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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

Detailed characterization of a five-dimensional phase space distribution

We image the five-dimensional phase space distribution of a hadron beam in unprecedented detail. The resolution and dynamic range of the measurement are sufficient to resolve sharp, high-dimensional features in low-density regions of phase space. We develop several visualization techniques, including non-planar slicing, to facilitate the identification and analysis of such features. We use these techniques to examine the transverse dependence of longitudinal hollowing and the longitudinal dependence of transverse hollowing in the distribution. Our results strengthen the claim that low-dimensional projections do not adequately characterize high-dimensional phase space distributions.

Hoover, Austin↗
NASA NTRS1994

Simulations of phase space distributions of storm time proton ring current

We use results of guiding-center simulations of ion transport to map phase space densities of the stormtime proton ring current. We model a storm as a sequence of substorm-associated enhancements in the convection electric field. Our pre-storm phase space distribution is an analytical solution to a steady-state transport model in which quiet-time radial diffusion balances charge exchange. This pre-storm phase space spectra at L approximately 2 to 4 reproduce many of the features found in observed quiet-time spectra. Using results from simulations of ion transport during model storms having main phases of 3, 6, and 12 hr, we map phase space distributions from the pre-storm distribution in accordance with Liouville's theorem. We find stormtime enhancements in the phase space densities at energies E approximately 30-160 keV for L approximately 2.5 to 4. These enhancements agree well with the observed stormtime ring current. For storms with shorter main phases (approximately 3 hr), the enhancements are caused mainly by the trapping of ions injected from open night side trajectories, and diffusive transport of higher-energy (greater than or approximately 160 keV) ions contributes little to the stormtime ring current. However, the stormtime ring current is augmented also by the diffusive transport of higher-energy ions (E greater than or approximately 160 keV) durinng stroms having longer main phases (greater than or approximately 6 hr). In order to account for the increase in Dst associated with the formation of the stormtime ring current, we estimate the enhancement in particle-energy content that results from stormtime ion transport in the equatorial magnetosphere. We find that transport alone cannot account for the entire increase in absolute value of Dst typical of a major storm. However, we can account for the entire increase in absolute value of Dst by realistically increasing the stormtime outer boundary value of the phase space density relative to the quiet-time value. We compute the magnetic field produced by the ring current itself and find that radial profiles of the magnetic field depression resemble those obtained from observational data.

Chen, Margaret W.↗
NASA NTRS1993

Positive phase space distributions and uncertainty relations

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Kruger, Jan↗
NASA NTRS2006

Pickup Ion Phase Space Distributions at Titan in a Three Dimensional Exosphere

The composition and structure of neutral exospheres imbedded in moving plasmas can be determined by measurements of the velocity distributions of their pickup ion progeny. In turn, the velocity distributions are dependent on the spatial structure of the neutral source gases. Since Titan's neutral exosphere extends into the Saturn's magnetosphere (or solar wind) and well above its ionopause, it serves as a good place to analyze such characteristics. They are analyzed using pickup ion measurements made by the Cassini Plasma Spectrometer (CAPS) at Titan [e.g., Hartle et al., 2006] and an ion kinetic model. An early version of the model [Hartle and Sittler, 2007] is an expression describing the phase space density of pickup ions, which is derived from the Vlasov equation with an ion source that explicitly accounts for the velocity and spatial variation of the exosphere source gases. The current version used here includes exosphere source gases in three dimensions. A fundamental parameter of the phase space densities is the ratio of the gyroradius to the neutral scale height alpha, = r(sub g)/H. Titan's exosphere structure yields pickup ions whose phase space distributions are beam-like when alpha >> 1 and fluid-like when alpha << 1. Downstream from the source peak, the light pickup ions, with alpha << 1, are easily observed because their phase space densities are almost uniform over the orbit phases. On the other hand, the phase space distributions of the heavier ions, with alpha >> 1, peak over narrow velocity and spatial ranges. This beam-like nature makes it considerably more difficult to observe heavy ions because their downstream positions and viewing directions are narrowly constrained. Examples of these extremes will be discussed.

