Large Bandwidth Radiation at XFELIgor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 2 Energy spread and Radiation Bandwidth -2 -1 0 1 2 0 20 40 60 80 100 120 2 0 ω ωρ ∆ (0)

Usage of corrugated structure for increase of the energy chirp

Large Bandwidth Radiation at XFEL

Igor Zagorodnov

S2E Meeting

DESY18. April 2016

Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 2

Energy spread and Radiation Bandwidth

-2 -1 0 1 20

20

40

60

80

100

120

02

ωω ρ∆

(0)x

x

E

E0

~ω ρ

ω∆

11gz L =

FEL bandwidth for negligible energy spread (1D simulation)

3~ 10 at EXFELρ −



0~ 0.1%

ωω∆



0 0

0 02

γ γ ω ωγ ω− −≈

2

21

22u Kλλ

γ

= +

The energy deviation (of electron) is equivalent to the wavelength deviation (of EM wave)

3% in bandwidth ~ 1.5% in energy spread

For 17.5 GeV we need energy spread of 260 MeV.


S2E simulations with over-compressionStart-to-End simulations done by Guangyao Feng, DESY.

�At the end of the linacE=17.5 GeV , Ipeak=~5.0kA, Q=0.5nC

�Beam energy at some key positions

1 130MeVE = 2 700MeVE = 3 2400 MeVE =

ASTRA+CSRTrack


S2E simulations with over-compression

Parameter settings for the bunch compressors

RF settings in accelerating modules

Linac3: accelerating on-crest

Start-to-End simulations done by Guangyao Feng, DESY.


S2E simulations with over-compressionStart-to-End simulations done by Guangyao Feng, DESY.

CSR impactOver compression


S2E simulations with over-compression

Parameter XFEL

Beam energy, GeV 17.5

Charge, pC 500

Beam average current, kA 3.75

FWHM bunch length, um 40

Emittance ��/��, um 0.64/1.09

Energy spread , keV 500

-30 -20 -10 0 10 20 300

1

2

3

4

5

[ ]kAI

[ ]MeVEσ[ ]µmxε

[ ]µmyε

[ ]GeVE

[µm]s [µm]s

50MeV


Flat structure with delayed layerFor flat structure (paper of Bane Stupakov, 2015)

12 10 tanh( )

( , ) sech ( ) ,2

ccx x

Z c XZ k k X ika X ak

a Xη

−− = − =

12 10 coth( )

( , ) csch ( )2

ssx

Z c XZ k k X ika

a Xη

−− = −

0 0 0( , , , ) ( , ) cosh( )cosh( ) ( , )sinh( )sinh( )cc ssx x x x x x xZ y y k k Z k k k y k y Z k k k y k y= +

0 0 0 , , 0 ,1

1( , , , , ) ( , , , )sin( )sin( ),

2x m x m x m xm

mZ x y x y k Z y y k k k x k x k

w w

π∞

=

= =∑

2a

- conductive layeriωµηκ

=Surface impedance

( )12 - dielectric layerikwη µ ε −= − −

For rectangular structure


Corrugated structure

12 mm

1.4 mm

g = 0.25 mmp = 0.5 mm2w = 12 mm2a = 1.4 mmh = 0.5 mmLength = 2&3 m

1 kη− <<

( )12 , , 1g

ikwp

η µ ε µ ε−= − − = << - equivalent dielectric layer

- high frequency behavior for any delayed layer


Corrugated structure wakes1

2 10 tanh( )( , ) sech ( ) ,

2cc

x x

Z c XZ k k X ika X ak

a Xη

−− = − =

12 10 coth( )

( , ) csch ( )2

ssx

Z c XZ k k X ika

a Xη

−− = −

02

X( , ) ( , )

2 cosh(X)sinh(X)cc ss

x x

Z cZ k k Z k k i

ka= =

02

X( , ) ( , )

2 cosh(X)sinh(X)cc ss

x x

Z cW k s W k s

a= =

0 0 0( , , , ) ( , ) cosh( )cosh( ) ( , )sinh( )sinh( )cc ssx x x x x x xW y y k s W k s k y k y W k s k y k y= +

