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Spin-Torque in Systems with Inhomogeneous Magnetization

The work performed during the grant period focused on the phenomenon of spin-transfer torque. This is a quantum mechanical effect whereby the angular momentum of conduction electrons is transferred to the magnetization of ferromagnetic structures. Our work on this subject began with phenomenological drift-diffusion and Landau-Lifshitz-Gilbert equations to demonstrate unambiguously that unpolarized current flow from a nonmagnet into a ferromagnet can produce a precession-type instability of the magnetization. We then used Boltzmann calculations appropriate to spin-valve type magnetic heterostructures composed of a non-magnetic thin film sandwiched between two thin film layers with uniform magnetization. Perhaps our most important paper dealt with quantum and semi-classical calculations of spin-transfer torque in systems with domain walls and other inhomogeneous distributions of magnetization. The latter work caused us to suggest that the Landau-Lifshitz approach to magnetic damping provided a clearer picture of the physics than the more popular (but formally equivalent) Gilbert approach to damping. Finally, we returned to our Boltzmann calculations and made a serious effort to analyze experimental data on current-induced magnetization in switching in magnetic spin-valve structures. Our work was part of a world-wide effort to study and harness the transport of the electron's spin and was one of the first sustained theoretical efforts in this direction in the United States. The payoff is just now being seen. In November of 2012, the Everspin Corporation announced the release of the first commercial spin-torque magnetoresistive random access memory.

36 MATERIALS SCIENCE↗

Utilizing Highly Scattered Light for Intelligence through Aerosols

This communication is the final report for the project Utilizing Highly Scattered Light for Intelligence through Aerosols funded by the Laboratory Directed Research and Development (LDRD) program at Sandia National Laboratories and lasting six months in 2019. Aerosols like fog reduce visibility and cause down-time that for critical systems or operations are unacceptable. Information is lost due to the random scattering and absorption of light by tiny particles. Computational diffuse optical imaging methods show promise for interpreting the light transmitted through fog, enabling sensing and imaging to improve situational awareness at depths 10 times greater than current methods. Developing this capability first requires verification and validation of diffusion models of light propagation in fog. For this reason, analytical models were developed and compared to experimental data captured at the Sandia National Laboratory Fog Chamber facility. A methodology was developed to incorporate the propagation of scattered light through the imaging optics to a pixel array. The diffusion approximation to the radiative transfer equation was found to predict light propagation in fog under the appropriate conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DRACO: An Overview [Slides]

DRACO (Diffusion ReACtiOn) is a diffusion and chemistry code designed to: 1) Operate on 3D with an unstructured grid defining an arbitrary geometry of interacting parts. 2) Generate its own meshes and use meshes created by other software. 3)Model the transport of any number of diffusing quantities: Concentrations, pressures, temperature, etc. 4) Allow diffusion coefficients to depend in an arbitrary way on concentration, temperature, position, time, etc. 5) Model general chemistry between concentrations with arbitrary reaction rates. 6) Allow arbitrary initial conditions, boundary conditions, and sources/sinks. 7) Allow all of the above to be specified by the user.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Constraining the Evolution of the Proton Distribution Function in the Heliotail

We use Interstellar Boundary Explorer (IBEX) measurements of energetic neutral atoms (ENAs) to constrain the proton (mostly pickup ion, PUI) distribution in the heliotail. In our previous study, we solved the Parker transport equation and found that the velocity diffusion coefficient $D(v)$ for PUIs is approximately $D(v)$ ~ 1.1 × 10 -8 km 2 s -3 ($v/v_0$) 1.3 , assuming the initial proton distribution processed by the termination shock (TS), $f_{p,0}$, is a kappa distribution with kappa index $ₖ_{p,0}$ = 1.63. In this study, we test different forms for $f_{p,0}$. We find that if $f_{p,0}$ is kappa-distributed and $D(v)$ = $D_0(v/v_0)^{1.3}$, any kappa index in the range 1.5 < $κ_{p,0}$ < 10 is consistent with IBEX data if $D_0 ~$ 0.8–1.3 × 10 -8 km 2 s -3 . While the case where $D(v)$ ∝ $v^{1.3}$ yields ENA fluxes that appear to best reproduce IBEX data for any $κ_{p,0}$, it is possible for $D(v)$ to scale close to $~v^{2/3}$ or $~v^2$ within our uncertainties by changing $D_0$. We also show that an upstream PUI filled-shell distribution that is heated by a quasi-stationary TS, generating a downstream filled-shell with large cutoff speed, yields an excess of ENAs > 2 keV compared to IBEX. However, using a fully kinetic particle-in-cell simulation to process a PUI filled-shell across the TS yields ENA spectra consistent with IBEX , reinforcing the significance of self-consistent, preferential PUI heating and diffusion at the TS. Interestingly, an upstream PUI distribution inferred from the particle-in-cell simulation to reproduce Voyager 2 observations of the nose-ward TS is inconsistent with IBEX observations from the heliotail, suggesting differences in the upstream PUI distribution or TS properties.

