Electron orbits in combined electromagnetic wiggler and axial guide magnetic fields

The interaction between a relativistic electron beam and an electromagnetic wiggler in the second stage of a free-electron laser is analyzed with emphasis on the effect of an axial guide magnetic field on such interaction. In particular, the single-particle trajectories in this configuration are treated; single-particle orbits are derived, and the stability of the orbits is discussed. Two classes of orbits corresponding to two regions of electron cyclotron frequencies are found, and both classes are shown to be stable in the case of an electromagnetic wiggler.