Three-dimensional free electron laser numerical simulations for a laser wiggler in the quantum regime

A compact tunable source of soft X-rays could be realized combining a state-of-the-art electron source with an intense counter-propagating laser pulse. If the source is operated in the quantum regime, the theoretical model predicts high monochromaticity (single-spike) and unprecedented temporal coherence for the emitted radiation. Here we present numerical simulations of the complete quantum model for an Free Electron Laser (FEL) with a laser wiggler in three spatial dimensions, based on a discrete Wigner function formalism taking into account the longitudinal momentum quantization. The numerical model includes the complete spatial and temporal evolution of the electron and radiation beams, with an explicit description of diffraction, propagation, laser wiggler profile and emittance effects. The contribution of each interaction term is studied independently, and the 3D results are contrasted with the 1D quantum FEL model neglecting transverse effects. Finally the parameter space for possible experiments is characterized, and a particular experimental case is discussed in detail.