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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↗

DOE OSTI2020

Statistical properties of homogeneous and isotropic turbulence in He II measured via particle tracking velocimetry

Despite being a quantum two-fluid system, superfluid helium-4 (He II) is observed to behave similarly to classical fluids when a flow is generated by mechanical forcing. This similarity has brought up the feasibility of utilizing He II for high Reynolds number classical turbulence research, considering the small kinematic viscosity of He II. However, it has been suggested that the nonclassical dissipation mechanism in He II at small scales may alter its turbulent statistics and intermittency. In this work, we report our study of a nearly homogeneous and isotropic turbulence (HIT) generated by a towed grid in He II. We measure the velocity field using particle tracking velocimetry with solidified deuterium particles as the tracers. By correlating the velocities measured simultaneously on different particle trajectories or at different times along the same particle trajectory, we are able to conduct both Eulerian and Lagrangian flow analyses. Spatial velocity structure functions obtained through the Eulerian analysis show scaling behaviors in the inertial subrange similar to that for classical HIT but with enhanced intermittency. The Lagrangian analysis allows us to examine the flow statistics down to below the dissipation length scale. Interestingly, abnormal deviations from the classical scaling behaviors are observed in this regime. Lastly, we discuss how these deviations may relate to the motion of quantized vortices in the superfluid component in He II.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Dynamic Motions of Topological Defects in Nematic Liquid Crystals under Spatial Confinement

Abstract Topological defects (TDs) have become a sensational topic due to their significant influence on the unusual optical and physiochemical characteristics of the material. To facilitate their application across a wide range of disciplines it is desirable to analyze and gain fundamental understanding of TDs in both equilibrium and nonequilibrium systems. Liquid crystals (LCs) are considered an ideal system for study given the direct visualization of TDs and a straightforward analyzation process. In addition to the equilibrium morphology of LC TDs, it is also of great interest to track and control the formation and annihilation of defects during thermodynamic processes. However, controlling the dynamic behavior of formed defects remains a challenge. Here, nematic LCs confined in a cell exhibiting surfaces with periodic anchoring conditions containing surface topography are relied on. The effects of patterned surface characteristics such as width, periodicity, and degree of curvature on defects dynamic motion, stabilization, and annihilation are explored. The computational experiments recapitulate the TDs transition path and provide free energy‐based predictions of critical distances for defect annihilation. Taken together, this simple approach offers a promising opportunity to control the dynamics of TDs in LCs through chemical patterned surfaces with topography.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Control of long-distance motion of single molecules on a surface

Spatial control over molecular movement is typically limited because motion at the atomic scale follows stochastic processes. Here, we used scanning tunneling microscopy to bring single molecules into a stable orientation of high translational mobility where they moved along precisely defined tracks. Single dibromoterfluorene molecules moved over large distances of 150 nanometers with extremely high spatial precision of 0.1 angstrom across a silver (111) surface. The electrostatic nature of the effect enabled the selective application of repulsive and attractive forces to send or receive single molecules. The high control allows us to precisely move an individual and specific molecular entity between two separate probes, opening avenues for velocity measurements and thus energy dissipation studies of single molecules in real time during diffusion and collision.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Fast Dynamic Aperture Optimization with Reversal Integration

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.

36 MATERIALS SCIENCE↗

NASA NTRS1972

Analog analysis of a tracked air-cushion vehicle.

The dynamics of tracked air-cushion vehicles considered for high-speed ground transportation systems are examined using a vehicle model represented by a one-degree-of-freedom system. The respective equations of motion are derived, and the control system is discussed. The equations obtained for the cushion are solved using an analog computer. The computer showed the effect of the control technique on the relative motion between vehicle and guideway.

Leatherwood, J. D.↗

NASA NTRS1989

Joint-space adaptive control of a 6 DOF end-effector with closed-kinematic chain mechanism

The development is presented for a joint-space adaptive scheme that controls the joint position of a six-degree-of-freedom (DOF) robot end-effector performing fine and precise motion within a very limited workspace. The end-effector was built to study autonomous assembly of NASA hardware in space. The design of the adaptive controller is based on the concept of model reference adaptive control (MRAC) and Lyapunov direct method. In the development, it is assumed that the end-effector performs slowly varying motion. Computer simulation is performed to investigate the performance of the developed control scheme on position control of the end-effector. Simulation results manifest that the adaptive control scheme provides excellent tracking of several test paths.

