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NASA NTRS1990

Gamma-Ray Observatory - The next great observatory in space

The Gamma-Ray Observatory (GRO) which is part of NASA's Great Observatories space program is presented. The GRO is equipped with the Burst and Transient Source Experiment (which detects low-energy gamma-ray photons from 20 keV to 600 keV and locates sources of gamma-ray bursts), the Oriented Scintillation Spectrometer Experiment (which detects celestial gamma rays from 100 keV to 10 MeV and identifies the elements producing these rays by measuring the ray's spectra and time variability), the Imaging Compton Telescope (which images gamma rays with energies from 1 to 30 MeV created when cosmic rays interact with interstellar matter), and the Energetic Gamma-Ray Experiment Telescope (which detects high-energy photons associated with the most energetic processes occurring in nature). After the energies of photons from each source are classified, the gamma-ray mechanisms can be modelled. Nuclei, radioactive isotopes, and nuclear reactions can be identified, and the physical conditions at the radiation's source can also be modelled. From these models, theories can be developed about the creation of elements in the explosion and collapse of giant stars, the acceleration of charged particles to velocities approaching the speed of light, and the destruction of matter and antimatter.

Neal, Valerie↗

NASA NTRS1990

Applications of ultrashort laser pulses in science and technology; Proceedings of the Meeting, The Hague, Netherlands, Mar. 12, 13, 1990

Topics discussed are on the generation of high-intensity femtosecond lasers, the high-repetition and infrared femtosecond pulses, and physics of semiconductors and applications. Papers are presented on the femtosecond pulse generation at 193 nm; the generation of intense subpicosecond and femtosecond pulses; intense tunable subpicosecond and femtosecond pulses in the visible and infrared, generated by optical parametric oscillators; a high-efficiency high-energy optical amplifier for femtosecond pulses; and the generation of solitons, periodic pulsing, and nonlinearities in GaAs. Other papers are on ultrafast relaxation dynamics of photoexcited carriers in GaAs, high-order optical nonlinear susceptibilities of transparent glasses, subnanosecond risetime high-power pulse generation using photoconductive bulk GaAs devices, femtosecond studies of plasma formation in crystalline and amorphous silicon, and subpicosecond dynamics of hot carrier relaxation in InP and GaAs.

Antonetti, Andre↗

NASA NTRS1993

Analytical and experimental investigation of the feasibility of accelerated lifetime testing of materials exposed to an atomic oxygen beam

The interaction of atomic particles with surfaces is of both scientific and technological interest. Past work emphasizes the measurement of high-energy sputtering yields. Very little work utilized low-energy beams for which chemical and electronic effects can be important. Even less work has been carried out using well-defined low-energy projectiles. The use of low-energy, reactive projectiles permits one to investigate surface processes that have not been well characterized. As the energy of the projectile decreases, the collisional cascades and spikes, that are common for high-energy projectiles, become less important, and chemical and electronic effects can play a significant role. Aspects of particle-surface interactions are of concern in several areas of technology. For example, the erosion, desorption, and glow of surfaces of spacecraft in orbit are important in the arena of space technology. The materials studied under this contract are of possible use on the exterior portions of the power generation system of Space Station Freedom. Under the original designs, Space Station Freedom's power generation system would generate potential differences on the surface as high as 200 volts. Ions in the plasma that often surround orbiting vehicles would be accelerated by these potentials leading to bombardment and erosion of the exposed surfaces. The major constituent of the atmosphere, approximately 90 percent, in the low earth orbit region is atomic oxygen. Since atomic oxygen is extremely reactive with most materials, chemical effects can arise in addition to the physical sputtering caused by the acceleration of the oxygen ions. Furthermore, the incident oxygen ions can remain embedded in the exposed surfaces, altering the chemical composition of the surfaces. Since the effective binding energy of a chemically altered surface can be quite different from that of the pure substrate, the sputtering yield of a chemically altered surface is usually different also. The low-energy O+ sputtering yield measurements, reported here, will help quantify the erosion rates for materials exposed to the low-earth orbit environment. These measurements are of technological importance in another respect. In most surface analysis techniques, a surface is bombarded with ions, electrons or photons. Information concerning the structure of the surface and near-surface bulk, abundance of impurities and defects, as well as other surface properties are obtained either from the desorbed species or from the scattered projectiles. Because of their low penetration depth, low-energy ions provide an advantage over other techniques because they provide information that is more indicative of conditions on the surface rather than integrated effects arising from deeper in the bulk. A better understanding of the microscopic processes involved in these interactions is not only of basic scientific interest, but will also aid the scientific community by increasing the accuracy and usefulness of these surface analysis techniques.

