Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Distribution function”

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 667 records · Page 37

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.↗

Characterization of Downstream Ion Energy Distributions From a High Current Hollow Cathode in a Ring Cusp Discharge Chamber

The presence of energetic ions produced by a hollow cathodes operating at high emission currents (greater than 10 Angstroms) has been documented in the literature. As part of an ongoing effort to uncover the underlying physics of the formation of these ions, ion efflux from a high current hollow cathode operating in an ion thruster discharge chamber was investigated. Using a spherical sector electrostatic energy analyzer located downstream of the discharge cathode, the ion energy distribution over a 0 to 60 eV energy range was measured. The sensitivity of the ion energy distribution function to zenith angle was also assessed at 3 different positions: 0, 15, and 25 degrees. The measurements suggest that the majority of the ion current at the measuring point falls into the analyzer with an energy approximately equal to the discharge voltage. The ion distribution, however, was found to be quite broad. The high energy tail of the distribution function tended to grow with increasing discharge current. Sensitivity of the profiles to flow rate at fixed discharge current was also investigated. A simple model is presented that provides a potential mechanism for the production of ions with energies above the discharge voltage.

Foster, John E.↗

Theoretical Investigation of the High-Altitude Cusp Region using Observations from Interball and ISTP Spacecraft

A fundamental goal of magnetospheric physics is to understand the transport of plasma through the solar wind-magnetosphere-ionosphere system. To attain such an understanding, we must determine the sources of the plasma, the trajectories of the particles through the magnetospheric electric and magnetic fields to the point of observation, and the acceleration processes they undergo enroute. This study employed plasma distributions observed in the near-Earth plasma sheet by Interball and Geotail spacecraft together with theoretical techniques to investigate the ion sources and the transport of plasma. We used ion trajectory calculations in magnetic and electric fields from a global Magnetohydrodynamics (MHD) simulation to investigate the transport and to identify common ion sources for ions observed in the near-Earth magnetotail by the Interball and Geotail spacecraft. Our first step was to examine a number of distribution functions and identify distinct boundaries in both configuration and phase space that are indicative of different plasma sources and transport mechanisms. We examined events from October 26, 1995, November 29-30, 1996, and December 22, 1996. During the first event Interball and Geotail were separated by approximately 10 R(sub E) in z, and during the second event the spacecraft were separated by approximately 4(sub RE). Both of these events had a strong IMF By component pointing toward the dawnside. On October 26, 1995, the IMF B(sub Z) component was northward, and on November 1-9-30, 1996, the IMF B sub Z) component was near 0. During the first event, Geotail was located near the equator on the dawn flank, while Interball was for the most part in the lobe region. The distribution function from the Coral instrument on Interball showed less structure and resembled a drifting Maxwellian. The observed distribution on Geotail, on the other hand, included a great number of structures at both low and high energies. During the third event (December 22, 1996) both spacecraft were in the plasma sheet and were separated bY approximately 20 R(sub E) in the y direction. During this event the IMF was southward.

Ashour-Abdalla, Maha↗

Lower hybrid drift instability in nonthermal plasmas

Lower hybrid drift instability (LHDI) is driven by the cross-field current and operates in the vicinity of the lower-hybrid frequency, between the ion- and electron-gyro frequencies, and with wavelengths between the electron and ion thermal gyro radii. The free energy source that drives this instability resides in the density gradient associated with an inhomogeneous plasma. The existing literature on LHDI assumes that the charged particle distribution function is given by a Maxwellian form, but the space plasma is pervasively observed to feature nonthermal characteristics. This paper extends the theory of LHDI to nonthermal plasmas. The generalized theory of LHDI is, thus, applicable to various space plasma environments characterized by nonthermal plasma velocity distribution functions.

Arya, Neetasha (ORCID:0009000236075605)↗

Particle Acceleration in Relativistic Alfvénic Turbulence

Abstract Strong magnetically dominated Alfvénic turbulence is an efficient engine of nonthermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations δ B 0 and the guide field B 0 . If δ B 0 ≪ B 0 , the particle magnetic moments are conserved, and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in log-normal tails of particle energy distribution functions. Conversely, if δ B 0 ≳ B 0 , interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to power-law tails of the energy distribution functions.

