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Results for “PHASE SPACE”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Single-Shot Reconstruction of Electron Beam Longitudinal Phase Space in a Laser Wakefield Accelerator

We report on a single-shot longitudinal phase-space reconstruction diagnostic for electron beams in a laser wakefield accelerator via the experimental observation of distinct periodic modulations in the angularly resolved spectra. Such modulated angular spectra arise as a result of the direct interaction between the ultrarelativistic electron beam and the laser driver in the presence of the wakefield. A constrained theoretical model for the coupled oscillator, assisted by a genetic algorithm, can recreate the experimental electron spectra and, thus, fully reconstructs the longitudinal phase-space distribution of the electron beam with a temporal resolution of approximately 1.3 fs. In particular, it reveals the slice energy spread of the electron beam, which is important to measure for applications such as x-ray free electron lasers. In our experiment, the root-mean-square energy spread retrieved is bounded at 9.9 MeV, corresponding to a 0.9%–3.0% relative spread, despite the overall GeV energy beam having approximately 100% relative energy spread.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Non-resonant Raman optical activity from phase-space electronic structure theory

In order to model experimental non-resonant Raman optical activity, chemists must compute a host of second-order response tensors (e.g., the electric-dipole–magnetic-dipole polarizability) and their nuclear derivatives along a set of vibrational modes. While these response functions are almost always computed within a Born–Oppenheimer (BO) framework, here we provide a natural interpretation of the electric-dipole–magnetic-dipole polarizability within phase space electronic structure theory, a beyond-BO model whereby the electronic structure depends on nuclear momentum (P) in addition to nuclear position (R). By coupling to nuclear momentum, phase space electronic structure theory is able to capture the asymmetric response of the electronic properties to an external field, in so far as for a vibrating (non-stationary) molecule, $\frac{∂μ}{∂B}$≠$\frac{∂m}{∂F}$, where μ and m are the electrical linear and magnetic dipoles, and F and B are electric and magnetic fields. As an example, for a prototypical methyloxirane molecule, we show that phase space electronic structure theory is able to deliver a reasonably good match with experimental results in a manner that is formally invariant to gauge origin G 0 —provided that one uses a complete basis or, alternatively, gauge invariant atomic orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Scattering theory in noncanonical phase space: A Drift-Kinetic collision operator for weakly collisional plasmas

After developing a scattering theory for grazing collisions in general noncanonical phase spaces, we introduce a guiding center collision operator in five-dimensional phase space designed for plasma regimes characterized by long wavelengths (relative to the Larmor radius), low frequencies (relative to the cyclotron frequency), and weak collisionality (where repeated Coulomb collisions induce cumulatively small changes in particle magnetic moment). The collision operator is fully determined by the noncanonical Hamiltonian structure of guiding center dynamics and exhibits a metriplectic structure, ensuring the conservation of particle number, momentum, energy, and interior Casimir invariants. It also satisfies an H-theorem, allowing for deviations from an equilibrium Maxwellian distribution due to the nontrivial kernel of the noncanonical guiding center Poisson tensor, spanned by the magnetic moment. We propose that this collision operator and its underlying mathematical structure may offer valuable insight into the study of turbulence, transport, and self-organizing phenomena in both laboratory and astrophysical plasmas.

Hamiltonian mechanics↗
DOE OSTI2025

Minimizing phase-space energies

A primary technical challenge for harnessing fusion energy is to control and extract energy from a nonthermal distribution of charged particles. The fact that phase space evolves by symplectomorphisms fundamentally limits how a distribution may be manipulated. While the constraint of phase-space volume preservation is well understood, other constraints remain to be fully appreciated. To better understand these constraints, we study the problem of extracting energy from a distribution of particles using area-preserving and symplectic linear maps. When a quadratic potential is imposed, we find that the maximal extractable energy can be computed as trace minimization problems. We solve these problems and show that the extractable energy under linear symplectomorphisms may be much smaller than the extractable energy under special linear maps. As a result, the method introduced in the present study enables an energy-based proof of the linear Gromov nonsqueezing theorem.

