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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Phase space distribution functions and energy distributions of dark matter particles in haloes

ABSTRACT For a spherical dark matter halo with isotropic velocity distribution, the phase space distribution function (DF), the energy distribution, and the density profile form a set of self-consistent description of its equilibrium state, and knowing one is sufficient to determine the other two. The Navarro–Frenk–White density profile (NFW profile) is known to be a good approximation to the spherically averaged density distribution in simulated haloes. The DARKexp energy distribution is also known to compare well with the simulated energy distribution. We present a quantitative assessment of the NFW and DARKexp fits to the simulated DF and energy distribution for a wide range of haloes in a dark-matter-only simulation from the IllustrisTNG Project. As expected, we find that the NFW fits work well except at low energy when the density at small radii deviates from the NFW profile. Further, the NFW and DARKexp fits have comparable accuracy in the region where both fit well, but the DARKexp fits are better at low energy because they require matching of the central gravitational potential. We also find an approximate relation between the energy scale parametrizing the DARKexp energy distribution and that defined by the characteristic density and radius of the NFW profile. This relation may be linked to the relaxation process during halo formation.

Astronomy & Astrophysics↗
DOE OSTI2023

Symmetry-mode analysis for local structure investigations using pair distribution function data

Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe2, where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. Here, the analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort, which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools, which converts the ISODISTORT output into a DiffPy-compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Modeling Short-Range Order in Disordered Rocksalt Cathodes by Pair Distribution Function Analysis

Pair distribution function (PDF) analysis is a powerful technique for the characterization of short-range order (SRO) in disordered materials. Accurate interpretation of experimental PDF data is critically reliant on the development of structural models that can account for local variations in site occupancies and bond lengths. To this end, we outline an approach to model SRO using first-principles calculations based on the cluster-expansion formalism. These methods are validated on neutron scattering data from two disordered rocksalt oxyfluorides, Li 1.3 Mn 0.4 Ti 0.3 O 1.7 F 0.3 and Li 1.3 Mn 0.4 Nb 0.2 Ti 0.1 O 1.7 F 0.3 . For each composition, we demonstrate that an average structure without any SRO fails to reproduce several key features in the experimental PDF. To pinpoint the origin of the suspected SRO in these materials, configurational and displacive effects were separately investigated using two disparate models. Special quasi-random structures were relaxed using density functional theory to account for local changes in bond lengths while maintaining a near-random ionic configuration. This leads to slightly improved accuracy but still misrepresents asymmetry in the first few peaks of the PDF. Monte Carlo simulations were performed to model configurational SRO on a fixed lattice, which by itself is shown to have a minimal influence on the PDF. Instead, we find that it is the bond length relaxations within environments created by SRO which controls the details of the PDF, thereby highlighting the subtle but important coupling between configurational and displacive SRO in disordered materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Plasma thermal transport with a generalized 8-moment distribution function

Moment equations that model plasma transport require an ansatz distribution function to close the system of equations. The resulting transport is sensitive to the specific closure used, and several options have been proposed in the literature. Two different 8-moment distribution functions can be generalized to form a single-parameter family of distribution functions. The transport coefficients resulting from this generalized distribution function can be expressed in terms of this free parameter. This provides the flexibility of matching the 8-moment model to some validating result at a given magnetization value, such as Braginskii’s transport, or the more recent results of Davies et al. [Physics of Plasma, 28, 012305 (2021)]. Here, this process can be thought of as solving for the 8-moment distribution function that matches the value of a transport coefficient given by a Chapman-Enskog expansion, while retaining the improved physical properties, such as finite propagation speeds and time dependence which belong to the hyperbolic moment models. Since the presented generalized distribution function only has a single free parameter, only a single transport coefficient can be matched at a time. However, this generalization process may be extended to provide multiple free parameters. The focus of this Brief Communication is on the dramatically improved thermal conductivity of the proposed model compared to the two base moment models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

