The Radiation Spot Size due to Wiggler Errors in a Free-Electron Laser Oscillator

We have developed an extended three-dimensional free-electron laser (3D FEL) code with source-dependent expansion to calculate the intensity of the radiation field and the spot size in a free-electron laser oscillator. The effect of the wiggler field errors was evaluated for the case of a planar wiggler generated by a magnet stack with parabolic shaped pole faces by using the extended three-dimensional equations in a free-electron laser oscillator based on the proposed FEL facility which is to be operated in the far-infrared and the infrared regions. The radiation spot size due to the wiggler field errors also have been analyzed for wiggler errors of ${\Delta}B/B=0.0$, 0.03, 0.06 and 0.09% at z = 1 m and z = 2 m. The effect of the diffraction of radiation field due to the wiggler field errors of ${\Delta}B/B=0.0$ and ${\Delta}B/B=0.09%$ at 200 passes was evaluated by using the extended 3D code that we developed. The variation of the curvature of the phase front and the effect of the radiation field intensity due to the wiggler field errors were also evaluated for B = 0.5 T and B = 0.7 T with the wiggler error of ${\Delta}B/B=0.09%$ at 200 passes and the results were compared to those of without errors. The intensity of the radiation, behavior of the radiation spot size and the variation of the curvature of the phase were highly sensitive to the wiggler error of ${\Delta}B/B$ > 0.09%, but were less sensitive to the wiggler errors for ${\Delta}B/B$ < 0.09% in a free-electron laser (FEL) oscillator based on the proposed FEL facility.