A relativistic theory for the unstable couplings of wave modes in a free-electron laser (FEL), in the Raman regime, is presented with the self-fields of the electron beam taken into account. Contrary to the usual investigations, relativistic terms to all orders of the wiggler amplitude are retained in the linearized equations. A dispersion relation for the unstable couplings of wave modes is derived. Numerical investigation of this dispersion relation reveals that self-fields reduce the growth rate for the FEL resonance, in group I orbits, and increases it somewhat, in group II orbits with Φ > 0. The growth rate of all of the couplings, in group II orbits with Φ < 0, is reduced by self-fields except for the Rc+ and Sc− coupling, which is increased. It is found that self-fields split the cyclotron mode of the right and left circularly polarized radiation into two separate modes and prevent the slow and fast space-charge waves from coupling to each other.
Pulsar emissions