Gain analysis of a strong-pump FEL operating at the fundamental and high harmonics

An analytical study of a planar wiggler FEL in the cold electron-beam strong-pump regime is presented. Such an FEL can lase at high odd harmonics due to the periodic variation in the longitudinal electron velocity, and can also emit superradiant emission at harmonic frequencies. Based on a parametric interaction approach, we develop an extended gain dispersion equation for a laser operating at the fundamental or high harmonics taking collective effects (Raman regime) into account. The analysis applies also to the case a_w (βγ) ∼ 1, where the customary use of the Taylor expansion of V₂ does not apply. This case is of interest mostly for mildly relativistic FELs, and allows excitation of very high harmonics.