Slippage and superradiance in the high-gain FEL

We describe the single-pulse high-gain free electron laser amplifier, taking into account propagation effects (slippage). We demonstrate the existence of two different dynamical regions characterized by a dimensionless parameter κ such that κ-1 is a measure of the gain of a photon on slipping through the electron pulse. In the long-pulse limit we find that only the leading region of the propagating radiation pulse exhibits the previous steady state behavior with peak power proportional to ne4/3 (where ne is the electron beam density). The trailing (slippage) region exhibits a spiking behavior with peak intensities reaching many times the saturated intensity predicted by steady state theory. In the short-pulse regime the peak power emitted by the electrons scales as ne2 which is typical of superradiant behavior. Furthermore, energy is extracted from the electrons in a continuous way, so that the efficiency of the superradiant FEL may be enhanced considerably.