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Following up the detailed three-dimensional analysis of the particle dynamics in a free electron laser with a helical wiggler and a uniform axial guide magnetic field, achieved by Rhimi et al. [1], we study the motion of the electrons in the neighborhood of the ideal trajectory. The normal modes ± of the quadratic Hamiltonian are analyzed numerically in both the normal and reversed-field configurations for different values of the ratio w/0. The electron trajectories are thus discussed. It is found that pseudo-circular and elliptic trajectories are characterizing both group-I and reversed-field group-II modes while the motion in the normal group-II mode is much more complicated.

Normal modes propagation in a helical free-electron laser with an axial guide field