FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
Dispersion Effects
on SASE at FLASH
Eduard PratFEL Beam Dynamics Meeting24 of November of 2008, Hamburg
SASE dependence on e- trajectorySASE vs e- energy for different dispersion scenariosSASE spectrum dependence on dispersion
Measurements done 11 & 15 October 2008 (total=1shift)Simulations done with Genesis 1.3
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE dependence on electron trajectoryMeasurements
-100 -50 0 50 1000
0.5
1
H19SEED kick [μrad]
SA
SE
pow
er [a
.u.]
-100 -50 0 500
0.5
1
V19SEED kick [μrad]
SA
SE
pow
er [a
.u.]
meas day1meas day2
day1: 450MeVday2: 495MeV
• FWHM: 100-105 µrad (x) / 90 µrad (y) (x>y because e- wiggling motion in the undulator is in x?)• Good reproducibility between different days
Measurements are averaged over 100 shots SASE energy taken by MCP detector (maximum around 20 µJ)
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE dependence on electron trajectory Simulations vs measurements
-5 0 5
x 10-5
0
500
1000
1500
s[m]
I[A]
Current
-5 0 5
x 10-5
0
1
2
3x 10-6
s[m]
ε u [m
]
Emittance
-5 0 5
x 10-5
960
965
970
975
980
985
s[m]
γ
Energy
-5 0 5
x 10-5
0
0.5
1
1.5
2
s[m]
Δγ
Energy Spread
SASE simulationsBunch length = 100e-4mGaussian current profile (Imax=1.5 KA)Energy chirp of ±1%Rest of conditions constant along the bunch: εu=2.2 μm, matched optics
Good agreement
-150 -100 -50 0 50 100 1500
0.2
0.4
0.6
0.8
1
kick [μrad]
SA
SE
pow
er [a
.u.]
meas2meas1SASE sim.SS. sim.
Idea: finding a “reasonable” input e- beam for Genesis with an orbit sensitivity as in reality.
Steady state simulations (SS): 1 single λTime-dependent: bandwidth
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE energy vs electron energyMeasurements
490 492 494 496 498 500 502 504 5060
0.2
0.4
0.6
0.8
1
electron energy [MeV]S
AS
E in
tens
ity [a
.u.]
initial caseextra dxdx correcteddx/dy corrected
FWHM goes from 0.82 to 1.72% after correcting dispersion in both planes ☺
5mm11mmdx/dy corrected
31mm12mmdx corrected
28mm48mmextra dx
30mm22mminitial case
dydxrms dispersion
1 2 3 4 5 6-100
-50
0
50
100
# BPM
Dx
[mm
]
1 2 3 4 5 6-60
-40
-20
0
20
40
# BPM
Dy
[mm
]
initial caseextra dxdx correcteddx/dy corrected
initial caseextra dxdx correcteddx/dy corrected
Energy change by varying ACC456 gradientMeasurements averaged over 100 points
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE energy vs electron energySimulations
1 2 3 4 5 6-0.04
-0.02
0
0.02
0.04
# BPM
DX
[m]
1 2 3 4 5 6-0.1
-0.05
0
0.05
# BPM
DY
[m]
initial case (meas.)initial case (prediction)after corr. (meas.)after corr. (prediction)
0.4 mrad-2.9 mraddy’
5 mm47 mmdy
1.9 mrad6.0 mraddx’
14 mm12 mmdx
After correctionInitial situation
From the dispersion measurement, the dispersion functions at the entrance of the undulator can be derived:D(s) = D(s0)*R11(s)+D’(s0)*R12(s)
-Orbit changes according to dispersion functions-Optics changes (magnets were not scaled)
Same beam conditions as before
No dispersion generated inside the undulator
Considered effects:
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE energy vs electron energySimulations vs measurements
Good agreement
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionMeasurements
25.5 26 26.5 2780
100
120
140
160
180
200
wavelength [nm]
inte
nsity
[a.u
.]
