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NASA NTRS1991

The modified plasma dispersion function

The modified plasma dispersion function (MPDF), based on the generalized Lorentzian (kappa) particle distribution function, is introduced, and a comprehensive set of graphs of the real and imaginary parts of the MPDF is presented. For any positive integral value of kappa, MPDF is calculated in closed form as a finite series. It is demonstrated how the MPDF approaches the plasma dispersion function in the limit as kappa yields infinity, a result to be expected since the kappa distribution function formally approaches the Maxwellian as kappa yields infinity. It is concluded that the MPDF can provide a tool in studying microinstabilities in plasmas when the particle distribution function is not only the standard generalized Lorentzian, but also of the Lorentzian type, including the loss-cone, bi-Lorentzian, and product bi-Lorentzian distributions.

Summers, Danny↗

NASA NTRS1998

Studies of the Intrinsic Complexities of Magnetotail Ion Distributions: Theory and Observations

This year we have studied the relationship between the structure seen in measured distribution functions and the detailed magnetospheric configuration. Results from our recent studies using time-dependent large-scale kinetic (LSK) calculations are used to infer the sources of the ions in the velocity distribution functions measured by a single spacecraft (Geotail). Our results strongly indicate that the different ion sources and acceleration mechanisms producing a measured distribution function can explain this structure. Moreover, individual structures within distribution functions were traced back to single sources. We also confirmed the fractal nature of ion distributions.

Ashour-Abdalla, Maha↗

NASA NTRS1973

Observations of collisionless drift waves.

Velocity distribution functions of both the electron and the proton component of the magnetospheric plasma are measured in 62 logarithmically spaced steps from 50 eV to 50 keV by an instrument carried upon the ATS-5 spacecraft in circular synchronous orbit (6.6 earth radii). Oscillations which appear to be collisionless drift waves having periods of several minutes or longer are found in this data. Linearized wave theory can be used to predict the theoretical perturbation distribution function in terms of the perturbing fields and the equilibrium distribution function. The functional dependence of the theoretical perturbation distribution function upon particle energy can then be compared with that of the measured perturbation.

Laquey, R. E.↗

NASA NTRS1975

Solar models of low neutrino-counting rate - The depleted Maxwellian tail

Evolutionary sequences for the sun are presented which confirm that the Cl-37 neutrino counting rate will be greatly reduced if the high-energy tail of the Maxwellian distribution of relative energies is progressively depleted. Thermonuclear reaction rates and pressure are reevaluated for a distribution function modified by the correction factor suggested by Clayton (1974), and the effect of the results on solar models calculated with a simple Henyey code is discussed. It is shown that if the depletion is characterized by a certain exponential dependence on the distribution function, the counting rate will fall below 1 SNU for a distribution function of not less than 0.01. Suggestions are made for measuring the distribution function in the sun by means of neutrino spectroscopy and photography.

Clayton, D. D.↗

NASA NTRS1999

Studies of the Intrinsic Complexities of Magnetotail Ion Distributions: Theory and Observations

We have studied the relationship between the structure seen in measured distribution functions and the detailed magnetospheric configuration. Results from our recent studies using time-dependent large-scale kinetic (LSK) calculations are used to infer the sources of the ions in the velocity distribution functions measured by a single spacecraft (Geotail). Our results strongly indicate that the different ion sources and acceleration mechanisms producing a measured distribution function can explain this structure. Moreover, individual structures within distribution functions were traced back to single sources. We also examined the intrinsic variability of the magnetotail during quiet and steady solar wind conditions and found that the magnetotail possess an intrinsic variability caused by the non-adiabatic acceleration and loss of current-carrying ions from the magnetotail current sheet.

