GENESIS simulations with Wakefields for XFEL

Igor Zagorodnov

BDGM, DESY

26.09.05

name symbol unit value

energy GeV 17.5

energy spread MeV 1.5

emmitance n mm-mrad 1.4

bunch charge Q nC 1

bunch length m 25

peak current IP kA 4.76

undulator period u cm 4.8

undulator parameter au 2.33

quadrupole length LQ cm 20

quadrupole gradient GQ T/m 17

section length Lsect m 5+1.1

total length Ltotal m 260

beta function (waist)x,

y,

m41.6

29.3

SASE 2 parameters

Parameters XFEL theory

22

1 0.13155[nm]2

us ua

, ,

41[ ]

34n

x y x y m

2 20 2

67 [ ]rR

s s

wz m

0.5( ) 37 [ ]r x y m

Parameters XFEL theory

1/ 22

3 0.52 [ ]2

JJ s l P

l A

A Icm

c I

1/31 3 0.16 [ ]B cm

23 34s

rBc

21

1 6.1e-4lc

2

33 20e-4lc

Gain parameter

Efficiency parameter

Diffraction parameter

Effective power of the input signal

13 6444 [ ]lnb

sh

c c

WP W

N N

Gain length*

0 (1+ ) 14 [m]g gL L

31[m]opt

Optimal beta-function

010 = 140 [m]sat gL L

Saturation length

* E.L.Saldin et al./Optics Communications 235 (2004) 415-420

0.13175 [nm]nums

22

1 0.13155[nm]2

us ua

Genesis steady state simulation

1 1.2 1.4 1.6 1.8

x 10-4

-10

-5

0

5x 10

4

head tail

Loss,

kV/nC/m

Spread,

kV/nC/m

Peak,

kV/nC/m

total 48 47 -101

-0.01 -0.005 0 0.005 0.01

-100

-50

0

||

kVW

nC m

[ ]s cm

.geom

.res

[ ]s m

headtail

||

VW

nC m

bunch

wakeELOSS= = - 48keV/m

-1 -1: 5.8e+7[ m ], =2.46e-14[sec]cond relaxcu

Scan with ELOSS = - 48keV/m

0.13180 [nm]0.13175 [nm]nums

Genesis steady state simulation

[m]z

[ m]s

Power

no wake (amplifier)

with wake (amplifier)

no wake (SASE)

with wake (SASE)

Genesis time dependent simulation

0 50 1000

1

2

3x 10

10

250

250

0.2wake

m

m

P

P

250

250

0.4wake

m

m

P

P

Amplifier model SASE model

75mmax0.13165 [nm](P )num

s 250mmax0.13175 [nm] (P )num

s

[ m]s

[W]P

0 50 1000

1

2

3x 10

10

no wake

with wake

[ m]s

[W]P

Taper optimization (steady state)

13 3 5w

w

ae

a

0 10 20 300

1

2

3

4

410 /w wa a

10250 [10 ]mP W Scan with ELOSS = - 100keV/m

2

0.019 ,0.048

5.068 3.04 80 ( )

w

w

w w w g mm

a B g g gg m

a B g

sec/ 0.9μm/sectiong N 3.694exp( (5.068 1.520 ))u u

g gB

37.5g m

0 50 1000

2

4

6

x 1010

0 50 1000

1

2

3x 10

10

Genesis time dependent simulation

with wake

250

250

0.4wake

m

m

P

P

SASE model

250

250

2wake taper

m

m

P

P

no wake

no wake

wake taper

[ m]s

[W]P

[ m]s

[W]P

Power (Gaussian bunch)

