Nuclear Instruments and Methods in Physics Research A 635 (2011) 121–126

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

n Corr

E-m1 Pr

journal homepage: www.elsevier.com/locate/nima

Pulse requirements for field integral measurements in pulsed wire method

Sumit Tripathi a,n, G. Mishra a,1, Vinit Kumar b, Sanjay Chouksey b, Ravi Kumar c

a School of Physics, Devi Ahilya University, Indore 452001, Indiab RRCAT, Indore 452001, Indiac IPR, Ahmedabad, India

a r t i c l e i n f o

Article history:

Received 29 September 2010

Received in revised form

20 January 2011

Accepted 20 January 2011Available online 2 February 2011

Keywords:

Free-electron laser

Undulator

Pulsed wire method

Magnetic field measurement

02/$ - see front matter & 2011 Elsevier B.V. A

016/j.nima.2011.01.117

esponding author.

ail address: stri_29sep@yahoo.co.in (S. Tripat

esent address. National Tsing Hua University

a b s t r a c t

The pulse requirements in pulsed wire measurements are verified for undulators with and without end

field corrections. For a perfect undulator, the second field integral is uniform along the length of the

undulator and the required pulse size is calculated by the distance of the sensor divided by the wave

velocity. The undulator without end field correction or with improper end field configuration requires

longer pulse sizes than the shimmed undulator for both first and second field integral results.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

In the pulsed wire method [1–22], a thin wire is stretchedalong the undulator axis. When a current pulse is passed throughthe wire, a force is exerted on the length of the wire. The forceevolves into a wave on the wire that propagates from theundulator region to a sensor located along the wire. The sensor’soutput versus time is proportional to the integral of the undulatorfield. The technique gives direct information on the first andsecond integrals of the field strength at appropriate pulse lengths.There are several factors, which limit the performance of the wiremethod in comparison to the Hall probe results. The accuracy [1]is limited due to the intrinsic properties of the wire such as wireimperfections, wire sag and dispersion due to the stiffness ofthe wire. The extrinsic parameters such as the wire oscillationscoming from the background room vibrations, airflow, lowsensitivity of the sensor, fluctuation of the optical components,poor signal noise ratio, distortion of the main signal from reflec-tion at the pulley end, wire misalignment along the undulatorintroduces errors in measurements. However apart from all thesedisadvantages the pulsed wire technique has special applicationsat select circumstances such as rapid online measurements oninstalled undulators without opening the vacuum systems. It hasthe advantages and ability for measuring directly both the fieldintegrals. Another important factor of the pulsed wire method is

ll rights reserved.

hi).

, Taiwan.

that both field components perpendicular to the wire can bemeasured simultaneously.

Over the years attempts were made to work out the measuringconditions of the pulsed wire techniques to improve its accuracy.Cu–Be wire is used for its low resistivity and low pulse heating.The wire characteristics allow the pulsed wire technique users touse thin wires of 100 mm diameter resulting in minimum disper-sion. High sensitivity, fast, reliable sensors to measure the wiredisplacement in the micrometer range have been developed. Thesensitivity of the laser-photodiode sensor reported are 40 mV/mm[6], 50 mV/mm [9] and 60 mV/mm [10], respectively, in the experi-ments with 100 mm diameter wire. Slotted optical switch with25 mV/mm [13] and 0.25 mV/mm [17] are used with 100 and200 mm wire diameters in the pulsed wire set-up, respectively.The wire vibrations are damped by passing the wire through anoil filled channel near each mount of the set-up [2].For decreasingthe sag, special thin hangers are used near the edge but outsidethe undulator magnet [9]. Oil bubble dampers are used towashout the effect of the reflected signals [9]. Efforts were madeto improve the signal to noise ratio. Reliable optical method [18]is reported for accurate measurement of wire sag. In the pastin most cases thin wires r100 mm diameter of Cu–Be areused [1–13]. Work on thick wire of 250 mm diameter Cu–Be arereported to get negligible effect of wire imperfections on pulsedwire method [14–21].

