Usage of corrugated structure for increase of the energy chirp Large Bandwidth Radiation at XFEL Igor Zagorodnov S2E Meeting DESY 18. April 2016
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 −
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 3
Energy spread and Radiation Bandwidth
0~ 0.1%
ωω∆
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 4
Energy spread and Radiation Bandwidth
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.
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 5
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 6
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.
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 7
S2E simulations with over-compressionStart-to-End simulations done by Guangyao Feng, DESY.
CSR impactOver compression
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 8
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 9
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 10
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 11
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− <<
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 12
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 13
Corrugated structure wakes
( )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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 14
Corrugated structure wakes
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 =
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 15
Corrugated structure wakes
-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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 16
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 17
0 2 4 6 8 10 12 14 160
10
20
30
40
50
60
Beam dynamics in corrugated structure
[ ]mz
[ ]mxβ
[ ]myβ
13 m
horizontal quadvertical
ASTRA tracking with wakefields.M.Dohlus et al. Fast Particle Tracking with Wakefields, 2012
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 18
Beam dynamics in corrugated structure
-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
Emittance �� 1.09 1.26
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 19
Beam dynamics in corrugated structure
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 20
Beam dynamics in corrugated structure
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 21
Beam dynamics in corrugated structure
Parameter Before After
Emittance �� 0.64 0.64
Emittance �� 1.09 1.37
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 22
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
Beam dynamics in corrugated structure
,0
x
x
εε
[ ]mz
,0
y
y
εε
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 23
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
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 24
-30 -20 -10 0 10 20 300
10
20
30
40
-30 -20 -10 0 10 20 300
10
20
30
40
SASE (“ideal” beam)
averaged
one shot
current[a.u]
Energy distribution at z=100 m
[GW]P
[µm]s
Energy distribution at z=175 m
[GW]P
[µm]s
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 25
-2 -1 0 1 20
0.5
1
1.5
0.098 0.099 0.1 0.1010
0.5
1
1.5
SASE (“ideal” beam)
averaged
[nm]λ
Spectrum[a.u.] Spectrum[a.u.]
0
[%]ωω
1.8%
FWHM
Spectrum at z=100 m
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 26
-2 -1 0 1 20
0.5
1
1.5
0.098 0.099 0.1 0.1010
0.5
1
1.5
SASE (“ideal” beam)
averaged
[nm]λ
Spectrum[a.u.] Spectrum[a.u.]
0
[%]ωω
2%
FWHM
Spectrum at 175 m
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 27
SASE
0 50 100 1500
1
2
3
4[mJ]E
[m]z
SASE, ALICE, for „real“ beam, 15 shots
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 28
-30 -20 -10 0 10 20 300
10
20
30
40
s [um]
SASE
averaged
one shotcurrent[a.u]
Energy distribution at z=100 m
[GW]P
[µm]s
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 29
-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
Spectrum[a.u.] Spectrum[a.u.]
0
[%]ωω
1.7%
FWHM
Spectrum at z=100 m
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 30
SASE
-30 -20 -10 0 10 20 300
20
40
60
80
100
averaged
one shotcurrent[a.u]
Energy distribution at z=175 m
[GW]P
[µm]s
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 31
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
Spectrum[a.u.] Spectrum[a.u.]
0
[%]ωω
2.2%
FWHM
Spectrum at z=175 m
Igor Zagorodnov | S2E Meeting| 18. April 2016 | Seite 32
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