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

z r r z PRISM-FFAG Magnet (2022.4) (1550) Field clamp D Pole F Pole C type (1345.1) (969.9) A Effective Aperture θ 100 cm (horizontal) B C 0 30 cm (vertical) 4 D Pole Thin Shape Field Clamp 2022.4 Length along beam axis : F Coil ~1.2 m 740 Slant pole shape 175 Field index = 4.6 θ 1550 Median Plane Cross section of F (6500) Distance from Machine Center magnet

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

3D axis field measurement tool Hall probe z y x

R4の高さ基準点 R1とR2の高さ基準点 R3の高さ基準点 Measurement region 300 Table 18.00° 18.00° 1000 R 7100 1020 R1 R3 R 205 6 5 800 0 0 165 R 5750 R2 R4 245 800 Pit 980

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.

y z Example of Distortion : Hall Probe Height variation arm_height_xy-3.dat 900 850 800 750 x δ h (mm) 0.4 700 650 0.2 600 550 y (mm) 0 500 450 -0.2 400 -0.4 350 300 -0.6 250 200 150 100 800 50 250 500 750 1000 600 0 400 -50 x (mm) y 200 0 250 500 750 1000 0 ( 0 m x (mm) Autolevel Hall probe m ) 2 2 δ h (mm) δ h (mm) 1.8 1.8 1.6 1.6 1.4 1.4 1.2 1.2 1 1 We measured Hall probe height 0.8 0.8 0.6 0.6 0.4 0.4 by autolevel changing x-y 0.2 0.2 0 0 -0.2 -0.2 -0.4 -0.4 position of Hall probe -0.6 -0.6 -0.8 -0.8 -1 -1 0 250 500 750 1000 0 200 400 600 800 x (mm) y (mm) Upper left ： 3D plot of Height variation of Hall probe Upper right ： Contour plot Height variation is ~ 1 mm Lower left ： Height variation as a function of x Lower right ： Height variation as a function of y

z y Angular Distortion Laser Angular Distortion was x measured by Laser set up on Hall probe arm Target This data is used to Hall probe 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.

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.

monitoring stability Fixed Hall probe Fixed Hall probe (2022.4) (1550) Field clamp D Pole ° 1 . 1 2.0° F Pole (1345.1) (969.9) 4.4° A 2.0° ° 0 1 4 . 1 D Pole B 2.5° C Field Clamp

Current fluctuation Trend of Monitoring Hall probe F pole D pole [Hour] [Hour] R1 R2

Current offset Run To obtain correction coefficient at each position, magnetic field has been measured changing coil current by 1 %. Run I F I D I F0 = 1444 A (F coil current) I D0 = 602.1 A (D coil current) 1 I F0 I D0 dI F = 0.01 x I F0 2 I F0 +dI F I D0 dI D = 0.01 x I D0 3 I F0 I D0 +dI D

Correction function „ ∂ B ( x , I ) « ∂ I F ( x ) − γ ∂ B ( x , I ) dM F + β ∂ B ( x , I ) dB ( x , I ) = α ∂ I D ( x ) dM D (25) ∂ I D ( x ) dB ( x , I ) = C F ( x ) dM F + C D ( x ) dM D (26) „ ∂ B ( x , I ) « ∂ I F ( x ) − γ ∂ B ( x , I ) C F ( x ) = α (27) ∂ I D ( x ) C D ( x ) = β ∂ B ( x , I ) (28) ∂ I D ( x ) A corrected magnetic field is obtained as B corr ( x ) = B meas ( x ) − C F ( x ) dM F − C D ( x ) dM D , (29) here, B meas is a measured value by 3D measurement tool. Obtained from the measurement where coil currents are changed by 1 %.

z y Correction results : F x = 0 mm Plotted line Region where F component is dominant x Bz (Gauss) k=dbz/bz*y/dy 4000 Correction OFF Correction OFF 20 x=0 cm x=0 cm 3000 15 10 2000 5 1000 6000 6500 7000 6000 6500 7000 y (mm) y (mm) Bz (Gauss) k=dbz/bz*y/dy 4000 x=0 cm x=0 cm Correction ON Correction ON 20 3000 15 2000 10 5 1000 6000 6500 7000 6000 6500 7000 y (mm) y (mm) Bz (Gauss)

