FREE-ELECTRON-LASER MODEL WITHOUT THE SLOWLY-VARYING-ENVELOPE APPROXIMATION

A mathematical model is presented which describes the evolution of ele ctromagnetic radiation in a free-electron laser (FEL), without any str ingent assumptions regarding the envelope of the radiation pulse. The derived set of equations is nearly identical to the traditional set, w hich needed the assumption of a slowly varying radiation amplitude and phase. Although rapid variations in the radiation envelope do have in fluence 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 b een realized sor far.