Chaotic electron dynamics for relativistic-electron-beam propagation through a planar wiggler magnetic field

It is shown that the motion of an individual test electron in a low-density relativistic electron beam propagating through a realizable planar wiggler magnetic field is nonintegrable and can become chaotic. The presence of chaos, which is induced by the transverse spatial inhomogeneities in the wiggler field, poses limits on the wiggler field amplitude and the beam size for beam propagation and free-electron-laser operation. An approximate condition that determines the onset of chaos-induced beam degradation is derived analytically and found to be in good qualitative agreement with the numerical simulations using the Poincar\'e map.