Instability mechanisms in storage-ring FEL oscillators

Abstract

The stability of operation for storage-ring FEL oscillators fed by a continuous electron beam is examined. The bunched-beam distribution, at steady state with a large-amplitude carrier signal, is found self-consistently for an arbitrary injected distribution. The dielectric response to small perturbations (sidebands) includes the nonuniformity from aperiodic beam bunching, the anisotropy from the unidirectional interaction with the radiation, and the cross coupling among symmetric upper and lower sidebands caused by the unharmonic (nonlinear) nature of the trapped-particle trajectories. The dominant contribution comes from resonances of the detuning δ = | ωs − ω0| between the sideband and the carrier frequencies, with combinations of the Doppler-upshifted synchrotron (bounce) and round-trip frequencies ωb and Ω respectively, δ; ⋍ 2γ2:(nωb + /Ω). For sideband frequencies corresponding to n ≠ 0, thermal effects are important. The growth rate scales as ωp2 and is proportional to the slope of the distribution across the trapped-particle island. However, the growth of sidebands in direct resonance with the round-trip frequency, δ; ⋍ 2γ2:/Ω, is independent of thermal effects. The growth rate then scales as ωp, and is proportional to the distribution gradients around the trapped-particle island. In effect, the resonance involves a macroparticle rotating with a frequency ωb in harmonic relation with Ω. It. is also shown that in all cases upper and lower sidebands decouple when the sideband growth length becomes much shorter than the synchrotron length.