Simulations for the HXRSS experiment with the 40 pC beam

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

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 • Focus on • Pulse characteristic in the SASE undulator • Pulse characteristic in the seeded undulator • Seed used power

3. Comments on simulations vs experiments • 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

4. 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, 092801 (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 24/1/2012 R. Iverson, H. Loos, Z. Huang, H.-D. Nuhn, Y. Ding, J. Wu, S. SpampinatiT.O. Raubenheimer,

5. Pulse in the SASE undulator • Measured quantity: 2.5m gain lengthand ≈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 brighterbeam • Beam parameter: energy spread 4 MeV, emittance 0.40. • Energy at crystal ~20µJ in very narrow pulses, gain length 3.1 m

7. Evolution of the pulse in the seeded undulator Seed energy Letargy • 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?)

8. Evolution of the pulse in the seeded undulator (continue) • 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 0.2-0.3 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

9. Seeded undulator start to end simulation Different colors for different tapering • 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

10. Simulation with high current beam • 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

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

12. END