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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Approximate Boltzmann distributions in quantum approximate optimization

Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7200 random MaxCut instances, with $n$ = 14–23 qubits and depth parameter $p$ ≤ 12 and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. Furthermore, we describe the rate of exponential scaling or effective temperature in terms of a series with a leading-order term $T$ ~ $C$ min /$n$ $\sqrt{p}$, with $C$ min the optimal solution energy. Using this scaling, we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Calculation Of The First Moment Of Energy Using D-T Reactivity Formalisms Under The Maxwell-Boltzmann Distribution--Part II

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of a nuclear fusion formalism is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium- Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hal reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell-Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. This report continues the step toward building understanding of nuclear fusion reactivity formalisms. It is part of a series of reports with the same goal, [5-10] and is the continuation of the Part I paper for defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, <$E$>, with the fusion cross-section, fusion reactivity and its derivative with ion-temperature. In Part I, three variants of the first moment <$E$> were analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment from Brysk. In Part II, attention is given to the definition of <$K$>, originally described as a ratio of moments from Brysk, and its relationship to the first moment definitions from Part I. One measure of the progress made in these documents is the identification that Brysk’s ratio of the second moment to the first moment ratio, <$K$>, does not correspond to his provided solution of the first moment of energy. Another measure of (our) progress from this work is the comparison of first moment variants. That comparison includes confirming the importance of cross sections defined in terms of energy. The analytical relationships we have developed among important physics quantities are useful tools in validation and verification (V&V). For example, we can calculate the kinetic energy as a mean or as a first moment, or as a function of the first moment. These analytically-determined values can be compared directly with numerically-determined values, supplied to the authors, representing <$E$>.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Wasserstein normalized autoencoder for anomaly detection

A novel anomaly detection algorithm is presented. The Wasserstein normalized autoencoder (WNAE) is a normalized probabilistic model that minimizes the Wasserstein distance between the learned probability distribution—a Boltzmann distribution where the energy is the reconstruction error of the autoencoder (AE)—and the distribution of the training data. This algorithm has been developed and applied to the identification of semivisible jets—conical sprays of visible standard model (SM) particles and invisible dark matter states—with the CMS experiment at the CERN LHC. Trained on jets of particles from simulated SM processes, the WNAE is shown to learn the probability distribution of the input data in a fully unsupervised fashion, such that it effectively identifies new physics jets as anomalies. The model exhibits stable, convergent training and recovers strong classification performance for a wide range of signals against the selected background process, for which a standard AE fails because of outlier reconstruction. In addition, the model improves upon standard normalized autoencoders while remaining fully agnostic to the signal. The WNAE directly tackles the problem of outlier reconstruction, a common failure mode of autoencoders in anomaly detection tasks.

Hayrapetyan, Aram [Yerevan Phys. Inst.]↗
DOE OSTI2023

Velocity-dependent J-factors for Milky Way dwarf spheroidal analogues in cosmological simulations

We study the impact of the dark matter velocity distribution modelling on signals from velocity-dependent dark matter annihilation in Milky Way dwarf spheroidal galaxies. Using the high resolution APOSTLE simulations, we identify analogues corresponding to Milky Way dwarf spheroidal galaxies, and from these directly determine the dark matter pair-wise relative velocity distribution, and compare to best-fitting Maxwell-Boltzmann distribution models. For three velocity-dependent annihilation models, p-wave, d-wave, and the Sommerfeld model, we quantify the errors introduced when using the Maxwell-Boltzmann parameterization. We extract a simple power-law relation between the maximum circular velocity of the dwarf spheroidal analogue and the peak speed of the Maxwell-Boltzmann distribution. We show that this relation can be used to accurately calculate the dark matter relative velocity distribution, and find that it allows us to estimate the dark matter annihilation signal without the need to directly calculate the relative velocity distribution for each galaxy. The scatter in the J-factors calculated from the analogues dominates the uncertainty obtained when compared to the J-factor as determined from the observational data for each dwarf spheroidal, with the largest scatter from d-wave models and the smallest from Sommerfeld models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Nonextensive hydrodynamics of boost-invariant plasmas

We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter q. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including q. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function (q → 1). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter q.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Ion energy distribution in an electron beam ion trap inferred from simulations of the trapped ion cloud

