Chaotic behaviour in a realizable helical-wiggler field

The motion of an individual electron for the case the wiggler magnetic field is described by a realizable helical wiggler is investigated. The dimensionless vector potential is considered to the leading-order vector potential for an ideal helical wiggler and the correction of the vector potential. Chaotic behaviour in a realizable helical wiggler field is examined for the expanded Hamiltonian in free-electron laser. We also analysed the focusing force provided by higher-order terms in the vector potential expansion, the effects of self-field, the particle trajectories and chaotic phenomena due to the wiggler field amplitude in a realizable helical wiggler by the numerical simulation.