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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.
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