79 ASTRONOMY AND ASTROPHYSICS↗

Electrochemical Impedance Spectroscopy and Cyclic Voltammetry Methods for Monitoring SmCl 3 Concentration in Molten Eutectic LiCl-KCl

Molten salt solutions consisting of eutectic LiCl-KCl and concentrations of samarium chloride (0.5 to 3.0 wt%) at 500 C were analyzed using both cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). The CV technique gave the average diffusion coefficient for Sm 3+ over the concentration range. Equipped with Sm 3+ diffusion coefficient, the Randles-Sevcik equation predicted Sm 3+ concentration values that agree with the given experimental values. From CV measurements; the anodic, cathodic, and half-peak potentials were identified and subsequently used as a parameter to acquire EIS spectra. A six-element Voigt model was used to model the EIS data in terms of resistance-time constant pairs. The lowest resistances were observed at the half-peak potential with the associated resistance-time constant pairs characterizing the reversible reaction between Sm 3+ and Sm 2+ . By extrapolation, the Voigt model estimated the polarization resistance and established a polarization resistance-concentration relationship.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Radiative shock structure.

Shock wave structure in ionized hydrogen, using Eddington approximation to solve Rankine- Hugoniot jump equation

DIFFUSION WAVE↗

A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate

A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.

Dow, J. W.↗

The present state of gamma-ray astronomy.

The current state of gamma-ray astronomy is reviewed in terms of the most recent experimental results that define, in either measured fluxes or upper limits, the cosmic photon spectrum in the energy range from 0.5 MeV to 10,000 TeV. Methods of research developed during the last 10 yr are discussed and specific results are cited. Cosmic gamma rays have been observed in two regions of the spectrum - from 0.5 to 6 MeV and from about 50 MeV to several hundred mega-electronvolts. Above 50 MeV, a strong concentration of intensity is observed in a band of directions around the galactic equator. In both spectral regions a diffuse background gamma ray flux, apparently isotropic and of extragalactic origin, is observed. Evidence of 50 MeV gamma-ray pulses from the Crab pulsar has been reported. No definite evidence of any other discrete gamma-ray source besides the galaxy itself has been observed at any energy.

Clark, G.↗

Implications of the reported low energy electron gradients

A recently reported measurement of a small electron gradient in the energy range from 1.9 to 8.4 MeV by Webber et al. (1973) is interpreted in terms of a large local value of the scattering mean free path for these particles. The possibility that the scattering mean free path may be large throughout the modulation region is then investigated under the assumption of an azimuthally symmetric modulation region of 5 AU extent, the applicability of the diffusion-convection-adiabatic energy loss transport equation, and a galactic origin for the low-energy electrons. The implications for the solar modulation of electrons and the interstellar electron spectrum are discussed.

Lezniak, J. A.↗

Bidirectional plant canopy reflection models derived from the radiation transfer equation

A collection of bidirectional canopy reflection models was obtained from the solution of the radiation transfer equation for a horizontally homogeneous canopy. A phase function is derived for a collection of bidirectionally reflecting and transmitting planar elements characterized geometrically by slope and azimuth density functions. Two approaches to solving the radiation transfer equation for the canopy are presented. One approach factors the radiation transfer equation into a solvable set of three first-order linear differential equations by assuming that the radiation field within the canopy can be initially approximated by three components: uniformly diffuse downwelling, uniformly diffuse upwelling, and attenuated specular. The solution to these equations, which can be iterated to any degree of accuracy, was used to obtain overall canopy reflection from the formal solution to the radiation transfer equation. A programable solution to canopy overall bidirectional reflection is given for this approach. The special example of Lambertian leaves with constant leaf bidirectional reflection and scattering functions is considered, and a programmable solution for this example is given. The other approach to solving the radiation transfer equation, a generalized Chandrasekhar technique, is presented in the appendix.