79 ASTRONOMY AND ASTROPHYSICS↗

Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F 2 n F 2 p for mirror nuclei He 3 and H 3

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions x B → 0 and x B → 1. The extrapolated F 2 ratio as quark momentum fraction x B → 1 is $\frac{F^n_2}{F^p_2}$ → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when x B → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high- x B , the proton quark distribution function ratio d/u is derived from the F 2 ratio and found to be d/u → 1/6. Our extrapolated values for both the $\frac{F^n_2}{F^p_2}$ ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. Finally, one such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated F 2 ratio at x B = 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A thermal/nonthermal approach to solar flares

An approach for modeling solar flare high-energy emissions is developed in which both thermal and nonthermal particles coexist and contribute to the radiation. The thermal/nonthermal distribution function is interpreted physically by postulating the existence of DC sheets in the flare region. The currents then provide both primary plasma heating through Joule dissipation, and runaway electron acceleration. The physics of runaway acceleration is discussed. Several methods are presented for obtaining approximations to the thermal/nonthermal distribution function, both within the current sheets and outside of them. Theoretical hard x ray spectra are calculated, allowing for thermal bremsstrahlung from the heated plasma electrons impinging on the chromosphere. A simple model for hard x ray images of two-ribbon flares is presented. Theoretical microwave gyrosynchrotron spectra are calculated and analyzed, uncovering important new effects caused by the interplay of thermal and nonthermal particles. The theoretical spectra are compared with observed high resolution spectra of solar flares, and excellent agreement is found, in both hard x rays and microwaves. The future detailed application of this approach to solar flares is discussed, as are possible refinements to this theory.

Benka, Stephen G.↗

Narrow-band Electrostatic Noise generated by an electron velocity space hole

Narrow-band Electrostatic Noise (NEN) is a common occurrence in the Earth's distant magnetotail. NEN is observed in a frequency range (100-316 Hz) that falls roughly between the electron and ion plasma frequencies. This mode may result from holes in the electron distribution function associated with slow shocks. An instability that is associated with this mode is studied using numerical simulations. The growth of the instability depends on the size and shape of the hole. The hole mode can also be driven unstable by either an anisotropy in the electron distribution function or an ion beam. In all these cases the instability saturates at a low level and only a fraction of the available free energy is released.

Richard, Robert L.↗

Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data

We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using nonstationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of the liquid structure. We demonstrate uncertainty propagation of the Gaussian process posterior to unmeasured quantities of interest. Experimental radial distribution functions of liquid argon and water with uncertainty quantification are provided as both a proof of principle for the method and a benchmark for molecular models.

Chemical structure↗

Computations of ion diffusion coefficients from the Boltzmann-Fokker-Planck equation

The Boltzmann-Fokker-Planck equation is solved with the Chapman-Enskog method of analysis for the velocity distribution functions of helium, carbon, nitrogen, and oxygen. The analysis is a perturbation scheme based on the assumption of a collision-dominated gas, and the calculations are carried out to first order. The elements considered are treated as trace constituents in an electron-proton gas. From the resulting distribution functions, diffusion coefficients are computed which are found to be 20-30% less than those obtained by Chapman and Burgers. In addition, it is shown that the return current of cold electrons needed to maintain quasi-neutrality in a plasma with a temperature gradient contributes a term in the thermal diffusion coefficient omitted erroneously in previous works. This added term resolves the longstanding controversy over the discrepancy between the coefficients of Chapman and Burgers, which are seen to be completely equivalent in the light of this analysis. The viscosity coefficient for an electron-proton gas is also computed and found to be 7% less than that obtained by Braginskii.

Roussel-Dupre, R.↗

Test particle calculations of pick-up ions in the vicinity of Comet Giacobini-Zinner

Ionization of cometary neutral molecules produces ions which are picked-up by the solar wind. The cometary ion pick-up process for Comet Giacobini-Zinner is studied using a test particle method in which trajectories are numerically calculated for several thousand ions whose initial locations were chosen randomly with probability proportional to the neutral density. The cometary ion distribution function was calculated at several locations upstream of the bow shock. Several types of magnetic fluctuations were included. Circularly and linearly polarized monochromatic waves result in less pitch-angle scattering of pick-up ions than turbulent fluctuations which have about the same amplitude. Some anisotropy remains in the distribution function just upstream of the shock, even for the turbulent fluctuations.

Cravens, T. E.↗

Electron beams and Langmuir turbulence in solar type III radio bursts observed in the interplanetary medium

Results are presented of in situ observations of electron beams, plasma waves, and associated solar type II radio emission in the interplanetary medium near 1 AU, which were provided by the ISEE-3 spacecraft. It is shown that electron beams are formed by the faster electrons arriving before the slower ones, following an impulsive injection at the sun. The resulting bump-on-tail in the reduced 1D distribution function is unstable to the growth of electrostatic electron plasma (Langmuir) waves. The Langmuir waves are observed to be highly impulsive in nature. The onset and temporal variations of the observed plasma waves are in good qualitative agreement with the wave growth expected from the evolution of the measured 1D distribution function. The lack of obvious plateauing of the bump-on-tail suggests that the waves were removed from resonance with the beam electrons by some wave-wave interaction.

