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NASA NTRS2007

Performance of the Lidar Design and Data Algorithms for the GLAS Global Cloud and Aerosol Measurements

The Geoscience Laser Altimeter System (GLAS) launched in early 2003 is the first polar orbiting satellite lidar. The instrument design includes high performance observations of the distribution and optical scattering cross sections of atmospheric clouds and aerosol. The backscatter lidar operates at two wavelengths, 532 and 1064 nm. For the atmospheric cloud and aerosol measurements, the 532 nm channel was designed for ultra high efficiency with solid state photon counting detectors and etalon filtering. Data processing algorithms were developed to calibrate and normalize the signals and produce global scale data products of the height distribution of cloud and aerosol layers and their optical depths and particulate scattering cross sections up to the limit of optical attenuation. The paper will concentrate on the effectiveness and limitations of the lidar channel design and data product algorithms. Both atmospheric receiver channels meet and exceed their design goals. Geiger Mode Avalanche Photodiode modules are used for the 532 nm signal. The operational experience is that some signal artifacts and non-linearity require correction in data processing. As with all photon counting detectors, a pulse-pile-up calibration is an important aspect of the measurement. Additional signal corrections were found to be necessary relating to correction of a saturation signal-run-on effect and also for daytime data, a small range dependent variation in the responsivity. It was possible to correct for these signal errors in data processing and achieve the requirement to accurately profile aerosol and cloud cross section down to 10-7 llm-sr. The analysis procedure employs a precise calibration against molecular scattering in the mid-stratosphere. The 1064 nm channel detection employs a high-speed analog APD for surface and atmospheric measurements where the detection sensitivity is limited by detector noise and is over an order of magnitude less than at 532 nm. A unique feature of the GLAS is a full acquisition of the surface return pulse, which has important application to the atmospheric transmission retrieval.

Spinhirne, James D.↗

NASA NTRS2015

Linear Mode HgCdTe Avalanche Photodiodes for Photon Counting Applications

An overview of recent improvements in the understanding and maturity of linear mode photon counting with HgCdTe electron-initiated avalanche photodiodes is presented. The first HgCdTe LMPC 2x8 format array fabricated in 2011 with 64 micron pitch was a remarkable success in terms of demonstrating a high single photon signal to noise ratio of 13.7 with an excess noise factor of 1.3-1.4, a 7 ns minimum time between events, and a broad spectral response extending from 0.4 micron to 4.2 micron. The main limitations were a greater than 10x higher false event rate than expected of greater than 1 MHz, a 5-7x lower than expected APD gain, and a photon detection efficiency of only 50% when greater than 60% was expected. This paper discusses the reasons behind these limitations and the implementation of their mitigations with new results.

HgCdTe↗

DOE OSTI2023

Analysis and Mitigation of Pulse-Pile-Up Artifacts in Plasma Pulse-Height X-ray Spectra

Pulse pile-up in pulse-height energy analyzers increases when the incident rate of pulses increases relative to the inverse of the dead time per pulse of the detection system. Changes in the observed energy distributions with incident rate and detector-electronics-formed pulse shape then occur. Here, we focus on weak high energy tails in X-ray spectra, important for measurements on partially ionized, warm (50–500 eV average electron energy), pure hydrogen plasma. A first-principles two-photon pulse-pile-up model is derived specific to trapezoidal-shaped pulses; quantitative agreement is found between the measurements and the model’s predictions. The model is then used to diagnose pulse-pile-up tail artifacts and mitigate them in relatively low count-rate spectra.

2-photon↗

NASA NTRSDate not supplied

Testing of A Photon-Counting Optical Ground Receiver With Emulated Space-to-Ground Link Effects

The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC) developed and previously characterized a photon-counting optical ground receiver system. The receiver is compliant with the Consultative Committee for Space Data Systems (CCSDS) Optical Communications Coding and Synchronization High Photon Efficiency (HPE) Standard. The standard will be used on the Optical Artemis-2 Orion (O2O) communications demonstration and the Deep Space Optical Communication (DSOC) project aboard the Psyche spacecraft. The receiver system consists of a fiber interconnect, up to sixteen superconducting nanowire single-photon detectors (SNSPDs), and a field programmable gate array (FPGA) based receive modem. Previously, the receiver system architecture was described and test results without emulated link effects were presented. SNSPD device properties, which impact detection jitter and time delay, can limit the receiver dynamic range, especially when operating with varying flux rates (>10 dB) between detectors. Codeword error-rate curves with and without simulated clock drifts attributed to Doppler shift and space transmitter clock differences are presented. Results with ±66 ppm clock differences show minimal performance impact (<0.2 dB). Test results show that the receiver dynamic range (>28 dB) is limited by changing SNSPD detection delays at high photon flux rates.

