自由电子激光中平衡态螺旋轨道的稳定性问题

PROBLEM OF STABILITY OF THE EQUILIBRIUM HELICAL ORBIT IN FREE-ELECTRON LASERS

本文用李亚普诺夫的运动稳定性理论成功地解决了具有均匀导向场和理想螺旋磁场自由电子激光中电子平衡态螺旋轨道的稳定性问题。利用李亚普诺夫第一方法,确定了轨道的不稳定区域;利用李亚普诺夫第二方法,严格地证明了高导向场区和低导向场区螺旋轨道的稳定性。

The problem of stability of the equilibrium helical orbit in free-electron lasers with a combined ideal helical wiggler and uniform axial guide field is successfully solved by means of the Lyapunov's stability theory of motion. The unstable region is determined with perturbation of initial energy taken into account by Lyipunov's first method. An appropriate Lyapuov's function is constructed; accordingly, the low and high guide field stable regions are shown rigorously.