自由电子激光的单粒子理论及其应用

EXACT SINGLE PARTICLE THEORY OF FREE ELECTRON LASER AND ITS APPLICATIONS

本文建立了圆极化摇摆场自由电子激光的单粒子理论,导出了电子未扰轨道及其稳定性判据和自由电子激光单程增益的表达式。单程增益由三项构成,其中第一项即自由电子激光不稳定性的增益与动力学理论得到的指数增益相符。第二项和和三项表明存在一对新的不稳定性——正不稳定性和负不稳定性。该理论没有对电子未扰轨道纵向速度作任何假设,不仅可以更合理地用于常规自由电子激光的研究,而且可以用于短周期摇摆器弱相对论自由电子激光研究。后者由于电子未扰轨道纵向速度比较低,已有的单粒子理论中所作的电子纵向速度约等于光速的假设不再成立。借助数值分析,我们发现:(1)稳定轨道Ⅱ的弱导引场区域也出现了动力学理论描述过的与自由电子激光互作用机理相悖的现象。(2)正不稳定性和负不稳定性在稳定轨道Ⅰ的导引磁场临界值附近可能严重影响自由电子激光的工作。(3)可以使用较弱的短周期摇摆场和较强的导引场产生高频率高增益相干受激辐射。

In this paper, an exact single particle theory of free electron laser (FEL) with a circularly polarized wiggler field and an axial guide magnetic field in the tenuous beam limit has been developed. The unperturbed electron orbits , their stable conditions and stability boundary of guide field , and the single pass gain have been derived out. The gain is composed of three dominant terms. The first term, which is the gain of FEL instability , has been found to be in excellent agreement with the exponential growth rate obtained by the previous kinetic theories . And the second and third terms represent the gains of a couple of new instabilities. Without assumption on the axial electron velocity, this theory is valid for conventional FELs and,especially, for small period wiggler FELs in which the electron beam energy is relatively lower.Thus the assumption commonly used in previous single particle theories that the axial electron velocity is approximately equal to the speed of light no longer remains exact. Numerical analyses indicate that the new instabilities will probably affect the FEL operation when the guide field increases to its stability boundary for the highest gain. The results also reveal that it is possible to use relatively weaker wiggler field to generate high gain radiations at high frequency with the help of a relatively stronger guide field. At last, two groups of parameters of such FELs using bifilar helical wigglers are presented.