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Investigation of the Longitudinal Electron Bunch Structure with LOLA
Michael Röhrs, Christopher Gerth, Holger Schlarb
21.11.2006 [email protected]
Outline
• Description of the measurements• Results:
– Longitudinal profile– Longitudinal phase space distribution– Slice emittance
• Error considerations for the measured slice emittance values
21.11.2006 [email protected]
LOLA in the FLASH linac
Beam direction
ACC23 BC2ACC45UND6 …. UND1 Dogleg LOLA BC3 ACC1 GUN
Q9ACC7 Q9/10ACC6
Horizontal Kicker
Off-axis screen
LOLA
OTR screen
Collimators
Sextupol
21.11.2006 [email protected]
Accelerator settings
• Energy: 677 MeV• Charge: 0.5 nC• SASE signal at 13.7 nm with 5 µJ average radiation
energy per bunch→ optics downstream of BC3 changed before the
measurements!• ACC1-phase: -9˚ • ACC23-phase: -25˚ • ACC45-phase: 0˚
21.11.2006 [email protected]
Longitudinal profile
21.11.2006 [email protected]
∆ t [ps]
x [m
m]
0 0.5 1 1.5 2-4
-2
0
2
0 0.5 1 1.5 20
0.5
1
ρ / ρ
max
∆ t [ps]
∆ tspike ≈ 65 fs (FWHM) Qspike ≈ 0.12 nC (23 %)
0
50
100
150
200
40 50 60 70 80 90 1000
5
10
15
20
25
30
35
∆ tspike [fs]
N
Ntotal = 100
Spike width: ~75 fs (FWHM) Resolution: ~50 fs (FWHM) Charge in spike: ~0.12 nC(23%) spike current: ~1.7 kA
Spike width statistics (100 bunches):
Longitudinal phase space
∆ t [ps]
δ [%
]
0 0.5 1 1.5 2
-0.5
0
0.5
0 0.5 1 1.5 2
0
0.1
0.2
0.3
σ δ [%
]
∆ t [ps]0 0.5 1 1.5 2
0
200
400
600
σ x [ µ m
]
0
0.1
0.2
density profile [a.u.]slice boundaries
Dispersion: 233 mm; Time resolution: ~ 50 fs; Energy spread resolution: ~ 0.06% (380 keV)
-200 -150 -100 -50 0 50
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
∆ t [fs]
δ [%
]
energy profile [a.u.]long. profile (lp) [a.u.]lp:low energy partlp:high energy part
Profile of the head
Head Tail
OTR-image
Slice energy spread:
21.11.2006 [email protected]
Slice emittance
• Resolution ~60 fs
• Proj. emittance: 13.5 mm mrad
• Slice mismatch < 1.5
0 0.5 1 1.50
5
10
15
20
ε xnorm
[mm
mra
d]
∆ t [ps]
∆ t [ps]
∆ x
[mm
]
0 0.5 1 1.5
-1
0
1
density profile [a.u.]slice boundaries
0
50
100
150
200
250
↔ SASE signal?
Head Tail
OTR-image
21.11.2006 [email protected]
Slice emittance: comparison of different methods
-0.5 0 0.5 1 1.5 20
5
10
15
20
∆ t [ps]
γ ε [m
m m
rad]
Comparison of different methods
Std. methodGauss fitTomogr.Tomogr.(90%)
0.5 1 1.5 20
1
2
3
4
5
∆ t [ps]
γ ε [m
m m
rad]
Comparison of different methods
Std. methodGauss fitTomogr.Tomogr.(90%)
Tail:
21.11.2006 [email protected]
Reconstructed phase space
0 0 . 5 1 1 . 50
5
1 0
1 5
2 0
ε xnorm
[mm
mra
d]
∆ t [ p s ]
∆ t [ p s ]∆
x [m
m]
0 0 . 5 1 1 . 5
- 1
0
1
d e n s i t y p r o f i l e [ a . u . ]s l i c e b o u n d a r i e s
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
x [mm]
x ′ [m
rad]
εxnorm = 12.8µ m
Q = 0.5 nC
-3 -2 -1 0 1 2 3
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Part of the head
Entire bunch:
x [mm]
x ′ [m
rad]
εxnorm = 15.2µ m
Q = 0.07 nC
-3 -2 -1 0 1 2 3
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Single slice (~60 fs) within the head:Main part of
the bunch
21.11.2006 [email protected]
Emittance of substructures in phase space
x [mm]
x ′ [m
rad]
90%
εxnorm = 4.7µ m
Q = 0.01 nC
εxnorm = 5.7µ m
Q = 0.05 nC
-3 -2 -1 0 1 2 3
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
x [mm]
x ′ [m
rad]
75%
εxnorm = 2.6µ m
Q = 0.009 nC
εxnorm = 3.8µ m
Q = 0.04 nC
-3 -2 -1 0 1 2 3
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Single slice (~60 fs) within the head
90% of the total charge (low intesityregions are cut):
x [mm]
x ′ [m
rad]
εxnorm = 7.2µ m
Q = 0.01 nC
εxnorm = 8.6µ m
Q = 0.06 nC
-3 -2 -1 0 1 2 3
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Subdivision of phase space
75% of the total charge:
21.11.2006 [email protected]
Dispersion
Reconstructed horizontal dispersion during the quadrupole scan:
∆ t [p s ]
x [m
m]
0 0 .5 1 1 .5 2-4
-2
0
2
0 0 .5 1 1 .5 20
0 .5
1
ρ / ρ
max
∆ t [p s ]
∆ ts p ik e ≈ 6 5 f s (F W H M ) Q s p ik e ≈ 0 .1 2 nC (2 3 % )
0
5 0
1 0 0
1 5 0
2 0 0
∆ t [p s ]
δ [%
]
0 0 .5 1 1 .5 2
-0 .5
0
0 .5
0 0 .5 1 1 .5 2
0
0 .1
0 .2
0 .3
σδ [%
]
∆ t [p s ]0 0 .5 1 1 .5 2
0
2 0 0
4 0 0
6 0 0
σx [ µ
m]
0
0 .1
0 .2
d e ns ity p ro f ile [a .u .]s lic e b o und a rie s
Tilt of the tail due to dispersion(?)
