Electron orbits in a free-electron laser with planar wiggler, axial magnetic field, and ion-channel guiding

The electron orbits in a free-electron laser with planar wiggler, axial magnetic field and ion-channel guiding are investigated. The wiggler magnetic field is taken to be static, plane polarized, transverse, radially independent, and sinusoidally varying along the free-electron laser axis. The relativistic equation of motion for a single electron is solved for the transverse coordinates and velocity components. An equation for function Φ, which determines the rate of change of axial velocity with energy, is derived and discussed. Numerical calculations are made to illustrate the effects of the two electron-beam guiding devices (axial magnetic field and ion-channel) on the electron trajectories. Some interesting results of simultaneous application of the two electron-beam guiding devices include the existence of the three groups of orbits, two singularity of function Φ, and two negative mass regimes. It is shown that only for group III orbits, the transverse velocity increases with increasing axial magnetic field in presence of constant ion-channel frequency. Since the gain of free-electron laser with planar wiggler is proportional to the mean-square-value of the transverse velocity, the gain for this group increases with increasing axial magnetic field.