Nguyen, Charles C.↗

NASA NTRS1991

Passive range estimation for rotorcraft low-altitude flight

The automation of rotorcraft low-altitude flight presents challenging problems in control, computer vision and image understanding. A critical element in this problem is the ability to detect and locate obstacles, using on-board sensors, and modify the nominal trajectory. This requirement is also necessary for the safe landing of an autonomous lander on Mars. This paper examines some of the issues in the location of objects using a sequence of images from a passive sensor, and describes a Kalman filter approach to estimate the range to obstacles. The Kalman filter is also used to track features in the images leading to a significant reduction of search effort in the feature extraction step of the algorithm. The method can compute range for both straight line and curvilinear motion of the sensor. A laboratory experiment was designed to acquire a sequence of images along with sensor motion parameters under conditions similar to helicopter flight. Range estimation results using this imagery are presented.

Sridhar, B.↗

NASA NTRS1993

Passive range estimation for rotorcraft low-altitude flight

Sridhar, B.↗

NASA NTRS1993

Passive range estimation for rotorcraft low-altitude flight

Sridhar, B.↗

NASA NTRS1993

Simulation development of a forward sensor-enhanced low-altitude guidance system

The requirement to operate aircraft at low-altitude near the terrain is common in the military community and essential for helicopters. The risk and crew workload in this flight regime is severe, with navigation, guidance, and obstacle avoidance demanding high attention. A guidance system relying on digitized terrain elevation maps has been developed that employs airborne navigation, mission requirements, aircraft performance limits, and radar altimeter returns to generate a valley-seeking, low-altitude trajectory between waypoints for display to the pilot. This system has been flight demonstrated to 150 ft above ground level altitude, and is primarily limited by the ability of the pilot to perform obstacle detection and avoidance. In this study, a wide field of view forward sensor has been modeled and incorporated in the guidance system for the purpose of relieving the pilot of the obstacle avoidance duty. The results of a piloted, motion-based simulation of this enhanced low-altitude guidance system is presented. Simulated flights to 50 ft altitude in the presence of obstacles were demonstrated while maintaining situational awareness and close tracking of the guidance trajectory.

Zelenka, Richard E.↗

NASA NTRS2002

Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence

When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.

Abedian, B.↗

NASA NTRS2005

[Summary of Research on Relationship Between Core Convective Structure and Intensity Change in Tropical Cyclones]

The downshear reformation of Tropical Storm Gabrielle (2001) was investigated using radar reflectivity and lightning data that were nearly continuous in time, as well as frequent aircraft reconnaissance flights. Initially the storm was a marginal tropical storm in an environment with strong 850-200 hPa vertical wind shear of 12-13 meters per second and an approaching upper tropospheric trough. Both the observed outflow and an adiabatic balance model calculation showed that the radial-vertical circulation increased with time as the trough approached. Convection was highly asymmetric, with almost all radar return located in one quadrant left of downshear in the storm. Reconnaissance data show that an intense mesovortex formed downshear of the original center. This vortex was located just south of, rather than within, a strong downshear left lightning outbreak, consistent with tilting of the horizontal vorticity associated with the vertical wind shear. The downshear mesovortex contained a 972 hPa minimum central pressure, 20 hPa lower than minimum pressure in the original vortex just three hours earlier. The mesovortex became the new center of the storm, but weakened somewhat prior to landfall. It is argued that dry air carried around the storm from the region of upshear subsidence, as well as the direct effects of the shear, prevented the reformed vortex from continuing to intensify. Despite the subsequent weakening of the reformed center, it reached land with greater intensity than the original center. It is argued that this intensification process was set into motion by the vertical wind shear in the presence of an environment with upward motion forced by the upper tropospheric trough. In addition, the new center formed much closer to the coast and made landfall much earlier than predicted. Such vertical shear-induced intensity and track fluctuations are important to understand, especially in storms approaching the coast. The structures of the highly sheared tropical storm Chantal During CAMEX-4 is also discussed.

