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An Improved Linear Model for the PSR: Process and Experimental Verification

An Improved Linear Model for the PSR: Process and Experimental Verification. Jeff Kolski USR Workshop 11/12/2010. LA-UR 10-07409. Slide 1. Outline. Introduction LANSCE Description of the baseline model

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An Improved Linear Model for the PSR: Process and Experimental Verification

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  1. An Improved Linear Model for the PSR: Process and Experimental Verification Jeff Kolski USR Workshop 11/12/2010 LA-UR 10-07409 Slide 1 Improved_Model

  2. Outline • Introduction • LANSCE • Description of the baseline model • Motivate study by introducing the baseline model’s shortcomings compared with measurement • Supporting Measurements • Betatron phase and tune measurement • Beta function measurement • Dispersion function measurement • Model improvement measurements • Orbit Response Matrix (ORM) • Magnet component characterization of the PSR extraction septa fringe fields • Ray tracing through the edge focusing of a rectangular dipole • An improved model • Experimental Verification of the improved model Improved_Model

  3. Los Alamos Neutron Science Center(LANSCE)

  4. Los Alamos Neutron Science Center (LANSCE) Ultra ColdNeutrons (UCN) ProtonRadiography (pRad) Ion SourcesSector J Isotope ProductionFacility (IPF) Switch Yard (SY) LDPM03 Area A TransitionRegion (TR) Central Control Room (CCR) CoupledCavityLinac (CCL)(805 MHz) Drift TubeLinac (DTL)(201 MHz) Jeff’s OfficeBuilding 6 LujanCenter ProtonStorageRing(PSR) WeaponsNuclearResearch(WNR) Google Maps

  5. Proton Storage Ring (PSR) Circumference = 90mBeam energy = 798 MeVRevolution frequency =2.8 MHzBunch length = 290 ns (73 m)Accumulation time = 625 μs= 1746 turns WM41 and WC41 ES41y RF Buncher ES43q RJM

  6. Introduction • Baseline Model is an extension of F. Neri’s psrdimad deck • Modifications • Quadrupole current to gradient length fits are assigned to the correct quadrupole and location in the ring. • Dipole edge focusing defined with the FINT parameter instead as a separate quadrupole element. • Extensions • The locations of the quadrupoles and dipoles (save RIBM09) are determined by the 2006 alignment data. Other element positions determined from a combination of other sources, S. Cousineau’s model, T. Spickermann’s model, and tape measurement. • Horizontal and vertical corrector magnets with constant current to kick gains for the vertical corrects from D. Fitzgerald. • BPMs are places 18 cm upstream of the center of the quadrupoles. • Magnet current and shunt input from a Save Accel data file. Improved_Model

  7. Baseline Model • Dipoles • Quadrupoles with current to gradient length fits • Vertical correctors • Horizontal correctors • Alignment data for fixed center of magnet to center of magnet distances • BPMs Improved_Model

  8. Baseline Model Predictions • Betatron Tune • Baseline model predicts the horizontal tune fairly well but not the vertical. • Betatron Phase • Baseline model predicts the betatron phases within the measurement error • Betatron Amplitude Functions • Baseline model predicts the beta functions fairly well • Dispersion Function • Baseline model does a good job at predicting the dispersion function Improved_Model

  9. Baseline Model Betatron Phase Improved_Model

  10. Supporting Measurements • The first set of supporting measurements will be employed to first establish an improved model • An improved model should make a better betatron tune prediction, especially in the vertical, than the baseline model. • An improved model should enhance, or at least maintain, the baseline model’s predictive capabilities for the beta and dispersion functions. • Once an improved model is shown to exist at one PSR operational set point, the improved model needs experimental verification at other PSR operating conditions. • Second, third, and forth sets of supporting measurements are collected at different PSR setups to experimentally verify the improved model. • The improved model should make better predictions of the measured quantities (tune, phase, and beta dispersion functions) than the baseline model. Improved_Model

  11. Betatron Phase and Tune Measurement • For near-on-axis injection, collect 30-40 turns of RingScan (RS) data at each BPM. • Fit the turn-by-turn BPM data to a cosine wave to obtain the phase at each BPM() and tune (). Improved_Model

  12. Beta Function Measurement • Quadrupole perturbation method • Measure the change in the tune with the RS data at four different shunt values for each quadrupole • Fit a line to calculate the slope of (KL) • The dominating error is thesystematic error due to the uncertainty in the fourth ordercurrent to gradient length fits,which is estimated as .1% as perD. Fitzgerald. • Mean Systematic Error For LargeBeta [4.960e-001 m, 4.035e-001 m] • Mean Systematic Error For SmallBeta [5.040e-002 m, 1.153e-001 m] Improved_Model

  13. Beta Function Measurement Improved_Model

  14. Dispersion Measurement • Momentum compaction factor method • Measure the time of flight (TOF) delay between the beam’s revolution period and the design, “moving” 2.8 revolution frequency at three different beam momentums. • Measure the CO from the RS data • The slope of a line fit to xCO(δ) is the dispersion function • Modify the phase of Mod48 and 47 to change the beam momentum • Momentum compaction factor is fairly constant with respect to the model parameters. Improved_Model

