Nonlinear orbits in free-electron lasers with a linear magnetic wiggler and a strong axial magnetic guide field

Single-particle trajectories in a free-electron-laser device consisting of a linear periodic wiggler superimposed on a strong uniform axial guide field are examined by a formalism suitable for perturbation analysis and adaptable to wigglers of arbitrary geometry. For motion locked on to a single resonance (between the gyromotion and the periodicity induced in the axial velocity by the wiggler) and for sufficiently weak wiggler fields, bounded oscillations of the gyroradius and of axial velocity are possible for a limited region of parameter and phase space. Optimal parameters for which the largest fraction of particles entering the drift chamber experience limited excursions in gyroradius and in axial velocity are determined. The mean drift of the guiding center off axis is used to determine the allowable length of the wiggler and of the drift tube for beam propagation. With increasing wiggler field bounded motion is eliminated, leading to transition between resonances, chaotic motion, and significant spread in the axial velocities of electrons. Comparison with experimental results is presented.