Free-Electron-Laser Model without the Slowly-Varying-Envelope Approximation

A mathematical model is presented which describes the evolution of electromagnetic radiation in a free-electron laser (FEL), without any stringent assumptions regarding the envelope of the radiation pulse. The derived set of equations is nearly identical to the traditional set, which needed the assumption of a slowly varying radiation amplitude and phase. Although rapid variations in the radiation envelope do have influence on the dynamics of the electrons, ignoring this fact does not cause excessive errors. Consequently, it is concluded that the region of validity of the traditional FEL equations is much larger than has been realized sor far.