Longitudinal Space Charge Micro-bunching in SDL (DUV-FEL)

1. Longitudinal Space Charge Micro-bunching in SDL (DUV-FEL) T. Shaftan, L. Carr, H. Loos, B. Sheehy, (BNL) Z. Huang, C. Limborg (SLAC) W.S. Graves (MIT/BATES) MICROBUNCHING AND BEAM BREAK-UP IN DUV-FEL ACCELERATOR, T. Shaftan, Z. Huang, L. Carr, W.S. Graves, C. Limborg, H. Loos, B. Sheehy, PAC 2003, Portland, Oregon

2. The DUVFEL Accelerator Accelerate bunch at RF zero-crossing of tank 4 Spectrometer dipole Size of the chirped beam image at the monitor 14 is proportional to the bunch length ! Positive RF slope Zero RF slope Negative RF slope RF gun 4.5 MeV Spectrometer dipole 200 MeV 135 MeV 75 MeV 35 MeV Chicane to FEL Tank 4 Tank 3 Tank 2 Tank 1 Beam Dump Monitors Focusing triplets Drive Laser 14 • Electron beam longitudinal diagnostics • For energy/time domain measurements we use TV monitor (Num. 14) located after 72° spectrometer dipole • “Zero-phasing” method of the bunch length measurement (single-shot !)

3. Motivation W.S. Graves, et al., PAC 2001, p. 2860 DUV FEL • “Zero-phasing” images from the • spectrometer dipole revealed spiky structure • with sub-picosecond period in the chirped • beam energy spectrum • Assuming that chirped bunch energy spectrum represents longitudinal density distribution  spikes could be treated as a spikes in the longitudinal bunch density (peak current) • Calculating FEL slippage length for lasing • at 266 nm as 70 um , follows that the spike • width is comparable or less than slippage length  must cause degradation of • FEL performance • Similar effect has been observed at TTF M. Huning et al., NIM A 475 (2001) p. 348 TTF

4. Modulation in RF gun drive laser We measure temporal profile of the laser (at 266 nm) by cross correlating it with the 120 fsec, 800 nm oscillator pulse in a nonlinear optical crystal (multi-shot measurement). This measurement has a resolution of ~200 fs, due to velocity mismatch in the crystal. Cross-correlation of the drive laser profile shows some amount of modulation (~5-10 %).

5. Structure with a Large Number Spikes • “Zero-phasing” image of uncompressed bunch with a large number of sharp spikes • Energy spectrum, derived from the image, • horizontal axis is scaled in picoseconds • Frequency spectrum of upper plot. Spectrum • shows modulation with harmonics in THz range. Harmonics  sharpness of the spikes. Time, ps Frequency spectrum (THz)

6. Modulation dynamics with Compression (~300 pC) 100 0° 1.42 ps • Dynamics at “high” (>200 pC) charge differs • from the dynamics at “low” charge • Uncompressed bunch profile is smooth • Experiment on modulation dynamics: • Keep chicane constant and increase chirping • tank phase (0-13-19-25 degrees) • Modulation shows up during compression • Process • Compression: a} decreases modulation period (C times); b) increases bunch peak current (C times) 50 0 0 2 4 6 8 100 -13° 1.24 ps 50 0 0 1 2 3 4 5 200 -19° 0.93 ps 100 0 0 1 2 3 4 -25° 0.43 ps 200 0 0 0.5 1 1.5 2 2.5

7. Sensitivity to the Chicane Strength 70 1 0.3 1.2 1.7 1.2 0.1 0.3 1.5 0.1 1.5 60 1 0.6 0.6 1.7 0.3 50 0.1 0.3 0.1 1.2 1 40 1.5 0.6 Chicane Current (A) 1.2 30 1 1.5 1.7 20 1.7 10 1.7 5 10 15 20 25 30 35 40 Tank 2 Phase (Degree) Isolines of constant bunch length • CSR-related effect ? should be sensitive to the bending radius in the chicane magnets • Experiment: maintain the final bunch length constant, while changing chicane strength  initial and final (post-compressed) bunch properties are the same for any chicane strength, so only collective effect should show up ! • Compression factor is 1-hR56 there is always a combination of h and R56 that will maintain a constant compression ratio • Result of the experiment: in general the modulation is insensitive to the chicane settings

8. Space Charge Model (courtesy of Z. Huang) • For an energy-modulated bunch, the horizontal profile by rf zero-phasing is also modulated with an enhanced amplitude • Space charge oscillation connects energy modulation with current modulation • Horizontal modulation appears much larger than the current modulation it intends to measure • “gain” = (amplitude of final energy modulation)/(initial density modulation) Space charge impedance per unit length for transversely uniform coasting beam in free space: • - energy, rb – bunch radius,  - modulation frequency Z. Huang, SLAC-PUB-9788

9. Simulation Beam parameters: E=65 MeV I=200 A rb=0.4 mm Ldrift=15 m mod=0.2 ps Emod= 20 keV Energy, MeV Time, ps

10. Modulation analysis An example of the chirped beam image. One of the interesting features here is evolution of the modulation wavelength along the bunch, corresponding to nonlinear chirp. Interpretation of double peaks on the left: “overmodulated” periods. Every couple of double spikes in this region represents a single modulation period. Tail of the bunch is folded back over, introducing bright region on the right side of the image (space charge). “Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL preprint.

