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SCU Measurements at LBNL

Diego Arbelaez (LBNL)

Superconducting Undulator R&D Review

Jan. 31, 2014

SCU R&D Review, Jan. 31, 2014

Introduction

Undulators must meet the trajectory and phase shake error requirements for the FELMagnetic field error sources

Random and systematic machining errors Assembly errors

Accurate 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 shake Keff

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Error Sources and Analysis

SCU R&D Review, Jan. 31, 2014

Error Analysis for Coil and Pole Tolerances

Coil error 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 (Pole)

100 μm errors

I1

I1 = 0.19 T-mm

I1 = 0.047 T-mm

100 μm errors

Second Field Integral Error (Coil)

δ = 0.21 T-mm2

δ = 0.94 T-mm2

Pole

h

l

Coil

d

w

* Tolerance = 50 T-mm2

SCU R&D Review, Jan. 31, 2014

Trajectory Error ScalingDetermine the standard deviation in the trajectory error for a random ensemble of undulator feature errors

Pole errors Characterized 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 N3/2

Coil errors Characterized by a displacement error (I2) Total trajectory error is a simple random walk of individual displacement errors

(i.e. ); scales with N1/2

Pole Errors Coil Errors

• Trajectory errors scale with the undulator length to the power of 3/2

SCU R&D Review, Jan. 31, 2014

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 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

Scaling of Trajectory and Phase Errors for Untuned Devices

linear increase with error size

quadratic increase with error size

LCLS-II requirementLu = 3.3 mEnd and central field tuning methods will be used to reduce the second integral error

SCU R&D Review, Jan. 31, 2014

• 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)

Simulated Trajectory with Field Correction

11 correctors Before correction After correction

Lu = 3.3 m

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Undulator Measurements at LBNL

SCU R&D Review, Jan. 31, 2014

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

Observation point (z = 0)

Bx(z)

Iz

y

x Traveling wave

SCU R&D Review, Jan. 31, 2014

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

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

;

I1

ct

Special cases:

z

SCU R&D Review, Jan. 31, 2014

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

Dispersive wave motion:

Undispersive wave motion:

Euler-Bernoulli BeamGeneral Solution

SCU R&D Review, Jan. 31, 2014

Experimental Validation

Wire motion detectorsWire position sensors (referenced to undulator fiducials)

Echo-7 Undulator

Wire Positioning stages

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

Fit to analytical expression

Wire motion from magnet at two locations Wave Speed

SCU R&D Review, Jan. 31, 2014

ECHO-7 First and Second Integral Measurement

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Firs

t In

tegr

alS

econ

d In

tegr

alBefore Dispersion Correction After Dispersion Correction

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SCU R&D Review, Jan. 31, 2014

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

SCU R&D Review, Jan. 31, 2014

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 currentTest Cryostat

In-vacuum Pulsed Wire System

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