HOM loss calculation of IP chamber Nakano Hiroshi

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

Beam parameters Nano beam option • sz (mm) = 6(LER)/6(HER) • n- = 3. 89 x 1010 • n+ = 6. 78 x 1010 • #bunch = 3425(LER, HER)

HOM calculation Gdfid. L: 3 D 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

Beam pipe data HER 15 mm 60 mrad(3. 438 deg) 10 mm Bended to use ports (pipes continue infinitely) LER

Calculation method Compare 6 ways of results ~30 mm ~400 mm port Window wake=yes Mesh size 0. 5 mm 1/1 model Is it long enough? Window wake=no *Window wake =Yes: use bunch-fixed grid =No: use pipe-fixed grid Mesh size 0. 3 mm 1/2 model Mesh size 1 mm Are mesh sizes good? Calculated in various crossing angles

Results of HER 6 ways agreed with each other within 10~20% Crossing angle big Loss factor big small 60 mrad 0. 0004 V/p. C ( ) 5. 3 [W]

Consideration 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. A B

Results with 0. 2 mm mesh Gdfid. L seems to work correctly. �OM losses from H and beams were calculated with 0. 2 mm mesh size to get more ‘accurate’ values. HER (r = 15 mm) 0. 000551 V/p. C (7. 3 W) LER (r = 10 mm) 0. 00145 V/p. C (58 W) 65 W

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

Type-1 HER *mesh size = 0. 2 mm, 1/2 model a b c loss factor 100 480 7. 0 0. 68 100 580 7. 0 100 680 7. 0 150 480 5. 5 0. 66 150 580 5. 5 150 680 5. 5 0. 90 b LER a 0. 77 c 0. 82 36~48 W (HER+LER) Check with finer mesh Loss factor -> 1. 2 * 10^-3[V/p. C] ( in case of mesh size = 0. 08 mm) 64 W

Type-2 *mesh size = 0. 13 mm, 1/2 model HER b’ HER / LER a’ b’ c loss factor 1. 9 / 2. 3 86 480 7. 3 2. 4 / 2. 1 165 480 5. 0 1. 8 / 2. 4 84 680 7. 5 165 680 5. 0 2. 1 / 2. 2 LER a’ c 115~119 W (HER+LER) Check with finer mesh Loss factor -> 2. 1 / 2. 4 * 10^-3[V/p. C] ( in case of mesh size = 0. 08 mm) 124 W

Summary • Gdfid. L 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 50 W~100 W - Larger for larger crossing angles