11. “Overmodulation” effect Measuring distance Ebetween “double spikes” we can determine amplitude of the energy modulation. where • is the energy modulation,  is the modulation frequency “Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL preprint.

12. Fourier spectrum of structure (with L.H. Yu) Time, ps Frequency spectrum (THz) Harmonics in the Fourier transform of energy spectrum Assuming chirped coasting beam with constant density and sinusoidal energy modulation, we can derive expression for the energy spectrum. This expression is valid for the case of “overmodulated” bunch as well Energy spectrum must contain a family of harmonics of modulation frequency “Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL-71490-2003-JA .

13. Sensitivity to the Transverse Beam Size 35 30 200 A 25 20 a G 15 10 40 A 5 0 0 20 40 60 80 100 large linac beam (1 mm) • Space charge force is a function of rb • Change the beam size of the compressed beam along the accelerator  effect on modulation ? 200 A 40 A small linac beam (250  m) Analytical calculations of “gain” in the modulation by Z. Huang 3 different lattice solutions  3 different RMS beam sizes along the accelerator

14. Results of the Experiment “Zero-phasing” profiles of the beam (300 pC) for different lattice solutions: Average RMS beam sizes along the accelerator: 0.25 mm, 0.5 mm, 1 mm

15. IR Radiation Measurements • Does modulation enhance any bunching in the bunch longitudinal density ? • Experiment: • Change the beam size  “modulated” and “non-modulated” bunch profiles • We measured CTR from metallic mirror, using IR detector and low-pass IR filters (cut-off of 40 µm, 100 µm, 160 µm) • Modulation wavelength = 90 µm (from “zero-phasing”)  expect enhancement of the coherent IR power in this spectral region if bunching • Result of the experiment: No difference is found between“modulated” and “non-modulated” beam conditions “Non-modulated”bunch profile “Modulated” bunch profile Bolometer signal, uVs Filters: >40 um >100 um >160 um Wavelength, um

16. Dependence on Energy 60 MeV • Space charge force is a function of  • Change the energy of the compressed beam (300 pC) along the accelerator   effect on modulation ? • Vary tank 3 energy, maintaining the same all other beam parameters (bunch length, transverse beam size, charge) 80 MeV 110 MeV

17. Initial chirped beam profiles (no compression) 0-phasing profiles without (a) and with chicane (b) Initial chirp = 0 in both situations (no compression) b) +90° -90° a) +90° -90°

18. (I) Results of the experiment • Number of modulation periods and modulation wavelength for different energies is different ! • Product is constant: bunch length is the same for different energies • Why ? “Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang, BNL-71491-2003-JA

19. Model of “Modulation versus Energy” experiment 16 m 1 m 3 m long linac section Space Charge “kicks” “Initial phase space” Beam: 70 MeV and other parameters of the experiment Slippage “kicks” “Final phase space”, spectrometer Assumptions: 1) Do not take into consideration bunch prehistory before chicane. We did not change anything but energy using tank after chicane. 2) Initial conditions at the end of the chicane  no initial energy modulation, certain amount of initial density modulation (spectral shape is unknown)

20. (II) Results of the experiment 50 MeV • Simulated normalized spectra of energy and density modulations for 50 MeV and 110 MeV • With energy increase average spectral frequency of energy modulation shifts toward higher freq. range • Therefore modulation wavelength decreases and number of modulation periods increases for higher energy • Another words: Plasma oscillations at different frequencies accumulate different phase advance while the bunch travels down to the accelerator. Initial density modulation Final energy modulation Final density modulation Initial density modulation Final energy modulation Final density modulation “Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang, BNL-71491-2003-JA 110 MeV

21. (III) Results of the experiment • Using technique for “overmodulated” bunch (#11), we processed measured data and found energy modulation amplitude for different energies. • Dashed line: simulation, assuming 6 % density fluctuations (and no initial energy modulation) at the end of the chicane-compressor. “Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang, BNL-71491-2003-JA

22. Summary & Conclusions • We observed a peculiar phenomena in the longitudinal phase space • Space charge oscillation transforms small longitudinal density modulation into energy modulation along the bunch • “Zero-phasing” shows spikes, corresponding to the energy modulation in the chirped bunch energy spectrum. • A space charge model of the phenomena is in fair agreement with experimental data (based on several assumptions have been made) • Complete understanding of the phenomena requires further analysis • Is this structure dangerous for accelerator performance ? • It increases the projected energy spread in the bunch and distorts longitudinal phase space • It does not affect compression for DUV FEL experimental conditions • magnetic system may convert this modulation into real spatial bunching

23. Acknowledgements • Research supported by DOE Contract No. DE-AC02-98CH10886 • We wish to thank D. Dowell, A. Doyuran,P. Emma, S. Krinsky, J.B. Murphy, J. Rose, X.J. Wang, Z. Wu, L.H. Yu for their help and many stimulating discussions.