Ashour-Abdalla, M.↗

NASA NTRS1974

Shock-wave structure in a partially ionized gas

The structure of a steady plane shock in a partially ionized gas has been investigated using the Boltzmann equation with a kinetic model as the governing equation and the discrete ordinate method as a tool. The effects of the electric field induced by the charge separation on the shock structure have also been studied. Although the three species of an ionized gas travel with approximately the same macroscopic velocity, the individual distribution functions are found to be very different. In a strong shock the atom distribution function may have double peaks, while the ion distribution function has only one peak. Electrons are heated up much earlier than ions and atoms in a partially ionized gas. Because the interactions of electrons with atoms and with ions are different, the ion temperature can be different from the atom temperature.

Lu, C. S.↗

NASA NTRS1998

Inner Magnetospheric Superthermal Electron Transport: Photoelectron and Plasma Sheet Electron Sources

Two time-dependent kinetic models of superthermal electron transport are combined to conduct global calculations of the nonthermal electron distribution function throughout the inner magnetosphere. It is shown that the energy range of validity for this combined model extends down to the superthermal-thermal intersection at a few eV, allowing for the calculation of the entire distribution function and thus an accurate heating rate to the thermal plasma. Because of the linearity of the formulas, the source terms are separated to calculate the distributions from the various populations, namely photoelectrons (PEs) and plasma sheet electrons (PSEs). These distributions are discussed in detail, examining the processes responsible for their formation in the various regions of the inner magnetosphere. It is shown that convection, corotation, and Coulomb collisions are the dominant processes in the formation of the PE distribution function, and that PSEs are dominated by the interplay between the drift terms. Of note is that the PEs propagate around the nightside in a narrow channel at the edge of the plasmasphere as Coulomb collisions reduce the fluxes inside of this and convection compresses the flux tubes inward. These distributions are then recombined to show the development of the total superthermal electron distribution function in the inner magnetosphere and their influence on the thermal plasma. PEs usually dominate the dayside heating, with integral energy fluxes to the ionosphere reaching 10(exp 10) eV/sq cm/s in the plasmasphere, while heating from the PSEs typically does not exceed 10(exp 8)eV/sq cm/s. On the nightside, the inner plasmasphere is usually unheated by superthermal electrons. A feature of these combined spectra is that the distribution often has upward slopes with energy, particularly at the crossover from PE to PSE dominance, indicating that instabilities are possible.

Khazanov, G. V.↗

NASA NTRS1998

Inner Magnetospheric Superthermal Electron Transport: Photoelectron and Plasma Sheet Electron Sources

Two time-dependent kinetic models of superthermal electron transport are combined to conduct global calculations of the nonthermal electron distribution function throughout the inner magnetosphere. It is shown that the energy range of validity for this combined model extends down to the superthermal-thermal intersection at a few eV, allowing for the calculation of the en- tire distribution function and thus an accurate heating rate to the thermal plasma. Because of the linearity of the formulas, the source terms are separated to calculate the distributions from the various populations, namely photoelectrons (PEs) and plasma sheet electrons (PSEs). These distributions are discussed in detail, examining the processes responsible for their formation in the various regions of the inner magnetosphere. It is shown that convection, corotation, and Coulomb collisions are the dominant processes in the formation of the PE distribution function and that PSEs are dominated by the interplay between the drift terms. Of note is that the PEs propagate around the nightside in a narrow channel at the edge of the plasmasphere as Coulomb collisions reduce the fluxes inside of this and convection compresses the flux tubes inward. These distributions are then recombined to show the development of the total superthermal electron distribution function in the inner magnetosphere and their influence on the thermal plasma. PEs usually dominate the dayside heating, with integral energy fluxes to the ionosphere reaching 10(exp 10) eV/sq cm/s in the plasmasphere, while heating from the PSEs typically does not exceed 10(exp 8) eV/sq cm/s. On the nightside, the inner plasmasphere is usually unheated by superthermal electrons. A feature of these combined spectra is that the distribution often has upward slopes with energy, particularly at the crossover from PE to PSE dominance, indicating that instabilities are possible.

