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Results for “power-law distribution”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Comparison of flare bremsstrahlung resulting from energetic thermal and nonthermal electrons

The paper investigates the behavior of the X-ray bremsstrahlung spectra resulting from two distinct types of electron distribution functions impinging on a target atmosphere during flare activity. A power-law distribution function is compared with two double-peaked Maxwellians. The results of these calculations show that it would be difficult to rule out multithermal interpretations for the emitted high-energy X-rays.

Davis, J.↗
NASA NTRS1976

Lossy radial diffusion of relativistic Jovian electrons

The radial diffusion equation with synchrotron losses is solved by the Laplace-transform method for near equatorially mirroring relativistic electrons. The evolution of a power-law distribution function is found, and the characteristics of synchrotron burnoff are stated in terms of explicit parameters for an arbitrary diffusion coefficient of a specific form. The peaking of the 10.4-cm volume emissivity from Jupiter at an L shell of about 1.8 provides an estimate of the diffusion coefficient in the radiation belts; one value is suggested as the appropriate modification, for an equatorial field strength of 4.2 G, of the Birmingham et al. (1974) result. Nonsynchrotron losses are included phenomenologically; from the phase-space densities reported by McIlwain and Fillius (1975), the particle lifetime is estimated. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

Barbosa, D. D.↗
NASA NTRS1977

Flare heating by energetic nonthermal electrons

A model has been developed which includes, in a self-consistent fashion, the energy degradation and attendant bremsstrahlung emission of a high-energy electron beam, heating of a flare plasma by the beam, and subsequent cooling by thermal conduction and radiation. To assist in the interpretation of experimental diagnostics, the model also characterizes the radiative behavior of iron ions present in the flare plasma. Electron deposition is described by the Fokker-Planck equation for an initial power-law particle distribution. Results are presented for the bremsstrahlung radiation emitted by the incident beam as it impinges on the disturbed atmosphere. A comparison is made between direct beam heating and thermal-conduction heating of the flare plasma. The radiation emitted by several selected spectral lines of Fe ions is determined as a function of time during and after deposition

Davis, J.↗
NASA NTRS1976

The protostellar origin of interstellar grains

A semiquantitative description of the origin of interstellar grains in a protostellar environment is given. Grains grow in the protostellar collapse phase and can be expelled by radiation pressure from stars of at least about 5 solar masses. A convective shell of grains forms in which shattering produces a power-law spectrum of fragments. A bimodal distribution of grain sizes, peaking at approximately 0.1 and 0.01 micron results. The effects of protostellar winds and rotation are considered.

Silk, J.↗
NASA NTRS1978

Observations of low-luminosity X-ray sources in Vela-Puppis

Results are presented for a study of the X-ray emission from a small portion of the galactic plane near galactic longitude 260 deg. This region contains at least six low-luminosity X-ray sources within about 10 deg of PSR 0833-45, which is near the center of the Gum nebula. The X-ray source 4U 0833-45, associated with the Vela pulsar, is observed at twice its 4U catalog intensity. The lack of X-ray pulsations at the pulsar period (greater than 99% nonpulsed), the nonthermal power-law spectrum, and models of the X-ray source distribution in this region suggest that a large fraction of the X-rays come from an extended source about 1 deg of arc in radius. The observation of a high-temperature (effective temperature at least 100 million K) spectrum in a field of view containing only Puppis A among known sources has led to the discovery of new OSO 8 source, OS 0752-39. Other spectra from this region are discussed.

Pravdo, S. H.↗
NASA NTRS1959

A Simple Method for Determining Heat Transfer, Skin Friction, and Boundary-Layer Thickness for Hypersonic Laminar Boundary-Layer Flows in a Pressure Gradient

A procedure based on the method of similar solutions is presented by which the skin friction, heat transfer, and boundary-layer thickness in a laminar hypersonic flow with pressure gradient may be rapidly evaluated if the pressure distribution is known. This solution, which at present is. restricted to power-law variations of pressure with surface distance, is presented for a wide range of exponents in the power law corresponding to both favorable and adverse pressure gradients. This theory has been compared to results from heat-transfer experiments on blunt-nose flat plates and a hemisphere cylinder at free-stream Mach numbers of 4 and 6.8. The flat-plate experiments included tests made at a Mach number of 6.8 over a range of angle of attack of +/- 10 deg. Reasonable agreement of the experimental and theoretical heat-transfer coefficients has been obtained as well as good correlation of the experimental results over the entire range of angle of attack studied. A similar comparison of theory with experiment was not feasible for boundary-layer-thickness data; however, the hypersonic similarity theory was found to account satisfactorily for the variation in boundary-layer thickness due to local pressure distribution for several sets of measurements.

