SCU Measurements at LBNL - PowerPoint Presentation

SCU Measurements at LBNL Diego Arbelaez (LBNL)Superconducting Undulator R&D ReviewJan. 31, 2014 1

Introduction Undulators must meet the trajectory and phase shake error requirements for the FELMagnetic field error sourcesRandom and systematic machining errors Assembly errorsAccurate fabrication methods will be used in order to minimize the initial device errorsEnd and central tuning methods will be incorporated on the prototypesSufficiently accurate measurement and tuning methods must be available to meet the requirements for:1st and 2nd field integral Phase and phase shakeKeff

Error Sources and Analysis 3

Error Analysis for Coil and Pole Tolerances Coil errorProduces no net kick (displacement does not grow with distance)Produces a phase error Pole errorProduces a net kick (displacement grows with distance) Second Field Integral Error (Pole)100 μm errors I1 I1 = 0.19 T-mm I 1 = 0.047 T-mm 100 μm errors Second Field Integral Error ( Coil ) δ = 0.21 T-mm 2 δ = 0.94 T-mm 2 Pole h l Coil d w * Tolerance = 50 T-mm 2

Trajectory Error Scaling Determine the standard deviation in the trajectory error for a random ensemble of undulator feature errorsPole errorsCharacterized by a kick error (I1)Total trajectory error is given by the sum of kick errors (K i) with a drift length (x-xi) (i.e. ); scales with N3/2Coil errorsCharacterized by a displacement error (I2)Total trajectory error is a simple random walk of individual displacement errors (i.e. ); scales with N 1/2 Pole Errors Coil Errors Trajectory errors scale with the undulator length to the power of 3/2

Second Integral Error LCLS-II requirement Phase Shake Random pole and coil errors with a given standard deviation are introduced using a Monte Carlo simulation for an undulator with length L u = 3.3 mCalculations performed for as-built undulator with no field tuning RMS machining errors of < 2μm were measured in the ½-m long LBL prototypeSecond field integral can be reduced to meet the requirements with end and central field correction mechanisms Scaling of Trajectory and Phase Errors for Untuned Devices l inear increase with error size quadratic increase with error size LCLS-II requirement L u = 3.3 m End and central field tuning methods will be used to reduce the second integral error

Random errors generated using CMM-measured distribution of machining errorsCorrector locations and excitation (same for all locations) of correctors is appliedOn average 11 correctors are needed to reduce the first and second integral errors to negligible levels over 3.3 mThe trajectory requirement is met for the entire range of operation with the only adjustment being the amplitude of the corrector current (same through all correctors)Simulated Trajectory with Field Correction 11 correctors Before correction After correction L u = 3.3 m

Undulator Measurements at LBNL 8

Field Measurement Technology Approaches Hall Probe (ANL)Local field measurementNeed to know the location of the hall probe to high accuracyStretched wire or coil scan (ANL)Obtain net first and second field integralsOnly length integrated information Pulsed wire (LBNL)Measure first and second field integralsMeasurements give integral values as a function of position along the length of the undulator

Pulsed Wire Method Description Tensioned wire between two pointsPart of the wire is in an external magnetic fieldA current pulse is applied to the wireThe wire is subjected to the Lorentz forceA traveling wave moves along the wireThe displacement at a given point is measuredThe displacement of the wire as a function of time is related to the spatial dependence of the magnetic field Observation point ( z = 0) B x (z ) I z y x Traveling wave

Analytical Solution (Dispersion Free) Solution for the wire motion at a given location as a function of timeA square current pulse with pulse width δt is assumed General solution: DC current: δt 0: : wire position at z = 0 as a function of time ρ : wire mass per unit length T : wire tension c : wave speed ; I 1 ct Special cases: z

Dispersion The flexural rigidity of the wire leads to dispersive behaviorThin wires with lower flexural rigidity are less susceptible to dispersionDispersive behavior can be predicted using Euler Bernoulli theory for bending of thin rods Dispersive wave motion: Undispersive wave motion: Euler-Bernoulli BeamGeneral Solution

Experimental Validation Wire motion detectors Wire position sensors (referenced to undulator fiducials) Echo-7 Undulator Wire Positioning stages

Wave Speed Measurement Wave speed obtained by placing the motion sensor in two different locations and measuring the phase difference as a function of frequency in the two signal Fit to analytical expression Wire motion from magnet at two locations Wave Speed

ECHO-7 First and Second Integral Measurement 15 First Integral Second Integral Before Dispersion Correction After Dispersion Correction

ECHO-7 Phase Error Phase error calculation with upstream and downstream detectors Comparison of the calculated phase errors for Hall Probe and PW measurements Wire damping introduces error in the field integral measurement which must be compensated in the calculation of phase errors 16

SCU Test System Cryogen-free cryostat (two cryo-coolers )Pulsed wire attachment at each end of the cryostatIn-vacuum pulsed wire measurementDecreased air damping overcome with passive damping at the ends and pulse cancelling with reverse currentTest Cryostat In-vacuum Pulsed Wire System

Measurement Plan Pulsed wire will be used as the main method during the R&D and commissioning phase for the field correction mechanism at LBNLThe pulsed wire method will be incorporated and used as one of the measurement methods in the ANL measurement systemAbsolute Keff measurements will be performed using the ANL hall probe system