Spectral width limits in “single mode” free electron lasers

Abstract

Sideband excitation near the carrier determines the minimum spectral width for steady-state FEL oscillators fed by continuous electron beams. A sideband separated by δω from the carrier resonates with harmonics of the upshifted bounce frequency for trapped particles, δω = n2γ z 2Ω . The nonlinear shift of the carrier phase velocity causes symmetric upper and lower sideband frequencies to decouple, accounting for the observed asymmetry in sideband spectra We focus on sidebands excited in the immediate vicinity of the carrier δω → 0, in resonance with particles trapped near the separatrix Ω → 0. For electrons distributed uniformly around their orbits the growth tends to zero as δω, Ω → 0, despite the infinite number of contributing harmonics. However, the distributions produced by injected electron beams are non-uniform around the trapped orbits, yielding finite growth rates. It is proved that if the carrier is stable to amplitude perturbations, then sidebands in the immediate vicinity Δω ω < 1 2N w are suppressed. This criterion does not apply to sidebands “far” from the carrier δω ∼ 2γ z 2Ω 0.