Document 7595435
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Transcript Document 7595435
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
Content
1. Introduction
2. Setup
3. Magnetic survey and alignment
• Permanent quadrupole magnets
• Super – conducting quadrupoles
4. Summary and Conclusion
5/24/2016
A. Temnykh, BNL NSLS, 6/1/06
2
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.
AC current with
resonance frequency
Lorenz forces
Maximum excitation if the
field location at maximum
standing wave amplitude
5/24/2016
No excitation if the
field in the node of
standing wave.
A. Temnykh, BNL NSLS, 6/1/06
3
Introduction (advanced)
• Equation for the string motion driving by AC current:
2x
2x
x
2 T 2 I t Bz ; x0, t xl , t 0
t
z
t
linear wir e density, T tension, decrement
I t I 0 exp it - driving AC current, B z transfers magnetic field
• Solution - sum of standing waves
n
x z , t xn sin z exp it ; xn - standing waves amplitudes
l
n
xn
I0
1
2 n2 i
Bn ; n
n T
l
A. Temnykh,
Vibrating wire
field-measuring
technique, Nuc.
Inst., A 399
(1997) 185-194
n
Bn - coefficien ts of a sinus waves expansion B( z ) Bn sin z
l
n
• Measuring xn one can find Bn and reconstruct B(z) !!!
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4
CESR final focusing quadrupole magnets survey /alignment setup
Wire geometry:
Basic Position
x(hor)
East End
West End
g
32 f12
Sag
f1[Hz]=
14.7
Sag[mm]=
1.418
y(vert)
z(long)
0
0
-3768.4
0
0
3768.4
Wire Shift from Basic Position
SC
PM
SC
Q0E/W – permanent quadrupole magnets
Q1E/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
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A. Temnykh, BNL NSLS, 6/1/06
x[mm]=
dx[mm]=
y[mm]
dy[mm]=
0
0
0
0
x[mm]
East end
West end
symmetric
assymetric
symmetric
assymetric
y[mm]
0
0
0
0
z[mm]
-3768.4
3768.4
Azimuth[mm]
z[mm]
x[mm]
y[mm]
East End
-3768.4
0.000
0.000
Q2E
-2079
0.000
-0.987
Q1E
-1166.9
0.000
-1.282
Q0E
-520
0.000
-1.391
IP
0
0.000
-1.418
Q0W
520
0.000
-1.391
Q1W
1166.9
0.000
-1.282
Q2W
2079
0.000
-0.987
West End
3768.4
0.000
0.000
5
Permanent magnets survey (analysis example)
Reconstructed horizontal
magnetic field, Bx(z)
Vertical standing wave amplitudes
Wire vertical
position at
Q0E,W
Y = 0.039mm
60
300
Vertical wire position 1.1mm
40
200
20
100
0
0
-20
-100
-200
-40
Standing wave order
-60
1
Y = -0.061mm
3
5
7
9
11
13
15
17
19
21
23
25
27
-300
29
z[cm] from IP
-300
-200
-100
0
100
300
Vertical wire position = 1.0mm
40
200
20
100
0
0
-20
-100
-40
-200
Standing wave order
z[cm] from IP
-60
-300
1
dy = - 0.1mm
differential
effect
200
300
60
3
5
7
9
11
13
15
17
19
21
23
25
27
29
-300
60
150
40
100
20
50
0
0
-20
-50
-200
-100
0
100
200
300
0.1mm differential effect
-40
Q0W
Q0E
-100
Standing wave order
z[cm] from IP
-60
-150
1
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3
5
7
9
11
13
15
17
19
21
23
25
27
29
-300
A. Temnykh, BNL NSLS, 6/1/06
-200
-100
Q0E
0
100
Q0W
200
300
6
Permanent magnets survey
(all SC quads turned off)
Vertical position survey
Horizontal position survey
300
300
ywire = -0.061mm
200
100
100
0
0
-100
-100
-200
xw = 0.07mm
200
-200
z[cm]
-300
z[cm]
-300
-300
-200
-100
Q0E
0
100
200
300
-300
-200
-100
Q0E
Q0W
150
0
100
Q0W
200
300
50
dywire = 0.1mm
effect
100
0
50
-50
0
-100
dxw = 0.1mm
effect
z[cm]
-50
z[cm]
-150
-300
-200
-100
Q0E
0
100
Q0W
200
300
PM quads vertical position:
Q0E -0.20mm, Q0W 0.11mm
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-300
-200
-100
Q0E
0
100
Q0W
200
300
PM quads horizontal position:
Q0E -0.14mm, Q0W 0.11mm
A. Temnykh, BNL NSLS, 6/1/06
7
Super-conducting magnets survey
For Q1E & Q1W survey the 4th order standing wave has been used.
