The effects of undulator phase errors on the Free Electron Laser small signal gain is analyzed and discussed.The gain reduction factor due to the phase error is given analytically for low-gain regimes,it shows that degradation of the gain is similar to that of the spontaneous radiation,has a simple exponential relation with square of the rms phase error,and the linear variation part of phase error induces the position shift of maximum gain.The result also shows that the Madey's theorem still hold in the presence of phase error.The gain reduction factor due to the phase error for high-gain regimes also can be given in a simple way.%对波荡器位相误差对自由电子激光小信号增益的影响进行了分析讨论.对低增益情况解析地给出了波荡器位相误差引起的增益降低因子.结果表明:与自发辐射类似增益的降低与位相误差的方差成简单的指数关系,位相误差的线性变化部分引起最大增益的位移,还表明波荡器位相误差存在时Madey定理仍然成立.对高增益情况也给出了波荡器位相误差引起的增益降低因子.
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