We have analyzed the effects of the wiggler error due to the electron beam's emittance, energy spreads, and higher-order modes in a free-electron laser (FEL) oscillator by using two electron beams of different energies based on the proposed FEL facility which is operated at a far-infrared and infrared regions. The three-dimensional (3D) effects in a FEL oscillator due to the wiggler error were calculated and an evaluation of the effect of the beam's emittance and energy spread was performed for the case of the coupled two-beam oscillator for phase shift errors and wiggler errors. The mode construction was studied on the higher-order modes of the wiggler for the various wiggler error parameters for FEL performance which is required for the high-quality electron beam. The radiation intensity at the fundamental mode was calculated for the rms phase shake in wiggler errors with sinus type, constant type, and parabolic type in the two-beam oscillator system using the 3D calculations. The results are compared with those of the fundamental modes without wiggler errors.