Albridge, Royal↗

NASA NTRS1993

Possible dust contamination of the early solar system

Measurements carried out over more than twenty years indicate a deficiency of neutrinos emitted from the deep interior of the Sun in conjunction with the neutrino flux expected from canonical solar models. The early measurements were sensitive only to high-energy neutrinos emitted from B-8 on a minor branch of the energy-producing nuclear reactions in the solar interior. Thus these measurements were not widely considered to be a definitive test of solar physics. However the more recent measurements, which are sensitive to lower energy neutrinos, produced primarily by the p-p reaction on the main energy-producing branch of the solar nuclear reactions, pose a far more significant mystery in physics. One possibility is that the Sun's interior opacity is lower than expected due to a paucity of elements. This paper discusses that the Sun formed from material less abundant in heavy elements than usually believed, and the subsequent contamination due to the settling of surrounding dust brought the abundance of heavy elements - in the protoplanetary nebula, and in the Sun's convective envelope - up to the currently observed value.

Levy, E. H.↗

NASA NTRS1994

Energetic ion distributions on both sides of the Earth's magnetopause

The Active Magnetospheric Particle Tracer Explorer/Charge Composition Explorer (AMPTE/CCE) spacecraft, with an apogee of approximately 8.8R(sub E) and an inclination of approximately 4.3 deg, sampled the outer dayside equatorial magnetosphere for extended time periods and often crossed into the magnetosheath whenever the solar wind pressure was sufficiently high to compress the magnetopause to less than 8.8R(sub E). We have analyzed ion distributions on both sides of the magnetopause in order to investigate any local time and energy dependence, giving information about physical processes at the magnetopause and the bow shock. Particle measurements are from the Charge Energy Mass (CHEM)(1.5 to 300 keV/e) and Medium-Energy Particle Analyzer (MEPA)(10 keV to 2 MeV) instruments. The wide total energy range (1.5 keV to 2 MeV) covered describes the magnetospheric distributions quite well, and for the purpose of this study, adequately describes the high-energy part of the shocked solar wind. Thus both solar wind and magnetospheric components can be recognized in a mixed particle distribution. Case studies of representative magnetopause crossings at dawn, noon, and dusk, as well as a survey of several other crossings, indicated: (1) a local time and energy dependence of magnetosheath spectra at energies greater than or equal to 50 KeV; spectra were harder at the duskside than at the dawnside and also correlated with magnetospheric activity, (2) constantly much higher intensities in the magnetosphere than in the magnetosheath at energies greater than 10 KeV and an earthward gradient in the subsolar magnetosheath. In addition to the steady state magnetosheath population there exists a burst-type component indicative of a magnetospheric source, and most of the time this is recognized as a flux transfer event. Overall, the results about the origin of the greater than or equal to 50 KeV magnetosheath ions are consistent with the continuous leakage of magnetospheric particles across a tangential discontinuity magnetopause, locally distributed according to magnetospheric drift paths. Magnetic reconnection, although present, should not be a dominant source on average, because it is not continuous in time. Fermi acceleration should not be dominant because it predicts the opposite local time asymmetry, and shock drift acceleration should be a minor contributor at E greater than or equal to 50 keV because of upper-energy cutoff limitations. Our observations also indicate a significant magnetospheric contribution to energies as low as approximately 10 KeV, where the magnetosphere-magnetosheath intensity gradient reverses. However, in orderto examine the relative strength and local time distribution of all possible sources at these energies, a detailed analysis is required.

Paschalidis, N. P↗

NASA NTRS1994

Particle acceleration mechanisms

High-energy particle acceleration is observed to proceed in a diverse variety of astrophysical sites ranging from the terrestrial aurorae to the most distant quasars. Particle acceleration is a fairly common channel for the release of large-scale kinetic, rotational, and magnetic energy. Physical mechanisms include electrostatic acceleration, stochastic processes, and diffusive shock energization. Cosmic-ray energy spectra have shapes which reflect escape, collisional, and radiative losses. The overall acceleration efficiency is controlled by the low-energy particle injection which may, in turn, feed back into the energization. Recent observational developments, which illustrate these general principles and raise fresh questions, are briefly summarized.

