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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

High-resolution lidar observations of sedimentation-induced size sorting of droplets near a laboratory cloud top

Cloud optical properties and precipitation, which are crucial to weather and climate, are strongly influenced by cloud microphysical properties that are still poorly understood. Here, we develop a high-resolution time-correlated single-photon-counting lidar and apply it to observe cloud microphysical properties at one-centimeter range resolution in a convection chamber under well-controlled conditions. Together with concurrent in-situ measurements and theoretical analysis, our lidar observations indicate that although turbulent mixing tends to homogenize the cloud in the bulk region, entrainment and sedimentation cause inhomogeneities in droplet concentrations near the cloud top. Specifically, the topmost region is directly affected by entrainment, and lidar profiles show clear evidence of entrained air and detrained cloud filament. The transition region below exhibits vertical size sorting of cloud droplets caused by sedimentation. Our results suggest that using a single sedimentation velocity for all cloud droplets, as is done in many atmospheric models, overlooks key physics relevant to the microphysical structure near the cloud top. In conclusion, our conceptual model used to describe these measurements can serve as a step toward improving the current modeling of processes in the cloud top region.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1984

Application of improved numerical schemes

Two approaches which accelerate the solution of the steady state Navier-Stokes equations are discussed. The SIMPLER algorithm, a revised version of SIMPLE, provides a more accurate pressure field for each iteration through the momentum equations, thereby speeding convergence. PISO (Pressure Implicit Split Operator), performs a secondary correction of the velocity and pressure fields (after the typical pressure correction) which enhances convergence. Both schemes account for terms neglected in the SIMPLE approach, but do so in slightly different ways. Two dimensional driven cavity flow and flow over a step were calculated to examine the effect of geometry on the performance of these schemes. Computations were carried out on a series of progressively finer grids. The effect of relaxation number on convergence rate was analyzed, using results from SIMPLE as criteria for performance correlation. Results show: (1) the improved schemes promoted convergence by up to 60% for the driven cavity and 40% for flow over a step; (2) for the driven cavity problem, the efficiency of PISO and SIMPLER increased as the number of nodes increased; and (3) to ensure faster convergence, higher relaxation numbers must be applied.

Neely, G. H.↗
NASA NTRS1985

A three-dimensional turbulent boundary layer undergoing transverse strain and streamwise pressure gradient

Results from an experimental investigation designed to provide data on both mean and turbulence quantities in the axisymmetric, swirling boundary layer (with and without pressure gradient) flowing over a stationary cylinder downstreams of a spinning cylindrical section are presented. The pressure gradient was introduced into the flow field by a 25.4 mm-high, forward-facing, circular step mounted on the stationary cylinder, the step height being nearly equal to the thickness of the approaching boundary layer. All the measurements were made at a nominal upstream reference Reynolds number of 2.4 x 10 to the 6th power/m (corresponding to an upstream reference velocity of 36 to 37 m/sec) with the rotation of the spinner set to make its peripheral speed equal the reference velocity. The data reported included measurements of surface pressure and the mean surface shear-stress vector taken with a miniature, directional, surface-fence gage. These measurements were supplemented by oil-flow visualization studies of the stationary cylinder. The data indicates that the streamwise pressure gradient controls the development of the streamwise component of wall shear, but leaves the peripheral component of wall shear practically unaffected.

Hebbar, S. K.↗
NASA NTRS1994

Backward-facing step measurements at low Reynolds number, Re(sub h)=5000

An experimental study of the flow over a backward-facing step at low Reynolds number was performed for the purpose of validating a direct numerical simulation (DNS) which was performed by the Stanford/NASA Center for Turbulence Research. Previous experimental data on back step flows were conducted at Reynolds numbers and/or expansion ratios which were significantly different from that of the DNS. The geometry of the experiment and the simulation were duplicated precisely, in an effort to perform a rigorous validation of the DNS. The Reynolds number used in the DNS was Re(sub h)=5100 based on step height, h. This was the maximum possible Reynolds number that could be economically simulated. The boundary layer thickness, d, was approximately 1.0 h in the simulation and the expansion ratio was 1.2. The Reynolds number based on the momentum thickness, Re(sub theta), upstream of the step was 610. All of these parameters were matched experimentally. Experimental results are presented in the form of tables, graphs and a floppy disk (for easy access to the data). An LDV instrument was used to measure mean velocity components and three Reynolds stresses components. In addition, surface pressure and skin friction coefficients were measured. LDV measurements were acquired in a measuring domain which included the recirculating flow region.