In this paper, we discuss pulse requirements for field integralmeasurements in the pulsed wire method. The pulse width iscalculated by the total length divided by the wave velocity for thesecond field integral for an undulator with perfect end fieldconfiguration. The total length is the undulator length plus the

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A1

B1

C1

Without pinhole , wire diameter = 250 µm

Out

put V

olta

ge (V

)

Distance (mm)-0.4

2.5

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put V

olta

ge (V

)

Distance (mm)

pinhole diameter 250 µm , wire diameter = 250 µm

A

BC

-0.4 -0.2 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4

Fig. 1. (a) Complete set-up of the pulsed wire, (b) undulator with shimming, (c) an opto-coupler mounted at XYZ translation stage, (d) calibration curve for the wire

diameter 250 mm in the absence of pin-hole and (e) calibration curve for the wire diameter 250 mm with pin-hole diameter of 250 mm.

S. Tripathi et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) 121–126122

S. Tripathi et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) 121–126 123

distance of the location of the sensor from the undulator. For anundulator without perfect end field configuration, the secondfield integral wanders away from the axis and the second field

-0.00005

0.00000

0.00005

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0.00025

Hall probe data (3) at 5.60ms (2) at 5.04ms (1)

Sec

ond

Inte

gral

(T*m

2 )

Distance (m)

1

23

0.0

-1.0

-0.5

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0.5 3,56

4

Hall probe (3) from pulse width 3.64ms (4) from pulse width 3.70ms (5) from pulse width 3.76ms (6)

Mag

netic

fiel

d (T

)

Distance (m)

-0.006

-0.004

-0.002

0.000

0.002

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0.006

Hall at 16

Firs

t Int

egra

l (T*

m)

0.1 0.2 0.3 0.4 0.5

0.0 0.1

0.0 0.1 0.2 0.3 0.4 0.5

Fig. 2. (a) Second field integral from the Hall Probe and pulsed wire method at a di

(b) magnetic field from the Hall Probe and pulsed wire method at a distance of 46 cm

from the Hall Probe and pulsed wire method at a distance of 25 cm with pulse widths

Probe and pulsed wire method at a distance of 5.2 cm with pulse widths of 2.20, 2.44 and

pulsed wire method at a distance of 46 cm with pulse widths of 160, 200 and 320 ms

integral measurement requires a longer pulse in comparison tothe perfect undulator. The first integral of an unshimmed undu-lator also requires a longer pulse than the shimmed undulator.

-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Hall probe data (3) from pulse width 5.60ms (2) from pulse width 5.04ms (1)

Mag

netic

fiel

d (T

)

12,3

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9

73,8

Hall probe (3) from pulse width 2.20ms (7) from pulse width 2.44ms (8) from pulse width 2.64ms (9)

Mag

netic

fiel

d (T

)

3

21

4

3

probe data (3) at 200µsec (1)0µsec (2) at 320µsec (4)

0.0Distance (m)

0.1 0.2 0.3 0.4 0.5

Distance (m)0.2 0.3 0.4 0.5

Distance (m)0.0 0.1 0.2 0.3 0.4 0.5

stance of 46 cm with pulse widths of 5.04 and 5.60 ms (unmatched undulator),

with pulse widths of 5.04 and 5.60 ms (unmatched undulator), (c) magnetic field

of 3.64, 3.70 and 3.76 ms (unmatched undulator), (d) magnetic field from the Hall

2.64 ms (unmatched undulator) and (e) first field integral from the Hall Probe and

(unmatched undulator).

-0.1

0.0000

0.0001

0.0002

3 Shim

2 ShimSec

ond

Inte

gral

(T*m

2 )

Distance (m)

Uncorrected

1 Shim

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Fig. 3. Pulsed wire result for the second field integral with shimming.

