1. 6D Characterization of Witness Beam before Injection in LWFA
B. Marchetti, D. Marx
1st EuPRAXIA Collaboration Week
DESY, June 2017

2. Outline
This talk will present ongoing numerical studies for Beam Characterization at the ARES-linac at SINBAD relevant for EuPRAXIA
How does the typical witness e-beam look like?
How does the lattice for diagnostics look like?
What do we mean with 6D Characterization of the Witness Beam?
Bunch Length
Longitudinal Phase Space
Slice emittance on different transverse planes (not covered by this talk)
3D Reconstruction of e-Bunch Charge

3. Overview of e-bunch Parameters
Witness beam for lwfa

4. Characteristics of Witness Beams
From EuPRAXIA parameter table LWFA with external injection:
At SINBAD we are investigating the range Q=0.5pC-30pC, especially the limit in the characterization of very low charge and ultra-short e-bunches.
Higher charges (up to 50 pC) and longer bunch lengths (up to 30fs) working points will allow to relax the requirements on the longitudinal and transverse resolution of the measurement.

5. Example of ultra-short probe for LWFA
Beam shape at the exit of the bunch compressor
Q=2.7 pC
Energy = 100 MeV
Transverse Normalized Emittance = 0.2 mm mrad
σt=0.461 fs

6. longitudinal charge profile reconstruction
Guidelines for Lattice Design, Resolution Calculation
longitudinal charge profile reconstruction

7. SINBAD-ARES linac SINBAD overview –
Cfr: U. Dorda et al. “SINBAD – The accelerator R&D facility under construction at DESY”, NIM A 829, p (2016).
Talk by J. Zhu describes examples of achievable working points suitable for LWFA
Dogleg to second experimental area
TDS + diagnostics beamline and experimental area
ARES linac
E=100MeV
Magnetic compressor
Temporary experimental area
Space for future possible energy upgrade

8. How does the considered diagnostics beamline look like?
RF cavity:
Frequency f = ω/(2π)
Peak deflection voltage Vy
Linac
Not to scale
Magnet & screen positions not yet fixed
For the moment we assume no matching lattice between the bunch compressor and the TDS

9. How does the considered diagnostics beamline look like?
RF cavity:
Frequency f = ω/(2π)
Peak deflection voltage Vy
Linac
Fig. Credits: D. Malyutin PhD thesis
Give bunch time-dependent kick => convert longitudinal to transverse
Variable polarization (see later in the talk) allows deflection at any angle

10. How does the considered diagnostics beamline look like?
RF cavity:
Frequency f = ω/(2π)
Peak deflection voltage Vy
Linac
Longitudinal Resolution:
e-bunch:
Energy E
Vertical emittance εy
Fig. Credits: D. Malyutin PhD thesis
High frequency ~12 GHz (X-band) allows 3-4 times higher resolution than S-band
RF cavity:
Frequency f = ω/(2π)
Peak deflection voltage Vy

11. Resolution Range EuPRAXIA case
εn=0.3mm*mrad
Δφ = π/2
f=12GHz
εn=1mm*mrad
Δφ = π/2
f=12GHz
Typical β function at ARES after magnetic bunch compression <30m.
If we want to avoid adding a matching section between BC and TDS we need to work with higher deflection voltages.

12. Longitudinal Beam Profile Characterization
Beam line & e-Bunch Parameters
V = 40MV
β(s0) = 6m (as from bunch compression)
Δφ = π/2
Q=2.7 pC
Energy = 100 MeV
εn= 0.2 mm mrad
σt=0.461 fs
Simulated Measured Streaked Screen
Longitudinal Resolution = 0.42 fs
Code used: Elegant
Space Charge OFF (implementation ongoing)
t [fs]
Screen resolution: 10μm
x [mm]

13. Technical Issues limiting Operation at High Voltage
RF Phase jitter:
RF Phase jitter causes transverse jitter of the beam on the screen in the direction of the streaking of the TDS.
~0.1deg RMS phase jitter can be tolerated during the calibration procedure by using a screen directly at the cavity exit. The bunch profile measurement is single shot.
The phase jitter will anyway have strong impact on the measurement time. For 10Hz operation we estimated a waiting time of about 30 seconds to get one shot on the high resolution measurement screen at 40MV.
For high charges and high rep. rates radiation issues might arise (many e-bunches lost along the diagnostics line).
Arrival time beam jitter effect is negligible if <10fs RMS
Temperature stability of the cavity.

