  We derive an effective Dicke model in momentum space to describe collective
effects in the quantum regime of a free-electron laser (FEL). The resulting
exponential gain from a single passage of electrons allows the operation of a
Quantum FEL in the high-gain mode and avoids the experimental challenges of an
X-ray FEL oscillator. Moreover, we study the intensity fluctuations of the
emitted radiation which turn out to be super-Poissonian.
