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DOE OSTI2020

Spatial and momentum imaging of the pion and kaon

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: ( b T 2 ) u π = 0.11 fm 2 , ( b T 2 ) s K = 0.08 fm 2 , and ( b T 2 ) u K = 0.13 fm 2 , and therefore the s quark in the kaon is much closer to the center of transverse momentum than the u quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD

Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments ⟨𝑥 2 ⟩ of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and 2+1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. Furthermore, this is the first direct calculation of these observables performed at the physical pion mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

A Drift‐Kinetic Method for Obtaining Gradients in Plasma Properties From Single‐Point Distribution Function Data

Abstract In this paper, we derive a new drift‐kinetic method for estimating gradients in the plasma properties through a velocity space distribution at a single point. The gradients are intrinsically related to agyrotropic features of the distribution function. This method predicts the gradients in the magnetized distribution function and can predict gradients of arbitrary moments of the gyrotropic background distribution function. The method allows for estimates on density and pressure gradients on the scale of a Larmor radius, proving to resolve smaller scales than any method currently available to spacecraft. The model is verified with a set of fully kinetic VPIC particle‐in‐cell simulations.

Wetherton, B. A.↗

DOE OSTI2020

Particlization in fluid dynamical simulations of heavy-ion collisions: The IS3D module

The IS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling of the Cooper–Frye formula which converts fluid dynamical information into local phase-space distributions for hadrons. The code package includes multiple choices for the non-equilibrium correction to these distribution functions: the 14-moment approximation, first-order Chapman–Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore to what extent heavy-ion experimental data are sensitive to different choices for δf n , presently the main source of theoretical uncertainty in the particlization stage. Here, we validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and space–time distributions to the Cooper–Frye formula.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.

neoclassical transport↗

DOE OSTI2024

Primordial non-Gaussianities with weak lensing: information on non-linear scales in the Ulagam full-sky simulations

Abstract Primordial non-Gaussianities (PNGs) are signatures in the density field that encode particle physics processes from the inflationary epoch. Such signatures have been extensively studied using the Cosmic Microwave Background, through constraining their amplitudes,f X NL , with future improvements expected from large-scale structure surveys; specifically, the galaxy correlation functions. We show that weak lensing fields can be used to achieve competitive and complementary constraints. This is shown via theUlagamsuite of N-body simulations, a subset of which evolves primordial fields with four types of PNGs. We create full-sky lensing maps and estimate the Fisher information from three summary statistics measured on the maps: the moments, the cumulative distribution function, and the 3-point correlation function. We find that the year 10 sample from the Rubin Observatory Legacy Survey of Space and Time (LSST) can constrain PNGs toσ(f NL eq ) ≈ 110,σ(f NL or, lss ) ≈ 120,σ(f NL loc ) ≈ 40. For the former two, this is better than or comparable to expected galaxy clustering-based constraints from the Dark Energy Spectroscopic Instrument (DESI). The PNG information in lensing fields is on non-linear scales and at low redshifts (z≲ 1.25), with a clear origin in the evolution history of massive halos. The constraining power degrades by ∼60% under scale cuts of ≳ 20 Mpc, showing there is still significant information on scales mostly insensitive to small-scale systematic effects (e.g., baryons). We publicly release theUlagamsuite to enable more survey-focused analyses.

Astronomy & Astrophysics↗

NASA NTRS1981

A statistical analysis of the low-energy geosynchronous plasma environment. I - Electrons. II - Ions

Data on the geosynchronous plasma environment between approximately 30 eV and 80 keV are analyzed statistically. Nearly 50 days of 10 minute averages of the first four moments of the distribution function from low-energy plasma detectors on the ATS-5 and ATS-6 geosynchronous satellites were used. The data were studied in terms of occurrence frequency, local time variations, and response to geomagnetic activity. These techniques revealed marked differences in the ATS-5 and ATS-6 data bases. When translated into a 2-Maxwellian representation, it was found that (1) the ATS-6 data covered an energy range not covered by ATS-5 (between 1 and 50 eV) and (2) there was a definite change in the ion plasma between the ATS-5 and ATS-6 measurements. Simple expressions are derived to simulate the relationship between the four moments, and a model is presented, which takes into account the ATS-5 and ATS-6 plasma variations. Despite the differences in the ion data, the accuracy of the four-moment representation was found valid for characterizing the geosynchronous electron population.