optical communications↗

NASA NTRSDate not supplied

Testing of A Photon-Counting Optical Ground Receiver With Emulated Space-to-Ground Link Effects

optical communications↗

NASA NTRS2011

Vacuum Nuller Testbed Performance, Characterization and Null Control

The Visible Nulling Coronagraph (VNC) can detect and characterize exoplanets with filled, segmented and sparse aperture telescopes, thereby spanning the choice of future internal coronagraph exoplanet missions. NASA/Goddard Space Flight Center (GSFC) has developed a Vacuum Nuller Testbed (VNT) to advance this approach, and assess and advance technologies needed to realize a VNC as a flight instrument. The VNT is an ultra-stable testbed operating at 15 Hz in vacuum. It consists of a MachZehnder nulling interferometer; modified with a "W" configuration to accommodate a hexpacked MEMS based deformable mirror (DM), coherent fiber bundle and achromatic phase shifters. The 2-output channels are imaged with a vacuum photon counting camera and conventional camera. Error-sensing and feedback to DM and delay line with control algorithms are implemented in a real-time architecture. The inherent advantage of the VNC is that it is its own interferometer and directly controls its errors by exploiting images from bright and dark channels simultaneously. Conservation of energy requires the sum total of the photon counts be conserved independent of the VNC state. Thus sensing and control bandwidth is limited by the target stars throughput, with the net effect that the higher bandwidth offloads stressing stability tolerances within the telescope. We report our recent progress with the VNT towards achieving an incremental sequence of contrast milestones of 10(exp 8) , 10(exp 9) and 10(exp 10) respectively at inner working angles approaching 2A/D. Discussed will be the optics, lab results, technologies, and null control. Shown will be evidence that the milestones have been achieved.

Lyon, R. G.↗

DOE OSTI2021

Characterization of the DUNE photodetectors and study of the event burst phenomenon

The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino physics experiment that will answer some of the most compelling questions in particle physics and cosmology. The DUNE far detectors employ silicon photomultipliers (SiPMs) to detect light produced by charged particles interacting in a large liquid argon time projection chamber (LArTPC). The SiPMs are photosensors consisting of an array of single-photon avalanche diodes (SPAD) operating in Geiger mode. Their high sensitivity and dynamic range, as well as the possibility to fill large surfaces with high-granularity sensors, makes them an ideal choice for DUNE. An international consortium of research groups is currently engaged in a systematic comparison of the performances of the SiPM models that have been custom developed for DUNE by two manufacturers. Such detailed studies, which include gain measurements and a structure study of the dark count rate at 77 K, are meant to determine the best choice of the photodetection system for DUNE, as well as characterize the response of the chosen detectors for the DUNE simulation. Moreover, an investigation of a newly observed phenomenon, in which quick bursts of tens of events at close range are collected in individual SiPMs, is being carried out, which potentially impacts the design of future models and their implementation in particle physics experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS2011