Jovic, Srba↗
NASA NTRS1995

Dynamic analysis of astronaut motions in microgravity: Applications for Extravehicular Activity (EVA)

Simulations of astronaut motions during extravehicular activity (EVA) tasks were performed using computational multibody dynamics methods. The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension mechanisms. These limitations can mask critical dynamic effects that later cause problems during actual EVA's performed in space. Methods of formulating dynamic equations of motion for multibody systems are discussed with emphasis on Kane's method, which forms the basis of the simulations presented herein. Formulation of the equations of motion for a two degree of freedom arm is presented as an explicit example. The four basic steps in creating the computational simulations were: system description, in which the geometry, mass properties, and interconnection of system bodies are input to the computer; equation formulation based on the system description; inverse kinematics, in which the angles, velocities, and accelerations of joints are calculated for prescribed motion of the endpoint (hand) of the arm; and inverse dynamics, in which joint torques are calculated for a prescribed motion. A graphical animation and data plotting program, EVADS (EVA Dynamics Simulation), was developed and used to analyze the results of the simulations that were performed on a Silicon Graphics Indigo2 computer. EVA tasks involving manipulation of the Spartan 204 free flying astronomy payload, as performed during Space Shuttle mission STS-63 (February 1995), served as the subject for two dynamic simulations. An EVA crewmember was modeled as a seven segment system with an eighth segment representing the massive payload attached to the hand. For both simulations, the initial configuration of the lower body (trunk, upper leg, and lower leg) was a neutral microgravity posture. In the first simulation, the payload was manipulated around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnal deviation limit by as much as 49. 8 deg and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position and the radius and speed of the circular trajectory were reduced by half. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m.

Newman, Dava J.↗
NASA NTRS2003

Simulating the Effect of Space Vehicle Environments on Directional Solidification of a Binary Alloy

Space microgravity missions are designed to provide a microgravity environment for scientific experiments, but these missions cannot provide a perfect environment, due to vibrations caused by crew activity, on-board experiments, support systems (pumps, fans, etc.), periodic orbital maneuvers, and water dumps. Therefore, it is necessary to predict the impact of these vibrations on space experiments, prior to performing them. Simulations were conducted to study the effect of the vibrations on the directional solidification of a dendritic alloy. Finite element ca!cu!attie?ls were dme with a simd2titcr based on a continuum model of dendritic solidification, using the Fractional Step Method (FSM). The FSM splits the solution of the momentum equation into two steps: the viscous intermediate step, which does not enforce continuity; and the inviscid projection step, which calculates the pressure and enforces continuity. The FSM provides significant computational benefits for predicting flows in a directionally solidified alloy, compared to other methods presently employed, because of the efficiency gains in the uncoupled solution of velocity and pressure. finite differences, arises when the interdendritic liquid reaches the eutectic temperature and concentration. When a node reaches eutectic temperature, it is assumed that the solidification of the eutectic liquid continues at constant temperature until all the eutectic is solidified. With this approach, solidification is not achieved continuously across an element; rather, the element is not considered solidified until the eutectic isotherm overtakes the top nodes. For microgravity simulations, where the convection is driven by shrinkage, it introduces large variations in the fluid velocity. When the eutectic isotherm reaches a node, all the eutectic must be solidified in a short period, causing an abrupt increase in velocity. To overcome this difficulty, we employed a scheme to numerically predict a more accurate value for the rate of change of fraction of liquid as the liquid in an element solidifies. The new method enables us to contrast results of simulations in which the alloy is subjected to no gravity or a steady-state acceleration versus simulations when the alloy is subjected to vibration disturbances; therefore, the effect of vibration disturbances can be assessed more accurately. To assess the impact of these vibration-perturbations, transient accelerometer data from a space shuttle mission are used as inputs for the simulation model. These on-orbit acceleration data were obtained from the Microgravity Science Division at Glenn Research Center (GRC- MSD) and are applied to the buoyancy term of the momentum equation in a simulation of a Pb-5.8 wt. % Sb alloy that solidifies in a thermal gradient of 4000 K/m and a translation velocity of 3 p d s . Figure 2 shows the vertical velocity of a node that begins in the all-liquid region and subsequently solidifies; the vibrations are applied at 5000 seconds in this simulation. An important difficulty, common to all solidification models based on finite elements or 2 The magnitudes of the velocity oscillations that are vibration-induced are very small and acceptable. The biggest concern is whether the concentration of the liquid near the dendrite tips is distorted because of the vibration-induced perturbations. Results for this case show no concentration oscillations present in the all-liquid region.

