longitudinal impedance budget from linac to sase2
DESCRIPTION
Longitudinal Impedance Budget from LINAC to SASE2. Igor Zagorodnov Beam Dynamics Group Meeting 13.11.06. SASE2. SASE1. (W.Decking). Wakefield sources Resistance of the pipe (r=25mm, L=456m, Aluminium) Collimators (r=2mm, L=50cm, 4 items, TIMETAL 6-4 ) - PowerPoint PPT PresentationTRANSCRIPT
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Longitudinal Impedance Budget from LINAC to SASE2
Igor Zagorodnov
Beam Dynamics Group Meeting
13.11.06
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SASE2
SASE1
(W.Decking)
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Wakefield sources
- Resistance of the pipe (r=25mm, L=456m, Aluminium)
- Collimators (r=2mm, L=50cm, 4 items, TIMETAL 6-4 )
- Kickers (r=10mm, L=10m, 3 items, R/Lm )
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500d mm
2 2b mm1 25b mm
Collimator (geometrical wake)
||( ) ( )QW s Z I s
|| 2 (0)eZ Z
0 1
2
(0) ln2
e Z bZ
b
|| 303Z
Diffractive regime: the geometrical wake repeats the bunch shape
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TIMETAL 6-4 alloy (Titanium)(E.Schutz MVA)
6 1 10.6 10 m
500d mm
2 2b mm1 25b mm
http://www.timet.com/timetal6-4frame.html
Collimator (resistive wake)
1
0
( ) ( )( ) 1
2 2s sZ ZR
Z iR c Z
0 sec
0 mrough
0 nmoxid
( ) ( ) ( )Ls s sZ Z Z
( )( )si
Z
( )LsZ i L
0( )1 i
0.5 ( 0.02 )oxid roughL
M.Dohlus. TESLA 2001-26, 2001K.L.F.Bane, G.V.Stupakov, SLAC-PUB-10707, 2004
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0 1 2
x 10-4
-3000
-2000
-1000
0
1000
TIMETAL 6-4 alloy (Titanium)
6 1 10.6 10 m
500d mm
2 2b mm1 25b mm
Geom. Res. Total
Loss 827 329 1156
Spread 501 359 829
Peak -1665 -823 -2411
/kV nC
|| /W kV nC
s m
Collimator
total
resistive
bunch
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0 1 2
x 10-4
-20
-10
0
10
20
Aluminium
7 1 13.66 10 m
456d m
1 25b mm
resistive total
Loss 6.6 7.4
Spread 5.9 6.5
Peak -14.5 -15.9
/ /kV nC m
|| / /W kV nC m
s m
Pipe (resistive+oxid layer+roughness)
resistive
bunch
-157.1 10 sec
600 mrough 5 nmoxid
(T.Wohlenberg)
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10d m
2 10b mm1 25b mm
Kicker (geometrical wake)
||( ) ( )QW s Z I s
|| 110Z
|| 2 (0)eZ Z
0 1
2
(0) ln2
e Z bZ
b
(T.Wohlenberg)
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6 1 10.76 10 m
Kicker (resistive wake)
1
7 2 612 1.1 10 1.3 10m mm
10d m
2 10b mm1 25b mm
0 sec 0 mrough
0 nmoxid
(T.Wohlenberg)
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0 1 2
x 10-4
-2000
-1000
0
1000
2000
Geom. Res. Total
Loss 300 894 1195
Spread 182 469 592
Peak -604 -1526 -1905
/kV nC
|| /W kV nC
s m
Kicker
totalresistive
bunch
10d m
2 10b mm1 25b mm6 1 10.76 10 m
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0 1 2
x 10-4
-1
-0.5
0
0.5
1x 10
4
Pipe (456m)
Collimators (4 items)
Kickers (3*10m)
Total
Loss 3359 4623 3584 11565
Spread 2963 3315 1777 7617
Peak -7248 -9645 -5714 -21636
|| /W kV nC
s m
TOTAL (LINAC to SASE2)
collimators
pipe bunch
kickers
/kV nC
0
51015
202530
354045
pipe collimators kickers
Loss
Spread
Peak
%
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Energy spread due to wakefields between LINAC and SASE 2
0 1 2
x 10-4
-0.1
-0.05
0
0.05
0.1
0.15
s m
0
%E
E
0 17.5 GeVE
bunch
0 0.5 1 1.5
x 10-4
3.416
3.418
3.42
3.422
3.424
3.426
x 104
s m
bunch
before SASE2
after LINAC
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Energy losses between LINAC and SASE2 vs. pipe radius R
5 10 15 20 25 300
0.05
0.1
0.15
0.2
5 10 15 20 25 300.06
0.08
0.1
0.12
0.14
0.16
5 10 15 20 25 300.1
0.2
0.3
0.4
0.5
0
%rmsE
E
0
%E
E
0
max%
E
E
Spread
[mm]R
Loss Peak
[mm]R [mm]R
With oxid layer and roughness
Geometrical+resistive
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0 1 2
x 10-4
-4
-2
0
2
4x 10
4
undulator pipe (42*5.1m)
intersection pipe (41*0.7m)
absorbers(41*0.3m items)
Total Total
(old geometry)*
Loss 9395 869 1689 1.19e4 1.11e4
Spread 16560 1723 1470 1.95e4 1.89e4
Peak -33789 -3435 -4200 -4.1e4 -4.0e4
|| /W kV nC
s m
TOTAL (SASE2)
undulator pipe
bunch
absorbers
/kV nC
pipe in intersection
(T.Wohlenberg)
* M. Dohlus et al, TESLA-FEL 2005-10
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Energy spread between LINAC and SASE2 vs. pipe radius R(normalized to the spread in SASE2)
10 20 30 40 500
50
100
150
2 2
2%
Linac SASErms
SASErms
E
E
Spread
[mm]R
total
collimators
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Conclusion
0
51015
202530
354045
pipe collimators kickers
Loss
Spread
Peak
Impact on FEL performance?(spectrum from SASE simulations?)
10 20 30 40 500
50
100
150
2 2
2%
Linac SASErms
SASErms
E
E
Spread
[mm]R
total
collimators
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Appendix A. Kick factors of flat and round collimators are equal
2b2b x
yround flat
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Appendix A. Kick factors of flat and round collimators are equal
0 0 0 0( , , , ) cos( )d dk r r k r
0 0 0( , , , )x dk x y x y k x
0 0 0( , , , )y dk x y x y k y
0 0 0( , , , )x xd xqk x y x y k x k x
0 0 0( , , , )y yd yqk x y x y k y k y
2b2b x
yround flat
xd xqk k xq yqk k
z
y
0yy=
0 0 0( , , , )y yd xdk x y x y k y k y
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Appendix A. Kick factors of flat and round collimators are equal
0 0 0( , , , )y dk x y x y k y0 0 0( , , , )y yd yqk x y x y k y k y
2b2b x
yround flat
0.5yd dk k 0.5xq xd dk k k
y yd yq dk k k k
Kick of the flat collimator is equal to the kick of the round one
z
y
0yy
=
=
=0.5
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Appendix B. XFEL collimator vs. cryomodule
1 25mmb
50d cm
2b
02 2
2 1
1 1
2long Z c
kb b
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Appendix B. XFEL collimator vs. cryomodule
b2,
mm
Kick,
V/pC/m
1 18*103
2 4.5*103
3 2.0*103
4 1.1*103
5 0.7*103
[V/pC/m/module]Kick
25 ~6.5
For the bunch with sigma=25mkm the kick from the collimator with apperture b2=2mm is equal to the kick of ~700 cryomoduoles
Emmitance growth?