Lin, R. P.↗

Self-consistent electrostatic potential due to trapped plasma in the magnetosphere

A steady state solution for the self-consistent electrostatic potential due to a plasma confined in a magnetic flux tube is considered. A steady state distribution function is constructed for the trapped particles from the constants of the motion, in the absence of waves and collisions. Using Liouville's theorem, the particle density along the geomagnetic field is determined and found to depend on the local magnetic field, self-consistent electric potential, and the equatorial plasma distribution function. A hot anisotropic magnetospheric plasma in steady state is modeled by a bi-Maxwellian at the equator. The self-consistent electric potential along the magnetic field is calculated assuming quasineutrality, and the potential drop is found to be approximately equal to the average kinetic energy of the equatorially trapped plasma. The potential is compared with that obtained by Alfven and Faelthammar (1963).

Miller, Ronald H.↗

Inclusive-photon production and its dependence on photon isolation in $pp$ collisions at $\sqrt{s}$ = 13 TeV using 139 fb -1 of ATLAS data

Measurements of differential cross sections are presented for inclusive isolated-photon production in $pp$ collisions at a centre-of-mass energy of 13 TeV provided by the LHC and using 139 -1 fb of data recorded by the ATLAS experiment. The cross sections are measured as functions of the photon transverse energy in different regions of photon pseudorapidity. The photons are required to be isolated by means of a fixed-cone method with two different cone radii. The dependence of the inclusive-photon production on the photon isolation is investigated by measuring the fiducial cross sections as functions of the isolation-cone radius and the ratios of the differential cross sections with different radii in different regions of photon pseudorapidity. The results presented in this paper constitute an improvement with respect to those published by ATLAS earlier: the measurements are provided for different isolation radii and with a more granular segmentation in photon pseudorapidity that can be exploited in improving the determination of the proton parton distribution functions. These improvements provide a more in-depth test of the theoretical predictions. Next-to-leading-order QCD predictions from JETPHOX and SHERPA and next-to-next-to-leading-order QCD predictions from NNLOJET are compared to the measurements, using several parameterisations of the proton parton distribution functions. The measured cross sections are well described by the fixed-order QCD predictions within the experimental and theoretical uncertainties in most of the investigated phase-space region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.

Modeling↗

A Search for Correlations between Turbulence and Star Formation in LITTLE THINGS Dwarf Irregular Galaxies

Turbulence has the potential for creating gas density enhancements that initiate cloud and star formation (SF), and it can be generated locally by SF. To study the connection between turbulence and SF, we looked for relationships between SF traced by FUV images, and gas turbulence traced by kinetic energy density (KED) and velocity dispersion (v {sub disp}) in the LITTLE THINGS sample of nearby dIrr galaxies. We performed 2D cross-correlations between FUV and KED images, measured cross-correlations in annuli to produce correlation coefficients as a function of radius, and determined the cumulative distribution function of the cross-correlation value. We also plotted on a pixel-by-pixel basis the locally excess KED, v {sub disp}, and H i mass surface density, Σ{sub HI}, as determined from the respective values with the radial profiles subtracted, versus the excess SF rate density Σ{sub SFR}, for all regions with positive excess Σ{sub SFR}. We found that Σ{sub SFR} and KED are poorly correlated. The excess KED associated with SF implies a ∼0.5% efficiency for supernova energy to pump local H i turbulence on the scale of the resolution here, which is a factor of ∼2 too small for all of the turbulence on a galactic scale. The excess v {sub disp} in SF regions is also small, only ∼0.37 km s{sup −1}. The local excess in Σ{sub HI} corresponding to an excess in Σ{sub SFR} is consistent with a H i consumption time of ∼1.6 Gyr in the inner parts of the galaxies. The similarity between this timescale and the consumption time for CO implies that CO-dark molecular gas has comparable mass to H i in the inner disks.

74 ATOMIC AND MOLECULAR PHYSICS↗

The stability of perfect elliptic disks. 1: The maximum streaming case

Self-consistent distribution functions are constructed for two-dimensional perfect elliptic disks (for which the potential is exactly integrable) in the limit of maximum streaming; these are tested for stability by N-body integration. To obtain a discrete representation for each model, simulated annealing is used to choose a set of orbits which sample the distribution function and reproduce the required density profile while carrying the greatest possible amount of angular momentum. A quiet start technique is developed to place particles on these orbits uniformly in action-angle space, making the initial conditions as smooth as possible. The roundest models exhibit spiral instabilities similar to those of cold axisymmetric disks; the most elongated models show bending instabilities like those seen in prolate systems. Between these extremes, there is a range of axial ratios 0.25 approximately less than b/a approximately less than 0.6 within which these models appear to be stable. All the methods developed in this investigation can easily be extended to integrable potentials in three dimensions.

Levine, Stephen E.↗

The electron Boltzmann equation in a plasma generated by fission fragments

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material show that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux but increases sharply in the presence of a sustainer electric field.

Hassan, H. A.↗