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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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At least 1,783 records · Page 99
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Optimization of ray-tracing simulations to confirm performance of the GP-SANS instrument at the High-Flux Isotope Reactor

The CG-2 beamline at the High Flux Isotope Reactor (HFIR) exhibits a notable discrepancy between observed count rates and the count rates we would expect based on a Monte-Carlo neutron ray-trace simulation. These simulations consistently predict count rates approximately five times greater than those observed in four separate experimental runs involving different instrument configurations. This discrepancy suggests that certain factors are causing losses in measurements that are not adequately accounted for in the simulation, in particular guide reflectivity or misalignment. To investigate these discrepancies, a high-dimensional simulation parameter approach is applied in order to understand the losses. Region of Interest (ROI) groups along the instrument are assigned to different surfaces of the guide components within the simulation. This allows the parameters of those guide components to be varied as a group to minimize the complexity of the search space. The result is an optimization of simulation parameters using an iterative scheme that aims to minimize the difference between experimentally measured count rates and simulated count rates across all tested collimator combinations. This proposed methodology holds the potential to reveal previously unrecognized sources of intensity loss in the CG-2 beamline at HFIR and improve the accuracy of simulations, leading to enhanced understanding and performance of the beamline for various scientific applications.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Round Robin Summary for ASTM Method C1733

This report was prepared to summarize the results of an inter- and intra-laboratory round robin of ASTM Method C1733-17 (now C1733-20a) Distribution Coefficients of Inorganic Species by the Batch Method. The testing used the sorption of cesium (Cs) to a standard reference soil from the San Joaquin Valley (Standard Reference Material 2709a). The data collected from the nine participants was used for a statistical analysis to assess the precision of the method and generate a precision and bias statement to update the C1733-20a standard.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Field validation of data-driven BSDF and peak extraction models for light-scattering fabric shades

Shading and daylighting systems affect cooling, heating, and lighting energy use by modulating solar radiation through the building façade. Characterizing shading systems holistically and accurately helps designers and engineers evaluate shading systems to achieve energy and non-energy performance goals. These complex fenestration systems can be modeled using Bidirectional Scattering Distribution Functions (BSDF), which map incident radiation to hemispherical distributions of outgoing radiation. Data-driven, tabulated BSDFs are derived from interpolated goniophotometer measured data, then sampled during the raytracing calculation. A peak extraction (PE) algorithm was developed to circumvent limits in BSDF angular resolution, where the specular peak is extracted during simulation by evaluating the BSDF in the through direction and surrounding region. The objective of this study was to validate this measurement and modeling workflow using field monitored data from a full scale testbed with eleven installed fabrics of different weaves, openness factors, and colors and assess the accuracy of the workflow under different adaptation and contrast conditions. Test conditions were limited to clear sky conditions with the sun in the field of view. Results showed that, for tensor tree datasets, vertical illuminance, solar luminance (2.5° apex), and daylight glare probability (DGP) were predicted to within a mean bias error (MBE) error of -456 lx (-12.3%), -3.46e5 (-38.4%), and -0.042 (-7.8%) when full PE occurred. With a binary classification of glare/ no glare, DGP was predicted accurately with a true positive rate of 0.98 and true negative rate of 1.0 using tensor tree data and less accurately with Klems BSDF data, particularly for cases of no glare. The workflow may be of insufficient accuracy to distinguish borderline performance between fabrics using the four-point glare scale, particularly under low adaptation, high contrast daylit conditions. Errors were due to reductions in peak shape and intensity across the BSDF interpolation and data reduction workflow. Future work is needed to better preserve measurement fidelity during interpolation and sampling, which in turn will improve PE performance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Characterization of CST Post-Processing AP-105 Hanford Tank Waste

The primary goal of the Tank Side Cesium Removal (TSCR) system, under development by Washington River Protection Solutions, LLC (WRPS), is to remove entrained solids and 137 Cs from the Hanford tank waste supernate to expedite production of low-activity waste. Ion exchange (IX) testing of 10.9 L of waste from Hanford tank 241-AP-105 (AP-105), performed by Pacific Northwest National Laboratory, used a lead-lag-polish column format, with a bed volume of 10 mL per column, to decontaminate tank waste supernate using crystalline silicotitanate (CST) as the IX media. The AP-105 Cs IX processing test, discussed elsewhere, resulted in a shorter transition zone (i.e., steeper load curve) than those defined by wastes from tanks 241-AP-107 and 241-AW-102.1 The shorter transition zone was indicative of a matrix effect retarding Cs capacity. Therefore, aliquots of spent CST from the lead, lag, and polish columns were subjected to a digestion protocol to quantify analytes retained by the CST and extrapolate the impact on Cs capacity. The spent CST was digested using a combination of 5 M HNO 3 and H 2 O 2 with vigorous heating and stirring. Due to the radiation dose accompanying the 137 Cs on the CST columns, a secondary Cs separation by ammonium molybdophosphate embedded in polyacrylonitrile (AMP-PAN) was performed to separate the 137 Cs from the CST so the samples could be contact-handled for analysis outside of a shielded facility.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Synthesizing, Compounding, and Characterizing a Heat Labile Polyurethane Foam