S. Tripathi et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) 121–126124

2. Field integral measurements

Fig.1(a) illustrates the total pulsed wire set-up. The details ofthe set-up are described in Refs. [18–21]. The undulator is ofNdFeB magnets and one period is of 5 cm. The magnet size is12.5 mm�12.5 mm�50 mm. There are six periods making thetotal length of the undulator as 30 cm. Four magnets with verticaland horizontal magnetization are used to build one undulatorperiod. The undulator has a mechanical gap varying system. Theminimum gap is 12 mm and the maximum gap can be varied upto 80 mm Fig.1(b). For a short pulse, the first integral reads [13]:

x1ðtÞ ¼�I0Dt

2mv

Z vt

0BuðzÞdz ð1Þ

Where I0 is the current injected in the wire,Dt is the current pulsewidth,n is the wave velocity of the acoustic wave in the wire and

given by v¼ffiffiffiffiffiffiffiffiffiffiffiffiffiT=m� �q

BuðzÞ is the magnetic field at z, T is the

tension andm is the mass per unit length of the wire.With a longer pulse the second integral is:

x2ðtÞ ¼�I0

2mv2

Z vt

0dz

Z z

0BuðuÞdu ð2Þ

The principle of the PWM is to translate the output voltageinto wire displacement in the sensor using a suitable calibrationfactor for the given wire. To construct the calibration graph, wemeasure the output voltage without a current in the wire andthe wire is moved across the opto-coupler in steps of 20 mm. Theoutput voltage records a maximum value when the wire is at thecenter of the opto-coupler and the output voltage decreases whenthe wire is moved to either side of the minimum position. Theopto-coupler Fig.1(c) has a slot opening of 3 mm�7 mm. Theopto-coupler characteristic with the slot is shown in Fig.1(d) andthe sensitivity was calculated to be E0.28 mV/mm. An earlierstudy with 250 mm diameter wire was carried out with thissensitivity [17]. We improved the sensitivity with a 250 mmsize pin-hole before the slot to get Fig.1(e), which resulted in asensitivity of 9.2 mV/mm. From the calibration graph (outputvoltage versus position), we can find two ranges of positionwhere this output voltage is linear with wire position. This rangeof position is chosen for better sensitivity of the output voltage tothe wire position because it has a sharp slope. In our case it isAu, Bu and A, B, respectively, for Fig.1(d) and (e). Then the wire isplaced on the almost middle position of this linear range whichis Cu and C point, respectively. The opto-coupler is placed on amovable rail to change the sensor locations (Fig.1(c)).

Fig. 2 presents the pulsed wire results for an unshimmedundulator. For the measurement, T ¼ 9:05N, I0 ¼ 1A. In Fig. 2(a) thesensor is located 46 cm away from the undulator. The solid line is theHall probe data. The undulator length is 30 cm. The wave velocity is152 m/s. The total length is 76 cm, the resulting pulse requirementfor the second field integral is 5 ms [20]. At the pulse width of5.04 ms, the Hall probe data and pulsed wire data mismatch resultedin an error ranging from 15% to 9% (bottom to top peak) in theirpeak values. The measurements were repeated for longer pulsewidths. The result is shown for 5.60 ms that closely matches withthe Hall probe data. At this pulse width, the magnetic field matcheswith the Hall probe data as shown in Fig. 2(b). The measurementsare repeated for several locations of the sensor. In Fig. 2(c) the sensorlocation is 25 cm away from the undulator end. It requires a pulselength of 3.7 ms, which is a bit longer than the calculated pulse sizeof 3.61 ms. In Fig. 2(d) the sensor location is 5.2 cm away fromthe undulator end. The pulse size required is 2.44 ms instead of2.31 ms. Fig. 2(e) presents the first integral results. For the firstintegral measurement, we set the upper limit of the pulse size asthe undulator period divided by the wave velocity i.e. E328 ms.

The pulse length is gradually decreased to find a reasonable close tothe Hall probe data at 200 ms. The mismatch increases furtherbeyond these pulse sizes. The disagreement between pulsed dataand the Hall probe data for the first integral is� 21%.

