magnetic survey of the cesr interaction region quadrupole magnets using vibrating wire technique

Magnetic survey of the CESR interaction region quadrupole magnets using vibrating wire

technique. Alexander Temnykh and Scott Chapman

Cornell University, Ithaca, NY 14850, USA

BNL NSLS, 6/1/06

04/19/23 A. Temnykh, BNL NSLS, 6/1/06 2

Content

1. Introduction 2. Setup3. Magnetic survey and alignment

• Permanent quadrupole magnets

• Super – conducting quadrupoles

4. Summary and Conclusion


AC current with resonance frequency

Maximum excitation if the field location at maximum standing wave amplitude

Introduction (basic)Vibrating wire setup is a stretched wire with AC current with natural wire vibrating frequencies. Standing wave amplitude and phase will depend on the location of the magnetic field.

No excitation if the field in the node of standing wave.

Lorenz forces


Introduction (advanced)• Equation for the string motion driving by AC current:

• Solution - sum of standing wavesA. Temnykh, Vibrating wire field-measuringtechnique, Nuc. Inst., A 399 (1997) 185-194

field magnetic transfers current, AC driving - exp

decrement tension, density, elinear wir

0,,0;

0

2

2

2

2

zBtiItI

T

tlxtxzBtIt

x

z

xT

t

x

nnn

nnn

n

nn

n

zl

nBzBB

T

l

nB

i

Ix

xtizl

nxtzx

sin)(expansion wavessinus a of tscoefficien -

;1

amplitudes wavesstanding -;expsin,

220

• Measuring xn one can find Bn and reconstruct B(z) !!!


CESR final focusing quadrupole magnets survey /alignment

setup

Basic Position f1[Hz]= 14.7Sag[mm]= 1.418

x(hor) y(vert) z(long)East End 0 0 -3768.4West End 0 0 3768.4

Wire Shift from Basic Position

x[mm]= 0 symmetricdx[mm]= 0 assymetricy[mm] 0 symmetricdy[mm]= 0 assymetric

x[mm] y[mm] z[mm]East end 0 0 -3768.4West end 0 0 3768.4

Azimuth[mm]z[mm] x[mm] y[mm]

East End -3768.4 0.000 0.000Q2E -2079 0.000 -0.987Q1E -1166.9 0.000 -1.282Q0E -520 0.000 -1.391IP 0 0.000 -1.418Q0W 520 0.000 -1.391Q1W 1166.9 0.000 -1.282Q2W 2079 0.000 -0.987West End 3768.4 0.000 0.000

Q0E/W – permanent quadrupole magnetsQ1E/W and Q2E/W super-conducting quadrupole

magnets in cryostats(1) – 7.536m long 0.1mm copper-beryllium wire (2) – precise moving stages with optical targets. (3) – constant tension mechanism.(4) – wire motion sensors

Wire geometry: 2132

gSag

f

PMSC SC


Permanent magnets survey (analysis example)

Wire vertical position at

Q0E,W

dy = - 0.1mm differential effect

Y = -0.061mm

Y = 0.039mm

Vertical standing wave amplitudes Reconstructed horizontal magnetic field, Bx(z)

Q0WQ0E

-60

-40

-20

0

20

40

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Standing wave order

-60

-40

-20

0

20

40

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Standing wave order

-60

-40

-20

0

20

40

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Standing wave order

-300

-200

-100

0

100

200

300

-300 -200 -100 0 100 200 300

Vertical wire position = 1.0mm

z[cm] from IP

-150

-100

-50

0

50

100

150

-300 -200 -100 0 100 200 300

0.1mm differential effect

z[cm] from IP

-300

-200

-100

0

100

200

300

-300 -200 -100 0 100 200 300

Vertical wire position 1.1mm

z[cm] from IP

Q0WQ0E


Permanent magnets survey(all SC quads turned off)

