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optics with SC
0 200 400 600 800 1000 1200 1400 16000
0.5
1
1.5
2x 10
10 energy/eV
0 200 400 600 800 1000 1200 1400 16000
50
100
150beta/m
mS
eV
myx
horizontalvertical
BC0 BC1 BC2
XFEL, design optics
momenta tracking
xxxx
xxxxC
xxxxxx
xxxxxxC
ds
d2
2
r
xrrx cp
Fppxxkx
r
xrrx cp
xFppxxxxkxx
r
xrrx cp
Fxppxxxxkxx
(non)linear self force
xxcpkxF rscx
space charge de-focusing
analytic expression for gaussian distributions with respect to slice or full bunchin the following: slice
space charge parameter scx kS 2ˆ
n
x
AI
zI
2
0 200 400 600 800 1000 1200 1400 16000
1
2
3
4
5
6space charge parameter, horizontal
0 200 400 600 800 1000 1200 1400 16000
1
2
3
4
5
6space charge parameter, vertical
0 200 400 600 800 1000 1200 1400 16000
0.5
1
1.5
2x 10
10 energy/eV
0 200 400 600 800 1000 1200 1400 16000
50
100
150beta/m
n
x
AI
I
2
ˆ
n
y
AI
I
2
ˆ
20 pC100 pC250 pC500 pC
1nC
1nC500 pC250 pC100 pC
20 pC
mS
eV
space charge parameter
0 200 400 600 800 1000 1200 1400 16000
0.5
1
1.5
2x 10
10 energy/eV
0 200 400 600 800 1000 1200 1400 16000
50
100
150beta/m
0 200 400 600 800 1000 1200 1400 16001
1.5
2
2.5
3
3.5
4mismatch parameter, horizontal
0 200 400 600 800 1000 1200 1400 16001
1.5
2
2.5
3
3.5
4mismatch parameter, vertical
space charge miss-match
eV
mS
250 pC500 pC
1nC
20 pC100 pC
Bmag,x
Bmag,y
match
0 200 400 600 800 1000 1200 1400 16000
50
100
150
2001 nC; beta function / m, horizontal
0 200 400 600 800 1000 1200 1400 16000
50
100
150
2001 nC; beta function / m, vertical
0 200 400 600 800 1000 1200 1400 16000
0.5
1
1.5
2x 10
10 energy/eV
0 200 400 600 800 1000 1200 1400 16000
50
100
150beta/m
optics with/without space charge
eV
mS
1 nC
mx
my
match
0 200 400 600 800 1000 1200 1400 16000
50
100
150
200250 pC; beta function / m, horizontal
0 200 400 600 800 1000 1200 1400 16000
50
100
150
200250 pC; beta function / m, vertical
0 200 400 600 800 1000 1200 1400 16000
0.5
1
1.5
2x 10
10 energy/eV
0 200 400 600 800 1000 1200 1400 16000
50
100
150beta/m
eV
mS
optics with/without space charge
250 pC
mx
my
match
0 200 400 600 800 1000 1200 1400 16000
100
200
300
400
500
60020 pC; beta function / m, horizontal
0 200 400 600 800 1000 1200 1400 16000
50
100
150
200
250
30020 pC; beta function / m, vertical
0 200 400 600 800 1000 1200 1400 16000
0.5
1
1.5
2x 10
10 energy/eV
0 200 400 600 800 1000 1200 1400 16000
50
100
150beta/m
eV
mS
optics with/without space charge
20 pC
mx
my
match
Astra simulations in preparation
SASE killer effect
analytic estimations (1d)
numerical estimation (1d) “rftweak”
full 3d calculation in preparation / running
160 165 170 175 180 185 1900
5
10
15
20
25
30
35
40
setup & optics
0
220
~
P
PKLcm L
I
uu
modulation amplitude
keV 550150
FLASH @ 19 nmundulator
laser
160 165 170 175 180 185 190 195 2000
5
10
15
20
25
30
35
40
A B C D E F G H
-1 -0.5 0 0.5 1
x 10-4
-1
-0.5
0
0.5
1x 10
6 start/before CHIC1
-1 -0.5 0 0.5 1
x 10-4
-1
-0.5
0
0.5
1x 10
6 after CHIC1/before CHIC2
-1 -0.5 0 0.5 1
x 10-4
-2
-1
0
1
2x 10
6 after CHIC2/before CHIC3
-1 -0.5 0 0.5 1
x 10-4
-1
-0.5
0
0.5
1x 10
7 after CHIC3/before UNDUL
A B C D
G HE F
-1 -0.5 0 0.5 1
x 10-4
0
500
1000
1500
2000before CHIC1
-1 -0.5 0 0.5 1
x 10-4
0
500
1000
1500
2000before CHIC2
-1 -0.5 0 0.5 1
x 10-4
0
500
1000
1500
2000before CHIC3
-1 -0.5 0 0.5 1
x 10-4
0
2000
4000
6000before UNDUL
B D
F H
100 keV modulation amplitude
~ 3 MeV rms energy spread
500 keV modulation amplitude
~ 3.5 MeV rms energy spread
first 3d simulation
current/A
beam linecoordinate/ mbunch coordinate/ m
250 keV modulation amplitude
near end of beam line
current/A
bunch coordinate/ m
/
current/A
beam linecoordinate/ mbunch coordinate/ m
current/A
beam line coordinate/ m
“side view”
period of plasma oscillation
120 m