  15. Beta Function Measurement Improved_Model

  16. Model Improvement Experiments • Model improvement experiments aim to test or correct the baseline model’s treatment of particular elements. • Observe an over focusing in the vertical of the baseline model. • Three possible sources for additional vertical focusing: • Quadrupoles • Extraction septa • Edge focusing of the dipoles • There are three model improvement experiments designed to quantify the vertical focusing in each of the above. • Orbit Response Matrix (ORM) • Beam-base measurements of the magnet multipole components of the extraction septa fringe fields • Ray tracing through the dipole edge focusing Improved_Model

  17. Orbit Response Matrix • The CO response to a dipole kick is • The orbit response at every BPM due to each corrector may be complied into a matrix • The ORM (R) may be measured experimentally, however the model can also produce a model ORM, R(p), dependent on the model parameters p. • Iteratively step through model parameter space to minimize (R - R(p))2 • Linear Optics from Closed Orbits (LOCO) is a Matlab based ORM analysis program with model parameters: quadrupole strengths, quadrupole rolls, positions, sextupole strength, octupole strength, BPM gains and tilts, and corrector kicks and coupling. Improved_Model

  18. ORM Measurement • 11 horizontal and 9 vertical correctors • 34 BPM (horizontal CO measurement at SRPM92 too unstable to use) • CO is measured by the RS data at three kick setting for each corrector • Baseline • Plus • Minus • Fit a line to xCO(ICor) to obtain theorbit response per unit currentof the corrector. • LOCO fit initially independent ofcorrector gain. Improved_Model

  19. Measured ORM Improved_Model

  20. Measured – LOCO ORM • Apply LOCO fitting Quadrupole Strengths, BPM gains, and corrector kicks • No coupling was fit in LOCO. • The x-x and y-y quadrants of the ORM on the orderor less than the coupling quadrants. Improved_Model

  21. LOCO Results: Quadrupole Strengths • LOCO results suggests ~2.5% systematic decrease in the defocusing quadrupoles without major alterations in the focusing quadrupoles. • 2.5% error was not found in power supply indications of read backs. Improved_Model

  22. LOCO Results: Corrector Kicks and BPM Gains • LOCO results suggest BPM gains all within ±.5% of 1 except for SRPM81x and 91x (Diamond Type BPMs) • LOCO results suggest a systematic degrease in the corrector gains. • LOCO does not distinguish between the 7″ and 11″ vertical correctors. Improved_Model

  23. LOCO Fitted Model • The LOCO fitted model: • Is the baseline model fit to data taken at one particular PSR set point • Is the baseline model with the LOCO fitted quadrupole strengths • Before the LOCO fitted model is heralded as the new improved model, it should first be tested against the baseline model and experimental measurements. Improved_Model

  24. Model Comparisons • Need a consistent comparison method to evaluate the quality of each model prediction with respect to the other models for a particular set of measured data. • Tune: • The error in the model prediction • Betatron phase and beta and dispersion functions: • The χ2 between model and measured Improved_Model

  25. LOCO Fitted Model Compared with Measurement Measured Tunes: [3.19150, 2.19793] • Although the LOCO fitted model predicts better tunes, it does not conserve the quality of the beta function prediction. • The LOCO fitted model is not the improved model. Improved_Model

  26. Characterization of the Magnetic Multipole Components of the PSR Extraction Septa Fringe Fields • Perform beam-based measurements to obtain the dipole, quadrupole, and sextupole components of the PSR extraction septa fringe fields. • The fringe fields of each extraction septum will be modeled as a thin lens multipole located at the upstream outer corner of the septum (location closest to the circulating beam with the peak magnetic field). • The motion of the circulating beam is influenced by both the fringe (field escapingthe ends) and leakage (field issuing from theside of the magnet) fields of each septum.The beam measured the integrated affects ofboth fields. Thus, leakage and fringe fieldwill be applied interchangeably. • Want an operational model, so measure themultipole components as a function trim coilcurrent. RODM02 RODM01 Improved_Model

  27. RODM02 Extraction Beam Pipe Trim Coil Circulating Beam Pipe Main Coil D Barlow

  28. Multipole Component Measurements • Take data with septa off for a baseline • Take data with septa on at trim coil current between -10 A and 10 A for comparison • Quadrupole Measurement • Measure the tune with RS data. Improved_Model

  29. Quadrupole Component RODM01 RODM02 Improved_Model

  30. Modeling the septa fringe fields • The results for the dipole, quadrupole, and sextupole multipole components as a function of trim coil current are fit to a fourth order polynomial. • The improved model reads the trim coil currents from the Save Accel data file and consults these fourth order current to magnetic multipole fits to obtain the strengths of each magnetic component. • Only the quadrupole component of the extraction septa fringe fields is included in the model for this search for an improved linear model. • Each extraction septa fringe field is modeled as a 1 cm quadrupole located at the upstream outer corner of the septa with strength determined by the trim coil current. Improved_Model

