A multi-frequency approach to free electron lasers driven by short electron bunches

Abstract

A multi-frequency model for free electron lasers (FELs), based on the Fourier decomposition of the radiation field coupled with the beam electrons, is discussed. We show that the multi-frequency approach allows for an accurate description of the evolution of the radiation spectrum, also when the FEL is driven by short electron bunches, of arbitrary longitudinal profile. We derive from the multi-frequency model, by averaging over one radiation period, the usual FEL equations modelling the slippage between radiation and particles and describing the super-radiant regime in high-gain FELs. As an example of application of the multi-frequency model, we discuss the coherent spontaneous emission (CSE) from short electron bunches.