SCU Measurements at LBNL Diego Arbelaez LBNL Superconducting

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

Introduction § Undulators must meet the trajectory and phase shake error § § requirements for the FEL Magnetic field error sources § Random and systematic machining errors § Assembly errors Accurate fabrication methods will be used in order to minimize the initial device errors End and central tuning methods will be incorporated on the prototypes Sufficiently accurate measurement and tuning methods must be available to meet the requirements for: § 1 st and 2 nd field integral § Phase and phase shake § Keff SCU R&D Review, Jan. 31, 2014

Error Sources and Analysis 3

Error Analysis for Coil and Pole Tolerances § Coil error Pole § Produces no net kick (displacement does not grow with distance) § Produces a phase error § Pole error § Produces a net kick (displacement grows with distance) Second Field Integral Error (Coil) h Coil d w l Second Field Integral Error (Pole) δ = 0. 94 T-mm 2 100 μm errors I 1 = 0. 19 T-mm δ = 0. 21 T-mm 2 100 μm errors * Tolerance = 50 T-mm 2 SCU R&D Review, Jan. 31, 2014 I 1 = 0. 047 T-mm I 1

Trajectory Error Scaling § Determine the standard deviation in the trajectory error for a random ensemble of undulator feature errors § Pole errors § Characterized by a kick error (I 1) § Total trajectory error is given by the sum of kick errors (Ki) with a drift length (x-xi) (i. e. ); scales with N 3/2 § Coil errors § Characterized by a displacement error (I 2) § Total trajectory error is a simple random walk of individual displacement errors (i. e. ); scales with N 1/2 Pole Errors • Trajectory errors scale with the undulator length to the power of 3/2 SCU R&D Review, Jan. 31, 2014 Coil Errors

Scaling of Trajectory and Phase Errors for Untuned Devices • • Random pole and coil errors with a given standard deviation are introduced using a Monte Carlo simulation for an undulator with length Lu = 3. 3 m Calculations performed for as-built undulator with no field tuning RMS machining errors of < 2μm were measured in the ½-m long LBL prototype Second field integral can be reduced to meet the requirements with end and central field correction mechanisms Second Integral Error Lu = 3. 3 m End and central field tuning methods will be used to reduce the second integral error linear increase with error size LCLS-II requirement SCU R&D Review, Jan. 31, 2014 Phase Shake LCLS-II requirement quadratic increase with error size

Simulated Trajectory with Field Correction • • Random errors generated using CMM-measured distribution of machining errors Corrector locations and excitation (same for all locations) of correctors is applied On average 11 correctors are needed to reduce the first and second integral errors to negligible levels over 3. 3 m The 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) Before correction After correction SCU R&D Review, Jan. 31, 2014 11 correctors Lu = 3. 3 m

Undulator Measurements at LBNL 8

Field Measurement Technology Approaches § Hall Probe (ANL) § Local field measurement § Need to know the location of the hall probe to high accuracy § Stretched wire or coil scan (ANL) § Obtain net first and second field integrals § Only length integrated information § Pulsed wire (LBNL) § Measure first and second field integrals § Measurements give integral values as a function of position along the length of the undulator SCU R&D Review, Jan. 31, 2014

Pulsed Wire Method Description § Tensioned wire between two points § Part of the wire is in an external magnetic field § A current pulse is applied to the wire § The wire is subjected to the Lorentz force § A traveling wave moves along the wire § The displacement at a given point is measured § The displacement of the wire as a function of time is related to the spatial dependence of the magnetic field y Traveling wave x z I Observation point (z = 0) SCU R&D Review, Jan. 31, 2014 Bx(z)

Analytical Solution (Dispersion Free) § Solution for the wire motion at a given location as a function of time § A square current pulse with pulse width δt is assumed ρ: wire mass per unit length T: wire tension c: wave speed General solution: Special cases: : wire position at z = 0 as a function of time DC current: ; δt I 1 ct z SCU R&D Review, Jan. 31, 2014 0:

Dispersion • The flexural rigidity of the wire leads to dispersive behavior • Thin wires with lower flexural rigidity are less susceptible to dispersion • Dispersive behavior can be predicted using Euler Bernoulli theory for bending of thin rods General Solution Dispersive wave motion: Undispersive wave motion: SCU R&D Review, Jan. 31, 2014 Euler-Bernoulli Beam

Experimental Validation Wire Positioning stages Wire motion detectors Wire position sensors (referenced to undulator fiducials) Echo-7 Undulator SCU R&D Review, Jan. 31, 2014

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 Wire motion from magnet at two locations Wave Speed Fit to analytical expression SCU R&D Review, Jan. 31, 2014

ECHO-7 First and Second Integral Measurement Second Integral First Integral Before Dispersion Correction 15 SCU R&D Review, Jan. 31, 2014 After Dispersion Correction

ECHO-7 Phase Error Wire damping introduces error in the field integral measurement which must be compensated in the calculation of phase errors Phase error calculation with upstream and downstream detectors 16 SCU R&D Review, Jan. 31, 2014 Comparison of the calculated phase errors for Hall Probe and PW measurements

SCU Test System § Cryogen-free cryostat (two cryo-coolers) § Pulsed wire attachment at each end of the cryostat § In-vacuum pulsed wire measurement § Decreased air damping overcome with passive damping at the ends and pulse cancelling with reverse current In-vacuum Pulsed Wire System Test Cryostat SCU R&D Review, Jan. 31, 2014

Measurement Plan § Pulsed wire will be used as the main method during the R&D and commissioning phase for the field correction mechanism at LBNL § The pulsed wire method will be incorporated and used as one of the measurement methods in the ANL measurement system § Absolute Keff measurements will be performed using the ANL hall probe system SCU R&D Review, Jan. 31, 2014