ABSTRACT A need exists for a packaging foam material that can be converted from solid to gaseous degradation products at reasonably low energy levels or temperatures, such as 100O C. This paper will primarily discuss the approaches currently being used to synthesize and characterize such a material. These approaches include the incorporation of novel polyols such as azo containing diols, polycarbonate diols, and polypropylene carbonate polyols into polyurethane foams. Characterization methods include NMR, FTIR, TGA, finite element analysis, impact strength, and others. This project will be funded for a duration of three years. Year 1 focused on developing the proposed test methods and producing an initial rigid polyurethane foam. Year 2 focuses on refining the materials and test methods. If appropriate, design of experiment (doe) techniques will be used to optimize components, component levels, density and other variables to attain required final material properties (TGA weight loss, impact strength, etc.). Year 3 focuses on scaling up to larger engineering quantities. The application for this material is in load securement for transportation of low level radioactive waste materials within the US Department of Energy (DOE) complex. Foam in place process equipment and operators will be shielded using this novel method over current practice. Current practice can involve time consuming methods of load securement in low level radiation environments. This new technique would eliminate exposure time securing the load and greatly improve the As Low As Reasonably Attainable (ALARA) conditions. The objective is to progress to higher Technical Readiness Levels (TRL) and larger pilot scale quantities. This paper discusses methodologies and presents current results to date.

Kranjc, Mark D.↗
DOE OSTI2020

Development of an optical sensor for measuring opacity changes in polyvinyl toluene scintillators

Polyvinyl toluene (PVT) based detectors are used in radiation portal monitors (RPMs) worldwide to detect the trafficking of illicit nuclear material. PVT scintillators, which are normally optically clear, have been observed to suffer internal fogging throughout their volume due to prolonged exposure to varying environmental conditions. These changes could lead to reduced performance for RPMs that utilize plastic scintillators. In this research, a proof of concept system, consisting of different color light emitting diodes (LEDs) and a single optical sensor (OS), were used to examine the change in light transmission through a PVT scintillator. This Optical Monitoring System (OMS), coupled with an environmentally exposed PVT detector, was tested in an environmental chamber where it was subjected to changes in temperature and humidity ranging from 55 °C at 100% relative humidity to –20 °C at 40% relative humidity. At temperatures below 10 °C, light transmission was reduced by 81% ± 8% for blue LEDs, 84% ± 5% for yellow LEDs, and 49% ± 4% for green LEDs. Similar reductions in detected light were not recorded when the OMS was tested with only air between the LEDs and OS. Therefore, the significant reductions in transmitted light were attributed to changes occurring within the PVT scintillator. These results indicate that a significant reduction in PVT opacity occurs due to wide environmental changes. A device such as the OMS could be used to track these changes and provide users an early indication that a portal monitor is suffering from reduced performance.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Using convolutional neural networks to detect edge localized modes in DIII-D from Doppler backscattering measurements

In H-mode tokamak plasmas, the plasma is sometimes ejected beyond the edge transport barrier. These events are known as edge localized modes (ELMs). ELMs cause a loss of energy and damage the vessel walls. Understanding the physics of ELMs, and by extension, how to detect and mitigate them, is an important challenge. In this paper, we focus on two diagnostic methods—deuterium-alpha (D α ) spectroscopy and Doppler backscattering (DBS). The former detects ELMs by measuring Balmer alpha emission, while the latter uses microwave radiation to probe the plasma. DBS has the advantages of having a higher temporal resolution and robustness to damage. These advantages of DBS diagnostic may be beneficial for future operational tokamaks, and thus, data processing techniques for DBS should be developed in preparation. In sight of this, we explore the training of neural networks to detect ELMs from DBS data, using D α data as the ground truth. With shots found in the DIII-D database, the model is trained to classify each time step based on the occurrence of an ELM event. The results are promising. When tested on shots similar to those used for training, the model is capable of consistently achieving a high f1-score of 0.93. Furthermore, this score is a performance metric for imbalanced datasets that ranges between 0 and 1. We evaluate the performance of our neural network on a variety of ELMs in different high confinement regimes (grassy ELM, RMP mitigated, and wide-pedestal), finding broad applicability. Beyond ELMs, our work demonstrates the wider feasibility of applying neural networks to data from DBS diagnostic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A novel high frequency, high bandwidth, three phase Mach–Zehnder optical data link

