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Brian McNeil, Neil Thompson, David Dunning & Brian Sheehy

Attosecond Pulse Trains from FEL Amplifiers. Brian McNeil, Neil Thompson, David Dunning & Brian Sheehy. Workshop on X-Ray FEL R&D LBNL October 23 - 25, 2008. Outline. Brief summary of ‘conventional’ cavity mode locked lasers Mode formation & locking in a SASE FEL amplifier

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Brian McNeil, Neil Thompson, David Dunning & Brian Sheehy

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  1. Attosecond Pulse Trains from FEL Amplifiers Brian McNeil, Neil Thompson, David Dunning & Brian Sheehy Workshop on X-Ray FEL R&D LBNL October 23 - 25, 2008

  2. Outline • Brief summary of ‘conventional’ cavity mode locked lasers • Mode formation & locking in a SASE FEL amplifier • 3D & 1D simulations in XUV & VUV • Application to High Harmonic attosecond structure • Improved models • Conclusions

  3. Brief summary of ‘conventional’ cavity mode locked lasers

  4. Ultra-short pulse generation This history of short pulse generation in ‘conventional’ lasers has developed from the first mode-locked lasers, through dye-lasers, Ti:Sapphire and now to High Harmonic Generation in gas jets. Since 1964, pulse durations have been reduced by ~ 5 orders of magnitude to ~130 as and very recently* to ~80 as. *E. Goulielmakis et al., Science 320,1614 (2008)

  5. n = 1 ω n=1 n = 2 s s n >> 2 * Cavity modes* perimeter = s s A repeated waveform generates a spectral comb • Envelope is atomic linewidth: gain bandwidth of lasing medium • Mode spacing ∆ωs=2πc/s • No of modes q = bandwidth/mode spacing

  6. Cavity mode-locking Sidebands • Mode-locking occurs when a fixed phase relationship develops between the axial modes. • Application of e.g. cavity length modulation causes axial modes to develop sidebands. • Cavity modulation at round trip frequency causes sidebands at mode spacing Δωs . Neighbouring modes couple and phase lock. • The the output consists of a one dominant repeated short pulse.

  7. Mode formation & locking in a SASE FEL amplifier* *

  8. Eg: s =10m, λ=10 nm, Nw = 50 q =107 Electron delayδ s= δ + Nwλ Nw period undulator n=1 n = 2 n =1 n = 3 s s ω Example: λ=12.4nm, N = 12, δ= 551nm s = 700nm# of modes: q = 2.35 Axial Modes from an amplifier FEL • For cavity FEL, gain bandwidth ~ 1/2Nw • No of modes within bandwidth q = s/2Nwλ • Too many modes to resolve & needs optics • Alternative: synthesise axial mode spectrum without cavity The spectrum is the same as a ring cavity of length s. Have synthesized a ring cavity of length equal to the total slippage between modules

  9. Axial mode analysis The analysis demonstrates that the axial modes generated are formally identical to those of a cavity. The ‘cavity’, however, is significantly shorter, so that only a few modes may fall under the gain bandwidth. This now allows coupling via a modulation introduced at a relatively large frequency. Similarities to DOK: V. N. Litvinenko, Nucl. Instrum. Methods Phys. Res., Sect. A 304, 463 (1991).

  10. Sidebands Axial mode coupling in the XUV

  11. Simulations (3D & 1D) in XUV & VUV

  12. Modelocking Simulations in Genesis 1.3 Interaction of e-beam and laser in modulator simulated Modulated e-beam propagated in undulator, including SHOTNOISE. Energy Modulation converted into BEAMFILE modulatede-beam e-beam Modulator Undulator Laser Chicane dispersion applied with 4-dipole chicane (IBFIELD, IMAGL, IDRIL) Undulator Radiation delayed using OFFSETRADF and ALIGNRADF parameters MODELOCKED SPIKES Repeat Until Saturation

  13. XUV Parameters

  14. Spike FWHM ~ 10fs SASE XUV-FEL @ 12.4nm

  15. Spike FWHM ~ 1 fs Mode-Coupled SASE XUV-FEL @ 12.4nm

  16. Spike FWHM ~ 400 as Ts From conventional cavity analysis: XUV SASE FEL amplifier with mode-locking

  17. XUV Output Comparison SASESpike FWHM ~ 10fs Mode-CoupledSpike FWHM ~ 1 fs Mode-LockedSpike FWHM ~ 400 as

  18. X-ray Parameters

  19. Spike FWHM ~ 23 as X-ray SASE FEL amplifier with mode-locking

  20. 1D Simulation: Mode locking mechanism

  21. Feasibility Typical FEL amplifier schematic: (4GLS XUV-FEL) FEL amplifiers are broken into a series of undulator sections. Between these sections it is necessary to accommodate phase-shifters, electron focussing elements and beam positioning monitors. Inclusion of electron bunch delay chicanes should not significantly affect this generic design. Note, typically the electron delay chicane will be independent of energy and of total length ~12-15cm. The chicanes are therefore easy to incorporate into an undulator lattice.

  22. Stability Chicane Magnet stability: Path length change: Require: where XUV X-ray Energy stability: E.g. in XUV case 2nd term is factor 10-5 smaller Energy spread: XUV X-ray

  23. Application to High Harmonic structure

  24. Amplified HHG – no modes* HHG *B W J McNeil, J A Clarke, D J Dunning, G J Hirst, H L Owen, N R Thompson, B Sheehyand P H Williams, Proceedings FEL 2006 Also - New Journal of Physics 9, 82 (2007)

  25. Amplified HHG – with modes HHG

  26. Amplified HHG – with modes P. M. Paul, et al. Science 292, 1689 (2001) and his the resonant harmonic of the HHG seed E.g. for operation at the h=65th harmonic of a Ti:Sapphire drive laser with :

  27. HHG spectrum Drive λ=805.22nm, h =65, σt=10fs Amplified HHG – retaining structure

  28. 1D Simulation: HHG amplification mechanism

  29. 1D Simulation: HHG amplification mechanism with energy modulated beam at multiple of mode spacing

  30. Further development: improved models for mode-locked case

  31. 39th harmonic Cannot modelfor fr=f39 Cannot modelfor fr=f39 Current computational codes e.g. Genesis Simulated spectrum For averaged FEL codes the minimum sample rate is: Nyquist freq. Freq. range for non-aliasing: => Freq. range that e.g. Genesis can simulate properly without aliasing is: Pulse lengths able to be modelled are limited!

  32. 1D enhanced frequency range model @ 12.4nm Spike width FWHM = 57as !(~1.4 optical cycles) 450 as: same as Genesis @12.4nm More modes now, therefore shorter spikes:

  33. Conclusions • Application of mode-locking techniques, stolen from ‘conventional’ cavity lasers, indicate possibility of generating attosecond pulse trains from FEL amplifiers • Method tested using full 3D simulation code used in design of e.g. XFEL and LCLS: predicts attosecond pulse trains in good agreement with analysis. • Method can be employed to amplify HHG pulses while retaining their attosecond structure • Evidence that mode-locking may be better than 3D models suggested when a numerical model accessing wider frequency space is used. “Potential advantages”: relatively easy to implement – modulator undulator and chicane inserts between undulator modules. Shorter pulses (~23as @ 1.5Å) in a train with variable time structure. “Practical difficulties”: more difficult to identify at this stage – more modelling required. Opens up possibility of stroboscopic interrogation of matter using light with the spatiotemporal resolution of the atom.

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