Abstract

Free-electron lasers with an axial guide field have been extensively studied. Freund et al.¹have discussed the single-particle trajectories and calculated small signal gain. These studies, based on perturbative solutions of electron equations of motion, seem to have neglected part of the contributions of the guide field to the overall axial oscillations and the transverse oscillations of the electrons bulk flow through the cavity. On taking these into account, we find that new radiation frequencies appear. From single-particle dynamics or through solutions of Vlasov-Maxwell equations it is found that small axial oscillations of the electron equilibrium distribution give rise to a loss (or gain) at an additional radiation frequency $~2{\omega }_b{\gamma }_0^2$ in addition to that at $2{\omega }_0{\beta }_0{\gamma }_0^2$ reported earlier; ω_bis the Larmor frequency of electron of energy γ₀mc², velocity β₀cis due to the axial magnetic field, and ω₀is the wiggler frequency. Significantly a three times bigger gain (or loss) is noticed at the same frequency $~2{\omega }_b{\gamma }_0^2$ due to the transverse oscillations of the electron equilibrium distribution. These two terms combine to give a net gain (or loss) at the new frequency.

© 1987 Optical Society of America