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

2. Beam parameters Nano beam option  z (mm) = 6(LER)/6(HER) n- = 3.89x10 10 n+ = 6.78x10 10 #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 60mrad (3.438deg) 15mm 10mm HER LER Bended to use ports (pipes continue infinitely)

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

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

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

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

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

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

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

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