Steady-state electron trajectories in a free electron laser with ion-channel and axial magnetic field in the presenceof self-fields

A theory of self-fields in a one-dimensionalhelical wiggler free electron laser with ion-channel guidingand axial magnetic field is presented. The steady-stateorbits under the influence of self-field are derived anddiscussed. The Φ function that determines the rate ofchange of axial velocity with energy is derived. Thenumerical results show the effects of self-fields and the twoelectron-beams guiding devices (ion-channel and axialmagnetic field) on the trajectories when used separatelyand simultaneously. The study shows that new unstableorbits, in the first part of the group I and II orbits, arefound. A detailed stability analysis of orbits is presented.