Field Measurement of PRISM-FFAG Magnet Y. Arimoto 13th, Apr. - - PowerPoint PPT Presentation

Field Measurement of PRISM-FFAG Magnet

• Y. Arimoto

13th, Apr. 2007@FFAG 2007 CNRS

Contents

PRISM-FFAG Magnet Field Measurement Apparatus Measurement Results

Current correction Comparison of three magnets Comparison to TOSCA calculation

Summary

PRISM-FFAG Magnet

C type Effective Aperture

100 cm (horizontal) 30 cm (vertical)

Thin Shape

Length along beam axis : ~1.2 m

Slant pole shape

Field index = 4.6

r θ z

Cross section of F magnet

Field Clamp Field clamp (1345.1) 4 B C (969.9) A (2022.4) (1550) F Pole D Pole D Pole

175 740 (6500) Distance from Machine Center 2022.4 F Coil 1550 Median Plane

r θ z

Measurement

Alignment tool Theodrite and Autolevel Measurement tool 3D axis robot Hall probe : MPT-141 (Group3 )

3D axis field measurement tool

Hall probe x y z

Measurement region

Pit

300

Table

R 7100 R 6 5 R 5750

18.00° 18.00° 165 245 205 980 R1とR2の高さ基準点 R3の高さ基準点 R4の高さ基準点 R1 R2 R3 R4

1000 1020 800 800

Analysis

Inclusion of mechanical distortion for 3d axis robot Correction of current fluctuation of power supply for main coil

Distortion of Measurement Tool

Measurement Tool have mechanical distortion. The position in x,y,z axis is deviated from expected position from motor pulse. The deviated position is corrected with measured Hall probe position by Auto-level and Theodorite.

Example of Distortion : Hall Probe Height variation

We measured Hall probe height by autolevel changing x-y position of Hall probe

arm_height_xy-3.dat

250 500 750 1000 200 400 600 800

• 0.6
• 0.4
• 0.2

0.2 0.4

x (mm) y ( m m ) δh (mm)

• 50

50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 250 500 750 1000

x (mm) y (mm)

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 250 500 750 1000

x (mm) δh (mm)

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 200 400 600 800

y (mm) δh (mm)

Upper left：3D plot of Height variation of Hall probe Upper right：Contour plot Lower left：Height variation as a function of x Lower right： Height variation as a function of y

y x z Autolevel Hall probe

Height variation is ~ 1 mm

Angular Distortion

Angular Distortion was measured by Laser set up

• n Hall probe arm

This data is used to correct Bx and By data Hall probe angle change from 0 to 1 mrad while measurement tool is moving from 0 mm to 800 mm.

y x z Hall probe Target Laser

Current Fluctuation

Unfortunately coil current power supply have current fluctuation The fluctuation is 1 ~ 2 % Magnetic field is fluctuating due to coil current fluctuation. Correction will be done by using offset current run and monitor Hall probe.

Fixed Hall probe

Field Clamp Field clamp (1345.1) 4.4° 2.0° 2.0° 1 . 1 ° 1 . 1 ° 4 2.5° C (969.9) A B (2022.4) (1550) F Pole D Pole D Pole

Fixed Hall probe monitoring stability

Current fluctuation

R1 R2 F pole D pole

Trend of Monitoring Hall probe

[Hour] [Hour]

Current offset Run

To obtain correction coefficient at each position, magnetic field has been measured changing coil current by 1 %.

Run IF ID 1 IF0 ID0 2 IF0+dIF ID0 3 IF0 ID0+dID

IF0 = 1444 A (F coil current) ID0 = 602.1 A (D coil current) dIF = 0.01 x IF0 dID = 0.01 x ID0

dB(x, I) = α „∂B(x, I) ∂IF (x) − γ ∂B(x, I) ∂ID(x) « dMF + β ∂B(x, I) ∂ID(x) dMD (25) dB(x, I) = CF (x)dMF + CD(x)dMD (26) CF (x) = α „∂B(x, I) ∂IF (x) − γ ∂B(x, I) ∂ID(x) « (27) CD(x) = β ∂B(x, I) ∂ID(x) (28) A corrected magnetic field is obtained as Bcorr(x) = Bmeas(x) − CF (x)dMF − CD(x)dMD, (29) here, Bmeas is a measured value by 3D measurement tool.

Correction function

Obtained from the measurement where coil currents are changed by 1 %.

