Magnetic Analysis Jin-Young Jung

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

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

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.)

B effective

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.

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

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

Second integral for 10 mm gap (HXU) internal shift: 15.6 mTm2 (requirement: ± 50 mTm2) displacement: 6.9 mTm2 internal kick: 0.528 mTm

Second integral for 7.2 mm gap (HXU) displacement: 6.8 mTm2 internal shift: -23.8 mTm2 (requirement: ± 50 mTm2) internal kick: -11 mTm

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

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.

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

Appendix

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