Blandford, R. D.↗

NASA NTRS1995

Pair cascades in extragalactic jets. 1: Gamma rays

A model of the approximately 0.1-10 GeV gamma-ray jets observed by the EGRET instrument on the Compton Gamma Ray Observatory (CGRO) is developed. It is shown that the soft X-ray background in an active galactic nuclei (AGN) contributes an opacity to pair production and that a gamma-ray photosphere or 'gamma-sphere' can be defined whose radius increases with gamma-ray energy E(sub gamma). It is proposed that the observed gamma-ray emission is due to inverse Compton scattering of the ambient soft X-rays by relativistic pairs accelerated in situ by shock fronts in a relativistic jet. For a wide range of assumed physical conditions, the emission at a given E(sub gamma) originates from near the associated gamma-spheres; emission from below the gamma-sphere initiates a cascade down to the energy where the gamma-rays can escape freely. In this model, the slope of the emergent gamma-ray spectrum is determined by the scattered, soft X-ray spectrum and the variation of the particle acceleration rate with jet radius. In general it is expected that the variation in the gamma-ray flux will be either slower or later at higher energy. It is also shown that the efficiency of conversion of energy from injected high-energy pairs to 0.1-10 GeV gamma-rays is typically high so that the models are radiatively efficient. It is argued that the observed gamma-ray jets are likely to be particle-dominated, though magnetically confined. The gamma-ray spectrum should continue down to an energy approximately 5 MeV emitted from an annihilation radius within which the pair content of the jet is limited by annihilation. This is probably the site of the beamed hard X-ray emission. It is speculated that the relativistic jets associated with radio-loud AGNs are powered electromagnetically by a spinning black hole and that they are collimated by an encircling MHD wind leaving the accretion disk at a slower speed. Powerful FR2 radio sources are formed when the hole spins rapidly and the relativistic core accelerates the MHD sheath; low-power FR1 sources ensue when the opposite occurs. Finally, it is suggested that the key factor which determines whether or not a given active nucleus can form a jet and a radio to gamma-ray nonthermal continuum is the central density of mass-losing stars which, when large, precludes the formation of a super-Alfvenic, collimating wind.

Blandford, R. D.↗

NASA NTRS1995

GRO: Black hole models for gamma-ray bursts

The Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) has established that the distribution of gamma-ray bursts (GRB's) is isotropic but is bound radially. This finding suggests that the bursts are either cosmological or they originate from an extended Galactic halo. The implied luminosities and the observed variability of the GRB's on time scales as short as one millisecond suggest that they originate from compact objects. We are presently studying black hole models for GRB's. Any such model must produce a non-thermal photon spectrum to agree with the observed properties. For a wide range of burst parameters the assumed bursting source consists of a non-thermal electron-positron-photon plasma of very high density. It seems possible to produce such a plasma in accretion onto black holes. In our on-going work, we are developing the kinetic theory for a non-equilibrium pair plasma. The main new features of our work are as follows: (1) We do not assume the presence of a thermal electron bath. (2) Non-thermal, high-energy pairs are allowed to have an arbitrary concentration and energy distribution. (3) There is no soft photon source in our model; initially all the photons in the plasma are either energetic X-rays or gamma-rays. (4) The initial energy distribution of the pairs as well as photons is arbitrary. (5) We collect the analytical expressions for the kinetic kernels for all relevant processes. And (6) we present a different approach to finding the time-evolution of pair and photon spectra, which is a combination of the kinetic-theory and the non-linear Monte-Carlo schemes. We have developed many Monte-Carlo programs to model various process, to take into account the time evolution, and to incorporate various physical effects which are unique to non-thermal plasmas. The hydrodynamics of fireballs in GRB's was studied before. Applying results from kinetic theory will improve our understanding of these systems.

Ruderman, Malvin↗

NASA NTRS1995

Laboratory electron exposure of TSS-1 thermal control coating

RM400, a conductive thermal control coating, was developed for use on the exterior shell of the tethered satellite. Testing was performed by the Engineering Physics Division to quantify effects of the space environment on this coating and its conductive and optical properties. Included in this testing was exposure of RM400 to electrons with energies ranging from 0.1 to 1 keV, to simulate electrons accelerated from the ambient space plasma when the tethered satellite is fully deployed. During this testing, the coating was found to luminesce, and a prolonged exposure of the coating to high-energy electrons caused the coating to darken. This report describes the tests done to quantify the degradation of the thermal control properties caused by electron exposure and to measure the luminescence as a function of electron energy and current density to the satellite.

