Electron Trajectories in a Combined Wiggler and Alternating Gradient Quadrupole Field

This paper reports on studies of electron trajectories in a combined wiggler and alternating gradient quadrupole field. The quadrupole field is assumed to vary continuously along the symmetry axis. The linearized equations of electron motion are solved analytically for a plane-polarized wiggler by using the two-scale perturbation method. A comparison with the numerical solution is presented, and the conditions for unstable trajectories are discussed.