Ponderomotive phase evolution in short-pulse FEL oscillators operating in the limit-cycle region

We have investigated the limit-cycle region of a short-pulse free electron laser (FEL) oscillator system. Using properly defined collective phase vari ables, we describe the electron dynamics and the phase evolution of the opt ical field in the limit-cycle region. In this research, we have observed th at electrons can be detrapped from the ponderomotive bucket due to the spat ial variation of the optical field, and we concluded that the limit-cycle o scillation of the short-pulse FEL oscillator system is a consequence of the electron detrapping.