Magnetic Analysis

Jin-Young Jung

1

Quarter period model for HXU

Slide 2

•Pole width : 4.2 cm•Pole height : 2.74 cm•Pole thickness: 0.53 cm•PM width : 5.5 cm•PM height : 3.39 cm•PM thickness : 1.07 cm

Quarter period model for SXU

Slide 3

•Pole width : 4.2 cm•Pole height : 5.04 cm•Pole thickness: 1.01 cm•PM width : 6.6 cm•PM height : 6.24 cm•PM thickness : 1.74 cm

Magnetic field and field roll off

Slide 4

HXU requirement

gap (mm) Beff (T) ∆B/B at x=0.4 mm ∆B/B7.2 1.28 *1.0E-05±1.9x10-6 5.4E-0520 0.29 6.7E-06±5.1x10-6 5.4E-05

* uses finer meshSXU requirement

gap (mm) Beff (T) ∆B/B at x=0.4 mm ∆B/B7.2 1.91 2.3E-05±2.6x10-6 1.5E-0436 0.25 3.2E-05±2.3x10-6 1.5E-04

• For calculation accuracy, results using finer mesh (mesh size: 0.05 mm in air gap region) are compared with the current model using less finer mesh (mesh size: 0.1 mm in air gap region) . • It shows there is not much difference in Beff (~0.1%) between the two models. • For better accuracy, it may need much finer mesh but it will take lots of computation time. (The finer mesh model took two days for computation.)

B effective

Slide 5

End design

Slide 6

• HXU end design is performed.

• HXU end for 10 mm gap is optimized and then applied for 7.2 mm gap and 20 mm gap.

• Scalar potential is normalized for the poles.

• SXU end using the HXU end design configuration is calculated for preliminary dimensions of the quote.

End design geometry for 10 mm gap HXU

Slide 7

• 2d results are compared with 3d and it has close match. • For optimization purpose and reducing computation time, 2d calculation is used.• 3d calculation for confirmation and full SXU design are not completed yet.

PM #1 PM #7PM #6PM #5PM #4PM #3PM #2

pole #1 pole #7pole #6pole #5pole #4pole #3pole #2

Scalar potential for poles (10 mm gap HXU)

Slide 8

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

Ideal scalar potential 1 -1 1 -1 0.75 -0.25 0 0

model scalar potential 1 -1.000 0.999 -1.018 0.758 -0.243 0.003 0.529

Second integral for 10 mm gap (HXU)

Slide 9

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-4.00E-05

-3.00E-05

-2.00E-05

-1.00E-05

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

2nd integral (HXU, 10 mm gap)

z (m)

2nd

inte

gral

(Tm

2)

internal kick: 0.528 mTm

internal shift: 15.6 mTm2

(requirement: ± 50 mTm2)displacement: 6.9 mTm2

Second integral for 7.2 mm gap (HXU)

Slide 10

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-1.00E-04

-8.00E-05

-6.00E-05

-4.00E-05

-2.00E-05

0.00E+00

2.00E-05

4.00E-05

6.00E-05

2nd integral (HXU, 7.2 mm gap)

z (m)

2nd

inte

gral

(Tm

2)

internal kick: -11 mTm

internal shift: -23.8 mTm2

(requirement: ± 50 mTm2)

displacement: 6.8 mTm2

Second integral for 20 mm gap (HXU)

Slide 11

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

-2.00E-05

-1.00E-05

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

6.00E-05

7.00E-05

8.00E-05

2nd integral (HXU, 20 mm gap)

z (m)

2nd

inte

gral

(Tm

2)

internal shift: 72.6 mTm2

(requirement: ± 50 mTm2)

internal kick: 18 mTm

displacement: 5.7 mTm2

End design performance vs. gap

Slide 12

• Due to the variations of Br values in end blocks, tuning is required for end poles.

7.2 mm gap

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

scalar potential 1 -1.000 0.999 -1.015 0.754 -0.249 0.006 -11

10 mm gap

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

scalar potential 1 -1.000 0.999 -1.018 0.758 -0.243 0.003 0.529

20 mm gap

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

scalar potential 1 -1.002 0.996 -1.024 0.769 -0.232 -0.001 18

Cost related to block size

Slide 13

• Peak field vs. pole block size: For higher magnetic field, much larger block volume is needed. Primary cost differential will be due to increased block volume Cost will approximately scale with pole height

HXUPole height Beff

125% +2.4%100% 100%75% -6.7%50% -19.0%

SXUPole height Beff

125% +1.4%100% 100%75% -2.9%50% -12.2%

50% 75% 100% 125%0.800

0.850

0.900

0.950

1.000

1.050

HXU SXU

Pole Height

B/B1

00

Appendix

Slide 14

Sensitivity matrix for perturbations in 1% Br change (HXU)

Slide 15

PM #5 Br -1% 10 mm gap

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

scalar potential 1 -0.999 1.001 -1.012 0.752 -0.245 0.002 -13.5

PM #6 Br -1% 10 mm gap

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

scalar potential 1 -1.000 0.998 -1.019 0.755 -0.24 0.005 0.6

PM #7 Br -1% 10 mm gap

pole #1 pole #2 pole #3 pole #4 pole #5 pole #6 pole #7entrance kick

(mTm)

scalar potential 1 -1.000 0.999 -1.018 0.758 -0.242 0.002 0.24