Tilt and long. Phase space distribution can me utilized to estimate dispersion
time
Energy
XOTR 17ACC7
OTR 5ECOL
0 2 4 6 8 10 12-50
0
50
100
150
200
scan indexD
[mm
]
→ Very large values
→ Tilt not solely due to dispersion?21.11.2006 [email protected]
Dispersion-corrected slice emittance
0 0.5 1 1.50
2
4
6
8
10
12
14
16
18
20
ε xnorm
[mm
mra
d]
∆ t [ps]
without disp. corr.with disp. corr.
Slice energy spread < 50keV assumed
21.11.2006 [email protected]
Large Dispersion because of optics?
Reconstructed beta-functions during the scan (single slice):
0 10 20 30 40 500
20
40
60
80
100
z [m]
β [m
]
startmiddleend
Kicker
Screen
0 2 4 6 8 10 12-100
0
100
200
300
400
scan index
tilt [µ
m/p
s]
measuredreconstr.
Measured and reconstructed tilt due to dispersion:
21.11.2006 [email protected]
Quadrupole gradient errors
21.11.2006 [email protected]
0.4 0.5 0.6 0.7 0.8 0.9 1 1.10
20
40
60
80
100
120
140
160
180
ε / ε0
N
• Monte Carlo simulation for 3% quadrupole gradient errors (1000 seeds, emittance of one slice):
0 2 4 6 8 10 1250
100
150
200
250
scan index
slic
e w
idth
[ µ m
] pS/S0 =2.9
measuredused transfer matchanged transfer mat.
• Comparison of measured and reconstructed slice widths:
Quadrupole gradient errors
0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.5
1
1.5
2
2.5
3
3.5
4
ε / ε0
p S/S0
Number of runs: 1000
Comparison of reconstructed and measured slice widths for random gradient errors :
Used transfer function
Errors from erroneous transfer matrices much smaller than expected
21.11.2006 [email protected]
21.11.2006 [email protected]
50 100 150 200 250 300 350 400 450
100
200
300
400
500
600
originalprocessed
50 100 150 200 250 300 350 400 450
100
200
300
400
500
600
Image analysis
• Algorithm to detect the image region covered by the bunch
• The remainder of the image is set to zero
original
→ nearly no influence of noise
Resolution limitation
• Pixel size: ~25 µm
0 10 20 30 40 500
50
100
150
200
250
slice index
slic
e w
idth
[ µ m
]
Minimum slice widths during the scan
• Minimum slice widths during the scan:
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
Pixelsize [σ]
rela
tive
beam
siz
e er
ror [
%]
Effect of binning on measured rms beam sizes (gaussian beam)
• Effect of binning on the calculated rms width for a gaussian distribution with standard deviation σ
21.11.2006 [email protected]
Conclusions
• Dispersion seems to be a significant error source for slice emittance measurements– Measure and correct dispersion before slice
emittance measurements if possible → smaller emittance values?
– Measurement of dispersion during the scan– Apply different optics?
21.11.2006 [email protected]
Image analysis 1
1. Local averaging; new pixel size e.g. 5x5 pixels
50 100 150 200 250 300 350 400 450
100
200
300
400
500
600
Original image with noise (background subtracted):
10 20 30 40 50 60 70 80 90
20
40
60
80
100
120
21.11.2006 [email protected]
Bad signal to noise ratio in single slices, noise largely influences calculated rms widths
Image analysis 2
4. Loop: add nearest neighbour pixels, if intensity > n*σ (e.g. n=3)
2. Determine mean value and variance σ^2 of noise from an intensity histogram
-50 0 50 100 150 2000
500
1000
1500
2000
Intensity [a.u.]
Num
ber o
f pix
els
Noise peak
Connected area with intensities above the noise level
10 20 30 40 50 60 70 80 90
20
40
60
80
100
120
3. Find pixel with maximum intensity
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Image analysis 35. Transformation back to original pixel size
21.11.2006 [email protected] 100 150 200 250 300 350 400 450
100
200
300
400
500
600
50 100 150 200 250 300 350 400 450
100
200
300
400
500
600
Comparison: resulting and original image
Optional:
• Boundary layers around the bunch area
• Iterative determination of the noise level, e.g. in case of synchrotron radiation
• Splitting of the image in case of inhomogenous background
