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 /spl Phi/, 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 /spl Phi/, 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.