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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 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

DEMONSTRATION OF A DATA-DRIVEN PHYSICS-BASED APPROACH FOR COMPUTATIONALLY EFFICIENT CFD PREDICTION OF TWO-PHASE BUBBLY FLOW

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale physics-guided data-driven approach, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. By defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. In a demonstration case of two-phase bubbly flow, the DFNN model well captured and corrected the unphysical “peaks” in the velocity and void fraction profiles near the wall in the coarse-mesh configuration, even for extrapolative predictions. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.

42 ENGINEERING↗
DOE OSTI2023

Reducing Uncertainty in Offshore Wind Energy Yield Estimates via a Metocean Reference Site

The offshore wind industry is burgeoning in the coastal waters of the United States, specifically along the Atlantic. For wind energy to be successful, reliable observations and model simulations are needed for resource assessment and forecasting. While many of these activities have already begun, there is currently an absence of observations at hub-height in these waters, with the closest available hub-height measurements usually taken onshore. Deployment of floating lidars has occurred through various federally funded projects, but only encapsulates time periods of a couple of years at best. Private industry is also beginning to leverage floating lidars, but this data is often proprietary, and not shared with the general public. In this work, we make the case for a metocean reference site for long-term offshore wind energy. Specifically, we quantify the impact of having a metocean reference site compared to other methods of determining hub-height winds and energy production. We use an offshore floating lidar to directly measure the wind resource, and compare these measurements to predictions derived from other widely-available surface meteorological variables. These prediction methods (vertical extrapolation, machine learning, and NWP output) produce a variety of vertical wind speed profiles, of which produce different energy yield estimates for a reference offshore turbine (Figure 1). While some methods perform reasonably well against the lidar, the uncertainty in these energy yield estimates has financial implications, further illustrating the need for long-term measurements in coastal waters.

machine learning↗
DOE OSTI2023

Experimental Aging and Lifetime Prediction in Grid Applications for Large-Format Commercial Li-Ion Batteries

Due to the growth of electric vehicle and stationary energy storage markets, the production and use of lithium-ion batteries has grown exponentially in recent years. For many of these applications, large-format lithium-ion batteries are being utilized, as large cells have less inactive material relative to their energy capacity and require fewer electrical connections to assemble into packs. And especially for stationary energy storage systems, where energy delivered is the only revenue source, the economics of these battery systems is highly dependent on cell lifetime. However, testing of large-format lithium-ion batteries is time consuming and requires high current channels and large testing chambers, making information on the performance of commercial, large-format lithium-ion batteries hard to come by. Here, accelerated aging test data from four commercial large-format lithium-ion batteries is reported. These batteries span both NMC-Gr and LFP-Gr cell chemistries, pouch and prismatic formats, and a range of cell designs with varying power capabilities. Accelerated aging test results are analyzed to examine both cell performance, in terms of efficiency and thermal response under load, as well as cell lifetime. Cell thermal response is characterized by measuring temperature during cycle aging, which is used to calculated a normalized thermal resistance value that may help estimate both cell cooling needs or to help extrapolate aging test results to different thermal environments. Cell lifetime is evaluated qualitatively, considering simply the average calendar and cycle life across a range of conditions, as well as quantitatively, using statistical modeling and machine-learning methods to identify predictive aging models from the accelerated aging data. These predictive aging models are then used to investigate cell sensitivities to stressors, such as cycling temperature, voltage window, and C-rate, as well as to predict cell lifetime in various stationary storage applications. Results from this work show that cell lifetime and sensitivity to aging conditions varies substantially across commercial cells, necessitating testing for specific cell formats to make quantitative lifetime predictions. That being said, all commercial cells tested here are predicted to reach at least 10-year lifetimes for stationary storage applications. Based on the aging test results and modeling, some cells are expected to be relatively insensitive to temperature and use-case, making them suited for simple use cases with little or no thermal management and simple controls, while the lifetime of other cells could be extended to 20+ years if operated with thermal management and degradation-aware controls.

battery↗
DOE OSTI2023

Maintaining Microstructure – The Path to Successful Technology Maturation in Fluidized Systems