Garrett, H. B.↗

NASA NTRS1995

The mosaic structure of plasma bulk flows in the Earth's magnetotail

Moments of plasma distributions observed in the magnetotail vary with different time scales. In this paper we attempt to explain the observed variability on intermediate timescales of approximately 10-20 min that result from the simultaneous energization and spatial structuring of solar wind plasma in the distant magnetotail. These processes stimulate the formation of a system of spatially disjointed. highly accelerated filaments (beamlets) in the tail. We use the results from large-scale kinetic modeling of magnetotail formation from a plasma mantle source to calculate moments of ion distribution functions throughout the tail. Statistical restrictions related to the limited number of particles in our system naturally reduce the spatial resolution of our results, but we show that our model is valid on intermediate spatial scales Delta(x) x Delta(z) equal to approximately 1 R(sub E) x 1000 km. For these spatial scales the resulting pattern, which resembles a mosaic, appears to be quite variable. The complexity of the pattern is related to the spatial interference between beamlets accelerated at various locations within the distant tail which mirror in the strong near-Earth magnetic field. Global motion of the magnetotail results in the displacement of spacecraft with respect to this mosaic pattern and can produce variations in all of the moments (especially the x-component of the bulk velocity) on intermediate timescales. The results obtained enable us to view the magnetotail plasma as consisting of two different populations: a tailward-Earthward system of highly accelerated beamlets interfering with each other, and an energized quasithermal population which gradually builds as the Earth is approached. In the near-Earth tail, these populations merge into a hot quasi-isotropic ion population typical of the near-Earth plasma sheet. The transformation of plasma sheet boundary layer (PSBL) beam energy into central plasma sheet (CPS) quasi-thermal energy occurs in the absence of collisions or noise. This paper also clarifies the relationship between the global scale where an MHD description might be appropriate and the lower intermediate scales where MHD fails and large-scale kinetic theory should be used.

Ashour-Abdalla, M.↗

DOE OSTI2025

A moment-conserving discontinuous Galerkin representation of the relativistic Maxwellian distribution

Kinetic simulations of relativistic gases and plasmas are critical for understanding diverse astrophysical and terrestrial systems, but the accurate construction of the relativistic Maxwellian, the Maxwell–Jüttner distribution, on a discrete simulation grid is challenging. Difficulties arise from the finite velocity bounds of the domain, which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here, we present a novel scheme for iteratively correcting the moments of the projected distribution applicable to all grid-based discretizations of the relativistic kinetic equation. In addition, we describe how to compute the needed nonlinear quantities, such as Lorentz boost factors, in a discontinuous Galerkin scheme through a combination of numerical quadrature and weak operations. The resulting method accurately captures the distribution function and ensures that the moments match the desired values to machine precision.

astrophysical plasmas↗

DOE OSTI2020

As a Matter of State: The Role of Thermodynamics in Magnetohydrodynamic Turbulence

Turbulence simulations play a key role in advancing the general understanding of the physical properties of turbulence and in interpreting astrophysical observations of turbulent plasmas. For the sake of simplicity, however, turbulence simulations are often conducted in the isothermal limit. Given that the majority of astrophysical systems are not governed by isothermal dynamics, we aim to quantify the impact of thermodynamics on the physics of turbulence, through varying adiabatic index, γ, combined with a range of optically thin cooling functions. Here, we present a suite of ideal magnetohydrodynamics simulations of thermally balanced stationary turbulence in the subsonic, super-Alfvénic, high ${\beta }_{{\rm{p}}}$ (ratio of thermal to magnetic pressure) regime, where turbulent dissipation is balanced by two idealized cooling functions (approximating linear cooling and free–free emission) and examine the impact of the equation of state by considering cases that correspond to isothermal, monatomic, and diatomic gases. We find a strong anticorrelation between thermal and magnetic pressure independent of thermodynamics, whereas the strong anticorrelation between density and magnetic field found in the isothermal case weakens with increasing γ. Similarly, the linear relation between variations in density and thermal pressure with sonic Mach number becomes steeper with increasing γ. This suggests that there exists a degeneracy in these relations with respect to thermodynamics and Mach number in this regime, which is dominated by slow magnetosonic modes. These results have implications for attempts to infer (e.g.,) Mach numbers from (e.g.,) Faraday rotation measurements, without additional information regarding the thermodynamics of the plasma. However, our results suggest that this degeneracy can be broken by utilizing higher-order moments of observable distribution functions.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1990

Solar wind proton velocity distributions - Comparison of the bi-Maxwellian based 16-moment expansion with observations

The purpose of this paper is to study the possible types of velocity distributions that can be obtained from the bi-Maxwellian based 16-moment expansion of the distribution function, assuming macroscopic parameter values characteristic of the range of solar wind conditions. While previous studies also took heat flow into account, the theoretical expansions for f and the definitions of the physical moments adopted in these studies were different from those used in this paper. The choice of the 16-moment expansion and corresponding moment definitions was motivated by the fact that this is the correct generalization of the widely-used Maxwellian-based 13-moment expansion to the case where the zeroth-order distribution is a bi-Maxwellian. It is found that most of the features characteristic of solar wind proton distributions can be reproduced with the 16-moment distribution, including the appearance of secondary peaks. It is also shown how each of the physically significant velocity moments affects the shape of the distribution function.