Vaughn, J. A.↗

NASA NTRS1995

Low-energy ion acceleration at quasi-perpendicular shocks: Transverse diffusion

The problem of ion injection and acceleration at quasi perpendicular shocks has been the subject of some debate over the past two decades. It is widely known that these shocks efficiently accelerate particles that are well in the high-energy tail of the distribution. However, the issue of injection, or the acceleration of low-energy ions, has yet to reach a consensus. The fundamental issue is whether there is enough diffusion normal to the magnetic field for the particles to remain near the shock. Since transverse diffusion is a physical process that is not well understood in space plasmas, this is an important, and difficult issue to address. In this report, we will investigate the ion injection problem by performing test particle orbit integrations using synthesized turbulent fields. These fields are fully three-dimensional so that transverse diffusion is possible (cross-field diffusion is not possible in geometries where the electromagnetic fields are less than three dimensional). The synthesized fields are produced by superimposing a three-dimensional wave field on a background field. For completeness, we will compare the results from this model with the more well-established theories, such as the diffusive approximation and scatter-free shock drift acceleration. We will also compare these results with other numerical simulation techniques such as the well known hybrid simulation, and other test-particle calculations in which the shock fields are specified to have less than three dimensions. We will also discuss some recent relevant observations and how these compare with our results.

Giacalone, J.↗

NASA NTRS1994

Inter-Agency Consultative Group for Space Science (IACG): Handbook of Missions and Payloads

The ACE spacecraft design is based on the Charge Composition Explorer (CCE) built by Johns Hopkins University (JHU) and the Applied Physics Lab (APL) for the AMPTE program. ACE is designed as a spinning spacecraft with its spin axis aligned to the Earth-Sun axis. The ACE launch weight will be approx. 633 kg, including 105 kg of scientific instruments and 184 kg of propellant. Using a Delta-class expendable launch vehicle, ACE will be launched into an L1 libration point (240 R(sub e)) orbit. Telemetry will be 6.7 kbps average, using tape recorder storage with daily readout to DSN. The experiment power requirement is approximately 76 W nominal and 96 W peak. The prime objective of the ACE mission is: (1) to determine accurate elemental and isotropic abundances including solar matter, local interstellar matter and local galactic matter; (2) to study the origin of elements and evolutionary processing in galactic nucleosynthesis, galactic evolution, origin and evolution of the solar system; (3) to study coronal formation and solar-wind acceleration processes; and (4) to study particle acceleration and transport, including coronal shock acceleration, stochastic flare acceleration, interplanetary shock acceleration, and interstellar acceleration and propagation. To accomplish this objective, ACE will perform comprehensive and coordinated determinations of the elemental and isotopic composition of energetic nuclei accelerated on the Sun, in interplanetary space, and from galactic sources. These observations will span five decades in energy, from solar wind to galactic cosmic ray energies, and will cover the element range from H-1 to Zr-40. Comparison of these samples of matter will be used to study the origin and subsequent evolution of both solar system and galactic material by isolating the effects of fundamental processes that include nucleosynthesis, charged and neutral particle separation, bulk plasma acceleration, and the acceleration of suprathermal and high-energy particles.

Source record↗

NASA NTRS1992

Multiple-scattering effects in quasielastic alpha-4He scattering

A multiple-scattering series for describing the quasielastic peak in nucleus-nucleus collisions is derived using the high-energy optical model. The effects of multiple knockout of target nucleons and internal excitation of the projectile are studied and found to be important for large energy loss and momentum transfers in inclusive alpha-4He scattering at 7 GeV/c. An approximate evaluation of higher-order inelastic collision terms is considered for forward-peaked wave functions and is demonstrated to be accurate.