We added metallic strips of ferro-core material of silicone steelCRGO to correct the second field integral. The strip is of the size5 cm�1.25 cm�0.039 cm. Three such stripes are required tocorrect the second field integral as shown Fig. 3. For the graphin Fig. 3, the sensor location is 34 cm away from the undulator.The pulse width of 4.44 ms for uncorrected and pulse width of4.22 ms for 3 shim were used in that set-up. The measurementsare repeated for different locations of the sensor. In Fig. 4(a) thesensor location is 46 cm. In this case the Hall probe data agreewith pulsed data at 5.08 ms and the pulsed data diverges awayfrom the Hall probe data at 5.60 ms. The second field integralFig. 4(a) data reproduces the correct magnetic field at 5.08 msshown in Fig. 4(b). In an unshimmed undulator the electrontrajectory wanders away from the axis. This increases the effectivebeam length in comparison to the shimmed undulator case. Thepulsed wire technique requires a pulse length that is calculated bythe total length. i.e. electron trajectory length plus the location ofthe sensor [20]. For a perfect undulator the electron trajectorylength is the undulator length. Hence the unshimmed undulatortakes a larger pulse length in comparison to the shimmed undu-lator. In Fig. 4(c),(d), we repeat our observations for other differentsensor locations. In Fig. 4(c), the sensor located at 25 cm distance,gives the required pulse size of 361 ms. In Fig. 4(d), the sensorlocation is 5.2 cm and pulse size used is 2.31 ms. The first integralresult gives the angular deviation of the beam path. In a perfectundulator the integral over the number of the undulator periodmust be zero. However in an imperfect undulator this is not zero.First field integral measurements require from mathematical pointof view a delta pulse; however, in an actual set-up a certain pulsewidth is still required for enough charge for a proper signal to noiseratio. In our experiment the shimmed undulator takes 160 ms pulsesize for first integral measurement in Fig. 4(e); while same resultreproduced at 200 ms pulse width for the unshimmed undulator.This indicates that the test undulator is still far from perfect. Wehave tried for a number of pulses sizes such as 320, 240, 180, 160,100 and 80 ms. The result for 160 ms is close to the Hall probe datain our set-up. It decreases again for shorter pulses. We could use upto 80 ms pulse in the set-up. For further decrease in pulse sizes weare unable to observe any significant oscillations .All the measure-ments are reported for a current level of 1 A. It is needed to raisethis current level to improve the signal noise ratio. There are alsomismatches of PWM data with the Hall probe data at the ends of

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Hall probe data (3) at 5.08ms (1) at 5.60ms (2)

Sec

ond

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Distance (m)

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Mag

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Hall probe (3) from pulse width 3.52ms (4) from pulse width 3.64ms (5) from pulse width 3.68ms (6)

Mag

netic

fiel

d (T

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Distance (m)0.0

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93,87

Hall probe (3) from pulse width 2.28ms (7) from pulse width 2.32ms (8) from pulse width 2.36ms (9)

Mag

netic

fiel

d (T

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Distance (m)

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4 223

5 1

Hall probe data (3) at 320 µsec (1) at 160 µsec (2) at 100 µsec (4) at 80 µsec (5)

Firs

t Int

egra

l (T*

m)

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0.000

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0.006

Hall probe data (3) at 46cm at 18.5cm at 11cm at 5.2cm

Firs

t Int

egra

l (T*

m)

at 160µs pulse width

0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5

0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4

0.0Distance (m)

0.0Distance (m)

0.1 0.2 0.3 0.4 0.5 0.50.1 0.2 0.3 0.4

Fig. 4. (a) Second field integral from the Hall Probe and pulsed wire method at a distance of 46 cm with pulse widths of 5.08 and 5.60 ms (matched undulator),

(b) magnetic field from the Hall Probe and pulsed wire method at a distance of 46 cm with pulse widths of 5.08 and 5.60 ms (matched undulator), (c) magnetic field from

the Hall Probe and pulsed wire method at a distance of 25 cm with pulse widths of 3.52, 3.64 and 3.68 ms (matched undulator), (d) magnetic field from the Hall Probe and

pulsed wire method at a distance of 5.2 cm with pulse widths of 2.28, 2.32 and 2.36 ms (matched undulator), (e) first field integral from the Hall Probe and pulsed wire

method at a distance of 46 cm with pulse widths of 80, 100, 160and 320 ms (matched undulator) and (f) first field integral from the Hall Probe and pulsed wire method at

different distances of 46, 18.5, 11 and 5.2 cm with a 160 ms pulse width (matched undulator).

