SCU Measurements

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

1IntroductionUndulators must meet the trajectory and phase shake error requirements for the FELMagnetic field error sourcesRandom and systematic machining errorsAssembly 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 shakeKeffSCU R&D Review, Jan. 31, 2014Error Sources and Analysis3Error Analysis for Coil and Pole TolerancesCoil errorProduces no net kick (displacement does not grow with distance)Produces a phase errorPole errorProduces a net kick (displacement grows with distance)

Second Field Integral Error (Pole)100 m errorsI1I1 = 0.19 T-mmI1 = 0.047 T-mm

100 m errorsSecond Field Integral Error (Coil) = 0.21 T-mm2 = 0.94 T-mm2PolehlCoildw* Tolerance = 50 T-mm2SCU R&D Review, Jan. 31, 2014Trajectory Error ScalingDetermine 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 (Ki) 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 N1/2

Pole ErrorsCoil Errors

Trajectory errors scale with the undulator length to the power of 3/2 SCU R&D Review, Jan. 31, 2014

Second Integral ErrorLCLS-II requirement

Phase ShakeRandom pole and coil errors with a given standard deviation are introduced using a Monte Carlo simulation for an undulator with length Lu = 3.3 mCalculations performed for as-built undulator with no field tuningRMS machining errors of < 2m were measured in the -m long LBL prototypeSecond field integral can be reduced to meet the requirements with end and central field correction mechanismsScaling of Trajectory and Phase Errors for Untuned Deviceslinear increase with error sizequadratic increase with error sizeLCLS-II requirementLu = 3.3 mEnd and central field tuning methods will be used to reduce the second integral errorSCU R&D Review, Jan. 31, 2014Random 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 correctionLu = 3.3 mSCU R&D Review, Jan. 31, 2014Undulator Measurements at LBNL8Field Measurement Technology ApproachesHall 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 informationPulsed wire (LBNL)Measure first and second field integralsMeasurements give integral values as a function of position along the length of the undulatorSCU R&D Review, Jan. 31, 2014Pulsed Wire Method DescriptionTensioned 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)Bx(z)IzyxTraveling waveSCU R&D Review, Jan. 31, 2014Analytical Solution (Dispersion Free)Solution for the wire motion at a given location as a function of timeA square current pulse with pulse width t is assumedGeneral solution:DC current:t 0:

: wire position at z = 0 as a function of time: wire mass per unit lengthT: wire tensionc: wave speed

;

I1

ctSpecial cases:zSCU R&D Review, Jan. 31, 2014DispersionThe 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

SCU R&D Review, Jan. 31, 2014Experimental Validation

Wire motion detectorsWire position sensors (referenced to undulator fiducials)Echo-7 UndulatorWire Positioning stagesSCU R&D Review, Jan. 31, 2014Wave Speed MeasurementWave 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 expressionWire motion from magnet at two locationsWave SpeedSCU R&D Review, Jan. 31, 2014ECHO-7 First and Second Integral Measurement15

First IntegralSecond Integral

Before Dispersion CorrectionAfter Dispersion CorrectionSCU R&D Review, Jan. 31, 2014ECHO-7 Phase Error

Phase error calculation with upstream and downstream detectors

Comparison of the calculated phase errors for Hall Probe and PW measurementsWire damping introduces error in the field integral measurement which must be compensated in the calculation of phase errors16SCU R&D Review, Jan. 31, 2014

SCU Test SystemCryogen-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 CryostatIn-vacuum Pulsed Wire System

SCU R&D Review, Jan. 31, 2014Measurement PlanPulsed 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 systemSCU R&D Review, Jan. 31, 2014