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NASA NTRS1974

Quaternion wave equations in curved space-time

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

Edmonds, J. D., Jr.↗

NASA NTRS1989

An imaging vector magnetograph for the next solar maximum

Researchers describe the conceptual design of a new imaging vector magnetograph currently being constructed at the University of Hawaii. The instrument combines a modest solar telescope with a rotating quarter-wave plate, an acousto-optical tunable prefilter as a blocker for a servo-controlled Fabry-Perot etalon, CCD cameras, and on-line digital image processing. Its high spatial resolution (1/2 arcsec pixel size) over a large field of view (5 by 5 arcmin) will be sufficient to significantly measure, for the first time, the magnetic energy dissipated in major solar flares. Its millisecond tunability and wide spectral range (5000 to 7000 A) enable nearly simultaneous vector magnetic field measurements in the gas-pressure-dominated photosphere and magnetically-dominated chromosphere, as well as effective co-alignment with Solar-A's X ray images. Researchers expect to have the instrument in operation at Mees Solar Observatory (Haleakala) in early 1991. They have chosen to use tunable filters as wavelength-selection elements in order to emphasize the spatial relationships between magnetic field elements, and to permit construction of a compact, efficient instrument. This means that spectral information must be obtained from sequences of images, which can cause line profile distortions due to effects of atmospheric seeing.

Mickey, D. L.↗

NASA NTRS1971

Signal broadening in the laser Doppler velocimeter.

Critical review of a recent paper in which Denison, Stevenson, and Fox (1971) discussed the sources of spectral broadening in the laser Doppler velocimeter. It is pointed out that, in their discussion, the above-mentioned authors indicated that the spread in wave vectors of the incident and detected fields and the finite length of time a scattering center stayed in the sample volume each contributed separately and independently to the observed spectral width of the scattered radiation. This statement is termed incorrect, and it is shown that the two effects are one and the same.

Angus, J. C.↗

NASA NTRS1979

Flux vector splitting of the inviscid equations with application to finite difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Steger, J. L.↗

NASA NTRS1979

Generalized lower-hybrid-drift instability

The theory of lower-hybrid-drift instability is extended to include a finite value of the component of wave vector parallel to the ambient magnetic field so that the analysis bridges the usual lower-hybrid-drift instability of flute modes and the modified-two-stream instability. The present theory also includes electromagnetic and ambient magnetic field-gradient effects. It is found that in the cold-electron limit the density and magnetic gradients can qualitatively modify the conclusion obtained in the early theory of the modified-two-stream instability. For example, even if the relative drift far exceeds the Alfven speed of the plasma, the instability may still persist. This result is in contrast to that established in the literature. When the electron temperature is finite, the problem is complicated. Numerical solutions are obtained for a number of cases.

Hsia, J. B.↗

NASA NTRS1981

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

Steger, J. L.↗

NASA NTRS1981

Interplanetary Alfvenic fluctuations - A stochastic model

The concept of minimum variance is investigated for nonplanar interplanetary Alfvenic fluctuations in which the field direction varies randomly. The theory of the random wandering of a vector of constant length is developed as a representation of the magnetic field, and it is found that the minimum variance tends to coincide with the mean field directions over the correlation time of the fluctuations. The Fokker-Planck limit of the theory is then developed and used to analyze the statistic distribution of field directions with and without a reflecting barrier. Results suggest that the tendency of the Alfvenic fluctuations to have a direction of minimum variance statistically aligned with the mean magnetic field may be purely a consequence of the randomness of the fluctuation and not imply that the fluctuations are necessarily plane waves. Extensive statistical studies of the observed directional variations of the interplanetary magnetic field are necessary to test this hypothesis.

Barnes, A.↗

NASA NTRS1982

Testing of turbulent seals for rotordynamic coefficients

A facility has been developed for dynamic testing of straight and convergent tapered seals with the capability of measuring the radial and tangential force components which result from a circular centered orbit. The test apparatus causes the seal journal to execute small-eccentricity centered circular orbits within its clearance circle. Dynamic measurements are made and recorded of the seal displacement-vector components, and of the pressure field. The pressure field is integrated to yield seal tangential and radial reaction-force components. Representative test data are provided and discussed for straight seals.

Childs, D. W.↗

NASA NTRS1983

First VHF auroral radar interferometer observations

Auroral plasma instabilities were investigated using the radar interferometer technique based on observations obtained with a 49.92 MHz, 20-25 KW peak power pulsed radar located in Ithaca, NY (42.5 degrees N, 76.4 degrees W). Strong auroral echoes obtained during several highly active periods were analyzed. Phase differences between the signals received on the two antennas were utilized to accurately determine the E-W position, within the scattering volume, of localized scattering centers, and changes in this phase were used to determine the corresponding velocity. The radial (essentially N-S) motion was described by the signal Doppler shift. It is found that these data provide detailed information on the turbulent structure of the echoing region and show clearly that different features in the Doppler power spectrum often represent signals coming from different locations. It is concluded that these data can be utilized to determine full horizontal velocity vectors and hence the horizontal electric field, usually with a time resolution of the order of 15-30 s.

