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At least 541 records · Page 30

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NASA NTRS1980

Variational description of the positive column with two-step ionization

The ionization balance in diffusion-dominated discharges may depend on both one- and two-step ionization processes. The Spenke diffusion equation describing such conditions is solved in this paper by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between the equation parameter, and the discharge dimensions, are derived for planar and cylindrical geometry and compared with exact computations for certain limiting cases.

Crawford, F. W.↗

NASA NTRS1981

Pseudospectral method for problems with nonperiodic boundary conditions

The capability of the pseudospectral technique and the time integration scheme for the time dependent nonperiodic problem is demonstrated. Significant improvements are shown in the accuracy for calculation of the two dimensional time dependent advection diffusion equation. The pseudospectral method is a viable alternative to the finite difference methods for the equation of the spatial deriviations.

Lee, H. N.↗

NASA NTRS1981

Magnetic field diffusion and dissipation in reversed-field plasmas

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

Drake, J. F.↗

NASA NTRS1980

Theory of positronium formation and positron emission at metal surfaces

The range of metallic surface processes available to the implanted positron is examined with a view to bare positron escape, positron surface state trapping, surface state detrapping, and positronium atom conversion. The stopping distance and its rms deviation are calculated. The effect of the elastic positron-ion core scattering, and the finite temperature corrections in the positron-phonon scattering are included. Overall conversion and emission efficiencies are calculated by solving an appropriate diffusion equation with boundary conditions set by the branching ratios for the surface processes. The temperature and incident energy dependence of the results for positronium atom conversion and positron emission efficiency are compared to experimental data.

Nieminen, R. M.↗

NASA NTRS1981

Hot oxygen atoms in the upper atmosphere of Venus

Using data obtained by an ultraviolet spectrometer on the Pioneer-Venus Orbiter, energy and altitude distribution of nonthermal oxygen atoms in the Venus atmosphere for typical daytime and nighttime conditions are calculated using two different numerical methods. Agreement is found between results obtained by the two-stream transport method and the diffusion equation technique. Dissociative recombination of molecular oxygen ions and charge exchange of atomic oxygen ions with the neutral hydrogen and oxygen gas are the source terms, and calculations show that the dissociative recombination term is the dominant one. It is shown that measured hot atom concentrations exceed estimates of the thermal hydrogen atom concentrations derived from Brinton et al. (1980) over most of the daytime exosphere, and the calculated concentrations do so to an even greater extent. It is concluded that hot oxygen atoms are an important component of the dayside exosphere of Venus, their most important effect being the absorption of solar wind.

Nagy, A. F.↗

NASA NTRS1981

Statistical acceleration of electrons by lower-hybrid turbulence

The statistical acceleration of electrons along an ambient magnetic field by large-amplitude lower-hybrid turbulence is discussed. Perturbations driven by a crossfield current and propagating nearly perpendicular to the applied magnetic field are considered. It is assumed that the instability saturates rapidly and that the fluctuating electric field is predominantly electrostatic. If the turbulence is characterized by a spectrum of small parallel wavenumbers, such that the parallel phase velocity of the waves is greater than the electron thermal velocity, then the turbulence can only accelerate electrons moving with large velocities along the magnetic field. The quasi-linear diffusion equation is solved using a Green's function technique, assuming a power law spectral energy density. The time evolution of an initial Maxwellian distribution is given and the time rate of change of the mean electron energy is calculated for various cases.

Wu, C. S.↗

NASA NTRS1981

Effect of shear stress on cell cultures and other reactor problems

Anchorage dependent cell cultures in fluidized beds are tested. Feasibility calculations indicate the allowed parameters and estimate the shear stresses therein. In addition, the diffusion equation with first order reaction is solved for the spherical shell (double bubble) reactor with various constraints.

Schleier, H.↗

NASA NTRS1982

Coupled hydromagnetic wave excitation and ion acceleration upstream of the earth's bow shock

A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.

Lee, M. A.↗

NASA NTRS1982

Ultrasonic determination of thermodynamic threshold parameters for irreversible cutaneous burns

In vivo ultrasonic measurements of the depth of conductive cutaneous burns experimentally induced in anesthetized Yorkshire pigs are reported as a function of burn time for the case in which the skin surface temperature is maintained at 100 C. The data are used in the solution of the one-dimensional heat diffusion equation with time-dependent boundary conditions to obtain the threshold temperature and the energy of transformation per unit mass associated with the transition of the tissue from the state of viability to the state of necrosis. The simplicity of the mathematical model and the expediency of the ultrasonic measurements in studies of thermal injury are emphasized.

