A dispersion relation for the plasma loaded free-electron laser (FEL), with a helical wiggler and an axial magnetic field is derived. The cold fluid formulation is used with self-fields of the electron beam taken into account. By solving the dispersion relation numerically the influence of self-fields on the FEL resonance and the two-stream instability is investigated. It was found that although self-fields have strong effect on the FEL resonance, their effects on the two-stream instability is much weaker.
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