0 0 0 , , 0 ,1

1( , , , , ) ( , , , )sin( )sin( ),

2x m x m x m xm

mW x y x y s W y y k s k x k x k

w w

π∞

=

= =∑

K. Bane, G. Stupakov, LCLS-II, TN-16-01, 2016

- independent from s

1 kη− <<


Corrugated structure wakes

-30 -20 -10 0 10 20 300

10

20

30

40

50

-30 -20 -10 0 10 20 300

500

1000

1500

2000

2500

3000

[µm]s [µm]s

||[MeV]W ,Q

MeV

mmyW

Current[a.u.]

ECHO

analytical

Current[a.u.]

ECHO

analytical

K. Bane, G. Stupakov, LCLS-II, TN-16-01, 2016

“0-order” approximation



( )1 1

10 0|| 2

2( ) 1 1

4 2

Z L Z c aZ k i i ik

ka a kg ca

α π ηπ π

− −− = + + = −

( ) 11 i

Lgk

πη α−

+=

- “surface” impedance

From paper of K. Bane, K. Yokoya , PAC 1999 for chain of pillbox cavities

0tanh( ) 40( , )

sinh(2 )

x

x

k a s

k a scc xa x

x

kW k s Z c e

k a

−

=

0coth( ) 40( , )

sinh(2 )

x

x

k a s

k a sss xa x

x

kW k s Z c e

k a

−

=

2

0 2 ( / )

g as

g p pπ α =

“First order” in paper of K. Bane, G. Stupakov, I. Zagorodnov, DESY 16-056

“0-order



2

0 0.1514mm8 ( / )

g as

g p pα = =

from paperof K.Bane SLAC-PUB-9663, 2003

from fit to ECHO (calculations for bunches with up to 2um RMS)

1.8 1.6

0 2.40.41 0.12mm

a gs

p= =

from Bane, Mosnier, Novokhatsky,Yokoya, ICAP 98.

0 5 10 15 20 250.4

0.45

0.5

0.55

0.6

0.6504

mm

s

-1mmxk0tanh( )0( , )

2 cosh( )sinh( )

x

x

k a s

k a scc xa x

x x

Z c kW k s e

k a k a

−

=

0 0.12 mms =



-30 -20 -10 0 10 20 300

5

10

15

20

25

30

35

-30 -20 -10 0 10 20 300

500

1000

1500

2000

2500

-40 -20 0 20 400

500

1000

1500

2000

2500

3000

[µm]s [µm]s

||[MeV]W,Q

MeV

mmyW

ECHOanalytical

Current[a.u.]

ECHO

analytical

[µm]s

,D

MeV

mmyW

Current[a.u.]

ECHO

analytical


Beam dynamics in corrugated structure

Patrameter Theoretical(0 order)

Numerical,ASTRA

(0 order)

Numerical,ASTRA

(1st order)

Emittance growth � ��⁄ 1.33 1.32 1.20

Energy spread in tail [keV] 67 66 45

Energy loss in tail [MeV] 45 45 35

230

40

1384 5

Z ceQ Ll

a E

ε π βε

= +

40µml =

34 40

4

2( )

256E x y

Z ceQLss

a l

πσ σ σ= +

0|| 2( )

16

Z ceQLW l

a

π=K. Bane, G. Stupakov, LCLS-II, TN-16-01, 2016

ASTRA tracking with wakefields.M.Dohlus et al. Fast Particle Tracking with Wakefields, 2012


0 2 4 6 8 10 12 14 160

10

20

30

40

50

60


[ ]mz

[ ]mxβ

[ ]myβ

13 m

horizontal quadvertical

ASTRA tracking with wakefields.M.Dohlus et al. Fast Particle Tracking with Wakefields, 2012



-20 -10 0 10 200

1

2

3

4

-20 -10 0 10 200

1

2

3

4

Parameter Before After6 mod.