Demars, H. G.↗

DOE OSTI2024

Far-from-equilibrium slow modes and momentum anisotropy in an expanding plasma

The momentum distribution of particle production in heavy-ion collisions encodes information about thermalization processes in the early-stage quark-gluon plasma. We use kinetic theory to study the far-from-equilibrium evolution of an expanding plasma with an anisotropic momentum-space distribution. We identify slow and fast degrees of freedom in the far-from-equilibrium plasma from the evolution of moments of this distribution. At late times, the slow modes correspond to hydrodynamic degrees of freedom and are naturally gapped from the fast modes by the inverse of the relaxation time, τ R − 1 . At early times, however, there are an infinite number of slow modes with a gap inversely proportional to time, τ − 1 . From the evolution of the slow modes we generalize the paradigm of the far-from-equilibrium attractor to vector and tensor components of the energy-momentum tensor, and even to higher moments of the distribution function that are not part of the hydrodynamic evolution. We predict that initial-state momentum anisotropy decays slowly in the far-from-equilibrium phase and may persist until the relaxation time. Published by the American Physical Society 2024

Brewer, Jasmine (ORCID:0000000230840663)↗

DOE OSTI2024

Moment extraction using an unfolding protocol without binning

Deconvolving (“unfolding”) detector distortions is a critical step in the comparison of cross-section measurements with theoretical predictions in particle and nuclear physics. However, most existing approaches require histogram binning while many theoretical predictions are at the level of statistical moments. We develop a new approach to directly unfold distribution moments as a function of another observable without having to first discretize the data. Our moment unfolding technique uses machine learning and is inspired by Boltzmann weight factors and generative adversarial networks (GANs). We demonstrate the performance of this approach using jet substructure measurements in collider physics. With this illustrative example, we find that our moment unfolding protocol is more precise than bin-based approaches and is as or more precise than completely unbinned methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Far-from-equilibrium slow modes and momentum anisotropy in expanding plasma

The momentum distribution of particle production in heavy-ion collisions encodes information about thermalization processes in the early-stage quark-gluon plasma. We use kinetic theory to study the far-from-equilibrium evolution of an expanding plasma with an anisotropic momentumspace distribution. We identify slow and fast degrees of freedom in the far-from-equilibrium plasma from the evolution of moments of this distribution. At late times, the slow modes correspond to hydrodynamic degrees of freedom and are naturally gapped from the fast modes by the inverse of the relaxation time, $τ$$^{–1}_{R}$. At early times, however, there are an infinite number of slow modes with a gap inversely proportional to time, τ –1 . From the evolution of the slow modes we generalize the paradigm of the far-from-equilibrium attractor to vector and tensor components of the energy momentum tensor, and even to higher moments of the distribution function that are not part of the hydrodynamic evolution. We predict that initial-state momentum anisotropy decays slowly in the far-from-equilibrium phase and may persist until the relaxation time.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Global weak solutions for a nonlocal multispecies Fokker–Planck–Landau system

The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker–Planck–Landau system for plasmas in the three-dimensional whole space is shown. The Fokker–Planck–Landau system is a simplification of the Landau equations assuming a linearized, velocity-independent, and isotropic kernel. The resulting equations depend nonlocally and nonlinearly on the moments of the distribution functions via the multispecies local Maxwellians. Furthermore, the existence proof is based on a three-level approximation scheme, energy and entropy estimates, as well as compactness results, and it holds for both soft and hard potentials.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

On the probability of cycle-slipping in first-order phase-locked loops.

The first-passage time boundary value problem for first-order phase-locked loops (PLL) is analyzed, and spectral representations are developed for the probability density function (pdf), the distribution function, and the moments of the first time to passage (or cycle-slip). For the sinusoidal PLL, an asymptotic formula, that is surprisingly accurate even at low loop SNR's and large frequency offsets, is obtained for the pdf of the time to cycle-slip, in terms of the mean time to slip.

La Frieda, J. R.↗

NASA NTRS1975

Distribution and moments of radial error

An investigation of the moments and probability distribution of the resultant of two normally distributed random variables is presented. This is the so-called generalized Rayleigh distribution which has many applications in the study of wind shear, random noise, and radar. The most general formula was derived, and two special cases were considered for which tables of the moments and probability distribution functions are included as an appendix. One of the special cases was generalized to n-dimensions.

White, R. G.↗

NASA NTRS1982

Plasma and magnetic field characteristics of magnetic flux transfer events

Plasma and magnetic field data from ISEE 1 and 2 are examined for 5 passes of the magnetopause region at 20 and 40 deg northern latitudes, and are presented in terms of moments of the distribution function, calculated from two-dimensional or three-dimensional data. Flux transfer events are characterized by a mixture of magnetosheath and magnetospheric particles, which supports the hypothesis that flux transfer events represent encounters of reconnected flux tubes. An excess pressure appears to be balanced by the tension of the ambient magnetic field lines as they are draped around the reconnected flux tube, and the different observed magnetic field signatures are consistent with expectations for encounters of the flux tubes at different relative locations. It is suggested that increased flow speeds are caused by continued reconnection at the low-latitude boundaries of the flux tubes.

Paschmann, G.↗