1. Fluctuations Study Update A. Lutman

2. Model description Undulator section I 1D FEL code Bunch shape: flat top Short Bunch Long Bunch length20 fs50 fs current2 kA Central energy 13695 Central energy deviation rho (5x10^-4) rho (5x10^-4) Uncorr. en. spread 0.2 rho Undulator section II 1D FEL code Keeps electron slice bunch energy, slice energy spread, or averages Uses as seed the forward Bragg diffracted beam Tapered / untapered operation Crystal Uses Yuri Shvid’ko time- domain formula for transmitted bragg radiation (Spatiotemporal response of crystals in x-ray Bragg diffraction P.R. ST AB 2012) Crystal thickness 104 um 004, symmetric Bragg @8333 eV

3. Undulator section I simulation s [um] intensity Relative slice energy (units of rho) slice uncorrelated energy spread (units of rho) s [um]

4. Undulator section I simulation z [m] Average Power (logscale) z [m] Uncorrelated average energy spread Diamond = chicane and crystal location

5. Monochromatic Wake After Crystal s [um] forward Bragg diffraction point response function Convolution with seed and electron bunch delayed

6. Monochromatic Wake After Crystal s [um] Some single shots Averages around different energies s [um] W W

7. Monochromatic Wake After Crystal W P(W) W Beam energy [MeV]

8. Monochromatic Wake After Crystal (Long Bunch) s [um] phase W Average Single shot

9. Untapered Radiator – Short Bunch case z [m] WW Single-Shot growth curveaverage growth curve All photon energies 1 eV bandwidth

10. Untapered Radiator – Short Bunch case Time domain (horizontal axis s [um],vertical axis power [W]) 10m20m30m 40m50m60m

11. Untapered Radiator – Short Bunch case – single shot spectra eV

12. Untapered Radiator – Short Bunch case – in 1 eV photon energy Horizontal: ebeam energy, vertical intensity 10m20m30m 40m50m60m All-energies

13. Untapered Radiator - in 1 eV – Short Bunch (fixed e beam energy) @ 0 m @ 10 m@ 30 m @ 50 m @ 70 m

14. Untapered Radiator – Short Bunch case – in 1 eV 10 MeV beam energy z [m]

15. Tapered Radiator 1 eV All ph.en. z [m] Average Power (logscale) 3-single shot spectra eV

16. Tapered Radiator – Short Bunch case 20m30m40m 50m60m70m 1 eV Horizontal: ebeam energy, vertical intensity

17. Tapered Radiator – Short Bunch case Relative energy rms 7.2 x 10 -4 Experimental Data Kmono measurement 05/15/2012 Fluctuations 72% Simulation Relative energy rms 5 x 10 -4 Fluctuations 67% Rho = 5 x 10 -4 Fit rms 3.5 x 10 -4 Rho = ~7 x 10 -4

18. Tapered Radiator - fluctuations z [m] std/avg

19. Conclusions Agenda Long bunch case (delay ?) 111 Asymmetric Laue reflection Changing chicane position Seed intensity is not gamma distributed for narrow electron beam energy filtering Position of bumps dependent on single shot realizations Simulation represents well spectral substructures in self-seeded spikes Starting with higher seed intensity does not mean reaching higher intensity: beam energy, uncorrelated energy spread, “bumps” position matter more Simulation shows lower fluctuation than experiment (different rho? different chicane position? Starting energy spread? Different taper?) Thanks to Z. Huang, J. Wu, J. Welch, Y. Ding J.Krzywinski, Y. Feng, Y. Shvyd’ko S. Spampinati