What defines the quantum regime of the free-electron laser?

The quantum regime of the free-electron laser (FEL) emerges when the discreteness of the momentum of the electron plays a dominant role in the interaction with the laser and the wiggler field. Motivated by a heuristic phase space approach we pursue two different routes to define the transition from the classical FEL to the quantum domain: (i) standard perturbation theory and (ii) the method of averaging. Moreover, we discuss the experimental requirements for realizing a Quantum FEL and connect them to today's capabilities.