First-principles calculations in plasma physics↗
DOE OSTI2025

Study of Particle Loss in Synchrotron Phase Space Injection for ESR Using Weak-Strong Beam-Beam Simulation with Nonlinear Lattice

In this report, we use tracking simulations to investigate synchrotron phase space injection for electron accumulation in the electron storage ring of the Electron Ion Collider. Our simulation model accounts for both beam-beam interactions and lattice nonlinearities. Specifically, we examine how particle loss is influenced by various parameters. Additionally, we conduct a theoretical analysis and derive an analytical formula for the rapid evaluation of particle loss. Our results demon strate the feasibility of synchrotron phase-space injection for the electron storage ring and provide insights to guide parameter selection for the design of the injection line.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Photon phase-space dynamics in a plasma wakefield accelerator

Frequency up-shifting of laser light in a beam-driven plasma wakefield has the potential to provide high-intensity sources of short wavelength radiation. Simulations have demonstrated that a laser pulse can undergo large frequency shifts, limited only by the drive beam energy, when the plasma density is tailored to match the accelerating phase of the wake to the group velocity of the pulse. Here, we study the dynamical evolution of photons in the 1D1P phase-space vicinity of the plasma wake-phase matching condition. Numerical calculations using a photon kinetic model are validated by direct comparison with 1D and quasi-3D particle-in-cell simulations. These calculations form the basis of a linear theory of the photon dynamics which reveals several important results, including scalings for the properties of the witness pulse and a self-similar solution for the photon phase-space dynamics. One prediction of the analytic theory is that the pulse can be compressed indefinitely, though the amount of compression would ultimately be limited by practical constraints. These results suggest that photon acceleration can provide a novel source of sub-femtosecond, short wavelength radiation.

XUV generation↗
DOE OSTI2024

Venturing into Unexplored Phase Space: Synthesis, Structure, and Properties of MgCo 3 B 2 Featuring a Rumpled Kagomé Network

MgCo 3 B 2 , a novel ternary boride in a previously unexplored phase space, was synthesized using the hydride route. In situ powder X-ray diffraction and DFT calculations aided in the discovery of this compound, whose structure was then determined by single-crystal X-ray diffraction. Like the closely related CeCo 3 B 2 , MgCo 3 B 2 crystallizes in centrosymmetric space group P6/mmm (a = 4.883(2) Å, c = 2.926(2) Å at 210 K, Z = 1). Unlike CeCo 3 B 2 , however, it adopts a disordered structure that features a rumpled Kagomé network of Co atoms, and Mg atoms fill the channels of a Co–B framework. Although the structural disorder leads to motifs that are similar to those observed in MgNi 3 B 2 and other related ternary borides, no evidence of an ordered superstructure was found by single-crystal X-ray diffraction or high-resolution powder X-ray diffraction. In the case of CeCo 3 B 2 , boron atoms occupy the center of regular Co 6 trigonal prisms; in MgCo 3 B 2 , boron atoms are shifted from the center of the prism to form B–B dimers with roughly the same length as those found in MgNi 3 B 2 . Magnetic susceptibility data exhibit an unusual temperature dependence that cannot be convincingly modeled by the modified Curie–Weiss equation, consistent with DFT calculations predicting a nonmagnetic ground state. Intrinsic susceptibility at 300 K is 1.42 × 10 –3 emu/mol Oe, which is comparable to that of paramagnetic YCo 3 B 2 and CeCo 3 B 2 with a similar structure and composition. Here, this study showcases the efficacy of combining several methodologies to discover new solids in unexplored phase spaces. This approach includes in situ PXRD data to monitor reactions of precursors upon heating, a diffusion-enhanced synthesis method, and DFT assessment of compound stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space

We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as μ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for μ = 0, while for very large values of μ, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as μ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.

AdS-CFT correspondence↗
DOE OSTI2024

Phase-space methods for neutrino oscillations: Extension to multibeams

The phase-space approach (PSA), which was originally introduced in Lacroix [] to describe neutrino flavor oscillations for interacting neutrinos emitted from stellar objects is extended to describe arbitrary numbers of neutrino beams. The PSA is based on mapping the quantum fluctuations into a statistical treatment by sampling initial conditions followed by independent mean-field evolution. A new method is proposed to perform this sampling that allows treating an arbitrary number of neutrinos in each neutrino beams. We validate the technique successfully and confirm its predictive power on several examples where a reference exact calculation is possible. We show that it can describe many-body effects, such as entanglement and dissipation induced by the interaction between neutrinos. Due to the complexity of the problem, exact solutions can only be calculated for rather limited cases, with a limited number of beams and/or neutrinos in each beam. The PSA approach considerably reduces the numerical cost and provides an efficient technique to accurately simulate arbitrary numbers of beams. Examples of PSA results are given here, including up to 200 beams with time-independent or time-dependent Hamiltonians. We anticipate that this approach will be useful to bridge exact microscopic techniques with more traditional transport theories used in neutrino oscillations. It will also provide important reference calculations for future quantum computer applications where other techniques are not applicable to classical computers. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Symmetry breaking as predicted by a phase space Hamiltonian with a spin Coriolis potential

