The theory for the two-stream free electron laser (FEL) consisting of a relativistic electron beam transporting along the axis of a helical wiggler in the presence of an axial guiding magnetic field is proposed and investigated. In the analysis, the effects of self-fields are taken into account. The electron trajectories and the small signal gain are derived. The characteristics of the linear-gain and the normalized maximum gain are studied numerically. The results show that there are seven stable groups of orbits in the presence of self-fields instead of two groups reported in the absence of the self-fields. It is also shown that the normalized gains of three groups decrease while the rest increase with the increasing of normalized cyclotron frequency W0. Furthermore, it is found that the two-stream instability and the self-field lead to a decrease in the maximum gain except for group 3. The results show that the normalized maximum gain is enhanced in comparison with that of the single stream.