For this work, we have inferred the energy distribution of trapped ions in an electron beam ion trap (EBIT) from simulations of the spatial distribution of Fe 13+ ions and a comparison with measured visible light images of the ion cloud. We simulated the cloud of Fe 13+ ions by computing ion trajectories in the EBIT for different ion energy distributions used to initialize the trajectories. We then performed a least-squares fit to infer the ion energy distribution that best reproduced the measured ion cloud. These best-fit distributions were typically non-Maxwellian. For electron beam energies of 395–475 eV and electron beam currents of 1–9 mA, we find that the average ion energy is in the range of 10–300 eV. We also find that the average ion energy increases with increasing beam current approximately as $\langle$E$\rangle$ ≈ 25 I e eV, where I e is the electron beam current in mA. We have also compared our results to Maxwell-Boltzmann-distribution ion clouds. We find that our best-fit non-thermal distributions have an $\langle$E$\rangle$ that is less than half that of the T from the best-fit Maxwell-Boltzmann distributions ($\langle$E$\rangle$/q)/T=0.41 ± 0.05.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Kinetic simulations of collision-less plasmas in open magnetic geometries

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

An improved synthetic signal injection routine for the Haloscope At Yale Sensitive To Axion Cold dark matter (HAYSTAC)

Microwave cavity haloscopes are among the most sensitive direct detection experiments searching for dark matter axions via their coupling to photons. When the power of the expected microwave signal due to axion–photon conversion is on the order of 10 −24 W, having the ability to validate the detector response and analysis procedure by injecting realistic synthetic axion signals becomes helpful. Here, we present a method based on frequency hopping spread spectrum for synthesizing axion signals in a microwave cavity haloscope experiment. It allows us to generate a narrow and asymmetric shape in frequency space that mimics an axion’s spectral distribution, which is derived from a Maxwell–Boltzmann distribution. In addition, we show that the synthetic axion’s power can be calibrated with reference to the system noise. Further, compared to the synthetic axion injection in the Haloscope At Yale Sensitive to Axion Cold dark matter (HAYSTAC) Phase I, we demonstrated synthetic signal injection with a more realistic line shape and calibrated power.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Thermodynamically consistent incorporation of the Langmuir adsorption model into compressible fluctuating hydrodynamics

For a gas–solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass–energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass–energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell–Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar, with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.

Adsorption↗
DOE OSTI2025

Dark Matter Velocity Distributions for Direct Detection: Astrophysical Uncertainties Are Smaller Than They Appear

The sensitivity of direct detection experiments depends on the phase-space distribution of dark matter near the Sun, which can be modeled theoretically using cosmological hydrodynamical simulations of Milky Way–like galaxies. However, capturing the halo-to-halo variation in the local dark matter speeds—a necessary step for quantifying the astrophysical uncertainties that feed into experimental results—requires a sufficiently large sample of simulated galaxies, which has been a challenge. In this Letter, we quantify this variation with nearly 100 Milky Way–like galaxies from the tng50 simulation, the largest sample to date at this resolution. Moreover, we introduce a novel phase-space scaling procedure that endows every system with a reference frame that accurately reproduces the local standard-of-rest speed of our Galaxy, providing a principled way of extrapolating the simulation results to real-world data. The ensemble of predicted speed distributions is well characterized by the standard halo model, a Maxwell-Boltzmann distribution truncated at the escape speed, though the individual distributions can deviate from it, especially at high speeds. The dark matter–nucleon cross section limits placed by these speed distributions vary by ∼ 60% about the median. This places the 1⁢𝜎 astrophysical uncertainty at or below the level of the systematic uncertainty of current ton-scale detectors, even down to the energy threshold. The predicted uncertainty remains unchanged when subselecting on those TNG 50 galaxies with merger histories similar to the Milky Way. Tabulated speed distributions, as well as Maxwell-Boltzmann fits, are provided for use in computing direct detection bounds or projecting sensitivities.

Milky Way↗
DOE OSTI2022

An improved synthetic signal injection routine for HAYSTAC

Microwave cavity haloscopes are among the most sensitive direct detection experiments searching for dark matter axions via their coupling to photons. When the power of the expected microwave signal due to axion-photon conversion is on the order of 10-24 W, having the ability to validate the detector response and analysis procedure by injecting realistic synthetic axion signals becomes helpful. Here we present a method based on frequency hopping spread spectrum for synthesizing axion signals in a microwave cavity haloscope experiment. It allows us to generate a narrow and asymmetric shape in frequency space that mimics an axion's spectral distribution, which is derived from a Maxwell-Boltzmann distribution. In addition, we show that the synthetic axion's power can be calibrated with reference to the system noise. Compared to the synthetic axion injection in HAYSTAC phase I, we demonstrated synthetic signal injection with a more realistic lineshape and calibrated power.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗
DOE OSTI2021

Velocity-dependent J-factors for annihilation radiation from cosmological simulations

Abstract We determine the dark matter pair-wise relative velocity distribution in a set of Milky Way-like halos in the Auriga and APOSTLE simulations. Focusing on the smooth halo component, the relative velocity distribution is well-described by a Maxwell-Boltzmann distribution over nearly all radii in the halo. We explore the implications for velocity-dependent dark matter annihilation, focusing on four models which scale as different powers of the relative velocity: Sommerfeld, s-wave, p-wave, and d-wave models. We show that the J-factors scale as the moments of the relative velocity distribution, and that the halo-to-halo scatter is largest for d-wave, and smallest for Sommerfeld models. The J-factor is strongly correlated with the dark matter density in the halo, and is very weakly correlated with the velocity dispersion. This implies that if the dark matter density in the Milky Way can be robustly determined, one can accurately predict the dark matter annihilation signal, without the need to identify the dark matter velocity distribution in the Galaxy.

