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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Energy distribution functions of kilovolt ions in a modified Penning discharge.

The distribution function of ion energy parallel to the magnetic field of a modified Penning discharge has been measured with a retarding potential energy analyzer. These ions escaped through one of the throats of the magnetic mirror geometry. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field have been made with a charge-exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and the parallel and perpendicular kinetic temperatures are equal within experimental error. These results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space, and result in an isotropic energy distribution.

Roth, J. R.↗
DOE OSTI2021

Statistical analysis of non-Maxwellian electron distribution functions measured with angularly resolved Thomson scattering

Angularly resolved Thomson scattering is a novel extension of Thomson scattering, enabling the measurement of the electron velocity distribution function over many orders of magnitude. Here, details of the theoretical basis of the technique and the instrument designed for this measurement are described. Angularly resolved Thomson-scattering data from several experiments are shown with descriptions of the corresponding distribution functions. A reduced model describing the distribution function is given and used to perform a Monte Carlo analysis of the uncertainty in the measurements. The electron density and temperature were determined to a precision of 12% and 21%, respectively, on average, while all other parameters defining the distribution function were generally determined to better than 20%. It was found that these uncertainties were primarily due to limited signal to noise and instrumental effects. Furthermore, measurements with this level of precision were sufficient to distinguish between Maxwellian and non-Maxwellian distribution functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1997

Ion Sources and Acceleration Mechanisms Inferred from Local Distribution Functions

This study investigates the sources of the ions up the complex and nonisotropic H(+) velocity distribution functions observed by the Geotail spacecraft on May 23, 1995, in the near-Earth magnetotail region and recently reported by Frank et al. [1996]. A distribution function observed by Geotail at -10 R(sub E) downtail is used as input for the large scale kinetic (LSK) technique to follow the trajectories of approximately 90,000 H(+) ions backward in time. Time-dependent magnetic and electric fields are taken from a global magnetohydrodynamic (MHD) simulation of the magnetosphere and its interactions with appropriate solar wind and IMF conditions. The ion population described by the Geotail distribution function was found to consist of a mixture of particles originating from three distinct sources: the ionosphere, the low latitude boundary layer (LLBL), and the high latitude plasma mantle. Ionospheric particles had direct access along field lines to Geotail, and LLBL ions convected adiabatically to the Geotail location. Plasma mantle ions, on the other hand, exhibited two distinct types of behavior. Most near-Earth mantle ions reached Geotail on adiabatic orbits, while distant mantle ions interacted with the current sheet tailward of Geotail and had mostly nonadiabatic orbits. Ions from the ionosphere, the LLBL, and the near-Earth mantle were directly responsible for the well-separated, low energy structures easily discernible in the observed and modeled distribution functions. Distant mantle ions formed the higher energy portion of the Geotail distribution. Thus, we have been successful in extracting useful information about particle sources, their relative contribution to the measured distribution and the acceleration processes that affected particle transport during this time.

Ashour-Abdalla, M.↗
DOE OSTI2022

diffpy.mpdf : open-source software for magnetic pair distribution function analysis

The open-source Python package diffpy.mpdf , part of the DiffPy suite for diffraction and pair distribution function analysis, provides a user-friendly approach for performing magnetic pair distribution function (mPDF) analysis. The package builds on existing libraries in the DiffPy suite to allow users to create models of magnetic structures and calculate corresponding one- and three-dimensional mPDF patterns. diffpy.mpdf can be used to perform fits to mPDF data either in isolation or in combination with atomic pair distribution function data for joint refinement of the atomic and magnetic structure. Examples are given using MnO and MnTe as representative antiferromagnetic compounds and MnSb as a representative ferromagnet.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The Stellar Velocity Distribution Function in the Milky Way Galaxy

