Electron orbits in combined electromagnetic wiggler and axial guide magnetic fields

The single-particle orbits due to a large amplitude, backward propagating electromagnetic wave and an axial guide magnetic field are derived, and the stability of the orbits are discussed. The large amplitude electromagnetic wave acts like a magnetostatic wiggler in a free-electron laser. Two classes of orbit are found corresponding to and , where Ω0is the electron cyclotron frequency, ωwand kware the frequency and wave vector of the electromagnetic wave, γ is the relativistic factor, and υ∥is the axial electron velocity. However, unlike the case of a magnetostatic wiggler, both classes of orbit are shown to be stable.