Fluctuations Study Update

A. Lutman

Magnetic chicaneUndulator section IIUndulaor section I

Crystal

Model description

Undulator section I

• 1D FEL code• Bunch shape: flat top

Short Bunch

Long Bunch

length 20 fs 50 fs

current 2 kA 2 kA

Central energy

13695 13695

Central energy deviation

rho(5x10^-4)

rho(5x10^-4)

Uncorr. en. spread

0.2 rho 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

Undulator section I simulation

s [um]

intensity

Relative slice energy(units of rho)

slice uncorrelated energy spread(units of rho)

s [um]

s [um]

Undulator section I simulation

z [m]

Average Power (logscale)

z [m]

Uncorrelated average energy spread

Diamond = chicane and crystal location

Monochromatic Wake After Crystal

s [um] s [um]

forward Bragg diffraction point response function

Convolution with seed and electron bunch

delayed

Monochromatic Wake After Crystal

s [um]

Some single shotsAverages around different energies

s [um]

W W

Monochromatic Wake After Crystal

W

P(W)

W

Beam energy [MeV]

Monochromatic Wake After Crystal (Long Bunch)

s [um] s [um]

phaseW

AverageSingle shot

Untapered Radiator – Short Bunch case

z [m] z [m]

W W

Single-Shot growth curve average growth curve

All photon energies1 eV bandwidth

Untapered Radiator – Short Bunch case

Time domain (horizontal axis s [um],vertical axis power [W])

10m 20m 30m

40m 50m 60m

Untapered Radiator – Short Bunch case – single shot spectra

eV

eV

eV

eV

Untapered Radiator – Short Bunch case – in 1 eV photon energy

Horizontal: ebeam energy, vertical intensity

10m 20m 30m

40m 50m 60m

All-energies All-energies All-energies

Untapered Radiator - in 1 eV – Short Bunch (fixed e beam energy)

@ 0 m

@ 0 m @ 0 m

@ 0 m

@ 10 m @ 30 m

@ 50 m @ 70 m

Untapered Radiator – Short Bunch case – in 1 eV

10 MeV beam energy

z [m]

Tapered Radiator

1 eVAll ph.en.

z [m]

Average Power (logscale)

3-single shot spectra

eV

eV

eV

Tapered Radiator – Short Bunch case

20m 30m 40m

50m 60m 70m

1 eVHorizontal: ebeam energy, vertical intensity

Tapered Radiator – Short Bunch case

Relative energy rms 7.2 x 10-4

Experimental DataKmono measurement 05/15/2012

Fluctuations 72%

Simulation

Relative energy rms 5 x 10-4 Fluctuations 67%

Rho = 5 x 10-4

Fit rms3.5 x 10-4

Rho = ~7 x 10-4

Tapered Radiator - fluctuations

z [m]

std/avg

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 toZ. Huang, J. Wu, J. Welch, Y. DingJ.Krzywinski, Y. Feng, Y. Shvyd’koS. Spampinati