Search NASA⌕ Search

SEARCH · Search NASA

Results for “distribution function moments”

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 37 records · Page 2

Energization and transport of ions of ionospheric origin in the terrestrial magnetosphere

The work of this grant has been predominantly focused on ion outflows from two data sets: Prognoz 7 and Dynamics Explorer. The Prognoz analysis studied ion densities, temperatures, and flow velocities in the magnetotail. The work performed under this contract consisted of developing a program to load the raw data, computing the background subtraction of a strong sun pulse, and using the net count to calculate the low order moments of the distribution function. The study confirms the results of ISEE with regard to the supply of plasma from the cusp as a major source of plasmasheet plasma and goes beyond this to discuss the use of ion velocities as a way to examine the motions of the magnetotail. The abstract of the work to be reported is included as an appendix. The work on the DE/Retarding Ion Mass Spectrometer is separated into two categories: (1) classification of low-energy ion flows from high-latitudes, and (2) studies of the polar wind. Major publications resulting from this work are also included as an appendix to this report. The polar wind is in a category by itself as a result of the thermal escape of hydrogen and helium because of ambipolar diffusion through the heavier, oxygen-dominated topside ionosphere. The analysis of the polar wind reports the flux variability as a function of season, magnetic activity, etc. Much effort has been expended under this grant to complete a follow on study of the thermal structure of the polar wind. Extensive display tools and analysis software have been developed and used in an attempt to carry out this thermal analysis. The present work uses a constrained fit scheme that combines the ion densities and flow velocities derived from Chandler et al. and a spacecraft potential derived from an empirical relation to the total ion density to determine the remaining fit parameter, the ion temperature, via a least squares fit to the RIMS data.

Waite, J. Hunter JR.↗

Energization and transport of ions of ionospheric origin in the terrestrial magnetosphere

This serves as a final report entitled Energization and Transport of Ions of Ionospheric Origin in the Terrestrial Magnetosphere. The work has been predominantly focused on ion outflows identified in two data sets: (1) Prognoz 7; and (2) Dynamics Explorer. The study analyzed ion densities, temperatures, and flow velocities in the magnetotail. The work performed under this contract consisted of developing a program to load the raw data, compute the background subtraction of a strong sun pulse, and use the net counts to calculate the low order moments of the distribution function. The study confirms the results of ISEE that the the cusp is a major source of plasmasheet plasma and goes beyond this to discuss the use of ion velocities as a way to examine the motions of the magnetotail.

Waite, J. H., Jr.↗

A Study of Ion Velocities Observed by TIDE and How It Relates to Magnetospheric Circulation

The high-latitude ion velocities measured by the Thermal Ion Dynamics Experiment (TIDE) instrument on the Polar spacecraft will be examined in relation to magnetospheric circulation. TIDE derives ion velocities from moments of measured distribution functions. Hydrogen and oxygen ions are E X B drifting in the polar cap and cleft regions with a speed of about 5-20 km/s at apogee (approximately 9 Re) and a speed of 1-2 km/s at perigee (approximately 1.8 Re). At perigee 0+ is typically seen flowing down in the polar cap and outflowing from the cleft. At the transition from downflowing to upflowing there is also seen a reversal in the ion convection. The convection at perigee is consistent with standard ionospheric convection models for given Interplanetary Magnetic Field (IMF) conditions. Convection at high altitude (approximately 8.9 Re) polar regions has not been studied very much since there have not been many satellites in this region. Unlike previous missions to this region TIDE in conjunction the Plasma Source Instrument (PSI) can measure ions with as low an energy as several electron Volts. The outflowing ions observed by TIDE at apogee are believed to be important to the overall circulation of the magnetosphere. The convection of these outflowing ions at apogee will be related to the IMF. This study tries to answer the question of how the IMF response of the convection influences the overall circulation of the magnetosphere.