First simultaneous global QCD analysis of dihadron fragmentation functions and transversity parton distribution functions

We perform a comprehensive study within quantum chromodynamics (QCD) of dihadron observables in electron-positron annihilation, semi-inclusive deep-inelastic scattering, and proton-proton collisions, including recent cross section data from Belle and azimuthal asymmetries from STAR. We extract simultaneously for the first time π + π − dihadron fragmentation functions (DiFFs) and the nucleon transversity distributions for up and down quarks as well as antiquarks. For the transversity distributions we impose their small- x asymptotic behavior and the Soffer bound. In addition, we utilize a new definition of DiFFs that has a number density interpretation to then calculate expectation values for the dihadron invariant mass and momentum fraction. Furthermore, we investigate the compatibility of our transversity results with those from single-hadron fragmentation (from a transverse momentum dependent/collinear twist-3 framework) and the nucleon tensor charges computed in lattice QCD. We find a universal nature to all of this available information. Future measurements of dihadron production can significantly further this research, especially, as we show, those that are sensitive to the region of large parton momentum fractions. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Orbit tomography of energetic particle distribution functions

Both fast ions and runaway electrons are described by distribution functions, the understanding of which are of critical importance for the success of future fusion devices such as ITER. Typically, energetic particle diagnostics are only sensitive to a limited subsection of the energetic particle phase-space which is often insufficient for model validation. However, previous publications show that multiple measurements of a single spatially localized volume can be used to reconstruct a distribution function of the energetic particle velocity-space by using the diagnostics' velocity-space weight functions, i.e. velocity-space Tomography. In this work we use the recently formulated orbit weight functions to remove the restriction of spatially localized measurements and present orbit tomography, which is used to reconstruct the 3D phase-space distribution of all energetic particle orbits in the plasma. Through a transformation of the orbit distribution, the full energetic particle distribution function can be determined in the standard {energy, pitch, r, z}-space. We benchmark the technique by reconstructing the fast-ion distribution function of an MHD-quiescent DIII-D discharge using synthetic and experimental FIDA measurements. We also use the method to study the redistribution of fast ions during a sawtooth crash at ASDEX upgrade using FIDA measurements. Lastly, a comparison between the orbit tomography and velocity-space tomography is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
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 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↗
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)↗
DOE OSTI2021

Measurements of Non-Maxwellian Electron Distribution Functions and Their Effect on Laser Heating

Electron velocity distribution functions driven by inverse bremsstrahlung heating are measured to be non-Maxwellian using a novel angularly resolved Thomson-scattering instrument and the corresponding reduction of electrons at slow velocities results in a ~40% measured reduction in inverse bremsstrahlung absorption. The distribution functions are measured to be super-Gaussian in the bulk (v/v th < 3) and Maxwellian in the tail (v/v th > 3) when the laser heating rate dominates over the electron-electron thermalization rate. Furthermore, simulations with the particle code quartz show the shape of the tail is dictated by the uniformity of the laser heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

EMPDF : inferring the Milky Way mass with data-driven distribution function in phase space

We introduce the emPDF (empirical distribution function), a novel dynamical modelling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state. emPDF determines the best-fitting potential by maximizing the similarity between instantaneous kinematics and the time-averaged phase-space distribution function (DF), which is empirically constructed from observation upon the theoretical foundation of oPDF (Han et al. 2016). This approach eliminates the need for presumed functional forms of DFs or orbit libraries required by conventional DF- or orbit-based methods. emPDF stands out for its flexibility, efficiency, and capability in handling observational effects, making it preferable to the popular Jeans equation or other minimal assumption methods, especially for the Milky Way (MW) outer halo where tracers often have limited sample size and poor data quality. We apply emPDF to infer the MW mass profile using Gaia DR3 data of satellite galaxies and globular clusters, obtaining enclosed masses of M (,r) = 26±8, 46±8, 90±13⁠, and 149±40 x 10 10 M ⊙ at r = 30, 50, 100⁠, and 200 kpc, respectively. These are consistent with the updated constraints from simulation-informed DF fitting (Li et al. 2020). While the simulation-informed DF offers superior precision owing to the additional information extracted from simulations, emPDF is independent of such supplementary knowledge and applicable to general tracer populations. emPDF is currently implemented for tracers with complete 6D kinematics within spherical potentials, but it can potentially be extended to address more general problems.

