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DOE OSTI2018

Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals

Monte Carlo phase space integration (MCPSI) is used to compute full dimensional and fully anharmonic, but classical, rovibrational partition functions for 22 small- and medium-sized molecules and radicals. Several of the species considered here feature multiple minima and low-frequency nonlocal motions, and efficiently sampling these systems is facilitated using curvilinear (stretch, bend, and torsion) coordinates. The curvilinear coordinate MCPSI method is demonstrated to be applicable to the treatment of fluxional species with complex rovibrational structures and as many as 21 fully coupled rovibrational degrees of freedom. Trends in the computed anharmonicity corrections are discussed. For many systems, rovibrational anharmonicities at elevated temperatures are shown to vary consistently with the number of degrees of freedom and with temperature once rovibrational coupling and torsional anharmonicity are accounted for. In conclusion, larger corrections are found for systems with complex vibrational structures, such as systems with multiple large-amplitude modes and/or multiple minima.

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

High-dimensional maximum-entropy phase space tomography

Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the reconstruction, but it is typically infeasible in high-dimensional spaces. In this paper, I review two recent approaches to high-dimensional entropy maximization. The first approach utilizes differentiable simulations and a class of generative models known as normalizing flows, whereas the second approach employs the method of Lagrange multipliers and Markov Chain Monte Carlo (MCMC) sampling. My aim is to provide a short explanation of each method using a common notation. I conclude by mentioning several unsolved problems in phase space tomography.

Hoover, Austin [ORNL] (ORCID:0000000153136962)↗
DOE OSTI2017

Grassmann phase space methods for fermions. II. Field theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space H{sub Γ}, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo–Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Phase space analysis for dynamics of three vortices of pure electron plasma trapped with Penning trap

A trilinear phase space analysis is applied for dynamics of three electron clumps confined with a Penning-Malmberg trap. We show that the Aref’s concept of phase space describe the observed features of the dynamics of three point vortices qualitatively. In vacuum, phase point P moves to physical region boundary in phase space, i.e. triangular configuration cannot be kept. With the addition of a low level background vorticity distribution (BGVD), the excursion of the clumps is reduced and the distance between P and stable point does not extend in the phase space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Driven electrostatic phase space vortices in a 1D weakly dissipative Vlasov–Poisson system

In this paper, the effect of collisions on driven electrostatic phase space vortices is analyzed by means of Eulerian simulation for two different collision models. It was demonstrated recently that in the absence of collisions, at late times, steady state phase space vortices manifest to form a plateau in the resonant region of the particle velocity distribution function, due to trapping of particles supporting multiextrema giant phase space vortices (PSVs). In the presence of collisions, over long time, this multiextrema plateau are found to smooth out, since collisions drive the velocity distribution toward Maxwellian, irrespective of how weak the collisions are as long as they are non-zero. In these conditions, kinetic processes and collisionality are found to be in competition, and the evolution of the plasma is found, therefore, to be a result of nontrivial combination of these two effects. An attempt has been made by means of numerical simulations to study the effect of weak collisionality on the electrostatic driven phase space vortices with two types of collision operators: (1) Bhatnagar–Gross–Krook (Krook) collision operator, where the colliding particles can be treated as isolated pairs and, (2) Fokker–Planck (FP) type collision operator (Zakharov–Karpman) in one dimension, where many weak collisions lead to particle diffusion in velocity space. It is shown that depending on the collision model used, the nature of smoothing in velocity space of giant PSVs results in qualitatively very different phase space structures. However, irrespective of the collision model used, excess density fractions over 10% are retained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 ↗
DOE OSTI2022

Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysis

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. In this work, we defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an invariant subspace based on the spectral properties of the Koopman operator. When the system evolution is known locally in several invariant subspaces in the state space of a dynamical system, a phase space stitching result is derived that yields the global Koopman operator. Additionally, in the case of equivariant systems, a phase space stitching result is developed to identify the global Koopman operator using the symmetry properties between the invariant subspaces of the dynamical system and time-series data from any one of the invariant subspaces. Finally, these results are extended to topologically conjugate dynamical systems; in particular, the relation between the Koopman tuple of topologically conjugate systems is established. The proposed results are demonstrated on several second-order nonlinear dynamical systems including a bistable toggle switch. Our method elucidates a strategy for designing discovery experiments: experiment execution can be done in many steps, and models from different invariant subspaces can be combined to approximate the global Koopman operator.