Astronomy & Astrophysics↗
DOE OSTI2021

Electron energy distributions in the extended gas nebulae associated with high-z AGN: Maxwell–Boltzmann versus κ distributions

ABSTRACT Emission line observations together with photoionization models provide important information about the ionization mechanisms, densities, temperatures, and metallicities in active galactic nuclei (AGN)-ionized gas. Photoionization models usually assume Maxwell–Boltzmann (M–B) electron energy distributions (EED), but it has been suggested that using κ distributions may be more appropriate and could potentially solve the discrepancies in temperatures and abundances found in HII regions and planetary nebulae. We consider the impact of the presence of κ distributions in photoionized nebulae associated with AGN and study how this might affect spectral modelling and abundance analyses for such regions. Using the photoionization code MAPPINGS 1e, we compute models adopting M–B and κ distributions of electron energies and compare the behaviour of emission line ratios for different values of κ, gas metallicity, density, ionization parameter, and SED slope. We find that the choice of EED can have a large impact on some UV and optical emission lines emitted by photoionized nebulae associated with AGN, and that the impact of adopting a κ distribution is strongly dependent on gas metallicity and ionization parameter. We compile a sample of line ratios for 143 type 2 AGN and compare our models against the observed line ratios. We find that for 98 objects, κ distributions provide a better fit to the observed line ratios than M–B distributions. In addition, we find that adopting κ-distributed electron energies results in significant changes in the inferred gas metallicity and ionization parameter in a significant fraction of objects.

Morais, S. G. (ORCID:0000000200927813)↗
DOE OSTI2023

Initial Fulcher band observations from high resolution spectroscopy in the MAST-U divertor

High resolution D$^*_2$ Fulcher band spectroscopy was used in the MAST-U divertors during Super-X and (shorter-legged) elongated divertor density ramps with D 2 fuelling from the mid-plane high-field side. In the Super-X case, the upper divertor showed ground state rotational temperatures of the D 2 molecules increasing from ~6000 K, starting at the detachment onset, to ~9000 K during deepening detachment. This was correlated with the movement of the Fulcher emission region towards the X-point, which is in turn correlated with the movement of the ionisation source. The increase in rotational temperature occurred throughout the divertor except near the divertor entrance, where ionisation was still the dominant process. Qualitative agreement was obtained between the lower and upper divertor. Similar rotational temperatures were obtained in the elongated divertor before the detachment onset, although the increase in rotational temperature during detachment was less clearly observed as less deep detachment was obtained. The measured vibrational distribution of the upper Fulcher state does not agree with a ground state Boltzmann distribution but shows a characteristically elevated population in the ν = 2 and ν = 3 bands in particular; which is strongly correlated to the rotational temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Distribution function of nuclei from $\mathcal{e}^±$ scattering in the presence of a strong primordial magnetic field

The amplitude of the primordial magnetic field (PMF) is constrained from observational limits on primordial nuclear abundances. Within this constraint, it is possible that nuclear motion is regulated by Coulomb scattering with electrons and positrons (e ± s), while e ± s are affected by a PMF rather than collisions. For example, at a temperature of 10 9 K, thermal nuclei typically experience ~ 10 21 scatterings per second that are dominated by very small angle scattering leading to minuscule changes in the nuclear kinetic energy of order $\mathcal{O}$(1) eV. In this paper the upper limit on the effects of a possible discretization of the e ± momenta by the PMF on the nuclear momentum distribution is estimated under the extreme assumptions that the momentum of the e ± is relaxed before and after Coulomb scattering to Landau levels, and that during Coulomb scattering the PMF is neglected. This assumption explicitly breaks the time reversal invariance of Coulomb scattering, and the Maxwell-Boltzmann distribution is not a trivial steady state solution of the Boltzmann equation under these assumptions. Here we numerically evaluate the collision terms in the Boltzmann equation, and show that the introduction of a special direction in the e ± distribution by the PMF generates no directional dependence of the collisional destruction term of nuclei. Large anisotropies in the nuclear distribution function are then constrained from big bang nucleosynthesis. Ultimately, we conclude that a PMF does not significantly affect the isotropy or big bang nucleosynthesis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