Optics with SC horizontal vertical BC0BC1BC2 XFEL, design optics.

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