qecol=84.49Aqecol=84.98Aqecol=85.18Aqecol=85.49Aqecol=86.49Aqecol=87.49Aqecol=88.48A
Widest spectrum and maximum power without dispersion Effects depend on the dispersion sign ↑QECOL ↓ λ(but not symmetrically): ↓QECOL ↑ λ
0 5 10 15 20 25-4
-2
0
2
4
#BPM
x [m
m]
0 5 10 15 20 25-2
0
2
4
#BPM
y [m
m]
•Every measurement averaged over 200 shots•Dispersion generated by varying QECOL current•Centroid orbit along the undulator kept constant
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
Dispersion generated when changing Q3/5ECOL current
1 2 3 4 5 6-0.04
-0.02
0
0.02
# BPM
DX
[m]
measurementsprediction
4.7 mraddx’
0.7 mmdx
Dispersion functions at the undulator entrance
Rms dispersion in the undulator: 15 mm
Decrease of 0.5 A decrease (0.6% of the current)
No dispersion generated inside the undulator
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionSimulations
Effect of the dispersion to SASE spectrum depends on the initialcorrelation between transverse coordinates and energy. In general we have the following relation:
Introducing dispersion changing Q3/5ECOL current, a linear component ηu is added
-1 0 1
x 10-4
0
500
1000
1500
s[m]
I[A]
Current
-1 0 1
x 10-4
960
965
970
975
980
985
s[m]
γ
Energy
SASE simulations
Similar beam conditions as beforeBunch length increased to 300e-4mCurrent increased for the head and the tail
Analysis restricted to horizontal offset x and the impact of DxConsidered dispersions:[0 +5cm -5cm]
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionSimulations
-1 0 1
x 10-4
-6
-4
-2
0
2
4
6x 10-4
s [m]
x [m
]
Horizontal offset
-1 0 1
x 10-4
960
970980
s [m]
γ
Energy
2.56 2.58 2.6 2.62 2.64
x 10-8
0
0.2
0.4
0.6
0.8
1
λ [m]
inte
nsity
[a.u
.]
Radiation spectrum
no disp+5cm-5cm
no disp+5cm-5cm
The spectrum becomes narrowerCentral wavelength does not change
No initial correlation x-energy / no off-set
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionSimulations
-1 0 1
x 10-4
-4
-2
0
2
4
6
8x 10-4
s [m]
x [m
]
Horizontal offset
-1 0 1
x 10-4
960
970980
s [m]
γ
Energy
2.58 2.6 2.62 2.64
x 10-8
0
0.2
0.4
0.6
0.8
1
λ [m]
inte
nsity
[a.u
.]
Radiation spectrum
no disp+5cm-5cm
no disp+5cm-5cm
Central wavelength depends on the dispersion sign
No correlation x-energy / non-zero off-set (+250 μm)
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionSimulations
-1 0 1
x 10-4
-1
-0.5
0
0.5
1x 10-3
s [m]
x [m
]
Horizontal offset
-1 0 1
x 10-4
960
970980
s [m]
γ
Energy
2.58 2.6 2.62
x 10-8
0
0.2
0.4
0.6
0.8
1
λ [m]
inte
nsity
[a.u
.]
Radiation spectrum
no disp+5cm-5cm
no disp+5cm-5cm
Effect to the spectrum width depends on the final correlation (can be narrower or wider)
Central wavelength does not change
Initial linear correlation x-energy
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionSimulations
-1 0 1
x 10-4
-10
-8
-6
-4
-2
0
2
4x 10-4
s [m]
x [m
]
Horizontal offset
-1 0 1
x 10-4
960
970980
s [m]
γ
Energy
2.56 2.58 2.6 2.62 2.64
x 10-8
0
0.2
0.4
0.6
0.8
1
λ [m]
inte
nsity
[a.u
.]
Radiation spectrum
no disp+5cm-5cm
no disp+5cm-5cm
The spectrum becomes narrowerCentral wavelength depends on the
dispersion sign
Initial quadratic correlation x-energy
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
SASE spectrum vs dispersionMeasurements
25.5 26 26.5 2780
100
120
140
160
180
200
wavelength [nm]
inte
nsity
[a.u
.]
qecol=84.49Aqecol=84.98Aqecol=85.18Aqecol=85.49Aqecol=86.49Aqecol=87.49Aqecol=88.48A
Linear + quadratic initial u-u’/energy correlation?Simulations are ongoing…
2.56 2.57 2.58 2.59 2.6 2.61 2.62 2.63 2.64
x 10-8
0
0.2
0.4
0.6
0.8
1
λ [m]
inte
nsity
[a.u
.]
Radiation spectrum
no disp+5cm-5cm
FEL Beam Dynamics / 24-11-08 Eduard Prat, DESY
Summary – Next steps
Summary
Dispersion correction improves sensitivity of SASE to electron energy
Introducing dispersion narrows the SASE spectrum and changes the central wavelength. An initial quadratic correlation u/u’-energy explains qualitatively the measurements.
Next steps
Fully simulate SASE wavelength vs dispersion (compare required initial u-u’/energy correlation with s2e simulations / measurements)
Repeat the measurements: see reproducibility, try to introduce dispersion with steerers in the MATCH section instead of QECOL.