NASA Discipline Radiation Health↗

DOE OSTI2024

Search for Heavy Neutral Leptons at the MINER$\nu$A detector

Heavy Neutral Leptons (HNL) are particles hypothesised to provide a mass generation mechanism for the active (observed) neutrino species, which are known to have nonzero mass from the definitive observation of neutrino oscillations. HNL are eigenstates of mass of the order $\mathcal{O}(0.1 − 1\,\,\mathrm{GeV}/c^{2})$, which mix into the active flavour eigenstates through the extended leptonic mixing matrix. Apart from neutrino mass, they could provide a natural dark matter candidate and a mechanism for matter-antimatter asymmetry in the early Universe, giving rise to today’s matter-dominated cosmos. Searches for HNL typically attempt to either confirm the existence of HNL through an excess in data that is most compatible with an HNL hypothesis, or by setting limits on the HNL parameter space $\left(M_{N4}, \left|U_{\alpha 4}\right|^{2}\right)$ in the case of statistically insignificant excess. Such searches are intensifying as part of a global research programme at both colliders and accelerator / atmospheric neutrino experiments. One such setting is the MINER$\nu$A experiment, located in the NuMI beamline at Fermilab. MINER$\nu$A has collected a large amount of data over seven years of operation to measure the cross-sections of neutrino-nucleus interactions necessary to drive systematic uncertainties down, in order for neutrino oscillation experiments to achieve sensitivity to CP violation in the neutrino sector. With the high-energy, high-intensity NuMI beam, and with good timing, position, and angular resolution leading to sensitivity to HNL decays, MINER$\nu$A is fertile ground for an HNL search, which is performed in this thesis. Specifically, a novel, experiment-agnostic and general simulation of HNL production and decay is presented and deployed; this simulation has been incorporated in the ubiquitous GENIE neutrino event generator for use with neutrino experiments in the future. The event selection and background characterisation is discussed in detail, including the primary background coming from charged-current coherent and diffractive pion production from neutrino-nucleus interactions, and constraints on the background using control regions from MINER$\nu$A data are derived. Finally, by means of a fake-data study given a background of $\mathcal{O}(500)$ events, the discovery potential and limit-setting capacity of MINER$\nu$A is demonstrated, and ways to improve this capacity are expounded upon.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

MAIA: A new detector concept for a 10 TeV muon collider

Muon colliders offer a compelling opportunity to explore the TeV scale and conduct precision tests of the Standard Model, all within a relatively compact geographical footprint. This paper introduces a new detector concept, MAIA (Muon Accelerator Instrumented Apparatus), optimized for $\sqrt{s}=10$ TeV $\mu\mu$ collisions. The detector features an all-silicon tracker immersed in a 5T solenoid field. High-granularity silicon-tungsten and iron-scintillator calorimeters surrounding the solenoid capture high-energy electronic and hadronic showers, respectively, and support particle-flow reconstruction. The outermost subsystem comprises an air-gap muon spectrometer, which enables standalone track reconstruction for high-momentum muons. The performance of the MAIA detector is evaluated in terms of differential particle reconstruction efficiencies and resolutions. Beam-induced background (BIB) simulations generated in FLUKA are overlaid with single particle gun samples to assess detector reconstruction capabilities under realistic experimental conditions. Even with BIB, reconstruction efficiencies exceed 95% for energetic tracks, photons, and neutrons in the central region of the detector. This paper outlines promising avenues of future work, including forward region optimization and opportunities for enhanced flavor/boosted object tagging, and addresses the technological assumptions needed to achieve the desired detector performance.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Large Neutrino "Collider"

We propose using current and future large-volume neutrino telescopes as ``Large Neutrino Colliders" (L$ν$Cs) to explore TeV-scale physics beyond the Standard Model. Cosmic neutrinos with energies above 100 PeV colliding with nucleons in the detector reach center-of-mass energies beyond the 14 TeV limit of the Large Hadron Collider (LHC). Using recently predicted and measured high-energy and ultra-high-energy neutrino fluxes from IceCube and KM3NeT, we estimate mass-scale sensitivities for representative new physics scenarios at 1--30 km$^3$ L$ν$Cs. Our results demonstrate that L$ν$Cs provide a novel avenue to probe multi-TeV particles with sensitivities comparable to, or even surpassing, those of the LHC.

Bai, Yang [Wisconsin U., Madison; Argonne]↗

DOE OSTI2026

Constraining high-energy neutrinos from tidal disruption events with IceCube high-energy starting events

Tidal disruption events (TDEs) have been proposed as candidate sources of high-energy neutrinos. Successful and choked jets, as well as the accretion disk, corona, wind, and outflow regions in a TDE have been examined and shown to produce TeV - PeV neutrinos. In this work, we use the IceCube 12.5 year high energy starting events (HESE) dataset and perform a maximum likelihood analysis to investigate the spatial and temporal correlations between HESE dataset and a selected sample of 89 TDEs. Our results indicate that the currently observed data do not show any significant correlation and hence is consistent with the background only hypothesis. Using this result, we place constraints on the fraction of TDEs harboring intrinsic jets ($f_{\rm jet}$) and the corresponding isotropic-equivalent cosmic ray (CR) energy ($\mathcal{E}_{\rm CR}$). We note that even with limited statistics, we can constrain the parameter space as $\mathcal{E}_{\rm CR} \lesssim 3 \times 10^{53}$ erg for $f_{\rm jet} \gtrsim 0.6$ at more than 90% C.L. Finally, we discuss the theoretical implications of our results and the limits on the all-sky diffuse neutrino flux from TDEs. With more observational data in the electromagnetic band for TDEs and neutrino observations from IceCube and KM3NeT, our analysis can be used to place stringent constraints on physical parameters associated with TDEs.