NASA Tech Briefs, November 2011

The topics include: 1) Flight Test Results from the Rake Airflow Gage Experiment on the F-15B; 2) Telemetry and Science Data Software System; 3) CropEx Web-Based Agricultural Monitoring and Decision Support; 4) High-Performance Data Analysis Tools for Sun-Earth Connection Missions; 5) Experiment in Onboard Synthetic Aperture Radar Data Processing; 6) Microfabrication of a High-Throughput Nanochannel Delivery/Filtration System; 7) Improved Design and Fabrication of Hydrated-Salt Pills; 8) Monolithic Flexure Pre-Stressed Ultrasonic Horns; 9) Cryogenic Quenching Process for Electronic Part Screening; 10) Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions; 11) Wheel-Based Ice Sensors for Road Vehicles; 12) G-DYN Multibody Dynamics Engine; 13) Multibody Simulation Software Testbed for Small-Body Exploration and Sampling; 14) Propulsive Reaction Control System Model; 15) Licklider Transmission Protocol Implementation; 16) Core Recursive Hierarchical Image Segmentation; 17) Two-Stage Centrifugal Fan; 18) Combined Structural and Trajectory Control of Variable-Geometry Planetary Entry Systems; 19) Pressure Regulator With Internal Ejector Circulation Pump, Flow and Pressure Measurement Porting, and Fuel Cell System Integration Options; 20) Temperature-Sensitive Coating Sensor Based on Hematite; 21) Standardization of a Volumetric Displacement Measurement for Two-Body Abrasion Scratch Test Data Analysis; 22) Detection of Carbon Monoxide Using Polymer-Carbon Composite Films; 23) Substituted Quaternary Ammonium Salts Improve Low-Temperature Performance of Double-Layer Capacitors; 24) Sustainably Sourced, Thermally Resistant, Radiation Hard Biopolymer; 25) Integrated Lens Antennas for Multi-Pixel Receivers; 26) 180-GHz Interferometric Imager; 27) Maturation of Structural Health Management Systems for Solid Rocket Motors; 28) Validating Phasing and Geometry of Large Focal Plane Arrays; 29) Transverse Pupil Shifts for Adaptive Optics Non-Common Path Calibration; 30) Qualification of Fiber Optic Cables for Martian Extreme Temperature Environments; 31) Solid-State Spectral Light Source System; 32) Multiple-Event, Single-Photon Counting Imaging Sensor; 33) Surface Modeling to Support Small-Body Spacecraft Exploration and Proximity Operations; and 34) Achieving Exact and Constant Turnaround Ratio in a DDS-Based Coherent Transponder.

Source record↗

NASA NTRS1992

Modeling the stellar contribution to the Galactic component of the diffuse soft X-ray background. I - Background fluxes and number counts

A combination of a stellar Galaxy model based on optical data, stellar X-ray luminosity functions derived from the full Einstein base, and a model for X-ray absorption derived from hydrogen column densities are used to estimate the contribution to the diffuse soft X-ray background flux from the main-sequence A, F, G, K, and M stars, and RS CVn stars, at various energies ranging from 0.1 to about 5 keV. Previous discrepancies between earlier estimates of the stellar contribution to the diffuse soft X-ray background are resolved; this stellar contribution to the diffuse soft X-ray background is found to be under 3 percent for photon energies less than energy I and J bands (about 0.8-2 keV), at a threshold sensitivity for point source detection about 10 exp -10 ergs/s sq cm. At low latitudes, stellar contribution estimates are less than 3 percent below 0.3 keV, 7-40 percent in the medium-energy bands, and 27-70 percent in the I and J bands. It is shown that while dM stars are the major contributors to the diffuse stellar flux, other stellar types contribute as much as 40 percent of this flux at the higher energies in the passband studied.

Kashyap, V.↗

NASA NTRS2003

Chandra X-Ray Observations of the Spiral Galaxy M81

A Chandra X-Ray Observatory ACIS-S imaging observation is used to study the population of X-ray sources in the nearby Sab galaxy M81 (NGC 3031). A total of 177 sources are detected with 124 located within the D(sub 25) isophote to a limiting X-ray luminosity of approx. 3 x 10(exp 36) ergs/s. Source positions, count rates, luminosities in the 0.3-8.0 keV band, limiting optical magnitudes, and potential counterpart identifications are tabulated. Spectral and timing analysis of the 36 brightest sources are reported including the low luminosity active galactic nucleus, SN 1993J, and the Einstein-discovered ultraluminous X-ray source X6. The nucleus accounts for approx. 86%, or 5 x 10(exp 40) ergs/s, of the total X-ray emission from M81. Its spectrum is well fitted by an absorbed power law with photon index 1.98 +/- 0.08, consistent with previous observations (average index 1.9). SN 1993J has softened and faded since its discovery. At an age of 2594 days, SN 1993J displayed a complex thermal spectrum from a reverse shock rich in Fe L and highly ionized Mg, Si, and S but lacking O. A hard X-ray component, emitted by a forward shock, is also present. X6 is spatially coincident with a stellar object with optical brightness and colors consistent with an O9-B1 main-sequence star. It is also coincident with a weak radio source with a flux density of approx. 95 microJy at lambda = 3.6 cm. The continuum-dominated X-ray spectrum of X6 is most closely reproduced by a blackbody disk model suggesting the X-ray source is an approx. 18 solar mass object accreting at nearly its Eddington limit.

