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HOM loss calculation of IP chambe r

# HOM loss calculation of IP chambe r

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## HOM loss calculation of IP chambe r

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1. HOM loss calculationof IP chamber Nakano Hiroshi 7-Jul-2009 (presented by Hitoshi Yamamoto) Thanks to Tetsuo Abe and other experts

2. Beam parameters • Nano beam option • sz (mm) = 6(LER)/6(HER) • n- = 3.89x1010 • n+ = 6.78x1010 • #bunch = 3425(LER,HER)

3. HOM calculation • GdfidL: 3D field calculation tool • Options • Two modes • Grid moves with bunch (window wake = yes) • Grid fixed to lab (window wake = no) • Symmtries • 1/2,1/4 etc. • Mesh sizes

4. Beam pipe data LER HER 15mm 60mrad(3.438deg) 10mm Bended to use ports (pipes continue infinitely)

5. Calculation method Window wake=yes Mesh size 0.5 mm 1/1 model 1/2 model Window wake=no Mesh size 0.3mm Mesh size 1mm Compare 6 ways of results ~30mm ~400mm port Is it long enough? *Window wake =Yes: use bunch-fixed grid =No: use pipe-fixed grid Are mesh sizes good? Calculated in various crossing angles

6. Results of HER Crossing angle big small Loss factor big small 0.0004 V/pC ( ) 5.3 [W] 6 ways agreed with each other within 10~20% 60mrad

7. Consideration A B If the change from “A” to “B” was slow, the loss factor might be small. EM will not stay A B At small angles, the change is quasi-static; penetration of field to the side chamber is ~zero.

8. Results with 0.2 mm mesh 0.000551 V/pC (7.3W) HER (r = 15mm) 0.00145 V/pC (58W) LER (r = 10mm) 65W GdfidL seems to work correctly. HOM losses from and beams were calculated with 0.2 mm mesh size to get more ‘accurate’ values.

9. New geometries IP HER r = 15mm before r = 10mm LER HER Type-1 IP LER HER Type-2 IP LER color: center of pipe All pipes have 10mm radius. dashed: beam trajectory Crossing angle of the beams is 60mrad.

10. Type-1 HER *mesh size = 0.2mm, 1/2 model b a b c loss factor LER 100 480 7.0 0.68 100 580 7.0 0.66 a 100 680 7.0 0.77 c 150 480 5.5 0.82 150 580 5.5 0.90 150 680 5.5 0.82 36~48W (HER+LER) Check with finer mesh Loss factor -> 1.2 * 10^-3[V/pC] ( in case of mesh size = 0.08mm) 64W

11. Type-2 c HER *mesh size = 0.13mm, 1/2 model b’ HER / LER LER a’ b’ c loss factor a’ 86 480 7.3 1.9 / 2.3 165 480 5.0 2.4 / 2.1 84 680 7.5 1.8 / 2.4 165 680 5.0 2.1 / 2.2 115~119W (HER+LER) Check with finer mesh Loss factor -> 2.1 / 2.4 * 10^-3[V/pC] ( in case of mesh size = 0.08mm) 124W

12. Summary • GdfidL gives stable(reliable) results • Within 10~20% • For different calculation modes, use of symmetries, length of wake calculation, mesh size, etc. • Crossing beam pipe designs for nano beam option have been evaluated for HOM • HOM loss is of order 50W~100W • Larger for larger crossing angles