Surveyed magnets
Q1E horizontal position survey, Jun 26 2003Q1E vertical position survey, Jun 26 2003 Q1W horizontal position survey, Jun 26 2003 Q1W vertical position survey, Jun 26 2003
0.8
0.6
0.6
Ay, ( I = 231A - bgr)
Q1E,
Ay, ( I =vertical
468A - bgr)
Ax / 233A - bgr
Q1E,
horizontal
- bgr
Ax / 466A
0.4
1
Ay ( I = 243A - bgr)
Q1W,
vertical
survey
Ay (I = 465A
- bgr)
Ax (I = 233A - bgr)
Q1W, horizontal
Ax ( I = 466A - bgr )
0.6
0.4
0.5
0.2
0.2
0.4
0
0
0
0.2
-0.2
-0.4
-0.2
0
-0.5
-0.6
-0.4
-0.2
-0.8
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
y = m1*(m0-m2)
1) I(Q1E)
=Error231A Value
Error
Value
0.0037142
0.51764
m1
0.0015816
1.0273
m1
x =-0.0016316
-0.010
+- 0.004mm
0.0041925
-0.0099784
m2
0.00090341
m2
NA
3.4489e-05
Chisq
6.2538e-06
Chisq
2)
I(Q1E)
=NANA466A
NA
0.99995
R
1
R
x = -0.002 +- 0.001mm
y = m1*(m0-m2)
5/24/2016
-0.6
-1
-0.4
-1
y[mm] relative beam line
y[mm] relative beam line
y[mm] relative beam line
x[mm] relative beam line
-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
1) I(Q1E) = 231A
y = 0.142 +- 0.007mm
2) I(Q1E) = 466A
y = 0.141 +- 0.010mm
y = m1*(m0-m2)
Value
m1
0.4
0.6
Error
-0.72215
0.0079553
Value
m1
-1
-0.8
-0.6
-0.4
-0.2
0
Error
-0.35641
0.0055902
0.2
0.4
1) I(Q1W) = 233A
x = -0.019 +- 0.001mm
2) I(Q1W) = 466A
x = -0.022 +- 0.002mm
Value
m1
0.6
Value
Error
-1.0394
0.0042463
m1
Error
-0.51289
0.0011806
m2
0.14191
0.0072887
m2
0.1415
0.010374
m2
-0.021668
0.0023629
m2
-0.019072
0.0013328
Chisq
0.00015822
NA
Chisq
7.8127e-05
NA
Chisq
4.5078e-05
NA
Chisq
3.4844e-06
NA
R
0.99988
NA
R
0.99975
NA
R
0.99998
NA
R
0.99999
NA
A. Temnykh, BNL NSLS, 6/1/06
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
1) I(Q1W) = 243A
Y = -0.159 +- 0.013mm
2) I(Q1W) = 465A
Y = -0.169 +- 0.018mm
m1
0.6
y = m1*(m0-m2)
y = m1*(m0-m2)
y = m1*(m0-m2)
y = m1*(m0-m2)
y = m1*(m0-m2)
Value
Error
0.73152
0.01689
Value
m1
Error
0.36437
0.012046
m2
-0.15875
0.012965
m2
-0.16859
0.018537
Chisq
0.00071317
NA
Chisq
0.00036276
NA
R
0.99947
NA
R
0.99891
NA
8
Super-conducting magnets survey
For Q2E & Q2W survey the 6th order standing wave has been used.
