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−