42 ENGINEERING↗
DOE OSTI2018

A new method for analyzing and visualizing plasma simulations using a phase-space tessellation

We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ~1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due to the deformable nature of the SIC volume elements. Here, by calculating momentum distributions, we show how SIC can capture low density tails in the spectrum using far fewer particles than are necessary for standard particle deposits. We calculate the charge density on spatial grids of increasing resolution to demonstrate the ability of SIC to reveal fine-scale details that are not accessible with standard particle deposits. Finally, we show how SIC can be extended to 3D and give an example of its use to calculate the charge density from 3D PIC simulations of the Weibel instability. These results motivate the future implementation of SIC directly in the simulation force calculation for a novel low-noise electromagnetic plasma simulation method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Validation of Varian TrueBeam electron phase–spaces for Monte Carlo simulation of MLC-shaped fields

Purpose: This work evaluates Varian’s electron phase–space sources for Monte Carlo simulation of the TrueBeam for modulated electron radiation therapy (MERT) and combined, modulated photon and electron radiation therapy (MPERT) where fields are shaped by the photon multileaf collimator (MLC) and delivered at 70 cm SSD. Methods: Monte Carlo simulations performed with EGSnrc-based BEAMnrc/DOSXYZnrc and PENELOPE-based PRIMO are compared against diode measurements for 5 × 5, 10 × 10, and 20 × 20 cm{sup 2} MLC-shaped fields delivered with 6, 12, and 20 MeV electrons at 70 cm SSD (jaws set to 40 × 40 cm{sup 2}). Depth dose curves and profiles are examined. In addition, EGSnrc-based simulations of relative output as a function of MLC-field size and jaw-position are compared against ion chamber measurements for MLC-shaped fields between 3 × 3 and 25 × 25 cm{sup 2} and jaw positions that range from the MLC-field size to 40 × 40 cm{sup 2}. Results: Percent depth dose curves generated by BEAMnrc/DOSXYZnrc and PRIMO agree with measurement within 2%, 2 mm except for PRIMO’s 12 MeV, 20 × 20 cm{sup 2} field where 90% of dose points agree within 2%, 2 mm. Without the distance to agreement, differences between measurement and simulation are as large as 7.3%. Characterization of simulated dose parameters such as FWHM, penumbra width and depths of 90%, 80%, 50%, and 20% dose agree within 2 mm of measurement for all fields except for the FWHM of the 6 MeV, 20 × 20 cm{sup 2} field which falls within 2 mm distance to agreement. Differences between simulation and measurement exist in the profile shoulders and penumbra tails, in particular for 10 × 10 and 20 × 20 cm{sup 2} fields of 20 MeV electrons, where both sets of simulated data fall short of measurement by as much as 3.5%. BEAMnrc/DOSXYZnrc simulated outputs agree with measurement within 2.3% except for 6 MeV MLC-shaped fields. Discrepancies here are as great as 5.5%. Conclusions: TrueBeam electron phase–spaces available from Varian have been implemented in two distinct Monte Carlo simulation packages to produce dose distributions and outputs that largely reflect measurement. Differences exist in the profile shoulders and penumbra tails for the 20 MeV phase–space off-axis and in the outputs for the 6 MeV phase–space.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2024

Four-dimensional phase-space reconstruction of flat and magnetized beams using neural networks and differentiable simulations

Beams with cross-plane coupling or extreme asymmetries between the two transverse phase spaces are often encountered in particle accelerators. Flat beams with large transverse-emittance ratios are critical for future linear colliders. Similarly, magnetized beams with significant cross-plane coupling are expected to enhance the performance of electron cooling in hadron beams. Preparing these beams requires precise control and characterization of the four-dimensional transverse phase space. In this study, we employ generative phase-space reconstruction techniques to rapidly characterize magnetized and flat-beam phase-space distributions using a conventional quadrupole-scan method. The reconstruction technique is experimentally demonstrated on an electron beam produced at the Argonne Wakefield Accelerator and successfully benchmarked against conventional diagnostics techniques. Specifically, we show that predicted beam parameters from the reconstructed phase-space distributions (e.g., as magnetization and flat-beam emittances) are in excellent agreement with those measured from the conventional diagnostic methods. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2014

The phase space and stellar populations of cluster galaxies at z ∼ 1: simultaneous constraints on the location and timescale of satellite quenching

