The effects of self-fields on the electron trajectory and gain in a two-stream electromagnetically pumped free-electronlaser with axial guiding field

A theory of a two-stream free-electron laser in a combined electromagnetic wiggler (EMW) is developed, in which we use an axial-guide magnetic field and take into account the effects of the self-fields. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear-gain, and the normalised maximum gain are studied numerically. The results show that there are nine stable groups of orbits in the presence of self-fields instead of seven groups reported in the absence of the self-field. It is also shown that the normalised gains of four groups of the orbits are decreasing and those for the rest of them are increasing with growing $\bar {\varOmega }_0 $. Furthermore, it is found that the two-stream laser with self-field enhances the maximum gain in comparison with the single stream case.