1. Magnetic Analysis
Jin-Young Jung

2. Quarter period model for HXU
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

3. Quarter period model for SXU
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

4. Magnetic field and field roll off
HXU
requirement
gap (mm)
Beff (T)
∆B/B at x=0.4 mm
∆B/B
7.2
1.28
*1.0E-05±1.9x10-6
5.4E-05 20
0.29
6.7E-06±5.1x10-6
* uses finer mesh
SXU
1.91
2.3E-05±2.6x10-6
1.5E-04 36
0.25
3.2E-05±2.3x10-6
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.)

5. B effective

6. End design 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.

7. End design geometry for 10 mm gap HXU
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 #2
PM #3
PM #4
PM #5
PM #6
PM #7
pole #1
pole #2
pole #3
pole #4
pole #5
pole #6
pole #7

8. Scalar potential for poles (10 mm gap HXU)
pole #1
pole #2
pole #3
pole #4
pole #5
pole #6
pole #7
entrance kick (mTm)
Ideal scalar potential 1 -1
0.75
-0.25
model scalar potential
-1.000
0.999
-1.018
0.758
-0.243
0.003
0.529

9. Second integral for 10 mm gap (HXU)
internal shift: 15.6 mTm2
(requirement: ± 50 mTm2)
displacement: 6.9 mTm2
internal kick: mTm

10. Second integral for 7.2 mm gap (HXU)
displacement: 6.8 mTm2
internal shift: mTm2
(requirement: ± 50 mTm2)
internal kick: -11 mTm

11. Second integral for 20 mm gap (HXU)
internal kick: 18 mTm
internal shift: 72.6 mTm2
(requirement: ± 50 mTm2)
displacement: 5.7 mTm2

12. End design performance vs. gap
7.2 mm gap
pole #1
pole #2
pole #3
pole #4
pole #5
pole #6
pole #7
entrance kick (mTm)
scalar potential 1
-1.000
0.999
-1.015
0.754
-0.249
0.006
-11
10 mm gap
entrance kick (mTm)
-1.018
0.758
-0.243
0.003
0.529
20 mm gap
-1.002
0.996
-1.024
0.769
-0.232
-0.001 18
Due to the variations of Br values in end blocks,
tuning is required for end poles.

13. Cost related to block size
HXU
Pole height
Beff
125%
+2.4%
100%
75%
-6.7%
50%
-19.0%
SXU
+1.4%
-2.9%
-12.2%
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

14. Appendix

15. Sensitivity matrix for perturbations in 1% Br change (HXU)
PM #5 Br -1%
10 mm gap
pole #1
pole #2
pole #3
pole #4
pole #5
pole #6
pole #7
entrance kick (mTm)
scalar potential 1
-0.999
1.001
-1.012
0.752
-0.245
0.002
-13.5
PM #6 Br -1%
-1.000
0.998
-1.019
0.755
-0.24
0.005
0.6
PM #7 Br -1%
0.999
-1.018
0.758
-0.242
0.24