Vertical position survey

-150

-100

-50

0

50

-300 -200 -100 0 100 200 300

z[cm]-50

0

50

100

150

-300 -200 -100 0 100 200 300

z[cm]

-300

-200

-100

0

100

200

300

-300 -200 -100 0 100 200 300

z[cm]-300

-200

-100

0

100

200

300

-300 -200 -100 0 100 200 300

z[cm]

Horizontal position survey

ywire = -0.061mm

dywire = 0.1mmeffect

xw = 0.07mm

dxw = 0.1mmeffect

Q0E Q0W

PM quads vertical position:Q0E -0.20mm, Q0W 0.11mm

PM quads horizontal position:Q0E -0.14mm, Q0W 0.11mm

Q0E Q0W

Q0E Q0W Q0E Q0W


-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Q1W vertical position survey, Jun 26 2003

Ay ( I = 243A - bgr)Ay (I = 465A - bgr)

y[mm] relative beam line

y = m1*(m0-m2)

ErrorValue

0.0120460.36437m1

0.018537-0.16859m2

NA0.00036276Chisq

NA0.99891R

y = m1*(m0-m2)

ErrorValue

0.016890.73152m1

0.012965-0.15875m2

NA0.00071317Chisq

NA0.99947R

1) I(Q1W) = 243AY = -0.159 +- 0.013mm2) I(Q1W) = 465AY = -0.169 +- 0.018mm

-1

-0.5

0

0.5

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Q1W horizontal position survey, Jun 26 2003

Ax (I = 233A - bgr)Ax ( I = 466A - bgr )


y = m1*(m0-m2)

ErrorValue

0.0011806-0.51289m1

0.0013328-0.019072m2

NA3.4844e-06Chisq

NA0.99999R

y = m1*(m0-m2)

ErrorValue

0.0042463-1.0394m1

0.0023629-0.021668m2

NA4.5078e-05Chisq

NA0.99998R

1) I(Q1W) = 233Ax = -0.019 +- 0.001mm2) I(Q1W) = 466Ax = -0.022 +- 0.002mm

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Q1E vertical position survey, Jun 26 2003

Ay, ( I = 231A - bgr)Ay, ( I = 468A - bgr)


y = m1*(m0-m2)

ErrorValue

0.0055902-0.35641m1

0.0103740.1415m2

NA7.8127e-05Chisq

NA0.99975R

y = m1*(m0-m2)

ErrorValue

0.0079553-0.72215m1

0.00728870.14191m2

NA0.00015822Chisq

NA0.99988R

1) I(Q1E) = 231Ay = 0.142 +- 0.007mm2) I(Q1E) = 466Ay = 0.141 +- 0.010mm

Q1E, vertical

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Q1E horizontal position survey, Jun 26 2003

Ax / 233A - bgrAx / 466A - bgr

x[mm] relative beam line

y = m1*(m0-m2)

ErrorValue

0.00371420.51764m1

0.0041925-0.0099784m2

NA3.4489e-05Chisq

NA0.99995R

y = m1*(m0-m2)

ErrorValue

0.00158161.0273m1

0.00090341-0.0016316m2

NA6.2538e-06Chisq

NA1R

1) I(Q1E) = 231Ax = -0.010 +- 0.004mm2) I(Q1E) = 466Ax = -0.002 +- 0.001mm

Q1E, horizontal

Super-conducting magnets surveyFor Q1E & Q1W survey the 4th order standing wave has been used.

Q1W, vertical surveyQ1W, horizontal

Surveyed magnets


Super-conducting magnets surveyFor Q2E & Q2W survey the 6th order standing wave has been used.

