Abstract
Echo-enabled harmonic generation (EEHG) is an external seeding concept for free-electron lasers (FELs) designed to produce fully coherent, transform-limited pulses of radiation down to soft x-rays. Like its cousin high-gain harmonic generation (HGHG), EEHG seeds the FEL with an electron beam that is density modulated at the lasing wavelength, such that the electrons coherently radiate and then collectively amplify the coherent pulse. In both schemes, the density-modulation is generated by precise laser-manipulation of the position and energies of the electrons within the beam. Because the FEL output is determined in large part by the electron beam distribution, this enables customizable x-ray beams with improved temporal coherence, stability, and flexibility. Unlike HGHG however, EEHG can access much higher harmonics in a single FEL amplification stage, and can produce cleaner FEL spectra that are less sensitive to initial electron beam distortions. Here we review the EEHG concept, the distinguishing features, recent experiments, and known challenges.
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Notes
- 1.
The resonant modulation wavelength is λm = λu(1 − βz) = λ1βz, where βz = vz∕c is the scaled longitudinal velocity of the electron beam in the undulator and λu is the modulator period. For highly relativistic beams βz ≈ 1, the modulation wavelength is essentially that of the laser λm ≈ λ1. The imprinted modulation also includes the forward slippage of the light one wavelength λ1 = 2π∕k1 per modulator period, as set by the resonance condition. However, the slippage is usually small compared to the laser pulse length or bunch length and thus typically ignorable.
- 2.
Inspection shows that the bunching vanishes for ξE = 0.
- 3.
Large initial energy structures like beam tails can negatively impact the spectrum, because they can fold over the phase space distribution in the large chicane. We refer instead to small energy structures that do not result in significant changes in the beam current profile.
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The author thanks G. Stupakov for helpful discussions and S. Khan for careful reading of the manuscript.
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Hemsing, E. (2020). Echo-Enabled Harmonic Generation. In: Jaeschke, E., Khan, S., Schneider, J., Hastings, J. (eds) Synchrotron Light Sources and Free-Electron Lasers. Springer, Cham. https://doi.org/10.1007/978-3-030-23201-6_57
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