Swartz, Douglas A.↗

NASA NTRS1992

A photon-phreak digs the LDEF happening

Radioactivities of the LDEF onboard experiments induced by gamma emitting rays in both intentional samples and spacecraft parts were examined. The long time greatly enhanced the ability to detect some of the longer lived nuclides, including: 2.6 yr Na-22 in Al and Fe; 5.3 yr Co-60 in Co, Ni, and In; 2.9 yr Rh-102 in In; and 38 yr Bi-207 in Pb. These radionuclides, along with such other as 33 yr Ar-42 in Ti, Fe, or Ni and 47 yr Ti-44 in the same elements, would be appropriate monitors of the high energy space radiation field on long round-trip voyages in the solar system. Additional candidate radionuclides are also discussed. Radiometric analysis of the LDEF samples was a substantial effort among a dedicated group of experts in low level counting, and highlights several important aspects of the procedures needed to achieve success in this kind of endeavor. Target elements should be chosen to differentiate between neutron and proton induced reactions, whenever this is feasible. Reactions should be chosen with a wide range of energy thresholds, to enable calculation of both intensity and energy spectra of the particle fluxes.

Smith, Alan R.↗

NASA NTRS1999

Diffuse Reflection of Laser Light From Clouds

Laser light reflected from an aqueous suspension of particles or "cloud" with known thickness and particle size distribution defines the "cloud radiative Green's function", G. G is sensitive to cloud thickness, allowing retrieval of that important quantity. We describe a laboratory simulation of G, useful in design of an offbeam Lidar instrument for remote sensing of cloud thickness. Clouds of polystyrene microspheres suspended in water are analogous to real clouds of water droplets suspended in air. The size distribution extends from 0.5 microns to 25 microns, roughly lognormal, similar to real clouds. Density of suspended spheres is adjusted so photon mean-free-path is about 10 cm, 1000 times smaller than in real clouds. The light source is a Nd:YAG laser at 530 nm. Detectors are flux and photon-counting PMTs, with a glass probe for precise positioning. A Labview 5 VI controls position and data acquisition, via an NI Motion Control board connected to a stepper motor driving an Edmund linear slider,and a 16-channel 16-bit NI-DAQ board. The stepper motor is accurate to 10 microns. Step size is selectable. Far from the beam, the rate of exponential increase in the beam direction scales as expected from diffusion theory, linearly with cloud thickness, and inversely as the square root of the reduced optical thickness, independent of particle size. Nearer the beam the signal increases faster than exponential and depends on particle size. Results verify 3D Monte Carlo simulations that demonstrate detectability of remotely sensed offbeam returns, without filters at night, with narrow bandpass filter in day.

Cahalan, R. F.↗

NASA NTRS2002

NASA's Photon-Counting SLR2000 Satellite Laser Ranging System: Progress and Applications

NASA's new unmanned SLR2000 system is designed to track, with millimeter precision and using single photon returns, a constellation of roughly 24 retroreflector-equipped satellites, which range in altitude from about 300 km to 20,000 km. Totally autonomous operation and a common engineering configuration are expected to greatly reduce station operations costs relative to NASA's current manned systems. The system has also been designed with a goal of significantly lowering replication costs. All of the prototype components and subsystems have been completed and tested and have substantially met the original specifications. The prototype system is presently undergoing final integration and testing in a dedicated shelter with an azimuth tracking dome synchronized to the optical tracking mount. The facility also features a number of security features such as security cameras and sensors designed to detect power or thermal control problems or entry by unauthorized personnel. Field tests are in progress. The present paper provides an overview of the various subsystems and test results to date. The meteorological subsystem, which has operated successfully in the field for almost three years, consists of several sensors which measure: (1) pressure, temperature, and relative humidity; (2) wind speed and direction; (3) ground visibility and precipitation; and (4) local cloud cover as a function of station azimuth and elevation (day and night). A "pseudo-operator" software program interprets the sensor readings and modifies satellite tracking priorities based on local meteorological conditions.

Degnan, John J.↗

NASA NTRS2001

A High-Speed, Event-Driven, Active Pixel Sensor Readout for Photon-Counting Microchannel Plate Detectors