Hartle, Richard↗
NASA NTRS1991

Phase space distribution of halo particles and detection of WIMPS

We calculate the velocity distribution of halo particles using realistic models for the density profiles of the Galactic disk, spheroid, and halo components. We get the resulting velocity distribution, which is different from the Maxwellian distribution of isothermal halo. We investigate the consequences concerning the time averaged count rate and the amplitude of the annual modulation in WIMPS detection experiments. Compared to the previous estimate based on the Maxwellian distribution, the time averaged count rate is up to 40 percent larger. On the other hand, the amplitude of the annual modulation is up to a factor of two larger.

Ryu, Dongsu↗
DOE OSTI2023

Revealing the dynamics of ultrarelativistic non-equilibrium many-electron systems with phase space tomography

The description of physical processes with many-particle systems is a key approach to the modeling of numerous physical systems. For example in storage rings, where ultrarelativistic particles are agglomerated in dense bunches, the modeling and measurement of their phase-space distribution is of paramount importance: at any time the phase-space distribution not only determines the complete space-time evolution but also provides fundamental performance characteristics for storage ring operation. Here, we demonstrate a non-destructive tomographic imaging technique for the 2D longitudinal phase-space distribution of ultrarelativistic electron bunches. For this purpose, we utilize a unique setup, which streams turn-by-turn near-field measurements of bunch profiles at MHz repetition rates. To demonstrate the feasibility of our method, we induce a non-equilibrium state and show that the phase-space distribution microstructuring as well as the phase-space distribution dynamics can be observed in great detail. Our approach offers a pathway to control ultrashort bunches and supports, as one example, the development of compact accelerators with low energy footprints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2011

Pickup Ion Distributions from Three Dimensional Neutral Exospheres

Pickup ions formed from ionized neutral exospheres in flowing plasmas have phase space distributions that reflect their source's spatial distributions. Phase space distributions of the ions are derived from the Vlasov equation with a delta function source using three.dimensional neutral exospheres. The ExB drift produced by plasma motion picks up the ions while the effects of magnetic field draping, mass loading, wave particle scattering, and Coulomb collisions near a planetary body are ignored. Previously, one.dimensional exospheres were treated, resulting in closed form pickup ion distributions that explicitly depend on the ratio rg/H, where rg is the ion gyroradius and H is the neutral scale height at the exobase. In general, the pickup ion distributions, based on three.dimensional neutral exospheres, cannot be written in closed form, but can be computed numerically. They continue to reflect their source's spatial distributions in an implicit way. These ion distributions and their moments are applied to several bodies, including He(+) and Na(+) at the Moon, H(+2) and CH(+4) at Titan, and H+ at Venus. The best places to use these distributions are upstream of the Moon's surface, the ionopause of Titan, and the bow shock of Venus.

Hartle, R. E.↗
DOE OSTI2026

Longitudinal Phase Space Tomography for the Booster Synchrotron

Efforts in the study of the longitudinal behavior of charged particles in the Fermilab Booster can be catalyzed with an image of the two-dimensional phase space distribution. In the past, tomography had been employed in the reconstruction of the phase space in accelerators such as the Recycler at Fermilab and the Proton Synchrotron Booster at CERN. However, such a capability had yet to realize for the Fermilab Booster synchrotron. In this work, the first successful tomographic phase space reconstruction of a low-energy Booster bunch is presented along with validation metrics. A numerical turn-by-turn model of the longitudinal particle dynamics in the Booster has been implemented, which utilizes a fast, map-based particle transport algorithm. Using a sinogram generated from the Wall Current Monitor signal, the iterative reconstruction algorithm recovers a discretized image of the original phase space distribution at variable resolution. The reconstruction result shows low root-mean-square error and a rapid convergence toward the solution, providing strong evidence of accuracy. Future and ongoing work includes modeling high-energy bunches above transition and using tomography to infer certain machine parameters such as synchronous phase, peak gap voltage, and synchronous energy in addition to the phase space distribution.