Astrophysics of Galaxies (astro-ph.GA)↗
DOE OSTI2022

Distribution Function Instead of Steady-State Assumption in Time-Series Simulation

The quasi-steady-state assumption in time-series simulation is inadequate to model phenomena of interest to energy system integration such as inverter clipping, sell-back of excess electricity to a utility and utility hosting capacity, and battery throughput. Researchers are working on stochastic modeling, higher-resolution time series data, and machine learning approaches to address this need. This poster describes a distribution function that allows a maximum value, minimum value, and shape to the curve that can vary within each time-step based only on data inputs at the resolution of that time step (eg. Hourly). The distribution function is not used to synthesize high-resolution data, rather scalar integrals are used to calculate the quantities of interest within each time step. The form of the distribution function shows significant reduction in error when compared to 1 minute data and commercial software employing the distribution function (HOMER Pro version 14.3 and higher) shows a much improved estimate of inverter clipping in an example.

battery↗
DOE OSTI2023

Cosmological constraints from the Subaru Hyper Suprime-Cam year 1 shear catalogue lensing convergence probability distribution function

Here we utilize the probability distribution function (PDF) of normalized convergence maps reconstructed from the Subaru Hyper Suprime-Cam (HSC) year 1 shear catalogue, in combination with the power spectrum, to measure the matter clustering amplitude S 8 = σ 8 $\sqrt {Ω_{m}/0.3}$. The large-scale structure’s statistical properties are incompletely described by the traditional two-point statistics, motivating our investigation of the PDF—a complementary higher-order statistic. By defining the PDF over the standard-deviation-normalized convergence map, we are able to isolate the non-Gaussian information. We use tailored simulations to compress the data vector and construct a likelihood approximation. We mitigate the impact of survey and astrophysical systematics with cuts on smoothing scales, redshift bins, and data vectors. We find S 8 = $0.860^{+0.066}_{–0.109}$ from the PDF alone and S 8 = 0.798$^{+0.029}_{–0.042}$ from the combination of the PDF and power spectrum (68% confidential level (CL)). The PDF improves the power-spectrum-only constraint by about 10%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Pair distribution function analysis of discrete nanomaterials in PDFgui

Pair distribution functions (PDFs) are a leading tool for atomic structure analysis of nanomaterials. However, the most widely used programs for refining atomic structure against PDF data are based on extended crystallographic models, which cannot be applied to discrete, whole nanoparticles. Furthermore, this work describes a straightforward approach to simulate and refine atomistic models of discrete clusters and nanoparticles employing widely used PDF modelling programs such as PDFgui that utilize extended crystallographic models. In this approach, the whole particle to be modelled is contained within an expanded, and otherwise empty, unit cell that is sufficiently large to avoid correlations between atoms in neighbouring unit cells over the r range analyzed. The PDF of the particle is simulated as a composite using two conventional `phases': one that calculates the atom–atom correlations and one that approximates the local number density. This approach is first validated for large nanoparticles that are well modelled by a conventional shape factor model, and then applied to simulate the PDF of discrete particles and low-dimensional materials (graphene and MXene) and to model the experimental PDF data for single-layer FeS nanosheets. A comparison of this approach with the DiffPy-CMI program, which calculates the PDF of discrete species, shows that the composite modelling approach is equally or more accurate. Example input files for implementing this approach within PDFgui and TOPAS, and recommendations for selecting model parameters for reliable application of this refinement strategy, are provided.

36 MATERIALS SCIENCE↗