Elliott, H. A.↗

A Multi-Sensor Water Vapor, Temperature and Cloud Climate Data Record: Status of Our MEaSUREs 2012 Project

- Our primary objectives: Incorporate all A-Train water vapor, including small-scale, horizontal and vertical water vapor structure from MODIS (Moderate Resolution Imaging Spectroradiometer) and GPS (Global Positioning System); Use MODIS cloud classification that is collocated at the pixel-scale over the full AIRS/AMSU (Atmospheric Infrared Sounder/Advanced Microwave Sounding Unit) swath; Extend summaries to PDFs (Probability Distribution Functions)/higher order moments of water vapor sorted by cloud classes; Establish robust, scale-dependent statistical relationships between cloud, temperature, and water vapor PDFs for the climate modeling community. - We will also: Update our current data record to new CloudSat/CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation) cloud classification; Provide merged AIRS and MLS (Microwave Limb Sounder) water vapor profiles using averaging kernels; Include temperature and water vapor from models (ECMWF - European Centre for Medium-Range Weather Forecasts) and re-analyses (MERRA - Modern Era-Retrospective Analysis for Research and Applications); Classify METOP-A (Meteorological Operational Satellite-A) and NOAA (National Oceanic and Atmospheric Administration) satellite water vapor with AVHRR (Advanced Very High Resolution Radiometer) during SNOs (Solar Neutrino Oscillations); Compare with the NVAP-M (re-analysis and extension of the NASA Water Vapor Project (NVAP)) water vapor climatologies; Use existing data sources and mature algorithms, and document processing algorithms.

Fetzer, Eric↗

Kinetic theory based new upwind methods for inviscid compressible flows

Two new upwind methods called the Kinetic Numerical Method (KNM) and the Kinetic Flux Vector Splitting (KFVS) method for the solution of the Euler equations have been presented. Both of these methods can be regarded as some suitable moments of an upwind scheme for the solution of the Boltzmann equation provided the distribution function is Maxwellian. This moment-method strategy leads to a unification of the Riemann approach and the pseudo-particle approach used earlier in the development of upwind methods for the Euler equations. A very important aspect of the moment-method strategy is that the new upwind methods satisfy the entropy condition because of the Boltzmann H-Theorem and suggest a possible way of extending the Total Variation Diminishing (TVD) principle within the framework of the H-Theorem. The ability of these methods in obtaining accurate wiggle-free solution is demonstrated by applying them to two test problems.

Deshpande, S. M.↗

Coincident POLAR/UVI and WIND Observations of Pseudobreakups

Using POLAR/UVI global images, we have identified a period of successive minor auroral activations during which WIND was making a perigee pass (X approx. - 11Re). These auroral brightenings are interpreted to be pseudobreakups due to the lack of global expansion. Large magnetic field fluctuations and high earthward ion velocity moments measured by the WIND spacecraft show a nearly one-to-one correspondence with the auroral intensifications. Analysis of the plasma parameters indicates that there is no difference in the behavior of the plasma during pseudobreakups as compared to substorm expansive phase onset. Inspection of the ion distribution functions during high velocity moment events reveals the presence of a two component plasma. The particles contributing to the large mean velocities are energetic ions from approx. 2-27 keV. We conclude that pseudobreakups are the ionospheric signature of high velocity moment events.

Fillingim, M. O.↗

The signature of parallel electric fields in a collisionless plasma

The presence of a parallel electric field in the magnetosphere should be apparent through its effect on particles. An analysis is made of particle trajectories in phase space for a steady state collisionless plasma. The analysis utilizes the concepts of distribution function, total energy, and magnetic moment because all three quantities are conserved in a steady state situation in the absence of collisions. Two methods are presented for using particle data to gain information on the potential distribution. The first method involves the use of measurements of both ion and electron distribution functions and invokes the principle of quasi-neutrality. The second method involves the observation of discontinuities in velocity space which can be interpreted in terms of the effect of the electric field on the apparent loss or source cone.

