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 55 records · Page 3

Analyses of convective flows and spatial gradients in energetic ion observations

Based on the measured anisotropy of three-dimensional energetic ion distributions obtained from the Medium Energy Particle Instrument experiment of the ISEE 1 spacecraft, bulk flow, epsilon x B convection, and pressure gradients in magnetospheric plasmas are measured with two techniques. In the first technique, using a Compton-Getting transform into the appropriate rest frame in an iterative fashion and converging to the unique velocity that removes the first-order anisotropy from the flux angular distribution, the actual measured angular distribution, and spectrum at each angle, are employed. The second technique uses a first moment of the distribution function in which the shift in velocity space of the distribution function is obtained at two phase space density values. The convection contribution to the velocity shift is assumed to be perpendicular to the pressure gradient contribution if an MHD generator condition is assumed, rendering the two shifts separable, and a gradient scale and a lower limit to the convection electric field are derived in one calculation.

Mitchell, D. G.↗

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.

Deng, Zheng-Tao↗

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↗

Propagation Pattern for Moment Representation of the Lattice Boltzmann Method

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This article extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

42 ENGINEERING↗

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.↗

Information-theoretic astrophysical uncertainties in the effective theory of dark matter direct detection

The impact of astrophysical uncertainties in direct detection searches can vary significantly across particle dark matter models and detector targets, due to the different velocity and momentum dependencies of the scattering cross section. We address these uncertainties for all operators of the nonrelativistic effective field theory of dark-matter/nucleon interactions, making use of the Kullback-Leibler (KL) information divergence to measure the deviation of the true dark matter velocity distribution from the Maxwell-Boltzmann form. This approach quantifies how astrophysical uncertainties affect each operator in the effective theory, without assuming any specific functional form for the velocity distribution. While for some operators the uncertainties are smaller than 1 order of magnitude for entropically motivated deviations from the Maxwell-Boltzmann form, for other operators, these uncertainties can be as large as three orders of magnitude near threshold. Furthermore, we identify the dependence of the scattering rate for various operators of the effective theory with different velocity-weighted moments of the velocity distribution, functionally analogous to the mean, variance, or skewness. This provides new analytic insight into which features of the velocity distribution are most relevant to detect a given particle dark matter model. Our technique is general and could be applied to a broader class of physics problems where a physical observable depends on the statistical moments of an uncertain theoretical distribution.

Herrera, Gonzalo [MIT, MKI; Harvard U.; Virginia T↗

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.↗

Formulation of 8-moment plasma transport with application to the Nernst effect

8-moment plasma models using two different distribution functions are used to study the Nernst effect and heat transport in dense plasma. These models are presented in hyperbolic form in contrast to traditional parabolic systems derived from perturbing the distribution function, as in Braginskii [Rev. Plasma Phys. 1, 205 (1965)]. The hyperbolic moment formulation can be solved implicitly in time with straightforward and fast local solvers. The numerical implementation of 8-moment models with the relaxation method in the PERSEUS code is also presented. To test 8-moment PERSEUS compared to Braginskii’s transport equations, a verification test for the Nernst thermomagnetic wave by Velikovich et al. [Phys. Plasmas 26, 112702 (2019)] is performed that confirms the presence of the same physics, but with slight differences in the transport coefficients, which are tabulated in the limits of high and low magnetization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Computing nuclear response functions with time-dependent coupled-cluster theory

We compute nuclear response functions by solving the time-dependent 𝐴-body Schrödinger equation, recording the time-dependent transition moment and extracting spectral information via Fourier transforms. The solution of the time-dependent many-body problem accounts for correlations on top of the mean field by taking advantage of a time-dependent formulation of coupled-cluster theory. As a validation, we focus on electric dipole transitions in 4 He and 16 O and compare moments of the response function distribution to the results of an equivalent static framework, finding negligible discrepancies. We investigate how proton and neutron densities evolve in time, and we see the traditional picture of soft and giant dipole resonances as collective oscillations of protons and neutrons emerging from our calculations in 16 O and 24 O. Furthermore, this method also allows us to investigate the behavior of the nucleus in the presence of a strong electric field. In that regime, the behavior of the system becomes chaotic. Qualitatively, the spectral information obtained in this limit is in line with previous time-dependent mean-field results.

Ab initio calculations↗

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↗