Emittance �� 0.64 0.68


Energy spread in tail [keV] 0 30

Energy loss in tail [MeV] 0 210

[ ]µmxε

[ ]µmyε

[ ]0.1 keVEσ

[ ]kAI [ ]kAI

[ ]0.1 keVEσ

[ ]µmxε

[ ]µmyε

[ ]MeVdE

[µm]s



0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 160.8

1

1.2

1.4

1.6

[ ]mz

,0

y

y

εε

,0

x

x

εε



Parameter after 1 module as

1 kick

after 1 module,10 kicks

after 6 modules,

60 kicks

Emittance growth ��

��,�1.20 1.32 1.06

Emittance growth ��

��,�1.20 1.11 1.15

Energy spread in tail[keV]

45 45 30

Energy Loss in tail[MeV]

35 35 210



Parameter Before After



Energy spread in tail [keV] 500 530

Energy loss in tail [MeV] 50 250

-30 -20 -10 0 10 20 300

1

2

3

4

5

-30 -20 -10 0 10 20 300

1

2

3

4

5

[ ]kAI

[ ]0.1 keVEσ[ ]µmxε [ ]µmyε

[ ]kAI

[ ]0.1 keVEσ[ ]µmxε [ ]µmyε

[ ]GeVE

[µm]s


0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16

1

1.2

1.4

1.6


,0

x

x

εε

[ ]mz

,0

y

y

εε


0 50 100 1500

0.5

1

1.5

2

2.5

3

3.5

SASE (“ideal” beam)

[mJ]E

[m]z

Genesis 1.3ALICE

SASE, ALICE vs. Genesis for „ideal“ beam


-30 -20 -10 0 10 20 300

10

20

30

40

-30 -20 -10 0 10 20 300

10

20

30

40


averaged

one shot

current[a.u]

Energy distribution at z=100 m

[GW]P

[µm]s


[GW]P

[µm]s


-2 -1 0 1 20

0.5

1

1.5

0.098 0.099 0.1 0.1010

0.5

1

1.5


averaged

[nm]λ

Spectrum[a.u.] Spectrum[a.u.]

0

[%]ωω

1.8%

FWHM

Spectrum at z=100 m


-2 -1 0 1 20

0.5

1

1.5

0.098 0.099 0.1 0.1010

0.5

1

1.5


averaged

[nm]λ


0

[%]ωω

2%

FWHM

Spectrum at 175 m


SASE

0 50 100 1500

1

2

3

4[mJ]E

[m]z

SASE, ALICE, for „real“ beam, 15 shots


-30 -20 -10 0 10 20 300

10

20

30

40

s [um]

SASE

averaged

one shotcurrent[a.u]


[GW]P

[µm]s


-2 -1 0 1 20

0.5

1

1.5

0.098 0.0985 0.099 0.0995 0.1 0.1005 0.101 0.10150

0.5

1

1.5

lambda [nm]

SASE

averaged

[nm]λ


0

[%]ωω

1.7%

FWHM

Spectrum at z=100 m


SASE

-30 -20 -10 0 10 20 300

20

40

60

80

100

averaged

one shotcurrent[a.u]


[GW]P

[µm]s


SASE

0.098 0.0985 0.099 0.0995 0.1 0.1005 0.101 0.10150

0.5

1

1.5

lambda [nm]-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

averaged

[nm]λ


0

[%]ωω

2.2%

FWHM

Spectrum at z=175 m


Conclusion

With 6 corrugated modules of total length 12 m we can obtain 2% radiation bandwidth at 17.5 GeV (0.1 nm radiation wavelength).

Parameter z=100 m z=175 m

Bunch charge, pC 500

Bunch energy, GeV 17.5

Radiation wavelength, nm 0.1

Bandwidth (FWHM), % 1.7 2.2

Radiation energy, mJ 2 3.5

Documents

Large Bandwidth Radiation at XFELIgor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 2 Energy spread and Radiation Bandwidth -2 -1 0 1 2 0 20 40 60 80 100 120 2 0 ω ωρ ∆ (0)