large bandwidth radiation at xfeligor zagorodnov | s2e meeting| 18. april 2016 | seite 2 energy...
TRANSCRIPT
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