High Compression in XFEL
Igor Zagorodnov 02.04.2012
DESY
0.155
0.03=
1 130MeVE =
Beam dynamics simulations for the European XFEL
1,1M
Gun
1,3M
2M 3M 4M
LH
DL 1BC 2BC 3BC2 700MeVE = 3 2400MeVE = 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 =
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]
Total
compr.
C
First
derivative
Z',
[m-1]
Second
derivative
Z'',
[m-2]
-78 3.5 -50 8 -20,…,-24 385 0 1000
Choosing of machine parameters
Macro-parameters
1 130MeVE = 2 700MeVE = 3 2400MeVE =
-10 0 10 20
13.995
14
14.005
14.01
-20 -10 0 10 20 300
0.5
1
1.5
R56,3=-20mm
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-20 -10 0 10 20 300
0.5
1
1.5
-10 0 10 20
13.94
13.945
13.95
13.9555kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
R56,3=-20.5mm
-20 -10 0 10 20 300
0.5
1
1.5
2
R56,3 =-20.8mm
-10 0 10 20
13.94
13.945
13.95
13.9555kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-20 -10 0 10 20 300
1
2
3
-10 0 10 20
13.935
13.94
13.945
13.95
13.955
R56,3 =-21 mm
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-20 -10 0 10 20 300
1
2
3
4
5
R56,3 =-21.3 mm
[MeV]Eσ-5 0 5 10 15
13.92
13.93
13.94
13.95
13.96
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
R56,3 =-21.6 mm
[kA]I
[MeV]Eσ[µm]xε[µm]yε
-10 0 10 200
2
4
6
8
-5 0 5 10 1513.9
13.92
13.94
13.96
13.98
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-10 0 10 200
2
4
6
8
10
R56,3 =-21.9 mm
[MeV]Eσ-5 0 5 10 15
13.9
13.92
13.94
13.96
13.98
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-5 0 5 10 150
2
4
6
8
R56,3 =-22.6 mm
0 5 10
13.92
13.93
13.94
13.95
13.96
13.97
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-4 -2 0 2 40
1
2
3
4
5
-2 -1 0 1 2
13.92
13.93
13.94
13.95
13.96
13.97
R56,3 =-22.6 mm (70% of particles)
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-10 -5 0 5 100
0.5
1
1.5
2
2.5
R56,3 =-23.2 mm (70% of particles)
-4 -2 0 2 413.98
13.99
14
14.01
14.02
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
-10 -5 0 5 100
0.5
1
1.5
2
R56,3 =-23.9 mm (70% of particles)
-5 0 5
13.93
13.935
13.94
13.945
13.95
13.955
13.96
13.965
5kA
I
Phase space
[MeV]Eσ
Current, emittance, energy spread
[µm]xε
[µm]yε
[µm]s [µm]s
bunch head
Beam core parameters vs. R56
20 21 22 23 240
10
20
30
40
50
20 21 22 23 240
5
10
15
20
25
20 21 22 23 240.2
0.3
0.4
0.5
0.6
20 21 22 23 240
1
2
3
4
[kA]I
[µm]slicexε [µm]slice
yε
[fs]tσ
56,3 [mm]R−56,3 [mm]R−
56,3 [mm]R−56,3 [mm]R−
95% of particles
70% of particles
20 21 22 23 240
2
4
6
8
20 21 22 23 24
0.35
0.4
0.45
0.5
0.55
0.6
0.65
20 21 22 23 240
2
4
6
8
20 21 22 23 240
10
20
30
40
50
[kA]I [MeV]Eσ
[µm]yε[µm]xε
56,3 [mm]R−
56,3 [mm]R−
56,3 [mm]R−
56,3 [mm]R−
95% of particles
70% of particles
Beam core parameters vs. R56
0 50 100 1500
0.5
1
1.5
2
0 50 100 15010
-6
10-4
10-2
100
102
20 21 22 23 240
0.1
0.2
0.3
0.4
0.5
20 21 22 23 240
0.5
1
1.5
2
2.5
3
[m]z
56,3 [mm]R− 56,3 [mm]R−
[m]z
[mJ]E[mJ]E
[mJ]E[mJ]E
60mz =
56.3 21.6mmR− =
56.3 20mmR− =
175mz =
Radiation energy vs. R56 without undulator wake (95% of particles)
0 50 100 1500
0.5
1
1.5
2
2.5
0 50 100 15010
-6
10-4
10-2
100
102
20 21 22 23 240
0.1
0.2
0.3
0.4
0.5
0.6
0.7
20 21 22 23 240
0.5
1
1.5
2
2.5
3
3.5
[mJ]E
[m]z
[mJ]E56.3 20mmR− =
56.3 21.6mmR− =
[m]z175mz =60mz =
[mJ]E
56,3 [mm]R−
[mJ]E
56,3 [mm]R−
Radiation energy vs. R56 with undul. wake and taper (95% of particles)
0 50 100 15010
-6
10-4
10-2
100
102
0 50 100 1500
0.5
1
1.5
2
2.5
3
20 21 22 23 240
0.5
1
1.5
2
2.5
3
20 21 22 23 240
0.2
0.4
0.6
0.8
1
1.2
[mJ]E
[m]z
[mJ]E56.3 20mmR− =
56.3 21.6mmR− =
[m]z175mz =60mz =
[mJ]E
56,3 [mm]R−
[mJ]E
56,3 [mm]R−
Radiation energy vs. R56 with undul. wake and taper (70% of particles)
14.0
20 21 22 23 240
0.2
0.4
0.6
0.8
1
1.2
1.4
60mz =
[mJ]E
Radiation energy vs. compression rate
[a.u.]I
56,3 [mm]R−
20 21 22 23 240
0.2
0.4
0.6
0.8
1
1.2
1.4
60mz =
[mJ]E
Radiation energy vs. compression rate
[a.u.]I
56,3 [mm]R−
0.155
0.03=
16
0.16≈
20 21 22 23 240
100
200
300
400
500
600
700175mz =
Radiation power vs. compression rate
[a.u.]I
56,3 [mm]R−20 21 22 23 24
0
50
100
150
200175mz =
max[GW]P
[a.u.]I
max[GW]P
56,3 [mm]R−