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Fluctuations Study Update

Fluctuations Study Update. A. Lutman. Model description. 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. Undulator section I 1D FEL code

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Fluctuations Study Update

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  1. Fluctuations Study Update A. Lutman

  2. Model description • 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 • Undulator section I • 1D FEL code • Bunch shape: flat top • 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 Relative slice energy (units of rho) intensity s [um] slice uncorrelated energy spread (units of rho) s [um] s [um]

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

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

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

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

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

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

  10. Untapered Radiator – Short Bunch case 30m 20m 10m 60m 50m 40m Time domain (horizontal axis s [um],vertical axis power [W])

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

  12. Untapered Radiator – Short Bunch case – in 1 eV photon energy 30m 20m 10m Horizontal: ebeam energy, vertical intensity All-energies All-energies All-energies 60m 50m 40m

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

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

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

  16. Tapered Radiator – Short Bunch case 40m 30m 20m Horizontal: ebeam energy, vertical intensity 1 eV 70m 60m 50m

  17. Tapered Radiator – Short Bunch case Experimental Data Kmono measurement 05/15/2012 Simulation Fit rms 3.5 x 10-4 Relative energy rms7.2 x 10-4 Relative energy rms5 x 10-4 Fluctuations 72% Fluctuations 67% Rho = 5 x 10-4 Rho = ~7 x 10-4

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

  19. Conclusions • 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?) Agenda Thanks to Z. Huang, J. Wu, J. Welch, Y. Ding J.Krzywinski, Y. Feng, Y. Shvyd’ko S. Spampinati • Long bunch case (delay ?) • 111 Asymmetric Laue reflection • Changing chicane position

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