30
Longitudinal Impedance Budget and Simulations for XFEL Igor Zagorodnov 14.03.2011 DESY
Longitudinal Impedance Budget and
Simulations for XFELIgor Zagorodnov
14.03.2011DESY
1 130 MeVE
Beam dynamics simulations for the European XFEL
1,1M
Gun
1,3M
2M 3M 4M
LH
DL 1BC 2BC 3BC2 700 MeVE 3 2400 MeVE 4 14GeVE
ASTRA ( tracking with 3D space charge, DESY, K. Flötmann)
W1 -TESLA cryomodule wake (TESLA Report 2003-19, DESY, 2003)
W3 - ACC39 wake (TESLA Report 2004-01, DESY, 2004)TM - transverse matching to the design optics
W3W1TM
4W1TM
64W112W1TM
Full 3D simulation method (200 CPU, ~10 hours)
CSRtrack (tracking through dipoles, DESY, M. Dohlus, T. Limberg)
1.6 kmz
ChargeQ,nC
Momentum compaction
factor in BC1
R56,1,[mm]
Compr.in BC1
C1
Momentum compaction
factor in BC2
R56,2,[mm]
Compr.in BC2
C2
Momentum compaction
factor in BC3
R56,3,[mm]
Totalcompr.
C
First derivative
Z',[m-1]
Second derivative
Z'',[m-2]
1 -100 3.5 -54 8 -20 121 0 2000
0.5 -89 3.5 -50 8 -20 217 0 1000
0.25 -78 3.5 -50 8 -20 385 0 1000
0.1 -71 3.5 -50 8 -20 870 0 1000
0.02 -67 3.5 -50 8 -20 4237 0 500
Choosing of machine parameters
Macro-parameters
1 130 MeVE 2 700MeVE 3 2400 MeVE
I. Zagorodnov, M. Dohlus, A Semi-Analytical Modelling of Multistage Bunch Compression with Collective Effects, Physical Review STAB 14 (2011), 014403.
-40 -20 0 20 40 600
1
2
3
4
5
Q=1 nCE
[kA]I
Phase space
[MeV]E
0.9 [μm]projx
3.5 [μm]projy
Current, emittance, energy spread
[μm]x[μm]y
[μm]s [μm]s
178fs
XFEL beam dynamic simulations for different charges (full)
bunch head
-40 -20 0 20 40 60
13.998
14
14.002
14.004
14.006
14.008
We have removed 6% of bad particles in the analysis
-60 -40 -20 0 20 40 60-200
-150
-100
-50
0
50
100
150
200
Mismatch and undulator wake Q=1nC||[kV/m]W
[μm]s-40 -20 0 20 40 60
0
0.5
1
1.5
2
2.5
xM
yM
[a.u]I
[μm]s
Total wake
resistive wake
bunch
Optimal taper for Q=1nC
ˆ 0.25opt
ˆˆ ˆ ˆ( )C z bz
ˆ 0.5opt optb
ˆ ˆ ˆ( ) 0.125C z z
21 2 0.5u udK dk kdz kK dz
5 -14.8 10 mopt
dKdz
2 keV160m
mc de dz
-40 -20 0 20 40 600
5
10
15
20
SASE radiation Q=1 nC (ALICE, 360 CPU, ~30 min)
Averaged through 8000 slices
85mz
0 50 100 1500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
+Wake+Taper
+Wake
mJE
mz
GWP
μms
Accelerator wakes. Q=1nC
19%
42%4%
2%1%
1%1%
10%
14% 2%4%
COL CAV TDSBPMA OTRA BPMRTORAO KICK PIP20PUMCL FLANG
collimators
cavities
“warm” pipe
Accelerator wakes. Q=1nC
-50 0 50-50
0
50|| [MV]W
[μm]s [μm]s
5.3 4e 0
0
E EE
Full wake
Cavities wake
Full wake
Cavities wake
current
-50 0 500
20
40
60
80
0 50 100 1500
2
4
6
8
10
“Artificially” matched beam. Q=1nC
[μm]s
mJE
mz
5 -14.8 10 mopt
dKdz
all slices matched
at z=175 m
matched in peak current
With full accelerator and undulator wake
current
-50 0 500
5
10
15
20
25
0 50 100 1500
2
4
6
8
10
[μm]s
mJE
mz
full wake
(full wake) x 4
(full wake) x 8
GWP at z = 85 m
“Artificially” matched beam. Q=1nC
current
-50 0 500
5
10
15
20
25
0 50 100 1500
1
2
3
4
5
[μm]s
mJE
mz
full wake
(full wake) x 4
(full wake) x 8
GWP at z=85 m
Beam matched in the peak current. Q=1nC
current
-50 0 50
-5
0
5
10
15
20
25
-0.6 -0.4 -0.2 0 0.2 0.40
0.2
0.4
0.6
0.8
1
full wake
(full wake) x 4(full wake) x 8
Beam matched in the peak current. Q=1nC
0
0
%
FWHM=0.14%FWHM=0.23%FWHM=0.6%
0
0
E EE
[μm]s
Normalized spectrum at z=85 m
-20 -10 0 10 200
0.2
0.4
0.6
0.8
1
Q=250 pCE Phase space
[MeV]E
0.45 [μm]projx
1.5[μm]projy
Current, emittance, energy spread
[μm]x
[μm]y
[μm]s [μm]s
39fs
XFEL beam dynamic simulations for different charges (full)
bunch head
5kAI
We have removed 6% of bad particles in the analysis (Q=235 pC!)