Ebeid, Safi [Unlisted; Fermilab]↗
DOE OSTI2026

Longitudinal Phase Space Tomography for the Booster Synchrotron

Efforts in the study of the longitudinal behavior of charged particles in the Fermilab Booster can be catalyzed with an image of the two-dimensional phase space distribution. In the past, tomography has been extensively employed in the reconstruction of the phase space in accelerators such as the Recycler at Fermilab and the Proton Synchrotron Booster at CERN. However, such a capability had yet to realize for the Fermilab Booster synchrotron. In this work, the first successful tomographic phase space reconstruction of a low-energy Booster bunch is presented along with validation metrics. A numerical turn-by-turn model of the longitudinal particle dynamics in the Booster has been implemented, which utilizes a fast, map-based particle transport algorithm. Using a sinogram generated from the Wall Current Monitor, the iterative reconstruction algorithm recovers a discretized image of the original phase space distribution at variable resolution. The reconstruction result shows low root-mean-square error and a rapid convergence toward the solution, providing strong evidence of accuracy. Future and ongoing work includes modeling high-energy bunches above transition and using tomography to infer certain machine parameters such as synchronous phase, peak gap voltage, and synchronous energy in addition to the phase space distribution.

Ebeid, Safi [Unlisted]↗
DOE OSTI2026

Longitudinal Phase Space Tomography for the Booster Synchrotron (Abstract Only)

Efforts in the study of the longitudinal behavior of charged particles in the Fermilab Booster can be catalyzed with an image of the two-dimensional phase space distribution. In the past, tomography has been extensively employed in the reconstruction of the phase space in accelerators such as the Recycler at Fermilab and the Proton Synchrotron Booster at CERN. However, such a capability had yet to realize for the Fermilab Booster synchrotron. In this work, the first successful tomographic phase space reconstruction of a low-energy Booster bunch is presented along with validation metrics. A numerical turn-by-turn model of the longitudinal particle dynamics in the Booster has been implemented, which utilizes a fast, map-based particle transport algorithm. Using a sinogram generated from the Wall Current Monitor, the iterative reconstruction algorithm recovers a discretized image of the original phase space distribution at variable resolution. The reconstruction result shows low root-mean-square error and a rapid convergence toward the solution, providing strong evidence of accuracy. Future and ongoing work includes modeling high-energy bunches above transition and using tomography to infer certain machine parameters such as synchronous phase, peak gap voltage, and synchronous energy in addition to the phase space distribution.

Ebeid, Safi [Unlisted, US]↗
DOE OSTI2025

Parton distribution functions from scalar light-front parton gas model

Here, we propose an application of a microcanonical ensemble with light-front kinematics to model the phase-space distribution of relativistic constituents of a bound state. These constituents denoted by partons are treated as classical spin-zero particles confined inside the bound state with inter-parton collisions as their only interaction. The microcanonical molecular dynamics ensemble is applied to obtain the phase-space distribution of such a thermodynamic system. We sample this phase-space distribution using Monte Carlo algorithms to obtain the parton distribution functions (PDFs) in scenarios with 3, 4, and 5 identical partons. In addition PDFs when a selected number of massless partons are mixed with 3 massive partons are also presented.

Microcanonical ensemble↗
NASA NTRS1991

Ion distributions at the dayside magnetopause

Ion phase space distribution, from the AMPTE UKS ion instrument, for a crossing of the dayside magnetopause on October 2, 1984, during typical southward IMF conditions are presented. D-shaped field-aligned phase space distributions of magnetosheath plasma earthward of and hot magnetospheric ions sunward of the magnetopause current layer are observed. The existence of such D-shaped magnetosheath plasma distributions has been predicted as a signature of reconnection. In addition, the observed ion distributions are in stress balance across the magnetopause, and the de Hoffman-Teller frame velocity obtained from the stress balance calculation is in agreement with the observed distribution function cutoff speed. These new observations thus provide further evidence that, at least for southward IMF conditions, reconnection is an important mechanism by which solar wind plasma penetrates into the magnetosphere.

Smith, M. F.↗
DOE OSTI2023

Phase Space Reconstruction from Accelerator Beam Measurements Using Neural Networks and Differentiable Simulations

Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying assumptions or require specialized diagnostics to infer high-dimensional (> $2D$) beam properties. In this Letter, we introduce a general-purpose algorithm that combines neural networks with differentiable particle tracking to efficiently reconstruct high-dimensional phase space distributions without using specialized beam diagnostics or beam manipulations. Furthermore, we demonstrate that our algorithm accurately reconstructs detailed 4D phase space distributions with corresponding confidence intervals in both simulation and experiment using a single focusing quadrupole and diagnostic screen. This technique allows for the measurement of multiple correlated phase spaces simultaneously, which will enable simplified 6D phase space distribution reconstructions in the future.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Demonstration of a Novel Phase-Space Painting Method in a Coupled Lattice to Mitigate Space Charge in High-Intensity Hadron Beams