In inertial confinement fusion, hydrogen isotopes are fused together under high pressures and temperatures. Typically, the duration of these experiments is incredibly short, on the order of around 60–150 ps. Due to the high radiation environment, a detector’s signal is typically data linked far distances to a protected location. The diagnostic challenge for fusion reaction history measurements is to measure signals of interest maximizing dynamic range while also maintaining time resolution on the order of 10 ps. In this work, we present a new experimental optical data link used to efficiently transport diagnostic signals over great distances to the recording system while not restricting the dynamic range. The concept of a three phase Mach–Zehnder modulator system is introduced as well as a description of the physical prototype. The initial results from testing at the OMEGA facility show that this system is a viable method for signal transportation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

(U) A Linear Response Model Predicts Reactivity From a Density Profile

We tested the ability to predict the system reactivity, described by alpha, given a density profile using a simple linear system response. We generated a suite of 1-dimensional density profiles that consisted of nominal density, a discontinuity, and a decay. These profiles were prescribed a functional form and the mass was conserved in all cases. From these density profiles, we calculated the alpha value of the 3-dimensional system.We calculated a linear response function given a training set of the 1-dimensional density profiles, and the system reactivity described by alpha. We tested the robustness of the response function using the remaining test data. Our results showed very good agreement between the predicted and calculated test values, where the distribution of alpha differences was centered about zero and had a standard deviation of 0.005 gens/shake. The predicted and calculated alpha values did not significantly differ (t=-0.0009 p<0.99). We used Singular Value Decomposition (SVD) to reduce the matrix rank by retaining95% of the cumulative singular value contributions. This reduced the matrix rank by 91.7%. We generated the linear response matrix and calculated the difference between the predicted and calculated alpha values. Using the reduced order matrix, we showed good agreement between the predicted and calculated alpha values where the distribution of differences was centered near zero, the standard deviation was 0.006 gens/shake, and the statistical t-test showed good agreement (t=0.02, p<0.98). These results show a linear relationship between a series of 1-dimensional density profiles,where the mass was conserved, and the system reactivity. The next steps of this work will be to investigate the linear response using 2-dimensional density profiles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Analysis of Air-Purifying Respirator (APR) and Powered Air-Purifying Respirator (PAPR) Cartridge Performance Testing on Hanford Tanks BY-108 and BY-110 Volume 2: Raw Analytical Data

As the Tank Operations Contractor for U.S. Department of Energy operations at the Hanford site in Washington State, Washington River Protection Solutions (WRPS) is responsible for managing highly radioactive wastes stored in tanks at Hanford. WRPS tests air-purifying respirator (APR) and powered air-purifying respirator (PAPR) chemical cartridges commonly used by workers at Hanford Tank Farms to determine the period of time that the cartridges would provide adequate performance for APRs and PAPRs used to protect workers when exposed to a mixture of Chemicals of Potential Concern (COPC) from any vapors exiting headspaces in the storage tanks. The Occupational Safety and Health Administration (OSHA) Standard promulgated in Title 29 of the Code of the Federal Regulations (CFR) 1910.134(d)(3)(iii)(b)(2) specifies that for protection against gases and vapors, employers shall implement a schedule for cartridges to ensure that change-outs occur before the end of service life. The change schedule can be based on objective information or data that ensures cartridge change-outs occur before the end of their service life. The primary function of the WRPS Cartridge Test Program is to obtain objective data to determine service lives for the APR and PAPR cartridges used at Hanford Tank Farms. WRPS contracted with Pacific Northwest National Laboratory to analyze the test data and offer an independent analysis and any recommendations. This report summarizes data analysis of APR and PAPR cartridge testing on BY-110 and BY-108 headspace vapors, respectively. Two different APR cartridges from SCOTT Safety (Monroe, North Carolina) were assessed for the BY-110 headspace vapors, and two different PAPR cartridges—one from MSA Safety Inc. (Pittsburgh, Pennsylvania) and another from 3M (Maplewood, Minnesota)—were assessed for the BY-108 headspace vapors. Volume 1 of this report documents the testing, data analysis, results, conclusions, and recommendations resulting from the cartridge testing of vapors from the BY-110 and BY-108 headspaces. Volume 2 provides an introduction to the raw data, including analytical laboratory analysis results that supported the analysis and conclusions documented in Volume 1.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Design and Prototyping of a Novel Toroid Magnet System for the MOLLER Experiment at Jefferson Lab

