Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “dispersion relation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Wave evolution in the marginal ice zone - Model predictions and comparisons with on-site and remote data

The ocean-wave dispersion relation and viscous attenuation by a sea ice cover were studied for waves in the marginal ice zone (MIZ). The Labrador ice margin experiment (Limex), conducted off the east coast of Newfoundland, Canada in March 1987, provided aircraft SAR, wave buoy, and ice property data. Based on the wave number spectrum from SAR data, the concurrent wave frequency spectrum from ocean buoy data, and accelerometer data on the ice during Limex '87, the dispersion relation has been derived and compared with the model. Accelerometers were deployed at the ice edge and into the ice pack. Data from the accelerometers were used to estimate wave energy attenuation rates and compared with the model. The model-data comparisons are reasonably good for the ice conditions observed during Limex' 87.

Liu, A. K.↗

Current driven instabilities of an electromagnetically accelerated plasma

A plasma instability that strongly influences the efficiency and lifetime of electromagnetic plasma accelerators was quantitatively measured. Experimental measurements of dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries are reported. The measured critical wave parameters are in excellent agreement with theoretical instability boundary predictions. The instability is current driven and affects a wide spectrum of longitudinal (electrostatic) oscillations. Current driven instabilities, which are intrinsic to the high-current-carrying magnetized plasma of the magnetoplasmadynmic (MPD) accelerator, were investigated with a kinetic theoretical model based on first principles. Analytical limits of the appropriate dispersion relation yield unstable ion acoustic waves for T(i)/T(e) much less than 1 and electron acoustic waves for T(i)/T(e) much greater than 1. The resulting set of nonlinear equations for the case of T(i)/T(e) = 1, of most interest to the MPD thruster Plasma Wave Experiment, was numerically solved to yield a multiparameter set of stability boundaries. Under certain conditions, marginally stable waves traveling almost perpendicular to the magnetic field would travel at a velocity equal to that of the electron current. Such waves were termed current waves. Unstable current waves near the upper stability boundary were observed experimentally and are in accordance with theoretical predictions. This provides unambiguous proof of the existence of such instabilites in electromagnetic plasma accelerators.

Chouetri, E. Y.↗

Comparison of Non-Parabolic Hydrodynamic Simulations for Semiconductor Devices

Parabolic drift-diffusion simulators are common engineering level design tools for semiconductor devices. Hydrodynamic simulators, based on the parabolic band approximation, are becoming more prevalent as device dimensions shrink and energy transport effects begin to dominate device characteristic. However, band structure effects present in state-of-the-art devices necessitate relaxing the parabolic band approximation. This paper presents simulations of ballistic diodes, a benchmark device, of Si and GaAs using two different non-parabolic hydrodynamic formulations. The first formulation uses the Kane dispersion relationship in the derivation of the conservation equations. The second model uses a power law dispersion relation {(hk)(exp 2)/2m = xW(exp Y)}. Current-voltage relations show that for the ballistic diodes considered. the non-parabolic formulations predict less current than the parabolic case. Explanations of this will be provided by examination of velocity and energy profiles. At low bias, the simulations based on the Kane formulation predict greater current flow than the power law formulation. As the bias is increased this trend changes and the power law predicts greater current than the Kane formulation. It will be shown that the non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation are limited due to the binomial approximation which was utilized in the derivation.

Smith, A. W.↗

Azimuthal spoke propagation in Hall Effect Thrusters

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall Effect Thrusters (HETs) that travel in the E × B direction and have been observed in many different systems. The propagation of azimuthal spokes are investigated in a 6 kW HET known as the H6 using ultra-fast imaging and azimuthally spaced probes. A spoke surface is a 2-D plot of azimuthal light intensity evolution over time calculated from 87,500 frames/s videos. The spoke velocity has been determined using three methods with similar results: manual fitting of diagonal lines on the spoke surface, linear cross-correlation between azimuthal locations and an approximated dispersion relation. The spoke velocity for three discharge voltages (300, 400 and 450 V) and three anode mass flow rates (14.7, 19.5 and 25.2 mg/s) yielded spoke velocities between 1500 and 2200 m/s across a range of normalized magnetic field settings. The spoke velocity was inversely dependent on magnetic field strength for low B-field settings and asymptoted at B-field higher values. The velocities and frequencies are compared to standard drifts and plasma waves such as E × B drift, electrostatic ion cyclotron, magnetosonic and various drift waves. The empirically approximated dispersion relation yielded a characteristic velocity that matched the ion acoustic speed for 5 eV electrons that exist in the near-anode and near-field plume regions of the discharge channel based on internal measurements. Thruster performance has been linked to operating mode where thrust-to-power is maximized when azimuthal spokes are present so investigating the underlying mechanism of spokes will benefit thruster operation.