1 1.2 1.4 1.6 1.8

x 10-4

-10

-5

0

5x 10

4

||

kVW

nC m

[ ]s cm

no wake with wake wake+taper[ ]z m

[ ]s m1800 1800 1800

[ ]s m [ ]s m

4 6 8 10 12

x 10-5

-1

0

1

x 105

2 4 6 8 10

x 10-5

-1

0

1

x 105

-5 0 5

x 10-5

-1

-0.5

0

0.5

1x 10

5Shape 0

Shape 3

head tail

headtail

.geom

.resist

headtail

-1 -1: 5.8e+7[ m ],

=2.46e-14[sec]cond

relax

cu

||

VW

nC m

[ ]s m

„Real“ shapes from Martin Dohlus

http://www.desy.de/~dohlus/2005.09.xfel_wakes

( ) ( )geomhiW s cZ s

3.36[ / ]hiZ m

Geometric wake?

pro section (6.1 m)

Loss,

V/pC

absorber 1 42

pumping slot 1 <0.2

pump 1 9

BPM 1

bellow 1 13

flange gap 1 6

Total geom. 70

Longitudinal wake for the case of the elliptical pipe (3.8mm)

-0.01 -0.005 0 0.005 0.01

-100

-50

0

||

kVW

nC m

[ ]s cm

( ) ( )geomhiW s cZ s

3.36[ / ]hiZ m The wake repeats the bunch shape

.geom

.resist

Genesis time dependent simulation (SASE)

250

0250

0.41gauss

m

shapem

P

P

0 50 1000

2

4

6

x 1010

0 50 1000

1

2

3x 10

10

3250

3250

0.15shape wake

m

shapem

P

P

3250

3250

1shape wake

m

shapem

P

P

250

250

0.4gauss wake

m

gaussm

P

P

250

250

2gauss wake

m

gaussm

P

P

Gaussian Shape 3

[ m]s

[W]P

[ m]s

[W]P

with wake

wake taper

no wake

Power

1 1.2 1.4 1.6 1.8

x 10-4

-10

-5

0

5x 10

4

4 6 8 10 12

x 10-5

-1

0

1

x 105

Genesis time dependent simulation (SASE)

250

0250

0.78gauss

m

shapem

P

P

0 50 1000

2

4

6

x 1010

0250

0250

0.37shape wake

m

shapem

P

P

0250

0250

1.4shape wake

m

shapem

P

P

250

250

0.4gauss wake

m

gaussm

P

P

250

250

2gauss wake

m

gaussm

P

P

Gaussian Shape 0

0 50 1000

1

2

3

4x 10

10

[ m]s

[W]P

[ m]s

[W]P

with wake

wake taper

no wake

Free space

With

wake

With

wake+taper

(32mkm / 260m)

Gaussian 1 0.4 2

Shape 0 0.8 0.8*0.37=0.3 0.8*1.4=1.1

Shape 3 0.4 0.4*0.15=0.06 0.4*1=0.4

Gaussian Shape 0 Shape 3

Power in a.u.

0 50 1000

2

4

6

x 1010

0 50 1000

2

4

6

x 1010

0 50 1000

2

4

6

x 1010

[ m]s

250 [W]mP

0 50 1000

2

4

6

x 1010

0.8 1 1.2 1.4 1.6

x 10-4

-1

0

1

x 105

4 6 8 10 12

x 10-5

-1

0

1

x 105

2 4 6 8 10

x 10-5

-1

0

1

x 105

Gaussian Shape 0 Shape 3

||

VW

nC m

[ ]s m

bunch

wake

0 50 1000

2

4

6

x 1010

0 50 1000

2

4

6

x 1010

[ m]s

250 [W]mP

13 3 5w

w

ae

a

wake taper

no wakewith wake

wake taper

wake taper

Taper:

Power

Gaussian

Shape 0

Shape 3

Conclusions

1. The wake field reduces the power at L=250 m by factor 2.5 for the Gaussian bunch and up to factor 7 by the “real” shape

2. The linear taper allows to avoid the degradation and to increase the power by factor 2 for the Gaussian bunch

Acknowledgements to Evgeny Schneidmiller and Martin Dohlus for the help

3. The same taper allows to avoid the degradation for other shapes too