  We analyze the dynamics of Free Electron Laser (FEL) devices, operating with
a bunched beam exhibiting a longitudinal phase space correlation. We show that
the presence of an energy-position correlation term is responsible for very
interesting effects like an enhancement of the peak output power, a shortening
of the laser pulses and an increase of the non linearly generated harmonic
intensities. We conjecture that the mechanism is due to a kind of energy
tapering effect associated with the correlation. We discuss the difference of
the dynamics with respect to an ordinary undulator tapering and the relative
advantages.
