Generalized gain-spread relation and optical guiding effect in high-gain free electron laser amplifiers

Abstract

We derive a generalized gain-spread relation for constant-wiggler free electron laser amplifiers which is valid for both low-gain and high-gain devices. It connects the energy spread of the electrons with the intensity and with the phase variation of the radiation field. This relation is discussed in the small-signal and in the exponential gain regimes. In the small-signal regime it reduces to Madey's theorem. In the exponential gain regime it is related to the effect of optical guiding of radiation in the electron beam. We demonstrate analytically and numerically that refractive guiding can take place near the wiggler entrance before gain guiding becomes appreciable.