Standing wave amplitude with sign versus string position

-0.6

-0.4

-0.2

0

0.2

0.4

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Q2W vertical position survey, Jun 26 2003

Ay / 182A - bgrAy / 366A - bgr


y = m1*(m0-m2)

ErrorValue

0.0094679-0.25394m1

0.021135-0.0010759m2

NA0.0002241Chisq

NA0.99861R

y = m1*(m0-m2)

ErrorValue

0.015308-0.51147m1

0.0169330.0059707m2

NA0.00058586Chisq

NA0.99911R

Vertical

1) I(Q2W) = 183AY = 0.006 +- 0.017mm2) I(Q2W) = 366AY = -0.001 +- 0.021mm

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Q2W horizontal position survey, Jun 26 2003



y = m1*(m0-m2)

ErrorValue

0.000610270.36372m1

0.0009717-0.028696m2

NA9.3108e-07Chisq

NA1R

y = m1*(m0-m2)

ErrorValue

0.00181240.72495m1

0.0014449-0.033389m2

NA8.2123e-06Chisq

NA0.99999R

Horizontal

1) I(Q2W) = 183Ax = -0.033 +- 0.001mm2) I(Q2W) = 366Ax = -0.029 +- 0.001mm

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Q2E vertical position survey, Jun 26 2003

Ay / 180A - bgrAy / 360A - bgr


y = m1*(m0-m2)

ErrorValue

0.00148550.25607m1

0.00324650.11907m2

NA5.5168e-06Chisq

NA0.99997R

y = m1*(m0-m2)

ErrorValue

0.00601790.51023m1

0.0065960.10923m2

NA9.0537e-05Chisq

NA0.99986R

Vertical

1) I(Q2E) = 180Ay = 0.109 +- 0.007mm2) I(Q2E) = 360Ay = 0.119 +- 0.003mm

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Q2E horizontal position survey, Jun 26 2003



y = m1*(m0-m2)

ErrorValue

0.0002404-0.35768m1

0.00039448-0.001165m2

NA1.4448e-07Chisq

NA1R

y = m1*(m0-m2)

ErrorValue

0.0031302-0.72092m1

0.0025417-0.0062884m2

NA2.4496e-05Chisq

NA0.99998R

Horizontal

1) I(Q2E) = 180Ax = -0.006 +- 0.002mm2) I(Q2E) = 360Ax = -0.001 +- 0.001mm

Q2W magnetic survey Q2E magnetic survey

Surveyed magnets


Magnetic Survey summaryMagnet Gradien

t [T/m]Length

[m]Horizontal position [mm]

Vertical position [mm]

Q2E 8.28 0.661 -0.004 0.114

Q1E 12.48 0.661 -0.006 0.142

Q0E 28.8 0.182 -0.140 -0.200

Q0W 28.8 0.182 0.110 0.110

Q1W 12.48 0.661 -0.020 -0.164

Q2W 8.28 0.661 -0.031 0.004

Over all survey precision ~ 0.07mm~0.050 mm from wire ends position optical survey~0.010 mm from magnetic survey


Wire position sensor signal as function of platform position.

(1) Wire is free(2) Wire is pressed against the “standard”

bar(3) Touch point.

(1)

(2)

(3)

Precise moving platform

wireOptical wire position sensor mounted on platform

Solenoid still yoke“Standard” bar

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

-2.3 -2.2 -2.1 -2 -1.9 -1.8 -1.7

hor_position_plus_face_2_3

AxDCAxDc / fit1AxDC / fit2

y = -1.5309 - 0.67819x R= 0.99889

y = -0.09938 + 0.011268x R= 0.57465

x[mm]

x* = -2.076 +- 0.002mm

Transferring of the wire position to outside world(resent development).