Bertram, Mitchel H.↗
NASA NTRS1974

Longitudinal aerodynamic performance of a series of power-law and minimum wave drag bodies at Mach 6 and several Reynolds numbers

Experimental data have been obtained for two series of bodies at Mach 6 and Reynolds numbers, based on model length, from 1.4 million to 9.5 million. One series consisted of axisymmetric power-law bodies geometrically constrained for constant length and base diameter with values of the exponent n of 0.25, 0.5, 0.6, 0.667, 0.75, and 1.0. The other series consisted of positively and negatively cambered bodies of polygonal cross section, each having a constant longitudinal area distribution conforming to that required for minimizing zero-lift wave drag at hypersonic speeds under the geometric constraints of given length and volume. At the highest Reynolds number, the power-law body for minimum drag is blunter (exponent n lower) than predicted by inviscid theory (n approximately 0.6 instead of n = 0.667); however, the peak value of lift-drag ratio occurs at n = 0.667. Viscous effects were present on the bodies of polygonal cross section but were less pronounced than those on the power-law bodies. The trapezoidal bodies with maximum width at the bottom were found to have the highest maximum lift-drag ratio and the lowest mimimum drag.

Ashby, G. C., Jr.↗
NASA NTRS1974

Boundary-layer transition and displacement thickness effects on zero-lift drag of a series of power-law bodies at Mach 6

Wave and skin-friction drag have been numerically calculated for a series of power-law bodies at a Mach number of 6 and Reynolds numbers, based on body length, from 1.5 million to 9.5 million. Pressure distributions were computed on the nose by the inverse method and on the body by the method of characteristics. These pressure distributions and the measured locations of boundary-layer transition were used in a nonsimilar-boundary-layer program to determine viscous effects. A coupled iterative approach between the boundary-layer and pressure-distribution programs was used to account for boundary-layer displacement-thickness effects. The calculated-drag coefficients compared well with previously obtained experimental data.

Ashby, G. C., Jr.↗
NASA NTRS1950

Approximate Turbulent Boundary-Layer Development in Plane Compressible Flow Along Thermally Insulated Surfaces with Application to Supersonic-Tunnel Contour Correction

Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.

BOUNDARY LAYER - WIND TUNNEL WALLS↗
NASA NTRS1973

A study of cosmic-ray positron and electron spectra in interplanetary and interstellar space and the solar modulation of cosmic rays

The differential energy spectra of cosmic-ray positrons and negatrons with energies between approximately 11 and 1500 MeV was measured during the period 1968-1971 using a balloon-borne magnetic spectrometer. These measurements fill a gap in the previously existing data and permit the determination of the interstellar spectra of cosmic-ray positrons and electrons. Knowledge of these spectra provides a crucial tool for studies of the distribution and density of matter and magnetic fields in the interstellar medium and the origin and dynamics of energetic particles contained in the fields. The differential energy spectrum of interstellar electrons may be represented as a power-law, j alpha T to the -1.8 power for 100 MeV approximately T approximately 2 GeV, but must flatten considerably at lower energies. From the measured electron charge composition, it is concluded that the majority of cosmic-ray electrons with energies above approximately 10 MeV originate in primary sources.

Cummings, A. C.↗
NASA NTRS1977

Energies of formation for ejecta blankets of giant impacts

Ejection energy-diameter scaling relations for impact craters are studied by assuming the energy is equal to a constant times the diameter raised to a (different) constant power. These scaling relations are derived from least-squares fits to calculated ejection energies over a range of crater diameters and vary according to ejection angle, ejecta blanket distribution, planetary radius, and the depth-diameter ratio. Extremely broad changes in ejection angle and ejecta blanket distribution result in relatively small changes in the total energy. The way in which the exponent in the scaling relation is dependent on the planetary radius of curvature as well as on the exponent of the power-law depth-diameter scaling relation is described. Two ejection energy-diameter scaling relations, one for simple craters with depth-diameter ratios of approximately 0.2 and the other for large complex craters, are presented. The scaling relations explicitly include target density, surface gravity, and planetary radius.