Scaling circulating fluidized bed risers has been a point of contention for nearly a century. There have been numerous attempts to define various methodologies. These have all fallen short of providing a robust approach, primarily due to a lack of maintaining microstructure dynamics – a key factor in maintain interphase heat and mass transfer. Recent work by the author put forward an approach based up maintaining dynamic similarity at different scales by ensuring that the microstructure remained similar by maintaining statistical and chaotic parameters across the scale. That work relied on a dimensionless regime map in which the x-axis was defined by the ratio of the solids flux to the saturation carrying capacity. This latter property was only good within the range of the data and it became evident that extrapolation beyond the limits of the data could induce unrealistic conditions. Therefore, literature was reviewed to develop a better correlation for the saturation carrying capacity. In doing so, a critical diameter concept was developed and applied to the correlations for both Geldart Group A and B materials. The critical diameter for Geldart Group A and B materials is 0.2 m and 0.3 m, respectively. The paper then gives examples on how to use the scaling approach to maintain dynamic similarity across the scales.<br>

Breault, Ronald↗
DOE OSTI2023

GCR: Class B Code Case

This PowerPoint presentation is for Joint ART Materials/AMMT Program Review, Germantown, MD, on June-5-8, 2023. It will discuss development to revamp the ASME Section III Division 5 Class B design rules. There will be a plan in the FY24 to assess extrapolation methods for other Class A materials, alternative strain range evaluations for fatigue damage, evaluation of Class B intersection point in D-diagram relative to material-specific Class A intersection points, and evaluation of new Class B rules against Class A rules based on Elastic-Perfectly Plastic (EPP) methodology and full inelastic analysis method, using sample problems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Industry Facing PV Degradation Prediction Tool and Database to Enable a 50 Year Life Module

The goal of this work is to create an online tool that can be used to search for degradation information and extrapolate PV module performance and durability to field exposure. A graphical user interface will aid in the understanding of the results. The prediction tool will be built modular and published open-source allowing users to expand on the existing framework.

degradation↗
DOE OSTI2022

Analysis of Correlation between Cold Weather Meteorological Variables and Electricity Outages

The significance of the impact of weather on the electric grid has grown as climate change continues to increase the frequency and intensity of extreme weather events. In recent years (2021-2022) in particular, extreme winter weather has affected the grid in locations in the US rarely exposed to extreme low temperatures, snow and icing conditions. Here we analyze the correlation between cold weather meteorological variables and electricity outages during two large winter storm events, Uri (February 2021) and Landon (February 2022) using Random Forest machine learning and Pearson’s correlation coefficient. Our geographical focus across the two storms is the state of Texas. Extrapolation of the method to winter weather impacts over other years and additional locations is proposed.

Dumas, Melissa↗
DOE OSTI2023

Temperature Uncertainty Modeling with Proxy Structural Data as Geostatistical Constraints for Well Siting: An Example Applied to Granite Springs Valley, NV, USA

Utilizing existing temperature and structural information around Granite Springs Valley, Nevada, we build 3D stochastic temperature models with the aim of evaluating the 3D uncertainty of temperature and choosing between candidate exploration well locations . The data used to support the modeling are measured temperatures and structural proxies from 3D geologic modeling, the latter considered "secondary" data. Two stochastic geostatistical techniques are explored for incorporating the structural proxies: cosimulation and local varying mean. With both the cosimulation and local varying mean methods, many equally likely temperature models (i.e., realizations) are produced, from which temperature probability profiles are calculated at candidate well locations. To aid in choosing between the candidate locations, two quantities summarize the temperature probabilities: Vprior and entropy. Vprior quantifies the likelihood for economic temperatures at each candidate location, whereas entropy identifies where new information has the most potential to reduce uncertainty. In general, the cosimulation realizations have smoother spatial structure, and extrapolate high temperatures at candidate locations that are located along the direction of the longest spatial correlation, which are down dip from existing temperature logs. The smooth realizations result in tight temperature probability profiles that are easier to interpret, but they have unrealistic temperature reversals in some locations because the cosimulation technique does not enforce a conductive geothermal gradient as a baseline (i.e., linearly increasing temperature with depth). The local varying mean results produce realizations with more realistic geothermal gradients, with temperatures increasing downward since a depth-temperature relationship is included. However, because they have much noisier spatial nature compared to cosimulation, it is harder to interpret the temperature probability profiles. The different local varying mean results allow the geologist to determine which proxy (e.g., dilation versus distance to fault termination) should be used given the specific geothermal system. In general, Vprior from local varying mean results identify locations that are close to high values for the structural proxies: areas with highe r probabilities for higher temperatures. The entropy results identify where uncertainty is greatest and therefore new drilling information could be most useful. Though these techniques provide useful information, even when applied to areas of sparse data, our comp arison of these two techniques demonstrates the need for new geothermal geostatistics techniques that combine the advantages of these two methods and that are tailored to the spatial uncertainty issues inherent in geothermal exploration.