S. Tripathi et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) 121–126 125

00.20

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Brm

s (T

)B

rms

(T)

for unmatched undulator

for matched undulator

Distance (cm)

10 20 30 40 50

0 10 20 30 40 50

Fig. 5. Comparison of the Brmsvalues with the Hall probe and PW methods for

unmatched and matched undulators.

S. Tripathi et al. / Nuclear Instruments and Methods in Physics Research A 635 (2011) 121–126126

the magnets. We have tried with a 160 ms pulse size at differentsensor locations and found that the pulsed wire data is close to theHall probe data (Fig. 4(f)) at all sensor locations as it should be.

In Fig. 5, we compared the Brms that comes from the Hall probeand the pulse wire method at different locations of the sensor. Assaid in the earlier sections, for the unmatched undulator, the Brms

for longer pulse widths are close to Brms from the Hall probe. As thesensor location moves away from the undulator end, the differencefrom the Hall probe data increases. For the matched undulator, Brms

from both the Hall probe data and the pulsed data matches withcalculated required pulse width. Again the differences between theHall probe data and the pulsed wire data increases with theincreased sensor locations away from the undulator end. For thematched undulator, the calculated pulse widths are shown with anasterisk mark. For the unmatched undulator the closely agreedpulse width is shown also with asterisk mark, which is higher thanthe matched undulator pulse width value.

3. Conclusions

We have discussed undulator field measurement in a pulsedwire set-up. The result of the measurement with a six periodundulator is presented and compared with the Hall probe data. Inpulsed wire experiment, there are several factors that affect theaccuracy and performance of the method. The wire imperfections,wire sag and dispersion due to stiffness of the wire affect theaccuracy. In our experiment with 250 mm wire diameter and shortundulator length of 30 cm, the effects of wire sag and dispersion,wire imperfections are negligible. The other possible sources oferror are due to background vibrations, poor signal to noise ratio,wire misalignment along the undulator length and fluctuations ofthe optical components. The sensitivity of the opto-coupler is alsoan important issue for the accuracy of the result. The opto-couplerworks on the principle of light interruption by the pulsed wire.The sensitivity of the opto-coupler depends on the aperture sizeon the IR-LED face and the wire diameter as well. A correct choiceof the sensitivity gives accurate wire position measurementand accurate field integral data. The present study points out thatthe pulse size is another important factor, which influences the

accuracy of the pulsed wire method. The result of the measure-ment both with and without end field corrected undulator isanalyzed. The unshimmed undulator requires longer pulse sizesthan the shimmed undulator for good match with the Hall probedata. The best result is achievable with the calculated pulse sizewhen the detector is close to the undulator in both the cases.

To conclude, we have verified the pulse size requirements forundulator field measurements in a pulsed wire set-up. To observethe second field integral of the magnetic field, a longer pulse size isrequired [22]. In our measurement set-up, during the duration ofthe impulse, the acoustic wave needs to pass the entire undula-tor plus the sensor distance giving the following conditions:Dtn4Lundþd for an undulator without proper end terminationand Dtn¼Lundþd for an undulator with proper end termination.Lund is the length of the undulator and d is the distance of the sensorfrom the undulator end. With the help of a short current pulse, thefirst integral of the magnetic field is measured. In the case of theunmatched undulator, the size of the short current pulse is longerthan the case of a matched undulator.

Acknowledgments

The authors are grateful to Dr. Ben Shepherd, DaresburyLaboratory, UK and Thomas Schmidt, PSI, Dr. S. Krishnagopal,BARC, Mumbai for various stimulating discussions on the pulsedwire measurement system. Financial support from BRNS-DAE isthankfully acknowledged.

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