The stellar velocity distribution function in the solar vicinity is reexamined using data from the Sloan Digital Sky Survey Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey’s DR16 and Gaia DR2. By exploiting APOGEE’s ability to chemically discriminate with great reliability the thin-disk, thick-disk, and (accreted) halo populations, we can, for the first time, derive the three-dimensional velocity distribution functions (DFs) for these chemically separated populations. We employ this smaller but more data-rich APOGEE+Gaia sample to build a data-driven model of the local stellar population velocity DFs and use these as basis vectors for assessing the relative density proportions of these populations over the 5 < R < 12 kpc and −1.5 < z < 2.5 kpc range as derived from the larger, more complete (i.e., all-sky, magnitude-limited) Gaia database. We find that 81.9% ± 3.1% of the objects in the selected Gaia data set are thin-disk stars, 16.6% ± 3.2% are thick-disk stars, and 1.5% ± 0.1% belong to the Milky Way stellar halo. We also find the local thick-to-thin-disk density normalization to be ρ {sub T}(R {sub ⊙})/ρ {sub t}(R {sub ⊙}) = 2.1% ± 0.2%, a result consistent with, but determined in a completely different way from, typical star-count/density analyses. Using the same methodology, the local halo-to-disk-density normalization is found to be ρ {sub H}(R {sub ⊙})/(ρ {sub T}(R {sub ⊙}) + ρ {sub t}(R {sub ⊙})) = 1.2% ± 0.6%, a value that may be inflated due to the chemical overlap of halo and metal-weak thick-disk stars.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Stability analysis of double-peaked proton distribution functions in the solar wind

Twelve proton velocity distribution functions as measured for different solar wind speeds by the plasma analyzer at the Helios spacecraft are modeled analytically by a superposition of two bi-Maxwellians. The stability of these distributions is investigated by solving the linear dispersion equation for parallel propagation of both left- and right-hand polarized modes. Due to the temperature anisotropy of the main proton component the presence of the resonant left-hand ion cyclotron instability is found to be typical for high-speed streams and is independent of an ion beam. The results indicate that the ratio of the beam density to total particle density and the beam drift velocity are generally close to the threshold values necessary to drive a highly unstable nonresonant right-hand mode. This instability is found for one proton distribution and is a consequence of the beam particles. It is concluded that both the ion cyclotron instability and the ion beam instability act as a regulating mechanism on the shape of solar wind double humped proton distribution functions.

Leubner, Manfred P.↗
DOE OSTI2024

Non-Thermal Solar Wind Electron Velocity Distribution Function

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Unusual electron distribution functions in the solar wind derived from the Helios plasma experiment - Double-strahl distributions and distributions with an extremely anisotropic core

Electron distribution functions with unusual features, which have been observed on rare occasions in the solar wind by the Helios probes, are presented. Two examples show a strong symmetric bidirectional anisotropy in the energy regime of the halo up to particle energies of 800 eV (double-strahl distributions). Another example shows an unusually strong bidirectional anisotropy in the energy regime of the core (below 150 eV). The infrequently observed double-strahl distributions provide evidence that magnetic field loops can exist in the solar wind where electrons are trapped. In addition, they provide evidence that in the case of electrons trapped in closed magnetic field structures the break in the energy spectrum separating the core from the halo is produced only by collisions. On the other hand, the class of distribution functions with strongly anisotropic cores indicates that in the case of 'open' magnetic field lines the break between core and halo is largely determined both by the interplanetary electrostatic potential and by collisions.

Pilipp, W. G.↗
NASA NTRS1986

Role of scattering distribution functions in spacecraft contamination control practices

A method for spacecraft optical surface contamination monitoring based on the bidirectional reflectance distribution function (BRDF) and the bidirectional transmittance distribution function (BTDF) is described. In the experimental set up, BRDF/BTDF measurements were made at 0.6328 microns using a 35-mW He-Ne laser light source. A correlation of the second order between BRDF and cleanliness levels was observed. It is suggested that bidirectional scattering distribution functions measured on witness mirrors can give information about contamination in clean rooms or vacuum chambers, and that they can be adopted to establish contamination control criteria.