3D temperature modeling↗
DOE OSTI2023

Dynamic Model Agnostic Reliability Evaluation of Machine-Learning Models Integrated in Instrumentation & Control Systems

In recent years, the field of machine learning (ML), specifically neural networks, has grown significantly and has spurred research in its applicability to digital instrumentation and control systems (DI&C). While ML models have shown promise in operational contexts, the trustworthiness of using such algorithms has not been adequately assessed. Failures of ML integrated systems are not well understood, and the lack of comprehensive risk modeling can degrade the trustworthiness in these systems. In recent reports by the National Institute for Standards and Technology (NIST) [1] and the Nuclear Regulatory Commission (NRC) [2], they indicate that trustworthiness in ML is a critical barrier and will play a vital role in the safe, accountable, and secure operation of intelligent systems. Thus, in this work, we demonstrate a dynamic model-agnostic method to quantify the relative reliability of AI/ML predictions by incorporating out-of-distribution (OOD) detection on the training dataset. It is well documented that most ML algorithms excel at interpolation (or near-interpolation) tasks but experience significant performance degradation at extrapolation. The method, referenced as the Laplacian distributed decay for reliability (LADDR), determines the difference between the operational and training datasets which can used to the relative reliability of AI/ML predictions. LADDR is then demonstrated on a feedforward neural network based digital twin used for the prediction of safety significant factors during a loss-of-flow transient. LADDR is used to demonstrate how training data can be used as evidence to support the relative reliability of ML/AI predictions enhancing the overall trustworthiness of the system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A review of cladding failure thresholds in RIA conditions based on transient reactor test data and the need for continued testing

Transient reactor experiments on light water reactor (LWR) fuel pins had been conducted since the beginning of the nuclear era to help determine core coolability and cladding failure thresholds. During one such test in November of 1993 at the CABRI transient test reactor on a test involving a high burnup fuel rod with a corroded Zircaloy-4 cladding it was first observed that cladding failures could occur prior to a departure from nucleate boiling (pre-DNB) at lower-than-expected peak radial average enthalpies. Thirteen additional tests would be performed in the CABRI reactor over the next decade on fuel rods with higher burnups [1]. Additionally, a larger testing program at the NSRR reactor in Japan with high burnup fuel would uncover a similar trend of pre-DNB ruptures in high burnup test rods at lower-than-expected peak enthalpies [2]. Numerous out of pile testing programs involving a variety of innovative mechanical testing techniques have been employed in an attempt to better quantify the failure thresholds of corroded zirconium alloy cladding in these rapid heating and loading conditions [3][4][5]. While previously interim guidance had been issued, in June of 2020 the NRC officially published updated regulatory guidance to account of these pre-DNB failures in Regulatory Guide 1.236 [6]. This paper will present an independent review of the publicly available transient reactor test database on higher burnup LWR pins conducted at the CABRI and NSRR reactors as well as review of a selection of published out of pile mechanical testing methods. The purpose of the review is to determine how well the new regulatory limits are supported by experimental data. The review will identify if additional transient reactor tests could provide additional support for the NRC guidance or identify the need for revisions. The evaluation will consider how far the existing database can be extrapolated when considering low hydrogen zirconium alloy claddings (with and without protective coatings) containing very high burnup (> 70 MWd/kgU) UO2 fuel pellets. Finally, the authors will suggest how out of pile mechanical tests can be used in conjunction with a limited number of transient reactor tests to develop cladding specific failure thresholds in RIA type transients.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Experimental Studies and Energy Modeling for Evaluating Performance of Various Deep Wall Retrofits

The Pacific Northwest National Laboratory, Oak Ridge National Laboratory, and the University of Minnesota conducted a three-year, multipart study on residential retrofit wall assemblies. The project, which was funded by the U.S. Department of Energy’s Building Technology Office, aimed to compare a range of residential wall retrofit systems that prioritized affordability, durability, and energy savings potential. The research team identified, constructed, tested, simulated, and analyzed the feasibility and economics of 16 wall retrofit assemblies (14 test configurations and two baseline configurations) that can be applied to the exterior side of existing walls (either with or without the existing cladding). The 16 wall assemblies were installed in an in-situ laboratory environment, to evaluate the ease of construction and study the thermal and hygrothermal performance of the walls. This paper presents the methodology used to evaluate the thermal performance of the walls and discusses the energy modeling results of the study. The results from the experiments were used to calibrate a THERM model of each wall assembly, which was then applied to a whole building using the EnergyPlus 8.6 simulation engine. A residential prototype building was used to extrapolate whole-building energy savings in each U.S. climate zone. To capture the conditions of the largest number of homes in the United States, the most frequent building characteristics (e.g., attic insulation level, window specifications, foundation insulation, etc.) were extracted from ResStock data and applied to the prototype model. Results from the energy modeling showed that the climate zones with the highest potential for retrofit savings are those which are heating-dominated (i.e., Cold and Very Cold climate designations). In these climate zones, heating and cooling energy savings due to the wall retrofits alone ranged from 21.5% to 38.2%.

