Raman free-electron laser with a coaxial wiggler

A one-dimensional theory of the stimulated Raman scattering mechanism for a coaxial free-electron laser (FEL) is developed. The beam-frame FEL dispersion relation and a formula for the lab-frame spatial growth rate are derived. A numerical study of the growth rate for the coaxial wiggler is made and compared with that for the helical wiggler. Except for a part of the group II orbits, the growth rate is found to be less than the helical wiggler. Relativistic effects due to the transverse oscillation of electrons in the wiggler field prevent the FEL operation from approaching magnetoresonance. In the absence of these relativistic mass effects, the calculations show a magnetoresonance associated with the first spatial harmonic and a much narrower resonance at the third spatial harmonic.