Croft, S. K.↗
NASA NTRS1972

Three dimensional potential and current distributions in a Hall generator with assumed velocity profiles

Three-dimensional potential and current distributions in a Faraday segmented MHD generator operating in the Hall mode are computed. Constant conductivity and a Hall parameter of 1.0 is assumed. The electric fields and currents are assumed to be coperiodic with the electrode structure. The flow is assumed to be fully developed and a family of power-law velocity profiles, ranging from parabolic to turbulent, is used to show the effect of the fullness of the velocity profile. Calculation of the square of the current density shows that nonequilibrium heating is not likely to occur along the boundaries. This seems to discount the idea that the generator insulating walls are regions of high conductivity and are therefore responsible for boundary-layer shorting, unless the shorting is a surface phenomenon on the insulating material.

Stankiewicz, N.↗
NASA NTRS1977

No new limit on size distribution of gamma-ray bursts

It is argued that the results of Carter et al. (1976), who derived an upper limit to the balloon intensity of small gamma-ray bursts at about 100 below the extrapolated known size spectrum and therefore concluded that the gamma-ray bursts are of galactic origin, are entirely consistent with the -1.5 index power-law extrapolation, so that no conclusion regarding the origin of gamma-ray bursts can be drawn. A reply of Carter et al. is published. Points at issue include: (1) whether a selection criterion of three successive 0.6-sec increases in the gamma-ray count rate ignores a significant or only a small number of events, (2) whether the spectra of all bursts extend below 100 keV, the satellite energy threshold, and (3) the required correction for the distortion of a horizontal, flat detector.

Cline, T. L.↗
NASA NTRS1972

Characteristics of the lunar photoelectron layer in the geomagnetic tail.

The charged particle lunar environment experiment, a part of the Apollo 14 lunar surface package, is an ion-electron spectrometer capable of measuring ions and electrons with energies between 40 eV and 50 keV. The instrument, with apertures 26 cm above the surface, has detected a photoelectron gas layer above the sunlit lunar surface. No detectable flux above 200 eV has been observed. Experimental data for periods while the moon was in the earth's magnetotail for electrons with energies 40 eV less than or equal to 200 eV follow a power-law spectrum. In the absence of photoelectrons with E greater than 200, we assume that the surface potential is at least 200 V. The modulation of this potential in the presence of intense plasma-sheet fluxes has been observed. Also, a detailed history of the Feb. 10, 1971, total lunar eclipse, to determine the source distribution of high-energy solar photons, is presented.

Reasoner, D. L.↗
NASA NTRS1975

Second-order small-disturbance solutions for hypersonic flow over power-law bodies

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.

Townsend, J. C.↗
NASA NTRS1975

Production of hard X rays in a plasma focus

A model of a plasma focus is examined wherein large axial electric fields are produced by an imploding current sheet during the final nanoseconds of the collapse phase and where the fields provide a mechanism for creating a beam of electrons of highly suprathermal energies. The expected bremsstrahlung radiation above 100 keV is calculated for such a beam, which has a power-law spectrum, both from electron-deuteron collisions in the focused plasma and when the beam reaches the wall of the device. It is concluded that, since the experimental results indicate little or no radiation above 100 keV originating in the walls, that the electrons in the beam must be decelerated after leaving the plasma and before reaching the wall. Comparisons with the results and the total energy of the device yield qualitative agreement with the expected angular distribution of hard X-rays and reasonable agreement with the total energy in accelerated electrons required to produce the observed total energy in hard X-rays by this mechanism.

Newman, C. E.↗
NASA NTRS1978

Photoelectric spectrophotometry of radio galaxies

The absolute energy distributions from 3200 to 10,000 A of 26 3CR radio galaxies are determined on the basis of spectrophotometric observations with the multichannel spectrometer of the Hale 5-m telescope. It is found that there is a continuous range of emission-line characteristics and UV excess in the sample and that a strong correlation exists between the nonthermal component luminosity and hydrogen emission, which favors the hypothesis that direct photoionization by the nuclear radiation is responsible for the emission lines observed. Calculations are performed which show that in almost all cases the power-law component model provides sufficient UV photons to produce the observed H-beta line. Indications are obtained that the optical nuclear component is related to the radio emission in some complex manner and that strong radio galaxies tend to be accompanied by UV excess and emission lines.

Yee, H. K. C.↗