Fig. 3: Principle of seeded FEL and spectral control.
From: Seeded free-electron laser driven by a compact laser plasma accelerator
a, The seeded FEL principle: an external seed laser periodically modulates, at its optical wavelength, the electron beam as it travels in the periodic magnetic field of an undulator. The microbunched electron beam finally emits coherent light at the wavelength of the density modulation period. b, FEL resonance condition: due to the chirps of the electron-beam energy and the seed wavelength, energy exchange between the electron beam and the seed laser can only occur at the longitudinal position t0 where the resonance condition λseed(t0) = λR(t0) is satisfied. This resonance location t0 is shifted (orange arrow) if the delay τ between the seed and the electron beam is varied. c, Undulator dispersion-induced modulation period stretching. As long as the electron beam traverses the undulator with an average longitudinal speed Vz, the undulator dispersion induces a stretching of the electron beam. The periodic modulation initiated by the seed laser at the resonant wavelength is thus stretched, leading to a FEL coherent emission redshifted with respect to the seed-laser optical wavelength. d, λFEL versus delay τ (Extended Data Fig. 2). τ = 0 corresponds to perfect synchronization between the seed and the electron beam. For τ < 0 (resp. τ > 0), the seed arrives before (resp. after) the electron beam at the undulator entrance. Experimental data are shown as grey dots, with the colour scale representing the charge of each single shot. The delay scan was carried out for a 4.3-mm-undulator gap. The model results are shown as a black dashed line, using equation (1) with Ee = 188.8 MeV, R56 = −1.8 mm, Leff = 1.87 m and D = −0.296 ps nm−1. Simulations are shown as red diamonds and use the same parameters as in Fig. 2, except for charge (100 pC), corresponding to a spectral charge density of 3 pC MeV−1.
