Short-Range Wakes in Elliptical Pipe Geometry

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Short-Range Wakes in Elliptical Pipe Geometry
Igor Zagorodnov Beam Dynamics Group
Meeting 05.09.05
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Pumping slot
Theoretical results (Bethe theory) only for
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Pumping slot
Effect of the slot is small.

• Accuracy estimation of the numerical results.
• Wake scaling for geometry parameters.

Used tools ECHO (time-domain), CST Microwave
Studio (modeling, meshing), Matlab (pre- and
postprocessing).
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Accuracy of 3D calculations
s mm dx s dy,dz s Loss,2D V/pC Error, 2D V/pC Loss, 3D V/pC Error, 3D V/pC
250 1/40 1/40 36.3097 ref.
250 1/20 1/20 36.2932 0.016
250 1/5 1/5 36.2369 0.07 36.2265 0.1
25 1/20 1/20 370.77 ref.
25 1/10 1/10 370.60 0.17
25 1/5 1/5 369.96 0.8
25 1/5 2 369.78 1
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Accuracy of 3D calculations
s mm dx s dy,dz s Loss,2D V/pC Error, 2D V/pC Loss, 3D V/pC Error, 3D V/pC
250 1/40 1/40 -0.8606 ref.
250 1/10 1/10 -0.8678 0.001
250 1/5 1/5 -0.8802 0.012 -0.8478 0.013
25 1/20 1/20 0.8639 ref.
25 1/10 1/10 -0.8619 0.002
25 1/5 1/5 -0.8859 0.02
25 1/5 2 -0.9380 0.17
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Scaling laws
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Scaling laws
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Out
In
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w mm q/(2p) s mm Loss V/pC
7 0.339 250 3.04-0.1
4 0.167 250 0.91-0.1
2 0.083 250 0.23-0.1
7 0.339 25 31.8-1
4 0.167 25
2 0.083 25 2.8-1
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w mm q/(2p) s mm Loss V/pC
7 0.339 250 -0.162-0.013
4 0.167 250 -0.065-0.013
2 0.083 250 -0.01-0.013
7 0.339 25 -0.247-0.17
4 0.167 25
2 0.083 25
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Scaling laws and extrapolation
w mm a, mm q/(2p) s mm Loss V/pC
7 4 0.339 250 -0.16
1 7.5 0.021 25 -0.005
w mm b, mm a, mm q/(2p) s mm Loss V/pC
7 10 4 0.339 250 3
1 20 7.5 0.021 25 0.2
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Energy method
(K. Zotter et al. , Impedances and Wakes , 1998
and K.L.F.Bane, I.A.Zagorodnov, SLAC-PUB-11388,
2005)
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Accuracy of the energy method
w mm s mm K_loss from time-domain V/pC K_loss from energy V/pC Error, V/pC
7 250 2.88 3.10 0.22
7 25 31.5 31.0 0.5
2 250 0.22 0.26 0.04
2 25 2.75 2.63 0.12
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Energy method
emm Mesh step in s Ellipse Ellipse with slot
0.25 2 2.89161337 2.89165659 4.32e-5
0.25 1 2.90553777 2.90560728 6.95e-5
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Round (a3.8, b3.3)
Energy method
Old pipe?
Direct time-domain with ECHO
The energy loss for the new smaller pipe is a
little smaller!
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Loss, V/pC Spread, V/pC Peak, V/pC
var1 84 33 -118
var2 42 16 -58
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Kick
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Longitudinal wake for the case of the elliptical
pipe (3.8mm)
pro section (6.1 m) Loss, V/pC Spread, V/pC Peak, V/pC
absorber 1 42 16 -58
pumping slot 1 lt0.2 lt0.1 gt-0.3
pump 1 9 4 -13
BPM 1
bellow 1 13 5 -18
flange gap 1 6 2.4 -8.5
Total geom. 70 25 -95
resistive (Cu) 6.1m 220 279 -542
resistive (Al) 6.1m 303 325 -660
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Shape dependence
Loss, V/pC Spread, V/pC Peak, V/pC
Gauss, cu/al 36/50 46/53 -89/108
Rect, cu/al 79/93 90/72 -256/243
copper
aluminum
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Power Loss (Gaussian bunch)
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Conclusion

• Loss and kick of the pumping slot are negligible
• Wake of the absorber is reduced by factor 2
• Resistive wake is dominant
• Non-smooth bunch shape (rectangular) increases
  the energy spread less than by factor 2