Chaotic Electron Trajectories in a Planar Wiggler Free-Electron Laser

The motion of an electron in a planar wiggler with an axial guide field is found to be nonintegrable. When taking into account the effects of self-fields of the beam, it is confirmed that the motion of an electron in a planar wiggler with a guide field may be chaotic. There is evidence of chaos from numerical calculations of nonzero Lyapunov exponents using different approaches of Benettin's method which are described and compared. Very accurate Poincaré maps are also performed.