Silicon array readouts for microchannel plate intensifiers offer several attractive features. In this class of detector, the electron cloud output of the MCP intensifier is converted to visible light by a phosphor; that light is then fiber-optically coupled to the silicon array. In photon-counting mode, the resulting light splashes on the silicon array are recognized and centroided to fractional pixel accuracy by off-chip electronics. This process can result in very high (MCP-limited) spatial resolution for the readout while operating at a modest MCP gain (desirable for dynamic range and long term stability). The principal limitation of intensified CCD systems of this type is their severely limited local dynamic range, as accurate photon counting is achieved only if there are not overlapping event splashes within the frame time of the device. This problem can be ameliorated somewhat by processing events only in pre-selected windows of interest or by using an addressable charge injection device (CID) for the readout array. We are currently pursuing the development of an intriguing alternative readout concept based on using an event-driven CMOS Active Pixel Sensor. APS technology permits the incorporation of discriminator circuitry within each pixel. When coupled with suitable CMOS logic outside the array area, the discriminator circuitry can be used to trigger the readout of small sub-array windows only when and where an event splash has been detected, completely eliminating the local dynamic range problem, while achieving a high global count rate capability and maintaining high spatial resolution. We elaborate on this concept and present our progress toward implementing an event-driven APS readout.

Kimble, Randy A.↗

NASA NTRS2002

A High-Speed, Event-Driven, Active Pixel Sensor Readout for Photon-Counting Microchannel Plate Detectors

Silicon array readouts for microchannel plate intensifiers offer several attractive features. In this class of detector, the electron cloud output of the MCP intensifier is converted to visible light by a phosphor; that light is then fiber-optically coupled to the silicon array. In photon-counting mode, the resulting light splashes on the silicon array are recognized and centroided to fractional pixel accuracy by off-chip electronics. This process can result in very high (MCP-limited) spatial resolution while operating at a modest MCP gain (desirable for dynamic range and long term stability). The principal limitation of intensified CCD systems of this type is their severely limited local dynamic range, as accurate photon counting is achieved only if there are not overlapping event splashes within the frame time of the device. This problem can be ameliorated somewhat by processing events only in pre-selected windows of interest of by using an addressable charge injection device (CID) for the readout array. We are currently pursuing the development of an intriguing alternative readout concept based on using an event-driven CMOS Active Pixel Sensor. APS technology permits the incorporation of discriminator circuitry within each pixel. When coupled with suitable CMOS logic outside the array area, the discriminator circuitry can be used to trigger the readout of small sub-array windows only when and where an event splash has been detected, completely eliminating the local dynamic range problem, while achieving a high global count rate capability and maintaining high spatial resolution. We elaborate on this concept and present our progress toward implementing an event-driven APS readout.

Kimble, Randy A.↗

DOE OSTI2025

Characterization of 6 Li-loaded pulse-shape-discriminating plastic scintillators

Lithium-loaded organic plastic scintillators combine sensitivity to γ rays with the ability to detect both fast and slow neutrons, making them valuable for applications in nuclear security and in basic nuclear and particle physics. The goal of this work is to characterize the neutron response of two custom lithium-loaded organic plastic scintillators developed at Lawrence Livermore National Laboratory. Both are ternary polystyrene-based formulations containing 1.5 wt.% 6 Li salts of isobutyric acid, but they differ in their primary and secondary dye compositions: one uses m-terphenyl as the primary fluor and with Exalite 404 as the wavelength shifter, whereas the other uses 2,5-diphenyloxazole (PPO) and 9,10-diphenyl-anthracene, respectively. The temporal response of the scintillators was measured via time-correlated single photon counting for γ-ray and neutron events. The proton light yield was measured using the double time-of-flight technique from 1.3 to 15 MeV at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. For the slow neutron response, an AmBe source moderated with polyethylene was used, and the light output from the 6 Li(n,α)t reaction was characterized. Differences in ionization quenching and temporal response were observed between the two materials with the PPO-containing scintillator exhibiting higher ionization quenching. These results provide performance benchmarks that can guide the design and optimization of future lithium-loaded plastic scintillators for use in basic science and applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1977

A focussing iron line crystal spectrometer for Spacelab

A crystal spectrometer system is described which employs conical focusing of 12 curved LiF crystal panels to minimize the detector size and reduce the background counting rate. The wavelength range from 1.70 to 1.98 A is covered, including the resonance lines of Fe XXV and Fe XXVI as well as the Fe I K-alpha line and absorption edge. Operation of the spectrometer is discussed, noting that diffracted X-rays are registered in one-dimensional position-sensitive detectors and that the arrival position of a photon in a detector is related to its wavelength due to the fixed curvature of the crystal panels in the dispersion plane. Some characteristics of the multianode position-sensitive detectors are reviewed along with the crystal arrangement and mounting. The instrument sensitivity is evaluated in relation to the strengths of 6.7-keV emission features detected by the Ariel 5 and OSO 8 proportional-counter spectrometers.

Catura, R. C.↗

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↗