The Thomas Jefferson National Accelerator Facility (JLab) has designed a unique spectrometer system to measure the weak interaction between electrons. The experiment ?Measurement of Lepton-Lepton Electroweak Reaction? (MOLLER) requires leveraging the recent 12 GeV electron beam upgrade and will run in JLab for 3 years. Focusing the signal for the MOLLER experiment requires five water-cooled toroidal magnets, each with unique geometry and with 7-fold symmetry. This system of magnets provides the magnetic field required to separate the incident beam electrons scattered from the target electrons (Møller scattering) and protons (elastic e-p scattering) in a liquid hydrogen target. The conceptual design was developed by the MOLLER collaboration and was given to JLab in the form of amp turns and physical location, with additional physics requirements. This paper presents prototyping of the coils and magnet support system and discusses the lessons learned during the process along with the plans for full magnet testing and installation. The JLab Magnet Group along with the MOLLER collaboration developed the specification document that includes keep out zones to design the set of magnets. JLab contracted the design of the first toroid magnet in the magnet (TM0) to Massachusetts Institute of Technology. The other four toroid magnets (TM1 through TM4) have been designed by JLab and are in the process of fabrication and assembly. Prototype coils of TM1-TM4 have been fabricated by Everson-Tesla Incorporated, PA (USA). The manuscript presents the unique challenges of the design, alignment, high current density, operating range, high radiation dose, and vacuum environment.

Kashy, David↗
DOE OSTI2024

Long-Term Performance of Ag/AgCl Reference Electrodes for Corrosion Potential Monitoring in Radioactive Tank Waste at the Hanford Site

This work studied the exposure effects of radioactive tank waste on the long-term performance of single junction Ag/AgCl reference electrodes for corrosion potential monitoring at the Hanford Site. Electrodes from three manufacturers with very different designs were studied using open-circuit potential and electrochemical impedance measurements in radioactive tank waste. Post-test analyses were conducted on some failed electrodes using destructive and nondestructive techniques. The intrusion of the aggressive and radioactive chemicals in tank waste through the porous frit materials was the primary mechanism that led to the clogging of frit, physical and chemical degradation of AgCl bonded to Ag wire, and alteration of the internal electrolyte. Radiolytic chemical species such as H2O2 and HNO3 may have also induced the degradation of the Ag wire. The extent of electrode degradation and failure probability highly depended on the electrode design and environmental conditions. Chemicals in tank waste had stronger effects than radiation on the long-term performance of the Ag/AgCl reference electrodes.

Materials Science↗
DOE OSTI2021

Portable unit for metabolic analysis

A portable unit for metabolic analysis includes a manifold in fluid communication with a mouth of a test subject. A conduit extends from the manifold and defines a flow channel through which the breaths of the test subject travels. A carbon dioxide sensor is attached to the conduit. The carbon dioxide sensor includes an intermediate support housing enclosing a volume disposed along the flow channel to define a first part of the flow channel, an inner support housing attached to a first side of the intermediate support housing, a plurality of IR LEDs mounted to an interior surface of the inner support housing, an outer support housing attached to a second side of the intermediate support housing, and a photodetector attached to the outer support housing. The photodetector faces the flow channel and receives IR radiation emitted by the plurality of LEDs.

Dietrich, Daniel L.↗
DOE OSTI2021

PreMevE Update: Forecasting Ultra-Relativistic Electrons Inside Earth's Outer Radiation Belt