14. 3D charge distribution reconstruction
Introduction of X-Band TDS Design with Variable Streaking Direction
3D charge distribution reconstruction

15. Novel X-Band TDS design with Variable Polarization
Variable Polarization Circular TE11 Mode Launcher
This new design allows for changing the streaking direction of the TDS.
A. Grudiev, CLIC-note-1067 (2016)
Collaboration working on first prototype
See “X-Band TDS Project”, MOPAB044, Proc. IPAC 2017
At DESY SINBAD, FLASH2, FLASHForward and potentially XFEL involved

16. Reconstruction of 3D Charge Distribution of the witness beam
Relies on streaking at multiple angles
Completely new measurement technique
Reference: MOPAB045, Proc. IPAC 2017
Principle:
Streak beam at different angles and measure intensity at screen
Identify the longitudinal slices for each streaking direction
Combine 1D transverse slice profiles from different streaking directions to form a 2D transverse slice profile
Stack longitudinal slices together to form complete 3D charge profile reconstruction

17. Tomographic Reconstruction – Input Beam
Input beam production simulated by J. Zhu
Input beam used for test simulations at the TDS
Example of correlation x-z that we wish to detect

18. Tomographic Reconstruction - Analysis
4 xy screen profiles [2D] out of 16.
Convert y to t and divide into slices (0.85 fs) [2D]
For each slice, take projection on x axis [1D] and combine using tomographic reconstruction (SART algorithm) [2D]
Stack slices [3D]
Screen resolution 20μm.

19. Tomographic Reconstruction – Final Result
Actual 3D e-beam distribution at the screen location
Reconstructed 3D distribution
Sixteen streaking angles (only 1 calibration needed)
Quadrupoles in the lattice OFF
Simulations in elegant
No space charge, no jitter, no misalignment effects so far included

20. Tomographic Reconstruction – Artefacts
Bunch length decreases with TDS off
Bunch length increases with TDS on
Slices don’t match up
Beam longitudinal phase space
@ TDS entrance
Induced Energy spread in the TDS
(Panofsky-Wenzel Theorem)
E=84MeV  velocity bunching effect!
This effect is frozen for highly relativistic beams

21. Longitudinal phase space measurement
Extension of the Lattice design for Energy Spread measurement, low Voltage measurement
Longitudinal phase space measurement

22. Longitudinal Phase Space Measurement
Reference: MOPAB046, Proc. IPAC 2017
Theoretical resolution achievable for dipole spectrometer:
Voltage of only 2MV per cavity (4MV in total) used to limit TDS induced energy spread
Dipole bending angle: 0.93 rad (53deg).
Simulations done with Elegant (CSR included)

23. Longitudinal Phase Space Measurement
Original (left) and reconstructed (right) slice energy spread
There is significant induced energy spread from the TDS visible in the reconstruction
The correlation is well reproduced

24. Conclusions
Longitudinal Characterization for low charge ultra-short Bunches has been discussed
Attosecond resolution is in principle possible by using high gradient X-band TDS
Limits for high TDS voltage operation are set by stability limits (RF jitter, temperature stability)
Space charge force introduces artefacts in the measurement and might play an important role especially at low energies and will be soon included in the study
A novel X-band TDS Design with Variable Polarization opens new opportunities for beam Characterization
Allows streaking of bunch at all angles
We have discussed 3D charge profile reconstruction using tomographic techniques, that would allow for characterization of the transverse vs longitudinal correlation of the charge profile, important both for LWFA and PWFA
Slice emittance measurements (e.g. via quadrupole scan) were not covered by this talk but complete the aimed characterization of the witness beam. Studies are foreseen.

25. Thank you for the attention !
Acknowledgements
The numerical studies presented in this talk are done by D. Marx.
Many thanks to: R. Aßmann, F. Christie, R. D‘Arcy, U. Dorda, M. Huening, J. Osterhoff, S. Schreiber, M. Vogt, J. Zhu, A. Grudiev (CERN), P. Craievich (PSI) for profitable discussions.
Thank you for the attention !