Khazanov, G. V.↗

DOE OSTI2026

Application of a Chemical Index to Aerosol Mass Spectrometry: Delta Plots and Functional Group Distributions

A better understanding of the chemical properties of organic aerosol (OA) particles will improve our ability to characterize their sources and predict their lifetime. The high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) is widely used to measure OA in real time using thermal vaporization followed by electron ionization (EI). EI creates fragment ions that can be assigned to functional groups using delta analysis, a method of classifying mass spectra according to the presence of different chemically related ion series. In this study, we demonstrate the application of delta analysis to characterize molecular structures using a new visualization method. We also use delta analysis to quantify the functional group distribution with an average absolute error of ∼5–6% for individual standard molecules, comparable to the error observed for OA mixtures from biomass and coal combustion fit with Fourier transform infrared spectroscopy. Finally, we apply delta functional group analysis to AMS positive matrix factorization (PMF) factors across seven different field campaigns and find a similar composition across the more oxidized factors with about 55% acid and 26% alcohol groups. The analysis method described here can be applied to any HR-ToF-AMS data set to provide quantitative relative functional group distributions for OA mixtures.

aerosol↗

NASA NTRS2001

Normal and abnormal tissue identification system and method for medical images such as digital mammograms

A system and method for analyzing a medical image to determine whether an abnormality is present, for example, in digital mammograms, includes the application of a wavelet expansion to a raw image to obtain subspace images of varying resolution. At least one subspace image is selected that has a resolution commensurate with a desired predetermined detection resolution range. A functional form of a probability distribution function is determined for each selected subspace image, and an optimal statistical normal image region test is determined for each selected subspace image. A threshold level for the probability distribution function is established from the optimal statistical normal image region test for each selected subspace image. A region size comprising at least one sector is defined, and an output image is created that includes a combination of all regions for each selected subspace image. Each region has a first value when the region intensity level is above the threshold and a second value when the region intensity level is below the threshold. This permits the localization of a potential abnormality within the image.

Heine, John J.↗

NASA NTRS1995

Ponderomotive effects on distributions of O(+) ions in the auroral zone

Test particle calculations are used to compute the effects of gravity and ponderomotive acceleration by shear Alfven wave oscillations on the distribution function of O(+) ions along auroral field lines, assuming an ionospheric Maxwellian source of the ions at 2000 km altitude with approximately 0.5 eV of thermal energy in the parallel component of velocity. The electric field model corresponds to a standing wave oscillation with a frequency approximately 1 Hz in the azimuthal direction superimposed on the background dipole field, in which the wave amplitude is either increasing or decreasing in time. The electric field is taken to be primarily in the perpendicular direction. The time varying wave produces broad distributions with widths of 2 to 10 times the initial 0.5-eV thermal energy of the Maxwellian source, and the density and flux of upward going O(+) ions at one Earth radius are both enhanced in this model. The oxygen ion distribution functions at 1 R(sub E) altitude resulting from interaction with waves whose amplitudes are increasing in time have a more gradual lower energy cutoff than do the distribution functions resulting from decaying waves. The high-energy part of the distribution functions in growing waves reflects the temperature of the Maxwellian source, while the high-energy part of the distributions resulting from decaying waves steepens with time, independent of the source temperature.

Witt, E.↗

NASA NTRS1992

Spaceflight alters immune cell function and distribution

Experiments are described which were performed onboard Cosmos 2044 to determine spaceflight effects on immunologically important cell function and distribution. Results indicate that bone marrow cells from flown and suspended rats exhibited a decreased response to a granulocyte/monocyte colony-stimulating factor compared with the bone marrow cells from control rats. Bone marrow cells showed an increase in the percentage of cells expressing markers for helper T-cells in the myelogenous population and increased percentages of anti-asialo granulocyte/monocyte-1-bearing interleulin-2 receptor bearing pan T- and helper T-cells in the lymphocytic population.