Mukhopadhyay, Mainak [Fermilab; Chicago U., KICP; ↗

DOE OSTI2025

Spatially Aware Linear Transformer (SAL-T) for Particle Jet Tagging

Transformers are very effective in capturing both global and local correlations within high-energy particle collisions, but they present deployment challenges in high-data-throughput environments, such as the CERN LHC. The quadratic complexity of transformer models demands substantial resources and increases latency during inference. In order to address these issues, we introduce the Spatially Aware Linear Transformer (SAL-T), a physics-inspired enhancement of the linformer architecture that maintains linear attention. Our method incorporates spatially aware partitioning of particles based on kinematic features, thereby computing attention between regions of physical significance. Additionally, we employ convolutional layers to capture local correlations, informed by insights from jet physics. In addition to outperforming the standard linformer in jet classification tasks, SAL-T also achieves classification results comparable to full-attention transformers, while using considerably fewer resources with lower latency during inference. Experiments on a generic point cloud classification dataset (ModelNet10) further confirm this trend. Our code is available at https://github.com/aaronw5/SAL-T4HEP.

Wang, Aaron [Illinois U., Chicago] (ORCID:00000003↗

DOE OSTI2025

A Novel Measurement of the Anomalous Muon Spin Precession Frequency in the Muon $g-2$ Experiment at Fermilab

The Muon $g-2$ Experiment operated at Fermi National Accelerator Laboratory (FNAL, or Fermilab) between 2018 and 2023 to produce the world's most precise measurement of the muon's \textit{anomalous magnetic moment}, $a_\mu = \frac{g_\mu - 2}{2}$, which expresses the relative deviation in the muon's $g$-factor from a baseline theoretical expectation that $g_\mu = 2$. In the Standard Model of particle physics, $g_\mu > 2$ and hence $a_\mu > 0$ by a calculable amount that depends on all possible interactions between the muon and all other fundamental particles, including any potentially undiscovered interactions beyond the Standard Model. For this reason, measurements of the electron anomaly $a_e$ and later the muon anomaly $a_\mu$ have helped guide the development of the Standard Model since the inception of quantum field theory, and the measured value of $a_\mu$ provides a valuable constraint for new hypotheses that extend the Standard Model. As of 2006, the leading measurement and Standard Model prediction for $a_\mu$ exhibited tension at the level of about three standard deviations, motivating an improved measurement at Fermilab that could test the tension more precisely. The experiment functions by storing a polarized beam of $\mu^+$ in a uniform magnetic field, which simultaneously induces circular motion and spin precession. As the stored muons undergo the Michel decay $\mu^+ \to e^+ + \nu_e + \bar{\nu}_\mu$, mediated by the parity-violating weak interaction, the rest-frame $e^+$ emission direction is correlated with the parent $\mu^+$ spin orientation. Boosting into the laboratory frame encodes this correlation in the decay $e^+$ energy, which is higher when the emission (i.e. $\mu^+$ spin direction) is aligned with the $\mu^+$ momentum, and lower when opposite. Detectors then count the rate of high-energy decay $e^+$, which modulates at the difference between the $\mu^+$ revolution and spin precession frequencies. This observed frequency, called the \textit{anomalous spin precession frequency} $\omega_a$, is directly proportional to $a_\mu$. The extraction of $\omega_a$ proceeds by fitting the time spectrum of detected $e^+$, which requires precise modeling of the $\omega_a$ oscillation as well as any perturbations from beam dynamics and detector acceptance. Using the $\omega_a$ analysis presented in this work, based on Runs 4 -- 6 of the Muon $g-2$ Experiment at Fermilab, we find that $a_\mu = 0.001\,165\,920\,738(162)$ with a relative uncertainty of 139 parts per billion.

Barrett, Tyler [Cornell U.]↗