We investigate the velocity versus position phase space of z ∼ 1 cluster galaxies using a set of 424 spectroscopic redshifts in nine clusters drawn from the GCLASS survey. Dividing the galaxy population into three categories, that is, quiescent, star-forming, and poststarburst, we find that these populations have distinct distributions in phase space. Most striking are the poststarburst galaxies, which are commonly found at small clustercentric radii with high clustercentric velocities, and appear to trace a coherent 'ring' in phase space. Using several zoom simulations of clusters, we show that the coherent distribution of the poststarbursts can be reasonably well reproduced using a simple quenching scenario. Specifically, the phase space is best reproduced if these galaxies are quenched with a rapid timescale (0.1 <τ {sub Q} < 0.5 Gyr) after they make their first passage of R ∼ 0.5 R {sub 200}, a process that takes a total time of ∼1 Gyr after first infall. The poststarburst phase space is not well reproduced using long quenching timescales (τ {sub Q} > 0.5 Gyr) or by quenching galaxies at larger radii (R ∼ R {sub 200}). We compare this quenching timescale to the timescale implied by the stellar populations of the poststarburst galaxies and find that the poststarburst spectra are well-fit by a rapid quenching (τ {sub Q} = 0.4{sub −0.4}{sup +0.3} Gyr) of a typical star-forming galaxy. The similarity between the quenching timescales derived from these independent indicators is a strong consistency check of the quenching model. Given that the model implies satellite quenching is rapid and occurs well within R {sub 200}, this would suggest that ram-pressure stripping of either the hot or cold gas component of galaxies are the most plausible candidates for the physical mechanism. The high cold gas consumption rates at z ∼ 1 make it difficult to determine whether hot or cold gas stripping is dominant; however, measurements of the redshift evolution of the satellite quenching timescale and location may be capable of distinguishing between the two.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

An Effective Method to Accurately Calculate the Phase Space Factors for β - β - Decay

Accurate calculations of the electron phase space factors are necessary for reliable predictions of double-beta decay rates and for the analysis of the associated electron angular and energy distributions. We present an effective method to calculate these phase space factors that takes into account the distorted Coulomb field of the daughter nucleus, yet it allows one to easily calculate the phase space factors with good accuracy relative to the most exact methods available in the recent literature.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

The phase space of z∼1.2 SpARCS clusters: Using Herschel to probe dust temperature as a function of environment and accretion history

We present a five-band Herschel study (100–500 μm) of three galaxy clusters at z∼1.2 from the Spitzer Adaptation of the Red-Sequence Cluster Survey. With a sample of 120 spectroscopically confirmed cluster members, we investigate the role of environment on galaxy properties utilizing the projected cluster phase space (line-of-sight velocity versus clustercentric radius), which probes the time-averaged galaxy density to which a galaxy has been exposed. We divide cluster galaxies into phase-space bins of (r/r{sub 200})×(Δv/σ{sub v}), tracing a sequence of accretion histories in phase space. Stacking optically star-forming cluster members on the Herschel maps, we measure average infrared star formation rates, and, for the first time in high-redshift galaxy clusters, dust temperatures for dynamically distinct galaxy populations—namely, recent infalls and those that were accreted onto the cluster at an earlier epoch. Proceeding from the infalling to virialized (central) regions of phase space, we find a steady decrease in the specific star formation rate and increase in the stellar age of star-forming cluster galaxies. We perform a probability analysis to investigate all acceptable infrared spectral energy distributions within the full parameter space and measure a ∼4σ drop in the average dust temperature of cluster galaxies in an intermediate phase-space bin, compared to an otherwise flat trend with phase space. We suggest one plausible quenching mechanism which may be consistent with these trends, invoking ram-pressure stripping of the warmer dust for galaxies within this intermediate accretion phase.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Predicting beam transmission using 2-dimensional phase space projections of hadron accelerators

We present a method to compress the 2D transverse phase space projections from a hadron accelerator and use that information to predict the beam transmission. This method assumes that obtaining at least three projections of the 4D transverse phase space is possible and that an accurate simulation model is available for the beamline. Using a simulated model, we show that—a computer can train a convolutional autoencoder to reduce phase-space information which can later be used to predict the beam transmission. Finally, we argue that although using projections from a realistic nonlinear distribution produces less accurate results, the method still generalizes well.

43 PARTICLE ACCELERATORS↗
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]↗