HOM loss calculationof IP chamber

Nakano Hiroshi

7-Jul-2009(presented by Hitoshi Yamamoto)

Thanks to Tetsuo Abe and other experts

Beam parameters

Nano beam option•z (mm) = 6(LER)/6(HER)• n- = 3.89x1010

• n+ = 6.78x1010

• #bunch = 3425(LER,HER)

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

Beam pipe data

60mrad(3.438deg)

15mm

10mm

HERLER

Bended to use ports

(pipes continue infinitely)

Calculation method

Window wake=yesMesh size 0.5 mm1/1 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

Results of HER

big small

big smallLoss factor

Crossing angle

60mrad

0.0004 V/pC ( )5.3 [W]

6 ways agreed with each otherwithin 10~20%

Consideration

If the change from “A” to “B” was slow, the loss factor might be small.

A B

EM will not stayBA

At small angles, the change isquasi-static; penetration of fieldto the side chamber is ~zero.

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

HER

HER

LER

LER

New geometries

Type-1

Type-2

color: center of pipe

dashed: beam trajectory

IP

IP

All pipes have 10mm radius.Crossing angle of the beams is 60mrad.

before

IP

HER

LER

r = 15mm

r = 10mm

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

Type-2

a’

b’

c 86 480 7.3

165 480 5.0 84 680 7.5165 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

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