Highest harmonic reachable by echo-enabled harmonic generation seeding
In plain words
Seeding an FEL with an external laser gives clean, stable pulses, but the seed frequency must be multiplied by large factors, and small random energy kicks to the electrons wash out the high harmonics.
Precise statement
In echo-enabled harmonic generation (EEHG), two laser modulators and two dispersive chicanes produce density bunching at harmonic $h$ of a seed laser of wavelength $\sim 2.6e-5\,\mathrm{cm}$. Determine the maximal $h$ at which EEHG gives bunching well above shot noise and lasing with near-transform-limited spectra, including intrabeam scattering and incoherent synchrotron radiation in the strong chicane, coherent synchrotron radiation, and seed-laser phase noise, and whether wavelengths near $1e-7\,\mathrm{cm}$ are reachable.
What would settle it
Measured bunching factor and spectral purity versus harmonic number at an EEHG facility, matched by a model of diffusive degradation.
Status in the literature
Unverified note
EEHG lasing in the soft x-ray range of a few nm, at harmonics of several tens, was reported at FERMI around 2019 (moderate confidence, not rechecked for 2024-2026).