Here, we perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ( 3 CH 2 , 2 CH$^{•}_{3}$, 3 O 2 ) going beyond the Born–Oppenheimer approximation and accounting for nuclear motion. According to a phase space approach that parameterizes electronic states (|Φ⟩) and electronic energies (E) by nuclear position and momentum [i.e., |Φ(R, P)⟩ and E(R, P)], we find that the presence of degenerate spin degrees of freedom leads to broken symmetry ground states. More precisely, rather than a single degenerate minimum at (R, P) = (R min , 0), the ground state energy has two minima at (R,P)=(R' min ,±P min ) (where R' min is close to R min ), dramatically contradicting the notion that the total energy of the system can be written in separable form as E = $\frac{P^2}{2M}$ + V el . Although we find that the broken symmetry solutions have small barriers between them for the small molecules, we hypothesize that the barriers should be macroscopically large for metallic solids, thus offering up a new phase-space potential energy surface for simulating the Einstein–de Haas effect.

Berry connection↗
DOE OSTI2026

Generative models on phase space

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be concentrated on a submanifold of the data embedding space. For high-energy physics data, consisting of collections of relativistic energy-momentum 4-vectors, this submanifold can enforce extremely strong physically-motivated priors, such as energy and momentum conservation. If these constraints are learned only approximately, rather than exactly, this can inhibit the interpretability and reliability of such generative models. To remedy this deficiency, we introduce generative models which are, by construction, confined at every step of their sampling trajectory to the manifold of massless N-particle Lorentz-invariant phase space in the center-of-momentum frame. In the case of diffusion models, the "pure noise" forward process endpoint corresponds to the uniform distribution on phase space, which provides a clear starting point from which to identify how correlations among the particles emerge during the reverse (de-noising) process. We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures, paving the way for future interpretability studies using generative models trained on simulated jet data.

Bogorad, Zachary [Fermilab]↗
DOE OSTI2025

Krylov complexity in mixed phase space

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.

chaos & nonlinear dynamics↗
DOE OSTI2025

Scaling relations in the phase-space structure of dark matter haloes

We present new scaling relations for the isotropic phase-space distribution functions (DFs) and energy distributions of simulated dark matter haloes. These relations are inspired by those for the singular isothermal sphere with density profile $\rho (r)\propto r^{-2}$, for which the DF satisfies $f(E) \propto r_{\mathrm{max}}^{-2}(E)$ and the energy distribution satisfies $\mathrm{ d}M/\mathrm{ d}E \propto r_{\mathrm{max}}(E)$, with $r_{\mathrm{max}}(E)$ being the radius where the gravitational potential equals energy $E$. For the simulated haloes, we find $f(E)\propto r_{\mathrm{max}}^{-2.08}(E)$ and $\mathrm{ d}M/\mathrm{ d}E \propto r_{\mathrm{max}}(E)$ across broad energy ranges. In addition, the proportionality coefficients depend on the gravitational constant and the parameters of the best-fitting Navarro–Frenk–White density profile. These scaling relations are satisfied by haloes over a wide mass range and provide an efficient method to approximate their DFs and energy distributions. Understanding the origin of these relations may shed more light on halo formation.

galaxies: haloes↗
DOE OSTI2026

Longitudinal Twiss parameters for tilted phase space ellipses

The longitudinal emittance ϵ s is usually defined under the implicit assumption that the longitudinal phase space distribution is erect, an assumption that is significantly incorrect near transition. This note generalizes the definition of e, to include tilted distributions, by introducing longitudinal Twiss functions β a , α s and γ s that are analogous to transverse Twiss functions. The evolution of these longitudinal parameters through RHIC transition is presented, for a typical set of simulation data.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Four-dimensional phase space tomography from one-dimensional measurements of a hadron beam

In this paper, we use one-dimensional measurements to infer the four-dimensional phase space density of an accumulated proton beam in the Spallation Neutron Source (SNS) accelerator. The reconstruction was performed by maximizing the distribution’s entropy subject to the measurement constraints and thus represents the most conservative inference from the data. The reconstructed distribution reproduces the measured profiles down to the noise level, and simulations indicate that the problem is reasonably well constrained. Similar measurements could serve as benchmarks for beam dynamics simulations in the SNS or hadron accelerators.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗
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)↗