Source record↗

DOE OSTI2024

Tropical Cyclone Wind Shear-Relative Asymmetry in Reanalyses

Abstract While tropical cyclones (TCs) are axisymmetric vortices to the first order, they often exhibit noteworthy structural asymmetries. These often result from environmental vertical wind shear, which tilts the vortex and induces a wavenumber 1 pattern in the circulation and precipitation fields. Reanalyses and climate models have improved in representing the TC structure and climatology, but their relatively coarse resolution and dependence on parameterized physics cast doubt on their ability to capture the asymmetric TC structure. We perform the most comprehensive process-oriented assessment of TC asymmetry to date in reanalyses. Specifically, we analyze the composite shear-relative TC structure in ERA5 and Climate Forecast System Reanalysis (CFSR), which vary in their resolutions, physical parameterization suites, and data assimilation techniques. These structures are compared with aircraft reconnaissance radar observations. In agreement with the observations, the strongest tangential winds are usually found left-of-shear, while inner core rainfall, ascent, vortex tilt, and low-level inflow are favored directly downshear or in the downshear-left quadrant. Outer rainband convection generally peaks in the downshear-right quadrant. Thermodynamic asymmetries are also apparent, with anomalous low-level moisture right-of-shear, midlevel warmth in the upshear-right quadrant (uptilt), and cloud properties suggestive of a realistic precipitation life cycle from growth to fallout. We also decompose rainfall contributions from the convective parameterization and large-scale cloud schemes and highlight the roles of vorticity advection, buoyancy advection, and diabatic processes in driving asymmetric vertical motions in the inner core and outer rainband regions. Our results suggest that process-level studies of TC asymmetry and TC–wind shear interaction under future warming are viable using climate models. Significance Statement Asymmetries are common in tropical cyclones (TCs), influencing their intensity, track, and hazards. Vertical wind shear often plays a leading-order role in causing these asymmetries. It is uncertain how well asymmetric structures and processes are captured in reanalyses and global climate models (GCMs) with grid spacings of 0.25° and coarser. In this study, we first evaluate TC asymmetry in reanalyses, which have the benefit of being forced by observations. This helps to assess whether the resolutions associated with GCMs sufficiently capture asymmetric structures and processes and motivates upcoming work with free-running GCMs to study how TC asymmetry may change in a warming climate.

Carstens, Jacob D.↗

NASA NTRS1986

The global tracking networks for crustal dynamics

Highly accurate Satellite Laser Ranging (SLR) and Very-Long-Baseline Interferometry (VLBI) have been implemented by the NASA Crustal Dynamics Project and many cooperating groups in many countries to form global SLR and VLBI networks for geodetic measurements of global plate motion, plate deformation, regional deformations in areas of high earthquake activity, and accurate measurements of the earth's polar motion and changes in rotation rate. These systems are measuring vector baselines between stations to an accuracy of 2-5 cm. New improvements being implemented will improve the accuracy to about 1 cm.

Coates, R. J.↗

NASA NTRS1972

Some higher order analyses of earth and lunar orbiters

The accurate modelling of the translational behavior of a drag-free satellite in an almost circular near-earth orbit is investigated. All short and long period position fluctuations in the satellite's coordinates down to 1 m are determined. The general zonal and tesseral harmonic effects are considered as well as lunar and solar effects. A noncanonical approach is followed. A mean orbital plane is chosen so that no short period out-of-plane fluctuations greater than second order occur. Short period radial and cross-track fluctuations and in-track fluctuations are computed. Long period and secular rates of the mean elements which define the slowly varying plane of reference are determined to third order in the small quantities. The equations of motion are integrated analytically away from critical inclination and tesseral resonance. The resonant situation of a sun-synchronous orbit is discussed as a special case. The long-period behavior of a lunar orbiter is also considered, including the effects due to the inclination of the earth's apparent orbit about the moon and those described by Cassini laws on the equations of motion. Both resonant and nonresonant low orbits, and high orbits are discussed.

Dasenbrock, R. R.↗

NASA NTRS1989

The glideslope approach

The problems associated with optimum approaches to an orbiting spacecraft at the completion of rendezvous are exacerbated when the maneuvering spacecraft is to dock with such large and extended structures as the NASA Space Station, which also has a torque equilibrium attitude due to which the docking port does not point directly into the orbital track. Attention is presently given to a candidate 'operationally optimum' approach to a local vertical-local horizontal stabilized target; this glideslope approach is derived on the basis of Hill's relative-motion equations, which have been expanded to encompass constant relative accelerations in a closed form solution. The motion is described in polar coordinates.

Pearson, Don J.↗

NASA NTRS1991

Applications of fuzzy logic to control and decision making

Long range space missions will require high operational efficiency as well as autonomy to enhance the effectivity of performance. Fuzzy logic technology has been shown to be powerful and robust in interpreting imprecise measurements and generating appropriate control decisions for many space operations. Several applications are underway, studying the fuzzy logic approach to solving control and decision making problems. Fuzzy logic algorithms for relative motion and attitude control have been developed and demonstrated for proximity operations. Based on this experience, motion control algorithms that include obstacle avoidance were developed for a Mars Rover prototype for maneuvering during the sample collection process. A concept of an intelligent sensor system that can identify objects and track them continuously and learn from its environment is under development to support traffic management and proximity operations around the Space Station Freedom. For safe and reliable operation of Lunar/Mars based crew quarters, high speed controllers with ability to combine imprecise measurements from several sensors is required. A fuzzy logic approach that uses high speed fuzzy hardware chips is being studied.

Lea, Robert N.↗