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A relativistic theory for Raman backscattering in the beam frame of electrons is presented and is used to find the growth rate of a free-electron laser (FEL), in the Raman regime. A one dimensional helical wiggler and an axial magnetic field are considered. The effects of static self-electric and self-magnetic fields, induced by the steady-state charge density and currents of the non-neutral electron beam, are taken into account to find the steady-state trajectories. The wiggler effects on the linear dispersion relations of the space-charge wave and radiation are included in the analysis. A numerical computation is conducted to compare the growth rate of the excited waves with nonrelativistic treatment. It was found that self-field effects increase the growth rate in the group II orbits and decrease it in the group I orbits. However, the wiggler effects on growth rate are stronger and increase the growth rate on both group I and group II orbits. Next, the growth rate under an ion-channel guiding, instead of an axial magnetic field, under similar condition is calculated and is studied numerically.
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