Sonnenfeld, Gerald↗

NASA NTRS1993

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗

NASA NTRS2005

Simulations of Evaporating Multicomponent Fuel Drops

A paper presents additional information on the subject matter of Model of Mixing Layer With Multicomponent Evaporating Drops (NPO-30505), NASA Tech Briefs, Vol. 28, No. 3 (March 2004), page 55. To recapitulate: A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The model is used to perform direct numerical simulations in continuing studies directed toward understanding the behaviors of sprays of liquid petroleum fuels in furnaces, industrial combustors, and engines. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and drops, respectively, and incorporates a concept of continuous thermodynamics, according to which the chemical composition of a fuel is described by use of a distribution function. In this investigation, the distribution function depends solely on the species molar weight. The present paper reiterates the description of the model and discusses further in-depth analysis of the previous results as well as results of additional numerical simulations assessing the effect of the mass loading. The paper reiterates the conclusions reported in the cited previous article, and states some new conclusions. Some new conclusions are: 1. The slower evaporation and the evaporation/ condensation process for multicomponent-fuel drops resulted in a reduced drop-size polydispersity compared to their single-component counterpart. 2. The inhomogeneity in the spatial distribution of the species in the layer increases with the initial mass loading. 3. As evaporation becomes faster, the assumed invariant form of the molecular- weight distribution during evaporation becomes inaccurate.

Bellan, Josette↗

DOE OSTI2024

Parallel expansion of a fuel pellet plasmoid

The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a ‘quasiequilibrium’ (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation.

Physics↗

NASA NTRS1971

Probe and radar electron temperatures in an isotropic nonequilibrium plasma.

Electron temperatures measured by electrostatic probes and radar backscatter are distinct physical quantities, the temperature from each technique determined from a different moment of the electron-distribution function. Numerical inequality of temperatures results from a non-Maxwellian electron-distribution function or, equivalently, from a nonequilibrium electron plasma. Probe and backscatter electron temperatures are studied for low- and high-energy (isotropic) distortions of the distribution function. The nonequilibrium plasma generally produces higher probe than backscatter temperatures; however, the temperature difference is small for distortions due to realistic photoelectron populations. If the ionosphere is in a highly nonequilibrium state, probe and backscatter temperatures would differ from the temperature characterizing the average electron kinetic energy, and a single temperature applicable to a variety of physical processes would no longer exist.

Hoegy, W. R.↗

NASA NTRS1982

Electromagnetic cyclotron-loss-cone instability associated with weakly relativistic electrons

The amplification of fast extraordinary mode waves at frequencies very close to the electron cyclotron frequency, due to the presence of a population of energetic electrons with a loss-cone type distribution, is studied. Low-energy background electrons are included in the analysis. Two types of loss-cone distribution functions are considered, and it is found that the maximum growth rates for both distribution functions are of the same order of magnitude. When the thermal effects of the energetic electrons are included in the dispersion equation, the real frequencies of the waves are lower than those obtained by using the cold plasma approximation. This effect tends to enhance the growth rate. An idealized case including a parallel electric field such that the distribution function of the trapped energetic electrons is modified is also considered. It is assumed that the parallel electric field can remove the low-energy background electrons away from the source region of radiation. Both these effects increase the growth rate.

Wong, H. K.↗

NASA NTRS1990

Shock-drift particle acceleration in superluminal shocks - A model for hot spots in extragalactic radio sources

Shock-drift acceleration at relativistic shock fronts is investigated using a fully relativistic treatment of both the microphysics of the shock-drift acceleration and the macrophysics of the shock front. By explicitly tracing particle trajectories across shocks, it is shown how the adiabatic invariance of a particle's magnetic moment breaks down as the upstream shock speed becomes relativistic, and is recovered at subrelativistic velocities. These calculations enable the mean increase in energy of a particle which encounters the shock with a given pitch angle to be calculated. The results are used to construct the downstream electron distribution function in terms of the incident distribution function and the bulk properties of the shock. The synchrotron emissivity of the transmitted distribution is calculated, and it is demonstrated that amplification factors are easily obtained which are more than adequate to explain the observed constrasts in surface brightness between jets and hot spots.

Begelman, Mitchell C.↗