Correction results : F

x = 0 mm

Region where F component is dominant

Correction ON Correction OFF Correction ON Correction OFF

1000 2000 3000 4000 6000 6500 7000

x=0 cm

y (mm) Bz (Gauss)

5 10 15 20 6000 6500 7000

y (mm) k=dbz/bz*y/dy

x=0 cm

1000 2000 3000 4000 6000 6500 7000

x=0 cm

y (mm) Bz (Gauss)

5 10 15 20 6000 6500 7000

y (mm) k=dbz/bz*y/dy

x=0 cm

Bz (Gauss)

y x z

Plotted line

Correction Result (BL Integral)

../blz-corr_OFF.out

500 1000 1500 x 10 2 580 600 620 640 660 680 700 720

BzL+ (Gauss*cm) BzL- (Gauss*cm)

BFL BDL

10000 20000 30000 580 600 620 640 660 680 700 720 5 5.5 6 6.5 580 600 620 640 660 680 700 720

BFL BDL

k value + 1

5.6 5.8 6 6.2 6.4 580 600 620 640 660 680 700 720

r (cm) F/D ratio

BFL = 55906.8,BDL = -9496.78, r=600 cm BFL = 86477.6,BDL = -14509.8, r=650 cm BFL = 133285,BDL = -21984.8, r=700 cm

../blz-corr_ON.out

500 1000 1500 x 10 2 580 600 620 640 660 680 700 720

BzL+ (Gauss*cm) BzL- (Gauss*cm)

BFL BDL

10000 20000 30000 580 600 620 640 660 680 700 720 5 5.5 6 6.5 580 600 620 640 660 680 700 720

BFL BDL

k value + 1

5.6 5.8 6 6.2 6.4 580 600 620 640 660 680 700 720

r (cm) F/D ratio

BFL = 56305.6,BDL = -9495.64, r=600 cm BFL = 86534.3,BDL = -14504, r=650 cm BFL = 133498,BDL = -21984.1, r=700 cm

Correction ON Correction OFF

r θ z

r θ k k F/D F/D r r

Design value Design value

R1 R2

Field Clamp Field clamp (1345.1) 4.4° 2.0° 2.0° 1 . 1 ° 1 . 1 ° 4 2.5° B C C (969.9) A A B (2022.4) (1550) F Pole D Pole D Pole

y=6335 mm R1

y x z

y=6975 mm

Comparison with other magnets

Magnetic field of the three magnets has been measured. These magnets are compared at red lines shown in right figure.

Magnets comparison (z=0mm)

y=6335 mm (R1) y=6975 mm (R1)

Bz Bz Ratio Diff. Diff. Ratio

2000 4000 200 400 600 800 1000

x (mm) Bz (Gauss)

y=6335 mm z=0 mm

• 0.1
• 0.05

0.05 0.1 200 400 600 800 1000

x (mm) Bz/Bz0-1

y=6335 mm z=0 mm

• 10
• 5

5 10 200 400 600 800 1000

x (mm) Bz-Bz0

y=6335 mm z=0 mm

2000 4000 200 400 600 800 1000

x (mm) Bz (Gauss)

y=6975 mm z=0 mm

• 0.1
• 0.05

0.05 0.1 200 400 600 800 1000

x (mm) Bz/Bz0-1

y=6975 mm z=0 mm

• 10
• 5

5 10 200 400 600 800 1000

x (mm) Bz-Bz0

y=6975 mm z=0 mm

F component : less than 0.2 % D component: 0.5 %

Mag#1 Mag#2 Mag#3 y x z Mag#2 / Mag#1 Mag#3 / Mag#1 ±1 %

Bi(r)=(1+δBi)B(r) i : cell ID number (1~10) δBi : random error- factor within error tolerance

200 400 600 800 1000 0.5 1 1.5 2 2.5 3 3.5

Error tolerance (+-%) 4D Acceptance (x106 mm*mrad2)

Error tolerance < 0.5 % by S. Nakaoka

4D acceptance was calculated when different random factors are applied to each triplets.

4D acceptance with field error

Shown at FFAG 2004 at FNAL

y=6335 mm y=6975 mm

Bz Bz Ratio Ratio

y x z

TOSCa vs measurement

tosca_vs_meas.kumac

• 1000

1000 2000 3000 4000 250 500 750 1000

x (mm) Bz (Gauss)

• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015 0.02 250 500 750 1000

x (mm) Bz_MEAS/Bz_TOS -1

• 1000

1000 2000 3000 4000 250 500 750 1000

x (mm) Bz (Gauss)

• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015 0.02 250 500 750 1000

x (mm) Bz_MEAS/Bz_TOS -1

y=6335 mm y=6975 mm

Difference between TOSCA and measurement is about 0.5 %.

TOSCA Meas.

Summary

The distortion of magnet measurement tool was measured. The coil-current fluctuation is successfully corrected. Difference between three magnets is less than 0.2 % for F component. This value is smaller than required difference to avoid acceptance decrease. Difference between TOSCA is about 0.5 %. Next study Errors of magnetic field should be estimated. Tracking with measured map