  31. Ray Tracing Through the Dipole Edge Focusing • Trace rays, parallel in the transverse, starting at the longitudinal center of the dipole through the magnetic fields from a TOSCA 3D simulation, D. Barlow. • The 25 rays begin initially on a 1 cm grid ranging between ±2 cm in both transverse directions. • The rays will receive a kick in the vertical due to the edge focusing. • From the ray tracing trajectories, we can measure the focal length of the edge focusing. Improved_Model

  32. Ray Tracing Trough the Common PSR Dipoles • A line may be fit to thebent trajectory of y(s). • The focal length of theedge focusing is thelength in s betweenwhere the verticalposition equals theinitial value and 0. Improved_Model

  33. Results of the Ray Tracing • The ray tracing results suggesta systematic increase in the focallength of the edge focusing inall dipole types. Improved_Model

  34. Constraining the Edge Focusing Focal Lengths in the Improved Model • We can constrain the focal lengths of the edge focusing in the improved model to those derived from the ray tracing. • Three parameters that determine the edge focusing focal length: the edge angle (β), gap height (g), and the fringe field integral (FINT, κ). where and • Chose to constrain the FINT because theedge angle and gap height are physicalparameters. • Ray tracing suggests the common PSRbenders have a FINT parameter of .9,which is more representative of theumclamped Rogowski geometry. Improved_Model

  35. The Improved Model • The improved model is an extension of the baseline model • With the following modifications • The focal lengths of the rectangular dipole edge focusing is constrained via the fringe field integral to the results of the ray tracing. • With the following additions • The PSR extraction septa fringe fields modeled as 1 cm quadrupoles with gradient lengths from fourth order trim coil current to quadrupole strength fits from the septa characterization experiment. • Before we herald the improved model as the an enhanced linear model of the PSR, we need to establish that it makes better predictions than the baseline and LOCO fitted models. Improved_Model

  36. Improved Model Compared with the Baseline and LOCO Fitted Models and Measurement Measured Tunes: [3.19150, 2.19793] Improved_Model

  37. Model Verification • Now that the improved model has been established, the improved model needs experimental verification at other PSR set points. • Take several sets of RS reproducibility data sets • different quadrupole settings. • Ramp the power supplies in between quadrupole settings to reduce the affects of hysteresis. • Due to time constraints, the beta and dispersion functions were not measured at any quadrupole setting. • The RS data yields direct comparison with measurement for the betatron tune and phase, but not the beta and dispersion functions • Need a method to compare the model predicted beta and dispersion functions with the results of the RS reproducibility dataset. Improved_Model

  38. Comparing Model Prediction with RS Data • Beta function • The amplitude of the betatron oscillation may be written • Apply linear regression to fit for the action at the cost of one degree of freedom • Then the model comparison is • Dispersion function • The dispersion function can be related to the CO measurement spread • Constrain the BPM measurement error to ~.2 mm and fit for the pulse-to-pulse momentum spread and the covariance term at the cost of two degrees of freedom • Since measurement does not provide and error on the measurement spread, use the sum of squares as the comparison quality factor. Improved_Model

  39. RingScan2Measured Tunes: [3.22661, 2.21922] Improved_Model

  40. Model and Measured Betatron Phase Improved_Model

  41. RingScan3Measured Tunes: [3.80017, 2.38361] Improved_Model

  42. RingScan4Measured Tunes: [2.65383, 3.58292] Improved_Model

  43. Model and Measured Betatron Phase Improved_Model

  44. Model and Measured Betatron Phase Improved_Model

  45. Conclusions • We have constructed an improved model • With ~10 times vertical tune prediction • While maintaining or enhancing the beta and dispersion function predictions • We found the additional vertical focusing in the model to be located in the edge focusing of the dipoles in a misrepresentative fringe field integral parameter. Improved_Model

  46. Further Work • The focal lengths of the edge focusing are taken from 3D magnetic field calculations. It may be good to measure these focal lengths with the beam, possibly as a function of current in the bender. Possibly applicable in ORM. • Also, could take additional ORM data with ramped quadrupoles prior to measurement in order to fit for the uncertainty in the current to gradient length fits. RJM_IU_2010

  47. Acknowledgements • Special thanks to • R. Macek (LANL) • R. McCrady (LANL) • D. Barlow (LANL) • S.Y. Lee (Indiana University) • X. Haung (SLAC) RJM_IU_2010

  48. Additional Slides Improved_Model

  49. Multipole Component Measurements • Take data with septa off for a baseline • Take data with septa on at trim coil current between -10 A and 10 A for comparison • Dipole Measurement • Measure the CO with RS data. • Quadrupole Measurement • Measure the tune with RS data. Improved_Model

  50. Multipole Component Measurements • Sextupole Measurement • Measure the dispersion function with both septa off • Measure the “natural chromaticities” with both septa off by fitting a line to the (δ) and calibrate the dispersion measurement at LDPM03 • Turn septa on • Measure momentum with calibrated LDPM03 • Measure tune with the RS data Improved_Model

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