Whipple, E. C., Jr.↗

Solutions to bi-Maxwellian transport equations for radial solar wind beyond 28 R(S)

This paper presents solar wind solutions for radial flow between 28 solar radii and 1 AU using the bi-Maxwellian-based 16-moment set of transport equations. In addition to the number density, drift velocity, and parallel and perpendicular temperatures, the 16-moment equations account for the transport of both longitudinal and transverse thermal energies as well as stress. Also, using the 16-moment approximation for the distribution function and assuming plasma parameter values characteristic of the solar wind, contour plots are generated for the proton velocity distribution function. It is shown how the shape of these plots depends on various macroscopic plasma parameters.

Demars, H. G.↗

Consequences of magnetotail ion dynamics

The trajectories of a large ensemble of particles are calculated in a modified Tsyganenko magnetic field model with a uniform cross-tail electric field. The model magnetotail can be divided into several distinct dynamical regimes of ion motion. Near Earth, where the field lines are dipolar the adiabatic formalism is adequate. In the mid-tail and distant tail, guiding-center theory breaks down and must be replaced by a quasi-adiabatic formalism. There is an important transition region between the adiabatic and quasi-adiabatic regions where ion trajectories become more complicated and no simple analytical description holds. This wall region is characterized by rapid ion acceleration and a major loss of particles to the dusk flank. The moments of the ion distribution function are constructued from the ion trajectories, including density, temperature, and pressure in the x-z and x-y planes. In the noon-midnight meridian plane, parameters are relatively constant except near the Earth, while the x-y plots show strong gradients across the magnetotail. Magnetotail plasma convects earthward, drifts toward dusk, and is squeezed out of the tail in the near-Earth region. A thin current sheet forms in the quasi-adiabatic region, and the pressure tensor has significant off-diagonal terms at its edges. These terms are the result of quasi-adiabatic ion trajectories which lead to azimuthally asymmetric distribution functions capable of maintaining approximate stress balance across the current sheet. Simplified analytical descriptions provide further physical insight into ion dynamics that are observed.

Ashour-Abdalla, Maha↗

Spacecraft and Instrument Photoelectrons Measured by the Dual Electron Spectrometers on MMS

Secondary electrons are continuously generated via photoemission from sunlit spacecraft and instrument surfaces. These particles can subsequently contaminate low-energy channels of electron sensors. Spacecraft photoelectrons are measured at energies below that of a positive spacecraft potential and can be removed at the expense of energy resolution. However, fluxes of photoelectrons generated inside electron instruments are independent of spacecraft potential and must be fully characterized in order to correct electron data. Here we present observations of spacecraft and instrument photoelectron populations measured with the Dual Electron Spectrometers (DES) on NASA's Magnetospheric Multiscale (MMS) mission. We leverage observations from Earth's nightside plasma sheet taken during MMS commissioning and develop an empirical model of instrument photoelectrons. This model is used with DES velocity distribution functions to correct plasma moments and has been made publicly available on the MMS science data center for use by the scientific community.

photoelectrons↗

Statistics of Sxy estimates

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Freilich, M. H.↗

Comparison of generalized transport and Monte-Carlo models of the escape of a minor species

The steady-state diffusion of a minor species through a static background species is studied using a Monte Carlo model and a generalized 16-moment transport model. The two models are in excellent agreement in the collision-dominated region and in the 'transition region'. In the 'collisionless' region the 16-moment solution contains two singularities, and physical meaning cannot be assigned to the solution in their vicinity. In all regions, agreement between the models is best for the distribution function and for the lower-order moments and is less good for higher-order moments. Moments of order higher than the heat flow and hence beyond the level of description provided by the transport model have a noticeable effect on the shape of distribution functions in the collisionless region.

Demars, H. G.↗

Statistical properties of two sine waves in Gaussian noise.

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Esposito, R.↗

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.↗

Energy partitioning of gaseous ions in an electric field.

The partitioning of ion energy among thermal energy, drift energy, and random-field energy is studied by solution of the Boltzmann equation. An expansion in powers of the square of the electric field strength is obtained by Kihara's method. Numerical calculations for several ion-neutral force laws show that Wannier's constant mean-free-time model gives a reasonable first approximation. The formal extension to multicomponent mixtures is also given. The matrix elements obtained are tabulated, and can be used to study the field dependence of other moments of the ion-distribution function.

Hahn, H.-S.↗