Polk, James E.↗

Azimuthal Spoke Propagation in Hall Effect Thrusters

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall Effect Thrusters (HETs) that travel in the E x B direction and have been observed in many different systems. The propagation of azimuthal spokes are investigated in a 6 kW HET known as the H6 using ultra-fast imaging and azimuthally spaced probes. A spoke surface is a 2-D plot of azimuthal light intensity evolution over time calculated from 87,500 frames/s videos. The spoke velocity has been determined using three methods with similar results: manual fitting of diagonal lines on the spoke surface, linear cross-correlation between azimuthal locations and an approximated dispersion relation. The spoke velocity for three discharge voltages (300, 400 and 450 V) and three anode mass flow rates (14.7, 19.5 and 25.2 mg/s) yielded spoke velocities between 1500 and 2200 m/s across a range of normalized magnetic field settings. The spoke velocity was inversely dependent on magnetic field strength for low B-field settings and asymptoted at B-field higher values. The velocities and frequencies are compared to standard drifts and plasma waves such as E x B drift, electrostatic ion cyclotron, magnetosonic and various drift waves. The empirically approximated dispersion relation yielded a characteristic velocity that matched the ion acoustic speed for 5 eV electrons that exist in the near-anode and near-field plume regions of the discharge channel based on internal measurements. Thruster performance has been linked to operating mode where thrust-to-power is maximized when azimuthal spokes are present so investigating the underlying mechanism of spokes will benefit thruster operation.

Cylindrical Hall Thruster (CHT)↗

Effects of finite plasma beta on the lower-hybrid-drift instability

The local dispersion relation for the lower-hybrid-drift (LHD) instability is derived and analyzed, taking into account the finite-beta effects associated with transverse electromagnetic perturbations as well as with resonant and nonresonant electron-orbit modifications due to magnetic-field gradients. The influence of finite-beta effects on the LHD instability is calculated in a fully self-consistent manner for arbitrary values of electron-ion temperature ratio, local beta, cross-field ExB velocity/ion thermal speed ratio, and other plasma parameters. Stability properties are investigated analytically for the case of cold electrons, and the local dispersion relation is solved numerically in the parameter regime of most interest for high-density plasma pinches. The results show that for all parameter regimes studied, the net effect of finite plasma beta is to reduce the maximum growth rate of the LHD instability, although the details can vary, depending on the plasma parameters. Except in the limit where the electron/ion temperature ratio tends to zero, it is found that there is a critical value of plasma beta above which the LHD instability is completely stabilized.

Davidson, R. C.↗

Waves in frazil and pancake ice and their detection in Seasat synthetic aperture radar imagery

Measurements of wavelength and direction derived from SAR imagery obtained from Seasat in October 1987 are compared with a theoretical model of waves propagating into an ice cover composed of frazil and pancake ice. The dispersion relation for phase and group velocities is derived, and the existence of an upper frequency limit for propagation into the ice is found. The wave radiation pressure exerted on the ice is derived from the reflection coefficient at the ice edge; it is found to cause a slick of frazil ice backed by thicker floes to become more dense or thick with increasing penetration. When the frazil ice becomes transformed into pancake ice, the raised edges of the pancakes cause the ice to appear bright despite the fact that there are no waves present at the Bragg wavelength. Directional wave number spectra are derived outside and inside the ice cover. The change of wavelength and angle of refraction of the dominant wave entering the ice field are both found to be characteristic of the dispersion relation derived theoretically.

Wadhams, Peter↗

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗

Application of ERTS-1 imagery to the study of caribou movements and winter dispersal in relation to prevailing snowcover

The author has identified the following significant results. Habitat differentiation was determined feasible using output from MSS band 6 because of apparent high correlations between surface moisture and habitat type on the test area. Progressive early snow distribution was readily determined from MSS outputs, particularly bands 4 and 5. Approximately thirty thousand caribou migrated into the test area during the reporting period, and aerial reconnaissance data on distribution were obtained for selected areas within several days of satellite overflight.

Lent, P. C.↗

Application of ERTS-1 imagery to the study of caribou movements and winter dispersal in relation to prevailing snowcover

The author has identified the following significant results. Step-wise discriminate analysis has demonstrated the feasibility of feature identification using linear discriminate functions of ERTS-1 MSS band densities and their ratios. The analysis indicated that features such as small streams can be detected even when they are in dark mountain shadow. The potential utility of this and similar analytic techniques appears considerable, and the limits it can be applied to analysis of ERTS-1 imagery are not yet fully known.

Lent, P. C.↗

Application of ERTS-1 imagery to the study of caribou movements and winter dispersal in relation to prevailing snowcover

The author has identified the following significant results. A multiband classification scheme was applied to ERTS-1 MSS digital tape data in a portion of the Yukon Flats area. Primary analytic objectives of mapping the extent of recent wildfire burns and mature forest were realized illustrating application to moose and caribou biology. Additionally, the analysis indicated the presence of new lakes as well as disappearance of lakes present in 1956. Because this is an important waterfowl production area, similar analyses may have significant application potential to waterfowl biology for rapid updating of habitat information. Further field confirmation of this finding is required.

Lent, P. C.↗

User's Guide for Monthly Vector Wind Profile Model

The background, theoretical concepts, and methodology for construction of vector wind profiles based on a statistical model are presented. The derived monthly vector wind profiles are to be applied by the launch vehicle design community for establishing realistic estimates of critical vehicle design parameter dispersions related to wind profile dispersions. During initial studies a number of months are used to establish the model profiles that produce the largest monthly dispersions of ascent vehicle aerodynamic load indicators. The largest monthly dispersions for wind, which occur during the winter high-wind months, are used for establishing the design reference dispersions for the aerodynamic load indicators. This document includes a description of the computational process for the vector wind model including specification of input data, parameter settings, and output data formats. Sample output data listings are provided to aid the user in the verification of test output.

Adelfang, S. I.↗