Energetic electrons inside Earth's Van Allen belts pose a major radiation threat to spaceborne electronics that often play vital roles in modern society. Ultra-relativistic electrons with energies greater than or equal to two megaelectron-volt (MeV) are of particular interest, and thus forecasting these ≥2 MeV electrons has a significant meaning to all space sectors. Here, we update the latest development of the predictive model for MeV electrons in the outer radiation belt. The new version, called PREdictive MEV Electron (PreMevE)-2E, forecasts ultra-relativistic electron flux distributions across the outer belt, with no need for in situ measurements of the trapped MeV electron population except at the geosynchronous orbit (GEO). Model inputs include precipitating electrons observed in low-Earthorbits by NOAA satellites, upstream solar wind speeds and densities from solar wind monitors, as well as ultra-relativistic electrons measured by one Los Alamos GEO satellite. We evaluated 32 supervised machine learning models that fall into four different classes of linear and neural network architectures, and successfully tested ensemble forecasting by using groups of top-performing models. All models are individually trained, validated, and tested by in situ electron data from NASA's Van Allen Probes mission. It is shown that the final ensemble model outperforms individual models at most L-shells, and this PreMevE-2E model can provide 25-h (~1-day) and 50-h (~2-day) forecasts with high mean performance efficiency and correlation values. Our results also suggest that this new model is dominated by nonlinear components at L-shells <~4 for ultra-relativistic electrons, different from the dominance of linear components for 1 MeV electrons as previously discovered.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Design and Prototyping of a Novel Toroidal Magnet System for MOLLER Experiment at Jefferson Lab

The Thomas Jefferson National Accelerator Facility (JLab) has designed a unique spectrometer system to measure the weak interaction between electrons. The experiment— Measurement of Lepton-Lepton Electroweak Reaction (MOLLER)—requires leveraging the recent 12 GeV electron beam upgrade and will run in JLab for three years. Focusing the signal for the MOLLER experiment requires five water-cooled toroidal magnets, each with unique geometry and with 7-fold symmetry. The five magnets operate in a vacuum and provide the magnetic field required to separate the incident beam electrons scattered from the target electrons (Møller scattering) and protons (elastic e-p scattering) in a liquid hydrogen target. The conceptual design was developed by the MOLLER Collaboration and was given to JLab in the form of amp turns and physical location, with additional physics requirements. This article presents prototyping of the coils and magnet support system and discusses the lessons learned during the process along with the plans for full magnet testing and installation. The JLab Magnet Group along with the MOLLER Collaboration developed the specification document that includes keep out zones to design the set of magnets. JLab contracted the design of the first toroid magnet (TM0) of the magnet system to Massachusetts Institute of Technology. The other four toroid magnets (TM1 through TM4) have been designed by JLab and are in the process of fabrication and assembly. Prototype coils of TM1-TM4 were fabricated by Everson-Tesla Incorporated, PA (USA). Finally, this article presents the unique challenges of the design, alignment, high current density, operating range, high radiation dose, and vacuum environment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Accelerated Climate Model for Energy (ACME): Ocean and Sea-Ice Processes

The primary goal of this project was to understand the role of the ocean and sea-ice components in the evolution of the climate in both a high-resolution fully-coupled 1850 preindustrial control and present day transient climate simulations run using the Energy Exascale Earth System Model (E3SM), formerly known as the Accelerated Climate Model for Energy (ACME). Two distinct approaches to the initialization of the present day transients were tested: in the first, an ensemble of three transients used atmospheric reanalysis forced 0.1-degree ocean/sea-ice states, while a fourth transient was branched off the preindustrial control. Biases from the control were inherited by its successor transient, in particular, sea surface temperatures (SSTs) at high latitudes were too warm and too much northward meridional heat transport occurred in the North Atlantic Ocean. SSTs in the Northern Hemisphere and Atlantic meridional heat transport increased in the transients initialized from the ocean/sea-ice simulation over a 40-50 year period to largely resemble the transient branched off the control simulation. Excessive absorbed solar radiation (ASR) is considered to be responsible for the SST biases as well as the formation of mode waters in lighter density classes than in reality both in the Southern Ocean and the North Atlantic Ocean subtropical gyre. These mode waters ventilate the thermocline waters to the north of their formation sites explaining the excessive Atlantic meridional heat transport and some of the warming in the high-latitude North Atlantic Ocean after multiple decades.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

HIGH POWER COUPLER DEVELOPMENT FOR EIC

The synchrotron radiation loss in EIC Electron Storage Ring is as high as up to 10 MW. This energy loss will be compensated by 17 2K 591 MHz single-cell SRF cavities with a combined total of 34 high power fundamental power couplers. Each power coupler will operate 92% of revolution time CW and ~8% of revolution time with 400 kW forward power due to the beam abort gap. To satisfy the EIC needs, we developed two 500 kW standing-wave FPC designs at BNL based on either a BeO and an Al2O3 RF window. This paper will briefly summarize test results of the BeO window FPC, and describe the design development of the Al2O3 window based FPC.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Beam dynamics corrections in the measurement of the anomalous precession frequency at the Muon $g-2$ experiment at Fermilab