Westra, D. G.↗
NASA NTRS2015

Total Lightning Characteristics with Respect to Radar-Derived Mesocyclone Strength

Recent work investigating the microphysical and kinematic relationship between a storm's updraft, its total lightning production, and manifestations of severe weather has resulted in development of tools for improved nowcasting of storm intensity. The total lightning jump algorithm, which identifies rapid increases in total lightning flash rate that often precede severe events, has shown particular potential to benefit warning operations. Maximizing this capability of total lightning and its operational implementation via the lightning jump may best be done through its fusion with radar and radar‐derived intensity metrics. Identification of a mesocyclone, or quasi‐steady rotating updraft, in Doppler velocity is the predominant radar‐inferred early indicator of severe potential in a convective storm. Fused lightning‐radar tools that capitalize on the most robust intensity indicators would allow enhanced situational awareness for increased warning confidence. A foundational step toward such tools comes from a better understanding of the updraft‐centric relationship between intensification of total lightning production and mesocyclone development and strength. The work presented here utilizes a sample of supercell case studies representing a spectrum of severity. These storms are analyzed with respect to total lightning flash rate and the lightning jump alongside mesocyclone strength derived objectively from the National Severe Storms Laboratory (NSSL) Mesocyclone Detection Algorithm (MDA) and maximum azimuthal shear through a layer. Early results indicate that temporal similarities exist in the trends between total lightning flash rate and low‐ to mid‐level rotation in supercells. Other characteristics such as polarimetric signatures of rotation, flash size, and cloud‐to‐ground flash ratio are explored for added insight into the significance of these trends with respect to the updraft and related processes of severe weather production.

Stough, Sarah M.↗
DOE OSTI2022

Bayesian State-Space Modeling Framework for Understanding and Predicting Golden Eagle Movements Using Telemetry Data

Predicting raptor movements through a wind power plant under given atmospheric and topographical conditions is a crucial first step in the overall goal of quantifying the risk of turbine-related collisions and mortalities. Extracting behavioral traits of golden eagles (Aquila chrysaetos) from telemetry data requires the fusion of noisy and sparse movement data (location, heading, velocity) with a stochastic mathematical representation of the eagles' decision-making processes. In this study, we framed this problem in a Bayesian state-space framework where both observations and decision-making are assumed to be stochastic processes connected through hidden states (mode of flight, intent), and the unknown model parameters are assumed to be random variables that are calibrated using the available telemetry data. This framework allowed for rigorous consideration of underlying uncertainties while allowing for both data and prior biological knowledge to contribute to a probabilistic and predictive agent-based movement model. We implemented and applied the Bayesian framework to understand movement behavior of 23 GPS-tagged golden eagles travelling in the western US for years 2019 and 2020. Our preliminary findings show that the Bayesian state-space framework provides a robust inverse modeling apparatus to decode eagle behavioral characteristics from telemetry data. This study was primarily aimed at verifying and validating the framework with selected golden eagle tracks (both long- and short-ranged), with future research aimed at extending the framework to include multi-mode flight, consideration of atmospheric data and uplift mechanisms, eagle-to-eagle interaction, and eagle-to-turbine interaction.

Bayesian modeling↗
NASA NTRS1991

Radial velocity detection of extra-solar planetary systems

The goal of this program was to detect planetary systems in orbit around other stars through the ultra high precision measurement of the orbital motion of the star around the star-planet barycenter. The survey of 33 nearby solar-type stars is the essential first step in understanding the overall problem of planet formation. The program will accumulate the necessary statistics to determine the frequency of planet formation as a function of stellar mass, age, and composition.

