A theoretical study of electron trajectories and gain in a quadrupole wiggler free-electron laser (FEL) with ion-channel
guiding is presented. The relativistic equation of motion for a single electron in the combined quadrupole magnetic and
ion-channel electrostatic fields is solved for the steady-state electron velocity components. Next the electromagnetic
radiation copropagating with the electron beam in the FEL interaction region is analyzed and an equation for gain in the
low-gain-per-pass limit is then derived. The results of a numerical study of electron trajectories and gain in the presence
of the ion-channel guiding is presented and discussed. It is shown that all orbits of group I are unstable, while group II
have stable orbits as well as unstable orbits. Effects of ion-channel guiding on the gain are then investigated and shown
that gain enhancement is obtained due to the ion-channel guiding.
A theory for self-fields effects on dispersion relation in a free-electron laser with planar wiggler and ion-channel guiding
is presented. An equation is derived for dispersion relation in the presence of the electromagnetic radiation, space-charge
wave, ion-channel electrostatic field, and self-fields. Numerical solution of this equation is used to study growth rate. A
comparison between the growth rates in the presence and absence of self-fields shows that the growth rate decreases
considerably due to the self-fields.