short-range wakes in elliptical pipe geometry
DESCRIPTION
Short-Range Wakes in Elliptical Pipe Geometry. Igor Zagorodnov Beam Dynamics Group Meeting 05.09.05. Pumping slot. Theoretical results (Bethe theory) only for. Pumping slot. Effect of the slot is small. Accuracy estimation of the numerical results. Wake scaling for geometry parameters. - PowerPoint PPT PresentationTRANSCRIPT
Short-Range Wakes in Elliptical Pipe Geometry
Igor Zagorodnov
Beam Dynamics Group Meeting
05.09.05
1w mm width of the slot 5L m length of the slot
Pumping slot
25w m
Theoretical results (Bethe theory) only for .w
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).
0 lnhi
Z bZ
a 2
hiloss
z
Z ck
250 m
25 m
1( ln( / ))lossk O b a
37.2 /lossk V pC
372 /lossk V pC
in outW W W
Out In
2( ) /(2 )L b a
ba
[m]
dx
[dy,dz
[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
outlossk
1( ln( / ))outlossk O b a
Accuracy of 3D calculations
-5 0 5-15
-10
-5
0
5x 10-3
out V mW
pC
/s
250 m
25 m
1( )outW O
[m]
dx
[dy,dz
[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
inlossk
1( )inlossk O a
in outloss lossk k
Accuracy of 3D calculations
-5 0 50
0.5
1
1.5
2in V
WpC
/s
250
(3 )
m
D
(1), 0inW O
25
(3 )
m
D
25
(2 )
m
D
1 lnoutloss
bk O
a
1inlossk O
a
Scaling laws
Out In
2( ) /(2 )L b a
ba
( )w
1 lnoutloss
bk O
a
inlossk O
a
, ?
Scaling laws
w
a
b
w10h mm
4a mm
Out In
w10h mm
4a mm
w
[mm]
[m]
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
outlossk
1( )outlossk O
1.8( ) ?!outlossk O
w
-5 0 5-1.5
-1
-0.5
0
0.51.8 1.8
outW V
pC rad
/s
0.3392
1.8( ), 0,outW O w
0.1672
0.0832
250 m
w10h mm
4a mm
w
[mm]
[m]
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
inlossk
( ) ?!inlossk O
(1), 0inlossk O
in outloss lossk k
w
-5 0 5-0.05
0
0.05
0.1
0.15
0.2inW V
pC rad
/s
0.3392
( ), 0,inW O w
0.1672
0.0832
250 m
?error
w
1 1.8 lnoutloss
bk O
a
inlossk O
a
w
[mm]
a,
[mm]
[m]
Loss
[V/pC]
7 4 0.339 250 -0.16
1 7.5 0.021 25 -0.005
0.021 40.16 0.005
0.339 7.5inloss
Vk
pC
w
[mm]
b,
[mm]
a,
[mm]
[m]
Loss
[V/pC]
7 10 4 0.339 250 3
1 20 7.5 0.021 25 0.2
1.820
ln0.021 7.5
3 10 0.2100.339
ln4
outloss
Vk
pC
0.2loss
Vk
pC
Scaling laws and extrapolation
in outW W W 2out in eW W W
2 2 2 , 0in e e inW W W W if W
in outloss lossk k
( )ez ellipse ellipse slot zW w w w
(K. Zotter et al. , Impedances and Wakes …, 1998 andK.L.F.Bane, I.A.Zagorodnov, SLAC-PUB-11388, 2005)
w
Energy method
w
[mm]
[m]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
Accuracy of the energy method
[mm] Mesh step in
Ellipse Ellipse with slot
0.25 2 2.89161337 2.89165659 4.32e-5
0.25 1 2.90553777 2.90560728 6.95e-5
0
2w
Z c
0.03 0.12 /lossk V pC
, 0.001 /kick xk V pC( , 0, 0)
( , 0, 0)s
yx
W s x yW s x y ds
a
xy
xa
20h mm
2 2 5000 25 3 16 [ ]h L e mm
0.2 /lossk V pC
Energy method
3mm
3.3mm3.8mm
84 248 257 /loss s sk x y V pC
, 390 46 436 /kick x s wk x x x V pC
, 348 47 301 /kick y s wk y y y V pC
Energy method
85 /lossk V pC
Round (a=3.8, b=3.3)
0.5mm
15mm
3mm
7.6yw mm
2 351 /( )Dkickk V pC m
3 359 /( )Dkickk V pC m
Direct time-domain with ECHO
x
y
9yw mm
7.8yw mm 85 /lossk V pC
91 /lossk V pC
Old pipe?
The energy loss for the new smaller pipe is a little smaller!
2%Error
x
y0.5mm
15mm
3mm
7.6 mm
250 250 /84loss s sk x y V pC
, 390 46 /436kick x s wk x x x V pC
, 348 47 /301kick y s wk y y y V pC
1200 1200 /42loss s sk x y V pC
, 280 206 /486kick x s wk x x x V pC
, 78 208 /130kick y s wk y y y V pC
Loss,
V/pC
Spread,
V/pC
Peak,
V/pC
var1 84 33 -118
var2 42 16 -58
x
yKick
, /486kick xk x V pC
, /130kick yk y V pC
xy
xa
, 0.001 /slotkick xk V pC
, ,0.0001 0.01 /slot abskick x kick xk k V pC
pro section (6.1 m)
Loss,
V/pC
Spread,
V/pC
Peak,
V/pC
absorber 1 42 16 -58
pumping slot 1 <0.2 <0.1 >-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
Longitudinal wake for the case of the elliptical pipe (3.8mm)
-5 0 5
-300
-200
-100
0
100
200
300
-5 0 5-300
-200
-100
0
100
200
300
Shape dependence
-5 0 50
1000
2000
3000
4000
5000
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
-1 -1: 5.8e+7[ m ], =2.46e-14[sec]cond relaxcu -1 -1: 3.66e+7[ m ], =7.1e-15[sec]cond relaxal
copper aluminum
I A
VW
pC
VW
pC
/ zs
/ zs / zs
25z m
4000 [ ]bN bunches
10 [ ]repf Hz
1[ ]q nC
2b rep lossP N f q k
0.52geom
WP
m
, 1.4res Cu
WP
m
, 2res Al
WP
m
Power Loss (Gaussian bunch)
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