-10 0 10 20
13.995
14
14.005
14.01
-20 -10 0 10 20-200
-100
0
100
200
-2 -1 0 1 2 3x 10-5
0
0.5
1
1.5
2
2.5
3 ||[kV/m]W
[μm]s
xMyM
[a.u]I
[μm]s
Mismatch and undulator wake. Q=250 pC
Total wake
resistive wake
bunch
SASE radiation. Q=250 pC
5 -14.8 10 mopt
dKdz
0 50 100 1500
0.5
1
1.5
2
-15 -10 -5 0 5 10 150
5
10
15
20
25
30
35
40
Averaged through 2400 slices
60 mz
+Wake+Taper
+Wake
mJE
mz
GWP
μms
Accelerator wakes. Q=250 pC.
33%
22%4%1%11%
23%
2% 4%
COL CAV TDS
BPMA KICK PIP20
PUMCL FLANG
collimators
cavities
“warm” pipe
-20 -10 0 10 20-30
-20
-10
0
10
20
30
Accelerator wakes. Q=250 pC
|| [MV]W
[μm]s [μm]s
5.3 4e 0
0
E EE
Full wake
Cavities wake
Full wakeCavities wake
-20 -10 0 10 200
20
40
60
80
100
120
0 50 100 1500
1
2
3
4
“Artificially” matched beam. Q=250 pC
[μm]s
mJE
mz
all slices matched
at z=175 m GWP
-20 -10 0 10 200
10
20
30
40
0 50 100 1500
0.5
1
1.5
2
2.5
[μm]s
mJE
mz
full wake(full wake) x 4
(full wake) x 8
GWP
Beam matched in the peak current. Q=250 pC
at z=60 m
-20 -10 0 10 20-5
0
5
10
15
full wake
(full wake) x 4
(full wake) x 8
Beam matched in the peak current. Q=250 pC
-0.6 -0.4 -0.2 0 0.2 0.40
0.2
0.4
0.6
0.8
1Normalized spectrum at z=85 m
0
0
%
FWHM=0.29%
FWHM=0.30%
FWHM=0.38%
0
0
E EE
[μm]s
-2 -1 0 1 20
0.2
0.4
0.6
0.8
1
Q=20 pC
E
[MeV]E
0.14 [μm]projx
0.26 [μm]projy
Current, emittance, energy spread
[μm]x
[μm]y
[μm]s [μm]s
2fs
XFEL beam dynamic simulations for different charges (full)
bunch head
5kAI
-2 -1 0 1 2
13.995
14
14.005
Phase space
-2 0 2 4 6-40
-20
0
20
40
-2 -1 0 1 2x 10-6
0
0.5
1
1.5
2
2.5
3||[kV/m]W
[μm]s
xM
yM
[a.u]I
[μm]s
Mismatch and undulator wake. Q=20 pC
Total wake
resistive wake
bunch
SASE radiation. Q=20 pC
5 -14.8 10 mopt
dKdz
0 50 100 1500
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-2 -1 0 1 20
10
20
30
40
50
60
Averaged through 800 slices
50 mz
+Wake+Taper
+Wake
mJE
GWP
μms mz
Accelerator wakes. Q=20 pC
56%
9%3%
17%
11% 1% 3%
COL CAV TDS
KICK PIP20 PUMCL
FLANG
collimators
cavities
“warm” pipe
-2 -1 0 1 2 3-10
-5
0
5
10
Accelerator wakes. Q=20 pC
|| [MV]W
[μm]s [μm]s
5.3 4e 0
0
E EE
Full wake
Cavities wake
Full wake
Cavities wake
0 50 100 1500
0.1
0.2
0.3
0.4
0.5
“Artificially” matched beam. Q=20 pC
[μm]s
mJE
mz5 -14.8 10 m
opt
dKdz
all slices matched
at z=175 m
-2 -1 0 1 2 30
20
40
60
80
100
120
140
-2 -1 0 1 20
20
40
60
80
100
120
140
0 50 100 1500
0.1
0.2
0.3
0.4
0.5
[μm]s
mJE
mz
full wake
(full wake) x 4
(full wake) x 8
GWP
Beam matched in the peak current. Q=20 pC
at z=60 m
-2 -1 0 1 2-1
0
1
2
3
4
5
-0.5 0 0.5 10
0.2
0.4
0.6
0.8
1
dw/w [%]
Spectrum at 84.7999 m
full wake
(full wake) x 4
(full wake) x 8
Beam matched in the peak current. Q=20 pC
0
0
%
FWHM=0.55%
FWHM=0.58%
FWHM=1.0%
0
0
E EE
[μm]s
Normalized spectrum at z=85 m
Summary
Accelerator wakeBunch charge, nC
1 0.25 0.02
Energy in the radiation pulse at z=175 m, mJ
x1 9 2.3 0.46
x4 8 2.3 0.44
x8 6 2.3 0.43
Spectrum width at z=85m, %
x1 0.14 0.29 0.55
x4 0.23 0.30 0.58
x8 0.6 0.38 1.0
We have considered only the longitudinal wake in a quite coarse model (adding the accelerator wake at the undulator entrance). The transverse wakes are neglected.
