Abstract

In this paper 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 characterised by an adimensional parameter κ such that κ−1 is a measure of the gain of a photon on slipping through the electron pulse. We define the long pulse limit to be when κ ⪡ 1. In this case we find that only the leading region of the propagating radiation pulse exhibits the previous steady state behaviour with peak power proportional to ne43 (where ne is the electron beam density). The trailing (slippage) region exhibits a spiking behaviour with peak intensities reaching many times the saturated intensity predicted by steady state theory. The existence of the spiking may be related to the fact that the trailing region of the electron pulse experiences less radiation re-absorption than the leading region, so that slippage inhibits saturation. The energy extracted from the beam exhibits the usual oscillatory behaviour after saturation as predicted by the steady state theory. We define the short-pulse regime to be when κ ≳ 1. In this regime the peak power emitted by the electrons does not scale as ne43, as predicted by steady state theory, but scales as ne2 which is typical of superradiant behaviour. Furthermore, energy is extracted from the electrons in a continuous way, with no steady-state-type oscillatory behaviour, so that the efficiency of the superradiant FEL may be enhanced considerably.

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