Cantrell, J. H., Jr.↗

NASA NTRS1982

Heat generation in aircraft tires under free rolling conditions

A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.

Clark, S. K.↗

NASA NTRS1983

Heat generation in aircraft tires

Clark, S. K.↗

NASA NTRS1981

An empirical investigation of methods for nonsymmetric linear systems

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

Sherman, A. H.↗

NASA NTRS1983

Turbulent heating in solar cosmic ray theory

The heating of minor ions in solar flares by wave-wave-particle interaction with Langmuir waves, or ion acoustic waves, can be described by a diffusion equation in velocity-space for the particle distribution function. The dependence of the heating on the ion charge and mass, and on the composition of the plasma, is examined in detail. It is found that the heating mechanisms proposed by Ibragimov and Kocharov cannot account for the enhanced abundances of heavy elements in the solar cosmic rays.

Weatherall, J.↗

NASA NTRS1984

Turbulent heating in solar cosmic-ray theory

The heating of minor ions in solar flares by wave-wave-particle interaction with Langmuir waves, or ion acoustic waves, can be described by a diffusion equation in velocity-space for the particle distribution function. The dependence of the heating on the ion charge and mass, and on the composition of the plasma, is examined in detail. It is found that the heat mechanisms proposed by Ibragimov and Kocharov cannot account for the enhanced abundances of heavy elements in the solar cosmic rays.

Weatherall, J.↗

NASA NTRS1985

On the structure of the turbulent vortex

The trailing vortex generated by a lifting surface, the structure of its turbulent core and the influence of axial flow within the vortex on its initial persistence and on its subsequent decay are described. Similarity solutions of the turbulent diffusion equation are given in closed form and results are expressed in sufficiently simple terms that the influence of the lifting surface parameters on the length of persistence and the rate of decay of the vortex can be evaluated.

Roberts, L.↗

NASA NTRS1985

Propagation and secondary production of low energy antiprotons in the atmosphere

Current theories, in which the observed antiproton component is attributed strictly to secondary production in high energy inelastic collisions of protons with the interstellar medium or the atmosphere, apparently fail to explain the relatively high p vertical intensities measured at mountain and balloon altitudes. Therefore, a more careful calculation of the theoretical secondary intensity spectra is required before more exotic sources for these excess p's can be explored. A one dimensional diffusion equation is used to calculate the expected vertical intensity of p's due only to secondary production in the atmosphere; any assumed primary p spectrum is also included. Two adjustable parameters, the inelasticity and charge exchange in nucleon-nucleus collisions, were included in the algorithm. In order to obtain an independent estimate of their values the proton vertical intensities in the atmosphere were calculated, adjusting the parameters until the curves fit the experimental proton data, and then assumed that these values were identical in antinucleon-nucleus collisions.

Bowen, T.↗

NASA NTRS1985

Spatial distribution of cosmic rays in magnetic cycles of the Sun

The space-time distribution of cosmic ray (CR) density is determined from the solution of the anisotropic diffusion equation. The boundary problem is solved in a quasistationary axisymmetric case, taking into account the delay of cosmic rays relative to the cyclic variations of solar activity. The specificty of the modulation model is the use of the empirical dependence of the free path of particles for scattering on the observed latitudinal distribution of solar activity. Another specific feature of the model is an account of an additional effect due to the drift of charged particles towards the helio-equator plane or backward, depending on the direction of the total magnetic field of the Sun.

Alania, M. V.↗

NASA NTRS1985

Diffusion of strongly magnetized cosmic ray particles in a turbulent medium

Cosmic ray (CR) propagation in a turbulent medium is usually considered in the diffusion approximation. Here, the diffusion equation is obtained for strongly magnetized particles in the general form. The influence of a large-scale random magnetic field on CR propagation in interstellar medium is discussed. Cosmic rays are assumed to propagate in a medium with a regular field H and an ensemble of random MHD waves. The energy density of waves on scales smaller than the free path 1 of CR particles is small. The collision integral of the general form which describes interaction between relativistic particles and waves in the quasilinear approximation is used.

Ptuskin, V. S.↗