Cochran, William D.↗
NASA NTRS1994

An Experimental Study of the Flowfield on a Semispan Rectangular Wing with a Simulated Glaze Ice Accretion

Wind tunnel experiments were conducted in order to study the effect of a simulated glaze ice accretion on the flowfield of a semispan, reflection-plane, rectangular wing at Re = 1.5 million and M = 0.12. A laser Doppler velocimeter was used to map the flowfield on the upper surface of the model in both the clean and iced configurations at alpha = 0, 4, and 8 degrees angle of attack. At low angles of attack, the massive separation bubble aft of the leading edge ice horn was found to behave in a manner similar to laminar separation bubbles. At alpha = 0 and 4 degrees, the locations of transition and reattachment, as deduced from momentum thickness distributions, were found to be in good agreement with transition and reattachment locations in laminar separation bubbles. These values at y/b = 0.470, the centerline measurement location, matched well with data obtained on a similar but two dimensional model. The measured velocity profiles on the iced wing compared reasonably with the predicted profiles from Navier-Stokes computations. The iced-induced separation bubble was also found to have features similar to the recirculating region aft of rearward-facing steps. At alpha = 0 degrees and 4 degrees, reverse flow magnitudes and turbulence intensity levels were typical of those found in the recirculating region aft of rearward-facing steps. The calculated separation streamline aft of the ice horn at alpha = 4 degrees, y/b = 0.470 coincided with the locus of the maximum Reynolds normal stress. The maximum Reynolds normal stress peaked at two locations along the separation streamline. The location of the first peak-value coincided with the transition location, as deduced from the momentum thickness distributions. The location of the second peak was just upstream of reattachment, in good agreement with measurements of flows over similar obstacles. The intermittency factor in the vicinity of reattachment at alpha = 4 degrees, y/b = 0.470, revealed the time-dependent nature of the reattachment process. The size and extent of the separation bubble were found to be a function of angle of attack and the spanwise location. Three dimensional effects were found to be strongest at alpha = 8 degrees. The calculated separation and stagnation streamlines were found to vary little with spanwise location at alpha = 0 degrees. The calculated separation streamlines at alpha = 4 degrees revealed that the bubble was largest near the centerline measurement plane, whereas the tip-induced vortex flow and the model root-tunnel wall boundary-layer interaction reduced the size of the bubble. These effects were found to be most dramatic at alpha = 8 degrees.

Khodadoust, Abdollah↗
NASA NTRS2001

Seismic Study of the Dynamics of the Solar Subsurface from SoHO Observations

In collaboration with Dr. Baudin, we have developed and refined the new observational methodology for local helioseismology known as time-distance analysis. Global helioseismology study the solar oscillations as a superposition of resonant modes, whose properties (mode frequencies) reflect the global structure of the sun (sound speed stratification, rotation rate, etc). In contrast, local helioseismology look at the solar oscillations as wave packets whose propagation will be affected by perturbations of the media sampled. These local perturbations (sound speed or velocity flows) will modify the propagation time, that in turn can be used as a diagnostic tool for a given region. From a data reduction perspective, the processing of solar dopplergrams that result in time-distance maps, i.e. propagation times as a function of distance between bounces at the surface, is radically different from the methodology used for global mode analysis. We have, in a first step, further develop the programs needed to carry out such analysis. We have then applied them to NMI data set, and explore the trade-off between various averaging and filtering approaches - steps required to improve the signal-to-noise ratio of correlation maps - and the resulting stability and precision of the fitted propagation times. While excessive averaging (whether over space, propagation distance, or time) will reduce the diagnostic potential of the method, insufficient averaging lead to unstable fits, or uncertainties so large as to hide the information we seek. In a second phase, we have developed the analysis methodology required to infer local properties from perturbation in time propagation. Namely, we have developed time-distance inversion techniques, with an emphasis on inferences of velocity flows from time anomalies. Note also that during the period covered by this grant, all the investigators on this proposal (i.e., Drs. Baudin, Eff-Darwich, Korzennik, and Noyes) took part in the organization of the SOHO 6 /GONG 99 Workshop: Structure and Dynamics of the Interior of the Sun and Sunlike Stars, held on June 1-4 1999 at the Boston Park Plaza Hotel in Boston, Massachusetts, USA. it was very well attended by more than 160 participants from 26 countries from all over the world. The proceedings were published in two volumes as ESA SP-418, with Sessions I-III in Volume 1, and Sessions IV-VI in Volume 2 (1,000 pages in total). The complete contents are also included in digital form on a CD-ROM included with Volume 1. This CD-ROM also contains additional multi-media material that complements some of the contributions.