Nagda, Harshil↗
DOE OSTI2023

Dynamic Model Agnostic Reliability Evaluation of Machine-Learning Models Integrated in Instrumentation & Control Systems

In recent years, the field of data-driven neural network-based machine learning (ML) algorithms has grown significantly and spurred research in its applicability to instrumentation and control systems. While they are promising in operational contexts, the trustworthiness of such algorithms is not adequately assessed. Failures of ML-integrated systems are poorly understood; the lack of comprehensive risk modeling can degrade the trustworthiness of these systems. In recent reports by the National Institute for Standards and Technology, trustworthiness in ML is a critical barrier to adoption and will play a vital role in intelligent systems' safe and accountable operation. Thus, in this work, we demonstrate a real-time model-agnostic method to evaluate the relative reliability of ML predictions by incorporating out-of-distribution detection on the training dataset. It is well documented that ML algorithms excel at interpolation (or near-interpolation) tasks but significantly degrade at extrapolation. This occurs when new samples are "far" from training samples. The method, referred to as the Laplacian distributed decay for reliability (LADDR), determines the difference between the operational and training datasets, which is used to calculate a prediction's relative reliability. LADDR is demonstrated on a feedforward neural network-based model used to predict safety significant factors during different loss-of-flow transients. LADDR is intended as a "data supervisor" and determines the appropriateness of well-trained ML models in the context of operational conditions. Ultimately, LADDR illustrates how training data can be used as evidence to support the trustworthiness of ML predictions when utilized for conventional interpolation tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Pump-and-Treat Impacts on Aquifer Conditions and the Development of System-Wide Performance Strategies - 20377

The pump-and-treat (P and T) system on the Hanford Site's Central Plateau currently treats multiple contaminants within the 200-ZP-1 operable unit, including nitrate through its biological treatment processes. Although it was initially designed to support the 200-ZP-1 Remedial Action Objectives, the P and T system has evolved in use to address contaminants from other regions of the aquifer as well. The P and T influents are biogeochemically distinct, treating groundwaters with elevated concentrations of cyanide, uranium, technetium-99, and nitrate. Given the varying geochemical signatures from current and potential future sources, operational conditions, and amendments considered for treatment processes, there is a need to identify the impacts that the P and T effluent has on the aquifer, and how the aquifer affects P and T performance. To this end, laboratory efforts have focused on characterizing P and T effluent and its biogeochemical effects on the sediments through a series repacked column experiments. The P and T effluent is rich in particulate matter. A systematic inspection of this particulate matter in the P and T effluent showed significant levels of manganese/iron oxides, calcite crystals, relatively large organic matter molecules, and biomass. Therefore, the column experiments were designed and conducted for four different treatment systems: artificial groundwater, filtered P and T effluent, non-filtered P and T effluent, and chlorinated P and T effluent. Different levels of microbiologically- and geochemically-induced changes in the columns occurred and modified the flow systems. For example, physical filtration occurred in the sediments where the particulate material had accumulated in the top portion of the column. Reactive transport modeling of the laboratory experiments is being carried out so that the reaction network can be extrapolated to the field scale. These simulations will provide predictive evaluations of system performance based on P and T operational changes and aquifer mass loading and capacity estimates. This information can be used to address combined subsurface and operational challenges, such as the need for frequent well redevelopment to maintain injection capacity. This information also provides the technical basis for decisions related to the P and T system operations that support remedy optimization efforts and short- and long-term remedy decisions related to multiple operable units on the Hanford Site Central Plateau. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Characterization Strategy of a Limited Number of Radioactive Waste Effluent Tanks in View of Decommissioning a Large Number of Tanks - 20286

