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Impedance Budget from LINAC to SASE2. Igor Zagorodnov Beam Dynamics Group Meeting 3.12.07. overview wake sources = geometric & resistive (=surface effects) definitions (average & rms) collimator : geometric, surface effects, all ~40% - PowerPoint PPT Presentation
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Impedance Budget from LINAC to SASE2
Igor Zagorodnov
Beam Dynamics Group Meeting
3.12.07
overview
wake sources = geometric & resistive (=surface effects)
definitions (average & rms)
collimator: geometric, surface effects, all ~40%
pipe: surface effects ~40%
kicker: geometric, surface effects, all ~20%
total
total vs. pipe radius
comparison with effects in LINAC
comparison with SASE2 ~SASE2 / 2
total vs. pipe radius normalized to SASE2
SASE2
SASE1
(W.Decking)
-50 0 50 1000
1000
2000
3000
4000
5000
6000
Wakefield sources
- Resistance of the pipe (r ~ 20 mm, L=456 m, Aluminium)
- Collimators (r=2 mm, L=50 cm, 4 items, TIMETAL 6-4 )
- Kickers (r=10 mm, L=10 m, 3 items, R/Lm )
0.56 nСq 12.5 μm
[μm]s
[A]I
1 nСq 25 μm Bunch shape
from S2E simulationsby Martin Dohlus
( ) bunch shapes
2 2 ( ) ( ) energy lossQ W Q W s s ds
0.50.5 22 2 2( ) ( ) ( ) energy spreadQ W W Q W s W s ds
Collimator (geometrical wake)
||( ) ( )QW s Z I s
|| 2 (0)eZ Z0 1
2
(0) ln2
e Z bZ
b
|| 276Z
Optical approximation: the geometrical wake repeats the bunch shape.
500 mmd
2 2 mmb 1 20 mmb
TIMETAL 6-4 alloy (Titanium)(E.Schutz MVA)
6 1 10.6 10 m
http://www.timet.com/timetal6-4frame.html
Collimator (resistive wake)
1
0
( ) ( )( ) 1
2 2s sZ ZR
Z iR c Z
0 sec
300 nmrough
5 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
500 mmd
2 2 mmb 1 20 mmb
0 1 2
x 10-4
-2500
-2000
-1500
-1000
-500
0
500
1000
Geom. Res. Total
Loss 754 332 1086
Spread 457 365 791
Peak -1518 -833 -2272
/kV nC
|| /W kV nC
s m
Collimator
total
resistive
bunch
500 mmd
2 2 mmb 1 20 mmb
0 1 2
x 10-4
-30
-20
-10
0
10
20
30
Aluminium
7 1 13.66 10 m
456md
1 20 mmb
resistive total
Loss 8.4 9.0
Spread 8.5 9.3
Peak -19.8 -21
/ /kV nC m
|| kV/nC/mW
ms
Pipe (resistive+oxid layer+roughness)
wake
bunch
-157.1 10 sec
300 nmrough 5 nmoxid
(T.Wohlenberg)
Kicker (geometrical wake)
||( ) ( )QW s Z I s
|| 110Z
|| 2 (0)eZ Z
0 1
2
(0) ln2
e Z bZ
b
(T.Wohlenberg)
10 md
2 10 mmb 1 20 mmb
Kicker (resistive wake)
2.4 15 sece
300 nmrough
5 nmoxid
(T.Wohlenberg)
8 2 612 4.4 10 0.53 10m mm
6 1 11.9 10 m
10 md
2 10 mmb 1 20 mmb
0 1 2
x 10-4
-2000
-1500
-1000
-500
0
500
1000
1500
Geom. Res. Total
Loss 227 659 886
Spread 137 412 519
Peak -457 -1222 -1544
/kV nC
|| /W kV nC
s m
Kicker
total
resistive
bunch
10 md
2 10 mmb 1 20 mmb
M. Ivanyan, A. Tsakanian, Phys. Rev. ST-AB, 2006
• Analytical solution for the fields inside tube for finite Lorenz factor
• Perform the ultrarelativistic limit
A.W. Chao, SLAC-PUB- 2946, 1982A. Piwinski, DESY-94-068, 1994• Usual Approach
• Tube with finite thickness
Method: matching technique
Problem: fields are diverges in outer space for γ
Tube with infinite thickness
skin-depth < tube thickness
• Solution in General Case
B. Zotter, S. Kheifets, 1997.
A. Tsakanian
Ceramic Kicker Vacuum chamber: Ceramic with Titanium-Stabilized High Gradient Steel (TSHGS) coats
1-m 12-10 R/L - Resistance
m 0.7 - Thickness
-1-16 mΩ100.18946)(2.0841σ
TSHGS Parameters
m 0.9 -Lenght
m 0.01 - Radius
Vacuum Chamber Parameters
Impedance of XFEL Ceramic Kicker Vacuum Chamber with Metallic Coats.
410~tan
1.9
r
Ceramic Parameters
A. Tsakanian
Longitudinal monopole impedance as function of dimensionless wave number for several cases of vacuum chamber material: 1. Ceramic with TSHGS coats. 2. TSHGS single layer tube with finite and infinite thickness. 3. Copper single layer tube.
0sk
s0 characteristic distance: mcas 4.63/231
02
0
Monopole Term Longitudinal Impedance Per Unit LengthA. Tsakanian
transverse A.T.
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 4103 4343 2659 11105
Spread 4222 3164 1557 8682
Peak -9680 -9088 -4633 -22595
|| /W kV nC
s m
TOTAL (LINAC to SASE2)
collimators
pipebunch
kickers
/kV nC
0
10
20
30
40
50
pipe collimators kickers
Loss
Spread
%
5 10 15 20 25 300
0.05
0.1
0.15
0.2
0.25
5 10 15 20 25 300
0.05
0.1
0.15
0.2
Energy losses between LINAC and SASE2 vs. pipe radius R
0
%rmsE
E
0
%E
E
Spread
[mm]R
Loss
[mm]R
1( )O R1( )O R
0 0.5 1 1.5
x 10-4
3.414
3.416
3.418
3.42
3.422
3.424x 10
4
0 1 2
x 10-4
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Energy spread due to wakefields between LINAC and SASE 2
s m
0
%E
E
0 17.5 GeVE
bunch
Energy from S2E simulationsby Martin Dohlus
after LINAC
Before SASE2
bunch
1
2 3
4
5 6 7 8Katrin Schuett, ZM1Dirk Lipka, MDI
0 1 2
x 10-4
-5
0
5x 10
7
Geometric Total
Loss 0.69e4 1.77e4
Spread 0.33e4 1.89e4
Peak -1.2e3 -4.67e4
|| /W V nC
s m
TOTAL (SASE2)
Total wake
bunch
Geometric
/kV nC
(for comparison)
5 10 15 20 25 300
50
100
150
Energy spread between LINAC and SASE2 vs. pipe radius R(normalized to the spread in SASE2)
2 2
2%
Linac SASErms
SASErms
E
E
[mm]R
total
collimatorskickers
pipe
0
10
20
30
40
50
pipe collimators kickers
Loss
Spread
R=20mm