Korzennik, Sylvain G.↗
NASA NTRS2010

Understanding Solar Eruptions with SDO/HMI Measuring Photospheric Flows, Testing Models, and Steps Towards Forecasting Solar Eruptions

The Solar Dynamics Observatory (SDO) is carrying the first full-disk imaging vector magnetograph, the Helioseismic and Magnetic Imager (HMI), into an inclined geosynchronous orbit. This magnetograph will provide nearly continuous measurements of photospheric vector magnetic fields at cadences of 90 seconds to 12 minutes with 1" resolution, precise pointing, and unfettered by atmospheric seeing. The enormous data stream of 1.5 Terabytes per day from SAO will provide an unprecedented opportunity to understand the mysteries of solar eruptions. These ground-breaking observations will permit the application of a new technique, the differential affine velocity estimator for vector magnetograms (DAVE4VM), to measure photospheric plasma flows in active regions. These measurements will permit, for the first time, accurate assessments of the coronal free energy available for driving CMEs and flares. The details of photospheric plasma flows, particularly along magnetic neutral-lines, are critical to testing models for initiating coronal mass ejections (CMEs) and flares. Assimilating flows and fields into state-of-the art 3D MHD simulations that model the highly stratified solar atmosphere from the convection zone to the corona represents the next step towards achieving NASA's Living with a Star forecasting goals of predicting "when a solar eruption leading to a CME will occur." Our presentation will describe these major science and predictive advances that will be delivered by SDO/HMI.

Schuck, Peter W.↗
NASA NTRS1975

Lightning properties in Florida thunderstorms from video tape records

From video-tape recordings of lightning flashes to ground in convective daytime storms at the NASA Kennedy Space Center, Florida, and near Ocala, Florida, statistical data are presented for the flash-time duration, the number of strokes per flash, the time between all strokes, and the time between strokes having spatially separate channels. A daytime video tape 'photograph' of a stepped leader is reproduced. Finally, statistical data are presented for 13 long horizontal lightning discharges occurring along a line of nocturnal thunderstorms near Gainesville, Florida. These discharges all propagated horizontally near the freezing level (4.5 km) at an apparent average velocity between 5600 and 11,000 m/s for a typical distance of 2 to 3 km. Eleven of the 13 horizontal discharges were preceded by or occurred within 16.7 ms of a glow in the cloud roughly 0.5 km above the horizontal channel.

Brantley, R. D.↗
NASA NTRS1989

An experimental study of a reattaching supersonic shear layer

A Mach 1.83 fully developed turbulent boundary layer was separated at a 25.4 mm backward step and formed a free shear layer. The incoming boundary layer thickness, momentum thickness, and Reynolds number were approximately 8 mm, 0.5 mm, and 52x10 to the 6th/m, respectively. A two-component coincident LDV system was used to take velocity measurements of the incoming boundary layer, the free shear layer, and the reattached shear layer. The results confirmed the existence of organized structures in both the free and the reattached shear layer which was reported earlier based on the authors dynamic pressure measurements and Schlieren photographs.

