Electron trajectories in a free-electron laser with planar wiggler and ion-channel guiding

An analysis of quasi-steady-state electron trajectories in a planar wiggler with an ion channel and an axial magnetic field is presented. A tenth-degr ee polynomial equation for the average axial electron velocity and an equat ion for the function Phi, which determines the rate of change of axial velo city with energy, are derived. Numerical calculations are made to illustrat e the effects of the two electron-beam guiding devices on the trajectories when applied separately and simultaneously. Some interesting effects of the ir simultaneous application include the existence of three groups of orbits , two singularities of the function Phi, and two negative mass regimes. (C) 2001 American Institute of Physics.