Carosso, P. A.↗
DOE OSTI2024

Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalised kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, B $\vartheta$ /B, it generalises the drift kinetic theory of [Hazeltine Phys. Plasmas 15 (1973) 77] to the limit of B $\vartheta$ /B ~ 1 (e.g. to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalised gyrokinetic formalism of [Dudkovskaia et al. Plasma Phys. Control. Fusion 65 (2023) 045010], derived specifically to capture neoclassical equilibrium currents in gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of [Dudkovskaia et al. Nucl. Fusion 63 (2023) 016020] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. In conclusion, resolving ρ ~ ρ $\vartheta$ (or B $\vartheta$ ~ B), where ρ $\vartheta$ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Updated analyses of gluon distribution functions for the pion and kaon from the gauge-invariant nonlocal chiral quark model

In this work, we investigate the gluon distribution functions for the pion and kaon, in addition to the improved result of the valence-quark ones, in the gauge-invariant nonlocal chiral-quark model, in which the momentum dependence of the quark interactions is properly taken into account. We then analyze the gluon distribution functions, generated dynamically through the splitting functions in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi QCD evolution. By comparing with the recent lattice QCD results and Jefferson Lab angular momentum global analyses, it is found that the present numerical results for the gluon parton distribution functions for the pion exhibit a good agreement and the valence up-quark distribution results for the pion by reproducing the reanalyzed experimental data with a remarkable agreement. Our prediction on the gluon distribution functions for the kaon is also consistent with the recent lattice data for the kaon within the errors. Published by the American Physical Society 2024

Hutauruk, Parada. T. P. (ORCID:0000000242257109)↗
NASA NTRS1978

Radio evidence on the particle distribution functions in the corona following flares

This paper summarizes results of radio studies of the distribution functions (number, energy distribution, and pitch-angle distribution) of the energetic particles that are produced at the time of solar flares. The clues and constraints they impose on the mechanisms of acceleration are considered, bearing in mind that radio evidence implies that there are at least two stages of acceleration in many flares. The distribution functions of the particles resulting from first-phase acceleration, first- and/or second-phase, and second-phase acceleration are discussed.

Dulk, G. A.↗
NASA NTRS1987

The electron distribution function upstream from the earth's bow shock

A general analytic theory for the distribution function of particles backstreaming from an arbitrary shock in a magnetized plasma is presented. Particle motions are shown to be restricted to two-dimensional planes. A general form for the source term describing upstreaming particles accelerated at the shock is presented along with explicit source terms for planar and parabolic shocks. The origin and form of the escape velocity cutoff for a shock in a magnetized plasma are discussed. The distribution function upstream of a finite planar shock and a parabolic shock in two dimensions is calculated, and an analytic approximation of the cutoff velocity at points in the upstream region is derived. The theory is then applied to the earth's bow shock, calculating distribution functions and the nature and spatial variation of the cutoff velocity. The theory for the particle distribution upstream of the bow shock is compared with the model of Filbert and Kellogg (1979).

Cairns, Iver H.↗
NASA NTRS2001

Distribution functions of probabilistic automata

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Denotational semantics↗
NASA NTRS1989

A distribution function for double-bit upsets

A chord length distribution function for simultaneus path lengths in two parallelepipeds is developed, which is applicable to a unidirectional flux. The distribution function measures the probability for an ion trajectory to have a path length exceeding a specified value in one parallelepiped and to simultationsly have a path length exceeding another specified value in another parallelepiped.

Edmonds, L. D.↗
NASA NTRS1984

Distribution functions of intergalactic clouds

Width spectrum data derived from high-redshift QSO Ly-alpha absorption lines are used to study the statistical properties of intergalactic clouds. Several theoretical distribution functions for size and density are derived and tested against observational data for two types of line broadening: thermal and cosmological. Good agreement was found between the theoretical distribution functions and the observational data when the clouds were thermally broadened, and when distribution functions for both cloud size and width have a nonzero width. Attempts to fit the data with a single radius or density distribution function were unsuccessful.

Sherman, R. D.↗