The Muon $g-2$ experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon with an accuracy of 140 ppb (parts per billions). This accuracy, obtained by adding in quadrature a statistical and a systematic contribution of comparable value (100 ppb), will allow to reduce the experimental uncertainty (from the previous E821 experiment at BNL \cite{bnl}) of a factor of 4, and represents one of the most precise tests of the Standard Model (SM) theory of elementary particles. The first result on the Run-1 dataset \cite{prl} was released on April 7, 2021, showing a very good agreement with the previous result from BNL experiment, with a slightly better uncertainty. The corresponding experimental average increases the significance of the discrepancy between the measured and Standard Model prediction of 4.2$\sigma$ \cite{white_paper}.\\ \noindent The measured quantity is the muon magnetic anomaly a$_\mu$=$\frac{g_\mu-2}{2}$ where g$_\mu$ is the gyromagnetic factor of the muon. Dirac's equation predicts g$_\mu$ = 2, while radiative corrections, dominated by the QED contribution due to an exchange of a virtual photon, causes a per-mille correction on this quantity. By including all the SM contributions, a$_\mu$ is known at 370 ppb. The E989 experiment measures $a_\mu$ injecting positive muons with momentum of 3.1 GeV/$c$ polarized longitudinally in bunches (called $fills$) with an average rate of 12 Hz, in a storage ring of 14 meters diameter. Due to the parity violation in the weak muon decay, high energy positrons produced are emitted preferably in the muon's spin direction. By counting the number of positrons with energy greater then 1.7 GeV in function of the time, the frequency precession of the muon spin is measured, that together with the measurement of the magnetic field, allows to extract $a_\mu$. The positrons are detected with 24 electromagnetic calorimeters, that measure the energy and the arrival time of the positrons, each made of 54 crystals of lead fluoride (PbF$_2$) read by silicon photomultipliers (SiPM). Together with calorimeters, two tracking detectors are used to make non-destructive measurements of the muon beam characteristic by reconstructing the muon decay position extrapolating backward the decay positrons. The knowledge of the beam motion inside the ring plays a fundamental role in the analysis of $a_{\mu}$, where the measured anomalous precession frequency $\omega_a$ must be corrected for four main beam dynamics effects. A first correction is associated with the presence of an electric field responsible of the vertical focusing on the storage ring, where vertical direction is orthogonal to the orbit and horizontal direction is along the storage ring radius. Due to the oscillations in the vertical direction, the so called vertical betatron oscillations, a second correction is necessary to account for an average angle associated with the muon motion off the ideal orbit. A third correction is caused by lost muons in the ring which have a different spin phase at the injection respect to the decay ones. Finally, due to the correlation between the vertical and horizontal beam motion of the muons and the acceptance of the calorimeter, a correction (called ``phase-acceptance") arises. In Run1, due to the presence of two damaged resistors in one electrostatic quadrupole, this correction had a prominent role. The replacement of the damaged resistors before Run2 decreased this effect by one order of magnitude, and a further reduction in Run-3 was provided by an improved orbit.\\ \noindent The work of this Thesis focuses on the beam dynamics corrections on $\omega_a$. Due to the prominent role in Run-1 a special attention has been put to the phase-acceptance correction\footnote{The effect of this correction on the E821 BNL measurement of the $g-2$ has been evaluated to be within the quoted systematic error.}. Chapter \ref{ch:anomalous_magnetic_moment} introduces the anomalous magnetic moment of the muon. Chapter \ref{ch:early_experiment} describes the history of the Muon $g-2$ experiments. Chapter \ref{ch:theory} discusses the Standard Model prediction and possible new physics scenario. Chapter \ref{ch:muon_g2_experiment} describes the E989 experiment, whose experimental technique and the apparatus are discussed focusing on the improvements needed to reach the final goal on $a_\mu$ measurement. The original work of the Thesis is discussed in the last 5 chapters. Chapter \ref{ch:experiment_technique} presents the analysis technique to extract $\omega_a$, Chapter \ref{ch:beam_dynamics} describes the beam dynamics in the E989 experiment, Chapter \ref{ch:beam_dynamics_correction} discusses the beam dynamics correction to $\omega_a$, and Chapter \ref{sec:pa_corr} focuses on the phase acceptance correction. Finally Chapter \ref{ch:run23_analysis_improvements} contains the Run-2/3 improvements which are expected to allow for an increased precision ons the beam dynamics co...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