Pulsed to VW setup conversion(sensitivity study)

-0.01

-0.005

0

0.005

0.01

0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46

VW setup sensitivity demonstrationSecond order VW harmonic

as a function of compensating magnet current.Compensating magnet calibration

~100Gcm / 0.425A or ~0.25Gcm/0.001A

Data set 1, I_com (A2=0) = 0.4250 +- 0.0002 [A]Data set 2, I_com ( A2=0 ) = 0.4265+- 0.0005 [A]

I_com[A]

-400

-300

-200

-100

0

100

200

300

0.42 0.44 0.46 0.48 0.5 0.52 0.54

Second mode amplitudeas function of the compensating magnet current.Compensating magnet calibration 0.48A/100Gcm

or 0.2 Gcm / 0.001A(Oscilloscope measurement)

Icom[A]

y = m1 *(m0-m2)

ErrorValue

219.917168.9m1

0.00090650.48883m2

NA3345.4Chisq

NA0.99626R

Compensating current 0.489 +- 0.0009 A

Sensitivity ~ 0.2Gcm !


VW using for sextupole magnet alignment

Sextupole magnet example:10cm long, 30mm bore radius1.5T field on pole tip

-5

0

5

10

15

20

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Sextupole field BsL = 1.5e4G*cm/mm^2 *(x/30)^2

with 0.20Gcm RMS noise

x[mm]

Sextupole center fromquadratic fit:X = 0.0018 +- 0.0013mm


Conclusion

1. WV technique has been used for magnetic survey of permanent and super-conducting quadrupole magnets of IR of Cornell Electron Storage Ring (CESR). The survey has been done in situ with CLEO detector field turned ON.

2. The technique demonstrated ~0.010mm or better precision in the finding of the quadrupole magnet magnetic centers.

3. The factors limiting the overall survey precision are:a. Optical survey of the wire ends ~ 0.050mmb. Stages motion ~ 0.010mmBoth can be improved.

Note: fundamental mode frequency variation df/f ~ 5x10-4 produces the sag error ~0.002mm.

Vibrating Wire Sensitivity Testat NSLS

Alexander Temnykh1

and

George Rakowsky, Dave Harder & Mike Lehecka

June 1, 2006

1Cornell University


NSLS Pulsed Wire Bench Converted to Vibrating Wirefor Sensitivity Study

CALIBRATEDP-M DIPOLE(100 G-cm)

E-M DIPOLE

(VARIABLE)

PHOTO-OPTICALWIRE POSITION

DETECTORS(X & Y)

AUDIOOSCILLATOR

~56 Hz

125 µm BeCu WIRE

SCOPE

PC

1.4m~1.5m5.1m

X-Y-Z STAGES

X-Y-Z STAGE

~1kg

2nd HarmonicVibration Mode

Method: • Vary EM current to cancel PM dipole kick.• Measure wire vibration amplitude vs. current


Vibrating Wire Sensitivity Study

-0.01

-0.005

0

0.005

0.01

0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46

VW setup sensitivity demonstrationSecond order VW harmonic

as a function of compensating magnet current.Compensating magnet calibration

~100Gcm / 0.425A or ~0.25Gcm/0.001A

Data set 1, I_com (A2=0) = 0.4250 +- 0.0002 [A]Data set 2, I_com ( A2=0 ) = 0.4265+- 0.0005 [A]

I_com[A]

-400

-300

-200

-100

0

100

200

300

0.42 0.44 0.46 0.48 0.5 0.52 0.54

Second mode amplitudeas function of the compensating magnet current.Compensating magnet calibration 0.48A/100Gcm

or 0.2 Gcm / 0.001A(Oscilloscope measurement)

Icom[A]

y = m1 *(m0-m2)

ErrorValue

219.917168.9m1

0.00090650.48883m2

NA3345.4Chisq

NA0.99626R

Compensating current 0.489 +- 0.0009 A

Sensitivity ~ 0.2Gcm !


Using VW for Sextupole Magnet Alignment

Sextupole magnet example:10cm long, 30mm bore radius1.5T field on pole tip

-5

0

5

10

15

20

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Sextupole field BsL = 1.5e4G*cm/mm^2 *(x/30)^2

with 0.20Gcm RMS noise

x[mm]

Sextupole center fromquadratic fit:X = 0.0018 +- 0.0013mm

magnetic survey of the cesr interaction region quadrupole magnets using vibrating wire technique

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