新型Wiggler自由电子激光中的Madey定理

Charge and Current Waves of The Relativistic Beam in the Free Electron Laser

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。

In this paper, the relativistic electron beam is described as the motion equation of the electron, continuity equation and Poissons equation. When the electron beam has not the perturbation motion, the space charge is fully cancelled. Then, the equations can be linearized. The solution of these linearized equations is exponential function: exp(jωt-jk·r). The electron beam presents a charge density wave and a current density wave of the electron.