Surveyed magnets
Standing wave amplitude with sign versus string position
Q2W magnetic survey
Q2E magnetic survey
Q2W horizontal position survey, Jun 26 2003
0.6
Q2W vertical position survey, Jun 26 2003 Q2E horizontal position survey, Jun 26 2003
Ay / 182A - bgr
Ay / 366A - bgr
Ax / 183A - bgr
Ax / 366A - bgr
0.4
Q2E vertical position survey, Jun 26 2003
0.4
0.8
0.4
Ax / 180A - bgr
Ax / 366A - bgr
0.6
Ay / 180A - bgr
Ay / 360A - bgr
0.3
0.2
Vertical
0.2
Horizontal
0.2
0.4
0.1
0
0
0.2
0
-0.2
0
-0.2
-0.1
Horizontal
-0.2
-0.4
Vertical
-0.4
-0.6
-0.4
-0.6
-0.4
-0.2
0
0.2
0.4
1) I(Q2W) = 183A
x = -0.033 +- 0.001mm
2) I(Q2W) = 366A
x = -0.029 +- 0.001mm
y = m1*(m0-m2)
y = m1*(m0-m2)
Value
0.6
Value
Error
Error
R
5/24/2016
1
1) I(Q2W) = 183A
Y = 0.006 +- 0.017mm
2) I(Q2W) = 366A
Y = -0.001 +- 0.021mm
Value
-1
0.8
y = m1*(m0-m2)
Value
Error
-0.8
-0.6
-0.4
-0.2
0
Error
0.2
0.4
1) I(Q2E) = 180A
x = -0.006 +- 0.002mm
2) I(Q2E) = 360A
x = -0.001 +- 0.001mm
Value
0.6
y = m1*(m0-m2)
y = m1*(m0-m2)
Value
Error
Error
-0.72092
0.0031302
m1
-0.35768
0.0002404
m2
-0.0062884
0.0025417
m2
-0.001165
0.00039448
NA
Chisq
2.4496e-05
NA
Chisq
1.4448e-07
NA
R
0.99998
NA
R
-0.25394
0.0094679
m2
-0.0010759
0.021135
NA
Chisq
0.00058586
NA
Chisq
0.0002241
NA
R
0.99911
NA
R
0.99861
A. Temnykh, BNL NSLS, 6/1/06
1
-0.6
-0.4
-0.2
0
0.2
0.4
NA
NA
0.6
1) I(Q2E) = 180A
y = 0.109 +- 0.007mm
2) I(Q2E) = 360A
y = 0.119 +- 0.003mm
Value
0.8
y = m1*(m0-m2)
y = m1*(m0-m2)
m1
m1
9.3108e-07
Chisq
0.6
0.016933
0.0009717
NA
0.4
0.015308
0.00061027
-0.028696
NA
0.2
-0.51147
0.36372
m2
0.99999
0
0.0059707
m1
0.0014449
8.2123e-06
-0.2
m2
0.0018124
-0.033389
R
-0.4
m1
0.72495
m2
Chisq
-0.6
y = m1*(m0-m2)
m1
y[mm] relative beam line
-0.4
-0.6
-0.6
-0.8
-0.8
-0.3
x[mm] relative beam line
y[mm] relative beam line
x[mm] relative beam line
-1
-0.2
Value
Error
Error
m1
0.51023
0.0060179
m1
0.25607
0.0014855
m2
0.10923
0.006596
m2
0.11907
0.0032465
Chisq
9.0537e-05
NA
Chisq
5.5168e-06
NA
R
0.99986
NA
R
0.99997
NA
9
Magnetic Survey summary
Magnet
Gradient
[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
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10
Transferring of the wire position to outside world
(resent development).
Precise moving
platform
“Standard”
bar
wire
hor_position_plus_face_2_3
Optical wire
position sensor
mounted on
platform
-0.02
AxDC
AxDc / fit1
AxDC / fit2
-0.04
Solenoid still yoke
y = -1.5309 - 0.67819x R= 0.99889
-0.06
y = -0.09938 + 0.011268x R= 0.57465
(2)
Wire position sensor signal as function of
platform position.
x* = -2.076 +- 0.002mm
-0.08
-0.1
-0.12
-0.14
-2.3
(3)
-2.2
(1) Wire is free
(2) Wire is pressed against the
“standard” bar
(3) Touch point.
(1)
-2.1
-2
-1.9
-1.8
-1.7
x[mm]
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11
Pulsed to VW setup conversion
(sensitivity study)
Second mode amplitude
as function of the compensating magnet current.
