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
\Omega_{0} < \gamma(\omega_{w} + k_{w}\upsilon_{\parallel})
and
\Omega_{0} > \gamma(\omega_{w} + K_{w}\upsilon_{\parallel})
, where Ω
0
is the electron cyclotron frequency, ω
w
and k
w
are 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.