Beeth, D. R.↗

On the dynamics of agglomerating ensembles of clouds

It is shown that for dynamical time scales longer than 10 million years the ensemble of interstellar cold diffuse clouds may be described by equations of mass and momentum conservation where the pressure has the form p/v-squared/ where /v-squared/ is the mass averaged square velocity dispersion. Equilibrium cloud spectra are derived and an equation of state obtained. The equation of state undergoes a phase transition at a critical density close to the local interstellar gas density. At higher densities, more massive clouds are formed and the cloud fluid softens. It is suggested that this mechanism may naturally regulate the interstellar gas density if star formation is very efficient in the cooler high-density systems.

Cowie, L. L.↗

Analytical description of charged particle transport along arbitrary guiding-field configurations

Focused particle transport is analyzed in terms of partial differential equations which are applicable to arbitrary spatial variations of the mean free path and the focusing length. A distribution function for transport is written in two forms of the Boltzmann equation and a coefficient of spatial diffusion is defined. Changes from a nearly coherent propagation of flare particles in regions of strong focusing near the sun to ordinary diffusion in the outer solar system are described as supercoherent transitions. A solution to the steady state problem is developed and results are presented for a monopolar guiding field configuration with isotropic diffusion gradually giving way to anisotropy in a region suggestive of a collimated beam of particles streaming away from its source.

Earl, J. A.↗

Ion temperature variations in the daytime high-latitude F region

The Schunk and Sojka (1981a, b) high latitude ionospheric model is improved through the inclusion of thermal conduction and diffusion terms in the ion energy equation, permitting the study of daytime, high latitude F layer temperature variations in a region poleward of the auroral oval. It is found that ion temperature variation with solar cycle, season and geomagnetic activity closely follows the neutral atomic oxygen variation, and that meridional electric fields of more than 40 mV/m can cause larger ion temperature changes than those due to solar cycle, seasonal or geomagnetic activity variations. In the presence of meridional electric fields, there is an upward flow of heat from the lower ionosphere that also acts to raise ion temperatures at high altitudes. Zonal electric fields affect ion temperature indirectly, through electron density changes.

Schunk, R. W.↗

The diffusivity of hydrogen in Nb stabilized stainless steel

The evolution of hydrogen from 347 stainless steel has been studied by using a real time dynamic technique under ultrahigh vacuum conditions. Auger electron spectroscopy was used to determine the surface composition as a function of time and temperature. The surface film on the electropolished samples was found to be approximately 15 A thick and consisted of a carbon-oxygen complex and a metal oxide (FexOy). Upon heating to 400 C, the carbon-oxygen complex desorbed as CO and the remaining oxygen and carbon began to incorporate. Also at this temperature sulfur began to diffuse out of the bulk to the surface and at approximately 800 C formed a complete monolayer. At 900 C, carbon and oxygen virtually disappeared, leaving the monolayer of sulfur as the only surface contaminant. The hydrogen diffusivity was found to follow closely the equation D = 7.01 x 10 to the -7th exp(-48.0/RT) sq m per second over the entire temperature range studied, thus indicating that hydrogen evolution is not significantly affected by the changing surface composition. The somewhat higher value of the diffusivity obtained in this work compared to past measurements in austenitic stainless steels may indicate the importance of sample preprocessing and ultrahigh vacuum conditions in minimizing the effects of surface layers.

Outlaw, R. A.↗

Losses in Channels with Increased External Turbulence

An approximate method for determining the effect of the level of turbulence on the aerodynamic characteristics of convergent and diffuser channels is examined. A momentum equation for the boundary layer is in the method, introducing external flow turbulence on the basis of experimental values of the coefficient of friction and the form factor. It is found that at significant levels of external turbulence, losses must be considered not only in the boundary layer but also in the central region of the channel.

Zaryankin, A. Y.↗

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗

Computations of turbulent evaporating sprays

A computational study of turbulent evaporating sprays is reported. The major focus is to examine the sensitivity of the vaporization behavior of turbulent sprays to the transient liquid-phase processes. Three models considered to represent these processes are the thin skin, infinite diffusion, and diffusion limit models. Favre-averaged equations with k-epsilon-g turbulence model are employed for the gas phase. The Lagrangian approach with a stochastic separated flow method is used for the liquid phase where the effects of gas turbulence on droplet trajectories and interphase transport rates are considered using random-walk computations. Also the variable-property effects are considered in detail. Results indicate that, depending upon the boiling temperature and heat of vaporization of the fuel considered, the vaporization behavior of turbulent sprays may be quite sensitive to the modeling of transient liquid-phase processes. Thus, it is important that for most hydrocarbon fuels these processes be adequately represented in any comprehensive spray computations. The present results also provide further support to the conclusions of earlier studies which have been based on simplified spray configurations.

Aggarwal, S. K.↗