1. Soft X-Ray pulse length measurement
Alberto Lutman
Jacek Krzywinski
Juhao Wu
Zhirong Huang
Marc Messerschmidt …
17.February.2011

2. Soft X-Ray Pulse length Determination
Electron Beam
Spectrometer
SASE FEL Amplifier t T
Goal: recover T from the spectra
(correlation technique proposed by Jacek K.)

3. FEL transfer function in Exponential growth
Electron Beam
Current profile
tk is a random variable having probability density f(t)
Current Fourier Transform t
FEL transfer function in Exponential growth
The spectrometer transfer function
For Saturation, we run numerical simulations

4. Correlation of the radiation intensity at the exit of the spectrometer
Frequencies that we correlate
Single shot correlation,
to be:
averaged on many shots normalized
Single shot spectrum

5. Calculation of the G2 function for different profiles
To find an analytical expression for G2 we need just to plug in the f(t) function

6. Gaussian Electrons Profile* * G2
bunch
profile # #
M: “number of modes”
With our spectrometer resolution, the rms of the bell shape is due to the spectrometer bandwidth

7. Flat top vs Gaussian G2 We cannot distinguish between:
- Gaussian profile with rms length
- Flat Top profile with full length

8. Some adressed Issues Statistical Gain Central Frequency Jitter
Scales the measured function by
Central Frequency Jitter

9. Numerical Simulations
1) Verified that relations hold well enough in saturation
2) Recover bunch length and spectrometer bandwith
Bunch Length = 10 mm
40m
Exponential growth
60m
At saturation
100m
Deep saturation sm
2.99 x 10-5
3.00 x 10-5
3.06 x 10-5 BL
9.70 mm
9.79 mm
9.81 mm
1.47 x 10-5
1.48 x 10-5
1.51 x 10-5
9.53 mm
9.71 mm
10.02 mm

10. A Matalab GUI to process the data
Select a
Subset of the collected spectra
Plot spectra
and
Shot-to-shot recorded quantities
Datasets
Shot by shot quantities
Calculate G2
Function
Re-align
Spectra
Show Bunch Length Result

11. Bunch Length vs # of Undulators (2 November 2010 Data)
FWHM
Gaussian fs 13 16 19 22 25 28
Undulators

12. Spectrometer relative bandwidth (2 November 2010 Data)13 16 19 22 25 28
Undulators

13. Bunch Length vs different peak current (26 January 2011 Data)
FWHM
Gaussian fs
Peak current kA
Bunch Length using slotted foil
Measured Photon Bunch length
10 fs
13.5 fs
18 fs
27 fs

14. Next Steps Include cases with non monoenergetic electron bunch
- Two gaussian with different energies case
- Including a linear energy chirp
Analyze in detail data collected January
Finish to write the paper
Adapt the matlab GUI to be used in Control Room

15. THE END

16. Different pulses have different Gain
Electron arrivals density probability
T as a random variable with probability density p(t)
Gain is function of T (e.g. smaller T, gives higher peak current and higher gain)

17. Statistical gain and FEL gain depending on profile length
We are using indeed a different average profile
The correlation function is affected by the statistical gain
In case the gain is independent of T, the relation between G2 with and without the gain is the following:

18. Statistical gain and FEL gain depending on profile length
We can observe that
And get rid of this effect
Using the offset of G2
normalizing shot by shot each spectrum with its energy
Both approaches are not easy to apply when analyzing the real noisy spectral data

19. Double Gaussian Electrons Profile

20. Gaussian Electrons Profile
GASSIAN WITH SIGMA T

21. Flat Top Electrons Profile

22. Statistical Gain
Considering the model of incoherent radiation, the intensity at a certain frequency can be written
We let the charge C fluctuate, and correlate intensities at two different frequencies w’ and w’’
with

23. Spectra Central Frequency jitter
Considering the model of incoherent radiation, the intensity at a certain frequency can be written
We let the charge C fluctuate, and correlate intensities at two different frequencies w’ and w’’
with

24. Different pulses have different Gain
The G2 function is multiplied by

25. We can observe that for large
To get rid of the multiplicative effect we can:
Use the offset of G2s
normalize shot by shot each spectrum with its integral
Both approaches are not easy to apply when analyzing the real noisy spectral data

26. Numerical Simulations
Flat top electrons profile
Full Length = 10 um
Radiation Wavelength = 1.5 A
Rho = 4.5 x 10-4
Gain Length = 2.98 m
Undulator Length = 100 m
Number of Shots = 2000
Slippage Length = 0.5 um
Analytical theory has been dereived in the linear regime.
Simulation have been carried to determine if the theory is still applicable in saturation.
Simulations have been also done for Gaussian electrons profile

27. Power vs Undulator Distance
Gaussian electrons profile
Flat top electrons profile

28. Flat top electrons profile
Agreement:
Z=30m
Linear regime
Z=60m
saturation
Z=100m
Deep saturation

29. Flat top electrons profile2
Agreement:
Z=30m
Linear regime 2 2
Z=60m
saturation
Z=100m
Deep saturation

30. G2 function
Flat top electrons profile

31. Simulations with Peak Current Jitter

32. Shot by Shot quantities
For each shot, beside the spectra, other quantities have been recorded:
x-ray pulse energy
Electron bunch charge
Electron bunch energy
X and Y position
X and Y angle
Peak current

33. Filtering the datasets
Theory assumes that different shots differ only by the arrival time of the electrons.
This is not the case for the real data.
We use the data collected to filter and keep only a subset of the spectra
Filter:
- bunch charge
- bunch energy
- peak current

34. Correlation between Energy and First moment
The Gui allows to:
show each spectrum profile
plot recorded quantities
Spectra first moment
Electron bunch energy

35. Spectra Realignment Realign the spectra Saving around 50% shots
We can realign the spectra, using the strong linear correlation between electron bunch energy and first moment
We can either:
Realign the spectra
Saving around 50% shots
Use a smaller electron bunch energy window
Saving around 10% shots
Both approaches lead to the same bunch length result

36. Evaluation of the correlation function
We calculate the correlation function.
Interface leaves some freedom to:
- Deal with backgroud noise issue
- Deal with gain issue
Bunch length is calculated with flat top and gaussian models

37. Results from data collected November 2nd, 2010
Only 6 sets of data collected with:
200 lines/mm monochromator
3 kA peak current
Different number of undulators
Can be used to calculate the bunch length.
Other sets have:
Too low spectrometer resolution
Too low signal to noise ratio