In the high gain strong pump regime, the radiation field amplitude and phase can vary substantially over a wiggler period. Also, due to the periodic transverse motion, the longitudinal electron energy suffers large variations over the same distance. Because of these considerations, the spatial average that leads to the classical one‐dimensional free‐electron laser equations is not applicable here. Thus the rederived equations suitable for the high gain strong pump regime contain 2&pgr;/kwperiodic terms. Comparisons with the Electron Laser Facility (ELF) experiments of the Lawrence Livermore National Laboratory [Phys. Rev. Lett.54, 889 (1985);57, 2172 (1986); Phys. Rev. A35, 2184 (1987)] on the operational characteristics including the relative phase of the radiation field are made.