we have studied the startup and saturation characteristics of short-pulse free-electron laser oscillator system. First, we defined bunching phase $Θ_B$ and $ψ_B$ to describe collective behavior of electron motion. We have found that in stable operation, the optical field ``locks`` the phase to $π/2$ at the trailing edge, which gives the maximum gain. In short-pulse FEL oscillator system, even though the amplitude of the optical field doesn````t change much during the pass because of the low gain, electrons can experience large alteration of the field amplitude and phase due to the spatial variation of the optical field, which result in electron detrapping. This electron detrapping should not be ignored in limit cycle oscillation regime, where the bunches are torn apart and remerged with adjacent bunches.
It is known that the system goes chaotic when the cavity detuning is very small. If the current of electron beam is sufficiently small, but not too small to overcome loss of the resonator, we can operate the system stably even at the near cavity synchronism regime. In this case, electron dynamics exhibit quite chaotic motion, while the averaged output power and optical pulse shape is quite stable because the electron motion doesn‘t affect much to the optical field due to the low current. The output power in this operation is low too, because of the low gain, and there````s a transient bump in output power, which occurs, at small cavity detuning, due to the change of the matching condition during the amplification.
We studied the timing jitter effect in a short-pulse FEL oscillator system. It is shown that, at small cavity detuning regime, the timing jitter prevents the system from amplifying, or modulate the output with its profile. At large cavity detuning, the jitter effect is suppressed if the jitter amplitude is not large, and can be ignored.
We also reproduced DCD experiment via one dimensional Maxwell-Lorentz coupled particle simulation. By DCD technic...