Longitudinal Impedance Budget from LINAC to SASE2
Igor Zagorodnov
Beam Dynamics Group Meeting
13.11.06
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 )
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
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
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
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)
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)
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)
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
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
%
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
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
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
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
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
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
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