Providakes, J. F.↗

NASA NTRS1984

High time resolution studies of upstream ions

The influence of phi, the angle between the interplanetary magnetic field and the earth-sun vector on ions and electrons in the earth's bow shock, was investigated in terms of ISEE 2 data. A small phi was associated with intermediate energy upstream ions and reduced populations of low energy, about 1.6 keV, ion fluxes. The magnitude of phi was closely related to particular, constant energy levels, e.g., a phi of 40 deg and an energy of 30 keV and a phi of 75 deg and an energy of 6 keV. Ion fluxes are high in the angles form 60-80 deg and feature energies of 55-280 keV. The acceleration process up to the high energy levels in the 1-3 min interval from upstream to downstream occurs more rapidly than could be accounted for by a first-order Fermi process.

Anderson, K. A.↗

NASA NTRS1984

NLR activities in the field of wind tunnel wall interference

Measured field data as a boundary condition for calculating the interference flow field were applied. They are divided into two categories. In the first category, the field data must consist of distributions of a single velocity component, and an accurate estimate of the hypothetical free air contribution of the model to this component is required. The differences between measured values and estimated model contributions are attributed to wall interference and they establish the boundary condition. The associated field data measurements are simple, yet the necessary model representation generally is a serious drawback. The second category requires field data which consist of velocity vector distributions at the price of multicomponent measurements, but at the profit that no information at all is required about the model. In solid wall test sections, the price is reduced to virtually zero but the profit remains.

Smith, J.↗

NASA NTRS1985

The zero-frequency ion ring instability

The electrostatic zero-frequency ion ring instability with wave vector perpendicular to a uniform magnetic field B is examined through linear and second-order theory as well as by computer simulation. In the simulation ions are taken as magnetized particles; the electrons are described as a massless fluid subject to E x B motion. Saturation of the instability is primarily due to broadening of the ion ring distribution. A second-order theory provides an approximate criterion for the saturation amplitude, as does a simple trapping argument. Thus, for the simulation presented here, both quasi-linear and trapping effects contribute to saturation.

Gary, S. P.↗

NASA NTRS1985

Plasma irregularities associated with a morning discrete auroral arc - Radar interferometer observations and theory

A description is given of E region auroral plasma irregularities associated with an intense auroral morning arc observed over Fort Churchill by radar. The observations are compared with data from an all-sky camera (ASC) operated at Fort Churchill by the National Research Council of Canada. The particular event described was chosen because of the rapid variation in structure and motion of the arc as it traveled through the radar beam. The horizontal vector electron drift velocity and electric field along the poleward boundary of the morning discrete auroral arc was successfully measured with a radar interferometer. This instrument provided information concerning the temporal and spatial structure of the electrostatic plasma turbulence in the arc. The observations are described.

Providakes, J.↗

NASA NTRS1987

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗

NASA NTRS1987

A three-dimensional dual potential procedure for inlets and indraft wind tunnels

Rao, K. V.↗

NASA NTRS1987

Vibration analysis of quasi-symmetric structures

A computational technique is developed to reduce the size of the dynamical model of a large complex quasi-symmetric structure prior to free vibration analysis. The structure is discretized using a two-field mixed FEM model; the response vectors are decomposed into symmetric and antisymmetric components; the eigenvectors of the quasi-symmetric structure are approximated by a linear combination of a few preselected sets of symmetric and antisymmetric modes generated by the reduced-size model; global approximation vectors are selected and generated; and the resulting eigenvalue problem is significantly reduced via a classical Bubnov-Galerkin procedure. Numerical results for a shallow laminated anisotropic panel of quadrilateral planform are presented in extensive tables and graphs, demonstrating the effectiveness of the method.

Noor, Ahmed K.↗

NASA NTRS1988

Global and local Joule heating effects seen by DE 2

In the altitude region between 350 and 550 km, variations in the ion temperature principally reflect similar variations in the local frictional heating produced by a velocity difference between the ions and the neutrals. Here, the distribution of the ion temperature in this altitude region is shown, and its attributes in relation to previous work on local Joule heating rates are discussed. In addition to the ion temperature, instrumentation on the DE 2 satellite also provides a measure of the ion velocity vector representative of the total electric field. From this information, the local Joule heating rate is derived. From an estimate of the height-integrated Pedersen conductivity it is also possible to estimate the global (height-integrated) Joule heating rate. Here, the differences and relationships between these various parameters are described.

Heelis, R. A.↗

NASA NTRS1989

Plasma wave, magnetic field and energetic ion observations in the ion pick-up region of Comet Giacobini-Zinner

Simultaneous plasma wave, magnetic field, and energetic ion observations made by the ICE spacecraft in the extended ion pick-up region surrounding comet Giacobini-Zinner are examined to determine the conditions under which two characteristic wave emissions, electrostatic waves at a few kHz, and electromagnetic waves at a few tens of Hz, are generated. The data are consistent with the view that the kHz electrostatic emissions result from an instability of the pick-up photoelectron 'beam' produced when the angle alpha between the magnetic field and the solar wind velocity vector is less than about 60 deg, while the behavior of the tens of Hz electromagnetic waves suggests that they are generated by the pick-up ion 'ring' which is present when alpha exceeds about 60 deg.

Richardson, I. G.↗