convection, diffusion, and energy supply terms in the basic equation can change character.

Lerche, I.↗