Multiturn charge-exchange injection is the primary method of creating high-intensity hadron beams in circular accelerators, and phase space painting during injection enables tailoring of the accumulated phase space distribution. A technique we call eigenpainting allows injection of particles into a single mode of a coupled ring, providing full four-dimensional control of the phase space distribution. Under ideal conditions, uniform eigenpainting generates a linear-force equilibrium distribution in the transverse plane, with zero volume in four-dimensional transverse phase space, even including space charge. Here, we have implemented eigenpainting for the first time in the spallation neutron source accumulator ring. Injecting 8.8 μ⁢C of an 800 MeV beam, we obtain a final ratio of intrinsic transverse emittances of ≈2.4. We analyze the effect of space charge on the final distribution through comparison of the reconstructed phase space to particle-in-cell simulations.

Evans, Nicholas J. [Oak Ridge National Laboratory ↗
NASA NTRS2017

Simulation Study of Landau Damping Near the Persisting to Arrested Transition

A one-dimensional electrostatic filtered Vlasov-Poisson simulation study is discussed. The transition from persisting to arrested Landau damping that is produced by increasing the strength of a sinusoidal perturbation on a background Vlasov-Poisson equilibrium is explored. Emphasis is placed on observed features of the electron phase-space distribution when the perturbation strength is near the transition value. A single ubiquitous waveform is found perturbing the space-averaged phase-space distribution at almost any time in all of the simulations; the sole exception is the saturation stage that can occur at the end of the arrested damping scenario. This waveform contains relatively strong, very narrow structures in velocity bracketing (plus or minus velocity (sub res)) - the velocities at which electrons must move to traverse the dominant field mode wavelength in one of its oscillation periods - and propagating with (plus or minus velocity (sub res)) respectively. Local streams of electrons are found in these structures crossing the resonant velocities from low speed to high speed during Landau damping and from high speed to low speed during Landau growth. At the arrest time, when the field strength is briefly constant, these streams vanish. It is conjectured that the expected transfer of energy between electrons and field during Landau growth or damping has been visualized for the first time. No evidence is found in the phase-space distribution to support recent well-established discoveries of a second-order phase transition in the electric field evolution. While trapping is known to play a role for larger perturbation strengths, it is shown that trapping plays no role at any time in any of the simulations near the transition perturbation strength.

plasma simulation↗
NASA NTRS2009

Lunar Neutral Exposphere Properties from Pickup Ion Analysis

Composition and structure of neutral constituents in the lunar exosphere can be determined through measurements of phase space distributions of pickup ions borne from the exosphere [1]. An essential point made in an early study [ 1 ] and inferred by recent pickup ion measurements [2, 3] is that much lower neutral exosphere densities can be derived from ion mass spectrometer measurements of pickup ions than can be determined by conventional neutral mass spectrometers or remote sensing instruments. One approach for deriving properties of neutral exospheric source gasses is to first compare observed ion spectra with pickup ion model phase space distributions. Neutral exosphere properties are then inferred by adjusting exosphere model parameters to obtain the best fit between the resulting model pickup ion distributions and the observed ion spectra. Adopting this path, we obtain ion distributions from a new general pickup ion model, an extension of a simpler analytic description obtained from the Vlasov equation with an ion source [4]. In turn, the ion source is formed from a three-dimensional exospheric density distribution, which can range from the classical Chamberlain type distribution to one with variable exobase temperatures and nonthermal constituents as well as those empirically derived. The initial stage of this approach uses the Moon's known neutral He and Na exospheres to deriv e He+ and Na+ pickup ion exospheres, including their phase space distributions, densities and fluxes. The neutral exospheres used are those based on existing models and remote sensing studies. As mentioned, future ion measurements can be used to constrain the pickup ion model and subsequently improve the neutral exosphere descriptions. The pickup ion model is also used to estimate the exosphere sources of recently observed pickup ions on KAGUYA [3]. Future missions carrying ion spectrometers (e.g., ARTEMIS) will be able to study the lunar neutral exosphere with great sensitivity, yielding the necessary ion velocity spectra needed to further analysis of parent neutral exosphere properties.

Hartle, R. E.↗
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)↗