S. Spampinati, J.Wu, T.Raubenhaimer Future light source March, 2012 Simulations for the HXRSS experiment with the 40 pC beam

Focus on  Pulse characteristic in the SASE undulator  Pulse characteristic in the seeded undulator  Seed used power 2 Presentation aims  Comments on simulations vs experiments  Derive model of pulse evolution in SASE and seeded undulator from experimental observation  Benchmark with start to end simulations  Try ideal simulations model to match with experiment  Try to understand seeding efficiency and match with simulations

 Start to end simulation are a guidance  Some beam parameter (current beam profile) can be measured, even if indirectly, to confirm simulations  Only few accelerator configurations and beams can be simulated completely  Accelerator and beam change from shift to shift and from shot to shot  Ideal models can be used to catch physics Comments on simulations vs experiments

 Measurements of current of fs beam profile beam energy spectrometer ( Z.Huang, K.Bane, Y.Ding, and P Emma, Phys. Rev. ST Accel. Beams 13, (2010) )  The beam measured is not exactly the beam in the undulator but 1-1 correspondence exists  The beam profile change from shot to shot R. Iverson, H. Loos, Z. Huang, H.-D. Nuhn, Y. Ding, J. Wu, S. Spampinati T.O. Raubenheimer, 24/1/2012

5 Pulse in the SASE undulator  Measured quantity : 2.5m gain length and ≈20 µJ at crystal  Short length with low energy: short pulse length  Back extrapolation of measured power: Considering a shot noise power of some KW the pulse length should be shorter then fs  Start to end simulation confirm very short pulse formation  3.7 m gain length, energy ≈5µJ. Than we try simulations with a beam more bright

6 SASE undulator (U 3-15) with a more brighter beam  Beam parameter: energy spread 4 MeV, emittance  Energy at crystal ~20µJ in very narrow pulses, gain length 3.1 m

7 Seed energy Letargy Evolution of the pulse in the seeded undulator  Energy along seeded undulator (active length on x)  Fitting the data with exponential curve  gain length can be short like 3.5 m  3.5 lethargy length  Amplified energy is around 1 nJ considering interaction from the start  If the seed peak power is of the order of MW the FEL pulse length is <= 1fs (is gain length measurement in the seeded part correct?)

 experimental spectral relative bandwidth FWHM 8-5*10^-5  (FWHM PULSE DURATION)* (FWHM PULSE DURATION)=0.44  2.8-4*fs FWHM pulse duration for a Gaussian Fourier transform pulse  Lasing from a small part of the beam or chirp on the FEL pulse.  FEL pulse longer then 2.8 fs Then considering a gain length of 3.5 m the seed power is more like MW. This level of power prevent saturation even for such short gain length.  FEL pulse in the second undulator is longer than the SASE in the first undulator 8 Evolution of the pulse in the seeded undulator (continue)

9 Seeded undulator start to end simulation  For the optimum detuning of the second undulator the core starts to contribute to the pulse energy and this produce the shorter gain length  Gain length 5 m  Starting from 2MW seed power production of ≈250µJ Different colors for different tapering

 Wakes in the undulator no chirp  Gain length 5 m  Lasing on all the beam  Same detuning of the second undulator for narrow spectrum maximum energy  Seems very difficult to have gain length shorter than 5m Simulation with high current beam

11  Lasing from horns in the SASE undulators. Then the core starts to lase even if the horns still dominate  High current in the horn reduces gain length in the SASE undulator. It seems, from the experiments, that the Horns are very bright  Shorter Gain length in the experiment shorter than the simulated one  The shorter seed gain length observed in the experiments (<5m) requires a seed power below 0.2 MW  Gain length ≈ 5m is more compatible with MW level seed power

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