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用单粒子方法推导出了ＳｈｌｏｍｏＰｉｎｈａｓ提出的一种新型摆动器－磁场与ｚ轴无关的摆动器自由电子激光中的Ｍａｄｅｙ定理。结果表明：在这种摆动器自由电子激光中，Ｍａｄｅｙ定理第一部分形式不变；第二部分相差一个因子Ｍ０，它说明新型摆动器自由电子激光比普通摆动器自由电子激光有更高的能量转换效率。
A new type of oscillator proposed by Shlomo Pinhas is derived by using single-particle method. The Madey’s theorem in the free-electron oscillator of the oscillator has nothing to do with the z-axis. The results show that the first part of the Madey’s theorem does not change in this kind of oscillator free-electron laser and the second part is different by a factor M0, which shows that the new type of free-electron laser has a higher energy conversion than the conventional free-electron laser effectiveness.