PROBLEM OF STABILITY OF THE EQUILIBRIUM HELICAL ORBIT IN FREE-ELECTRON LASERS
自由电子激光中平衡态螺旋轨道的稳定性问题

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.