A Raman quantum free-electron laser model

Operation of a Quantum Free Electron Laser (QFEL) could provide a compact and fully coherent source of X- and γ-rays. Imperative to experimental realization is allowing for decoherence effects of either spontaneous emission or space-charge to take place, having opposing constraints. Here, for the first time, we present a one-dimensional QFEL Wigner model that includes longitudinal space-charge effects by quantizing the periodic potential derived from the Fourier components of the longitudinal electron beam density. The model is used to investigate steady-state QFEL gain and momentum state dynamics for a variety of space-charge regimes. We find increased saturation lengths and lower saturation intensity as a result of attenuated transitions in the two-level quantum system. In addition, we characterize a space-charge regime where specific transitions outside the QFEL bandwidth are targeted, such that the conventional description breaks down. These findings serve as a consistent theoretical extension of existing QFEL models.