Correction Result z r (BL Integral) Correction OFF Correction ON ../blz-corr_OFF.out ../blz-corr_ON.out 580 600 620 640 660 680 700 720 580 600 620 640 660 680 700 720 x 10 2 x 10 2 B F L B F L B F L = 55906.8,B D L = -9496.78, r=600 cm B F L = 56305.6,B D L = -9495.64, r=600 cm 30000 30000 B F L = 86477.6,B D L = -14509.8, r=650 cm B F L = 86534.3,B D L = -14504, r=650 cm B D L B D L 1500 1500 B z L + (Gauss*cm) B F L = 133285,B D L = -21984.8, r=700 cm B z L + (Gauss*cm) B F L = 133498,B D L = -21984.1, r=700 cm B z L - (Gauss*cm) B z L - (Gauss*cm) 20000 20000 1000 1000 10000 10000 R2 R1 500 500 θ 0 0 0 0 580 600 620 640 660 680 700 720 580 600 620 640 660 680 700 720 B F L 6.5 6.5 B F L B D L B D L 6 6 k value + 1 k value + 1 k k 5.5 5.5 Design value 5 5 r 580 600 620 640 660 680 700 720 580 600 620 640 660 680 700 720 6.4 6.4 F/D Design value F/D 6.2 6.2 F/D ratio F/D ratio 6 6 5.8 5.8 θ 5.6 5.6 580 600 620 640 660 680 700 720 580 600 620 640 660 680 700 720 r r r (cm) r (cm)

y z Comparison with other magnets B C A 4.4° 2.0° 2.0° 1 ° ° 1 . 1 . 1 2.5° (1345.1) F Pole Magnetic field of D Pole the three magnets R1 D Pole Field Clamp y=6975 mm has been measured. (1550) Field clamp (2022.4) y=6335 mm These magnets are compared at red lines shown in right figure. (969.9) 0 4 C x A B

Magnets comparison y z (z=0mm) Mag#1 Mag#2 / Mag#1 Mag#2 Mag#3 / Mag#1 y=6335 mm (R1) Mag#3 0.1 10 Bz (Gauss) Ratio y=6335 mm y=6335 mm y=6335 mm 4000 z=0 mm z=0 mm z=0 mm 0.05 5 Bz/Bz 0 -1 Bz-Bz 0 Bz 2000 0 0 -0.05 -5 0 -0.1 -10 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 Diff. x (mm) x (mm) x (mm) x y=6975 mm (R1) 0.1 10 Bz (Gauss) Ratio y=6975 mm y=6975 mm y=6975 mm F component : 4000 z=0 mm z=0 mm z=0 mm 0.05 5 Bz/Bz 0 -1 less than 0.2 % Bz-Bz 0 ±1 % Bz 2000 0 0 Diff. -0.05 -5 D component: 0.5 0 -0.1 -10 % 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 x (mm) x (mm) x (mm)

4D acceptance with field error 4D acceptance was calculated when by S. Nakaoka different random factors are applied to each triplets. 1000 4D Acceptance (x10 6 mm*mrad 2 ) 800 B i (r)=(1+ δ B i )B(r) 600 i : cell ID number (1~10) 400 δ B i : random error- 200 factor within error 0 tolerance 0 0.5 1 1.5 2 2.5 3 3.5 Error tolerance (+-%) Error tolerance < 0.5 % Shown at FFAG 2004 at FNAL

z y TOSCa vs measurement tosca_vs_meas.kumac 4000 0.02 Ratio B z (Gauss) B z_MEAS /B z_TOS -1 y=6335 mm 0.015 3000 0.01 Meas. 0.005 2000 Bz TOSCA 0 1000 -0.005 -0.01 y=6335 mm 0 -0.015 -1000 -0.02 0 250 500 750 1000 0 250 500 750 1000 x x (mm) x (mm) 4000 0.02 B z (Gauss) B z_MEAS /B z_TOS -1 y=6975 mm Ratio 0.015 3000 0.01 0.005 2000 Bz 0 1000 -0.005 -0.01 y=6975 mm 0 -0.015 -1000 -0.02 0 250 500 750 1000 0 250 500 750 1000 x (mm) x (mm) Difference between TOSCA and measurement is about 0.5 %.

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