A theory of electromagnetic-wave wiggler with ion-channel guiding is presented. Steady-state electron trajectories are obtained by solving the equations of motion for a single electron in a free-electron laser with electromagnetic-wave wiggler and ion-channel guiding field. The eighth-degree polynomial dispersion equation for electromagnetic and space charge waves in this configuration is derived. The characteristics of dispersion relation are analyzed in detail by numerical solutions. It is found that the growth rate for group I and II orbits has been affected by the presence of the ion-channel guiding and the growth rate for group II orbits is more affected.
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