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

A theory of self-fields in a one-dimensional helical wiggler free electron laser with ion-channel guiding and axial magnetic field is presented. the steady-state orbits under the influence of self-field are derived and discussed. the φ function that determines the rate of change of axial velocity with energy is derived. the numerical results show the effects of self-fields and the two electron-beams guiding devices (ion-channel and axial magnetic field) on the trajectories when used separately and simultaneously. the study shows that new unstable orbits, in the first part of the group i and ii orbits, are found. a detailed stability analysis of orbits is presented.