A theory of two-stream free-electron laser in a combined electromagnetic wiggler and an ion-channel guiding is developed. In the analysis, the electron trajectories and the small signal gain are derived by considering the effects of self-fields. Numerical calculations show that there are seven group's trajectories rather than nine groups reported in Mehdian and Saviz (2010 Chin. Phys. B 19(1), 014214). The comparison of the normalized gains and their corresponding normalized frequencies by employing the axial magnetic field and ion-channel guiding, with and without self-fields, in FEL has been studied numerically. The results show that the normalized maximum gain in FEL with axial magnetic is larger than that for using ion-channel guiding except in small region, but the results for their corresponding normalized frequencies are opposite.