In order to organize the D and D of the former effluent treatment facility at the CEA Cadarache Center (France), the key data to gather through the facility characterization are the following:: volumes and masses, liquid/solid distribution and specific activity. By studying the treatment processes and the history of the facility, families of tanks have been defined and a reference tank chosen for investigation in each family. The intrusive investigations (video, residue thickness, dose rate..), the gamma spectrometry measurements carried out on site on the residue samples and radiochemical results collected in laboratories, led us to conclude that there was a relative radiological homogeneity (for specific activity and Am-241/Cs-137 ratio) within each tank. The next step consisted in extrapolating the specific activity evaluated for the reference tanks, to the other tanks of each family by using data such as geometry, dose rate or the function of the tanks within the process. Thus, a cartography of the 130 tanks of the facility is available. Finally, the conclusions drawn from the radiological homogeneity of the tanks and their affiliation to homogeneous, well-identified tank clusters lead to a simple and efficient operational approach for the D and D of the 130 tanks of the facility. Indeed, because of the residue characteristics (homogeneous activity and strong differentiation of Cs/Am ratio), a sample collected when opening the tank, and measured on site by gamma spectrometry will allow us to validate the operational design and the emptying techniques defined during the D and D study phase thanks to the characterization of a limited number of reference tanks. (authors)

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

Hardware-in-the-Loop Evaluation for Potential High Limit Estimation-Based PV Plant Active Control: Preprint

This paper validates the effectiveness of an Artificial Intelligence (AI)-driven PV plant control and optimization approach, namely, the Automated Learner for Intermittency Control by Extrapolation (ALICE), in empowering PV plant as a dependable grid reliability service provider. The validation is performed in a realistic laboratory controller-hardware-in-the-loop (CHIL) environment, leveraging accurate PV plant modeling and standard industrial communication protocol. Simulation results, considering both varying weather conditions and active control scenarios, demonstrate the superior performance of ALICE in improving the grid service delivery precision and reducing the over-curtailment compared to a state-of-the-art approach, i.e., reference-control grouping based approach. Such a work could help mitigate risks and provide practical guidance during the field deployment of ALICE, while establishing a standardized testing framework for evaluating various PV active control strategies.

hardware-in-the-loop↗
DOE OSTI2024

Post-Deployment Characterization of Glass Fiber-Reinforced Thermoset and Thermoplastic Composite Tidal Turbine Blades: Preprint

In 2021, the National Renewable Energy Laboratory (NREL) supported Verdant Power with the most successful tidal energy deployment in U.S. history. Three of their tidal turbines were deployed as part of the Roosevelt Island Tidal Energy project. Initially, the three rotors were manufactured from glass fiber-reinforced epoxy composites. Midway through the deployment, one rotor was replaced with one manufactured at NREL. Instead, it was infused with a novel, infusible thermoplastic resin system. Since the deployment, one epoxy rotor and one thermoplastic rotor were returned to NREL for continued materials and manufacturing research. The two rotors underwent full-scale structural testing before being sectioned and cut into specimens for a variety of manufacturing quality tests, thermos-mechanical characterization, and evaluation of material performance in marine environments, to understand the key differences between the fiberglass reinforced epoxy and Elium composites used for the respective rotors. Matrix burnoff tests showed that the Elium blades had a considerably higher fiber volume fraction compared to the epoxy blades (61% vs. 49%). Environmental aging of the specimens showed that the epoxy laminates absorbed more water over the conditioning period, however, it was determined that the Elium laminates had higher diffusion coefficients, so initially absorbed water faster. Finally, one full epoxy blade and one full Elium blade were conditioned at ambient temperatures for up to 11 months, while taking periodic mass measurements. The datasets were extrapolated out to assume a full 20 year operational life span and it was determined that the blades would not reach full saturation during that time span.

composite manufacturing↗
DOE OSTI2023

High-Throughput Electric-Field-Assisted Sintering and Characterization Techniques for Materials Discovery

Despite improvements in computing and modeling capabilities, the performance of new materials, particularly those which deviate greatly in composition from well-studied materials (e.g., high-entropy alloys), can be difficult to simulate given the lack of available experimental property data. While some modeling techniques may attempt to predict the properties of these exotic materials, most are forced to make extrapolations from more traditional materials. To fulfill the need for accelerated material synthesis and property measurement, a high-throughput methodology has been developed. Utilizing electric-field-assisted sintering (EFAS), also known as spark plasma sintering (SPS), equipped with custom tooling, samples of differing alloy compositions can be produced simultaneously as a single alloy array. Several arrays have been produced with compositions spanning the Co-Cr-Fe-Mn-Ni alloy family, including many high-entropy alloys, while the novel array geometry has enabled the samples to be polished and characterized in parallel, using X-ray diffraction, scanning-electron microscopy, and laser-based thermal diffusivity measurements.

36 MATERIALS SCIENCE↗
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↗