Compensating magnet calibration 0.48A/100Gcm
or 0.2 Gcm / 0.001A
(Oscilloscope measurement)
VW setup sensitivity demonstration
Second order VW harmonic
as a function of compensating magnet current.
Compensating magnet calibration
~100Gcm / 0.425A or ~0.25Gcm/0.001A
0.01
300
Data set 1,
I_com (A2=0) = 0.4250 +- 0.0002 [A]
Data set 2,
I_com ( A2=0 ) = 0.4265+- 0.0005 [A]
Compensating current 0.489 +- 0.0009 A
200
0.005
100
0
0
-100
y = m1 *(m0-m2)
-200
m1
m2
Chisq
R
-300
-400
0.42
0.44
0.46
0.48
Icom[A]
0.5
Value
7168.9
0.48883
3345.4
0.99626
0.52
Error
219.91
0.0009065
NA
NA
0.54
-0.005
-0.01
0.39
0.4
0.41
Sensitivity ~ 0.2Gcm !
5/24/2016
A. Temnykh, BNL NSLS, 6/1/06
0.42
0.43
0.44
0.45
0.46
I_com[A]
12
VW using for sextupole magnet alignment
Sextupole magnet example:
10cm long,
30mm bore radius
1.5T field on pole tip
Sextupole field
BsL = 1.5e4G*cm/mm^2 *(x/30)^2
with 0.20Gcm RMS noise
20
15
10
Sextupole center from
quadratic fit:
X = 0.0018 +- 0.0013mm
5
0
-5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
x[mm]
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13
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 ~ 0.050mm
b. Stages motion ~ 0.010mm
Both can be improved.
Note: fundamental mode frequency variation df/f ~ 5x10-4
produces the sag error ~0.002mm.
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14
Vibrating Wire Sensitivity Test
at NSLS
Alexander Temnykh1
and
George Rakowsky, Dave Harder & Mike Lehecka
June 1, 2006
1Cornell
University
NSLS Pulsed Wire Bench Converted to Vibrating Wire
for Sensitivity Study
X-Y-Z
STAGE
CALIBRATED
E-M
P-M DIPOLE
DIPOLE
(100 G-cm) (VARIABLE)
125 µm
BeCu WIRE
PHOTO-OPTICAL
WIRE POSITION
DETECTORS
(X & Y)
X-Y-Z
STAGES
AUDIO
OSCILLATOR
~56 Hz
2nd Harmonic
Vibration Mode
~1kg
SCOPE
PC
~1.5m
5.1m
1.4m
Method: • Vary EM current to cancel PM dipole kick.
• Measure wire vibration amplitude vs. current
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16
Vibrating Wire Sensitivity Study
Second mode amplitude
as function of the compensating magnet current.
Compensating magnet calibration 0.48A/100Gcm
or 0.2 Gcm / 0.001A
(Oscilloscope measurement)
VW setup sensitivity demonstration
Second order VW harmonic
as a function of compensating magnet current.
Compensating magnet calibration
~100Gcm / 0.425A or ~0.25Gcm/0.001A
0.01
300
Data set 1,
I_com (A2=0) = 0.4250 +- 0.0002 [A]
Data set 2,
I_com ( A2=0 ) = 0.4265+- 0.0005 [A]
Compensating current 0.489 +- 0.0009 A
200
0.005
100
0
0
-100
y = m1 *(m0-m2)
-200
m1
m2
Chisq
R
-300
-400
0.42
0.44
0.46
0.48
Icom[A]
0.5
Value
7168.9
0.48883
3345.4
0.99626
0.52
Error
219.91
0.0009065
NA
NA
0.54
-0.005
-0.01
0.39
0.4
0.41
Sensitivity ~ 0.2Gcm !
5/24/2016
A. Temnykh, BNL NSLS, 6/1/06
0.42
0.43
0.44
0.45
0.46
I_com[A]
17
Using VW for Sextupole Magnet Alignment
Sextupole magnet example:
10cm long,
30mm bore radius
1.5T field on pole tip
Sextupole field
BsL = 1.5e4G*cm/mm^2 *(x/30)^2
with 0.20Gcm RMS noise
20
15
10
Sextupole center from
quadratic fit:
X = 0.0018 +- 0.0013mm
5
0
-5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
x[mm]
5/24/2016
A. Temnykh, BNL NSLS, 6/1/06
18