Samimy, M.↗
NASA NTRS1946

Waters Loads on the XJL-1 Hull as Obtained in Langley Impact Basin, TED No. NACA 2413.3

An investigation was conducted in the Langley impact basin of the water loads on a half scale model of the XJL-1 hull whose forebody has a vee bottom with exaggerated chine flare. The impact loads, moments, and pressures were determined for a range of landing conditions. A normal full-scale landing speed of 86 miles per hour was represented with effective flight paths ranging from 0.6deg to 11.6deg. Landings were made with both fixed trim and free-to-trim mounting of the float over a trim range of -15deg to 12deg into smooth water and into waves having equivalent full-scale length. of 120 feet and heights ranging from 1 to 4 feet. All data and results presented in this report are given in terms of equivalent full-scale values. Summary tables and illustrative plots are used in presenting the material. The following maximum values of load and pressure are those which are apropos for effective flight paths less than 6.5deg which was the maximum value obtained in tests with the XJL-1 hull model representing full-scale landings with vertical velocity of 4.5 feet per second into 4-foot waves. The maximum local pressure on the flat portion of the bottom is 130 pounds per square inch which was measured on a 2-inch-diameter circular area near the step. The maximum local pressure obtained in the curved area near the chines is 200 pounds per square inch. This pressure was also measured near the step.

Steiner, Margaret F.↗
NASA NTRS2012

Containerless Measurements of Density and Viscosity of Fe-Co Alloys

During the past years, extensive collaborative research has been done to understand phase selection in undercooled metals using novel containerless processing techniques such as electrostatic and electromagnetic levitation. Of major interest is controlling a two-step solidification process, double recalescence, in which the metastable phase forms first and then transforms to the stable phase after a certain delay time. The previous research has shown that the delay time is greatly influenced by the internal convection velocity. In the prediction of internal flow, the fidelity of the results depends on the accuracy of the material properties. This research focuses on the measurements of density and viscosity of Fe-Co alloys which will be used for the fluid simulations whose results will support upcoming International Space Station flight experiments.

Lee, Jonghyun↗
NASA NTRS2010

Understanding Solar Eruptions with SDO/HMI Measuring Photospheric Flows, Testing Models, and Steps Towards Forecasting Solar Eruptions

The imminent launch of Solar Dynamics Observatory (SDO) will carry the first full-disk imaging vector magnetograph, the Helioseismic and Magnetic Imager (HMI), into an inclined geosynchronous orbit. This magnetograph will provide nearly continuous measurements of photospheric vector magnetic fields at cadences of 90 seconds to 12 minutes with I" resolution, precise pointing, and unfettered by atmospheric seeing. The enormous data stream of ~1.5 Terabytes per day from SDO will provide an unprecedented opportunity to understand the mysteries of solar eruptions. These ground-breaking observations will permit the application of a new technique, the differential affine velocity estimator for vector magnetograms (DAVE4VM), to measure photospheric plasma flows in active regions. These measurements will permit, for the first time, accurate assessments of the coronal free energy available for driving CMEs and flares. The details of photospheric plasma flows, particularly along magnetic neutral-lines, are critical to testing models for initiating coronal mass ejections (CMEs) and flares. Assimilating flows and fields into state-of-the art 3D MHD simulations that model the highly stratified solar atmosphere from the convection zone to the corona represents the next step towards achieving NASA's Living with a Star forecasting goals of predicting "when a solar eruption leading to a CME will occur." This talk will describe these major science and predictive advances that will be delivered by SDO /HMI.

Schuck, Peter W.↗
DOE OSTI2023

Measurement of Beam Energy in the Fermilab's Linac taken at the transfer Line

Linac is the first machine in the Accelerator chain at Fermilab where 𝐻− particles are accelerated from 35 keV to 400 MeV and travel to the Booster where they are stripped. of the extra electrons to become protons. The Booster requires stable beam energy at injection. The Linac extraction energy tuning has been performed using two Beam Velocity Monitors (a.k.a Griffin detectors) to maintain stable relative energy between the Booster and the Linac. Our goal is to control the Linac energy parameters using Machine Learning techniques to increase reliability and quality of beam delivered from Linac. The first step is to understand the data from the Linac extraction diagnostics; and develop reliable, accurate methods for energy measurement and control before implementing machine learning. There were two methods of energy measurement implemented, and the results of these are compared. The first method was time of flight measurements using the Phase probes inside B eam Position Monitors (BPM) that provide the beam’s phase of arrival data. The second method used the relation between beam position data from the BPMs and dispersion values from the 400MeV MAD-X model to calculate momentum variation. The results of these two energy measurement methods compare well as the Linac energy is varied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