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, it is possible to change effective detuning during the FEL oscillation, In our numerical simulation, we have scanned δL from gain-maximizing value to saturation power-maximizing value, and have observed that both quick saturation and large saturation power can be obtained simultaneously. The power spectrum of the DCD system follows the saturation characteristics of the final desynchronism stage, so it was much broader compared with that of large detuning.
Finally, we suggested the feedback control of cavity detuning for the short-pulse free-electron laser system to achieve very high power,very short pulse length, relatively good spectrum, and very stable operation. Using feedback control, we have found the steady-state near the zero cavity detuning regime, and it doesn‘t depend on the initial condition the system has started.
Though the feedback control scheme gives very nice output profile of short-pulse free-electron laser system, it has a few difficulties in experimental realization. As an alternative, we tried the given cavity detuning profile, which is fitted from the feedback controlled cavity detuning profile. The results are fair, though not satisfactory, and has an advantage of good feasibility. We guess that the suggested detuning profile would be one of the best DCD profile without feedback, and can be applied to short-pulse FEL oscillator system to enhance the performance.
짧은 전자빔 펄스를 사용하는 자유전자레이저 오실레이터 시스템을 일차원 컴퓨터 시뮬레이션 코드를 사용하여 모사실험하고 공진기 디튜닝 효과를 조사하였다. 우선 전빔의 번칭 위상을 정의하고 이를 사용하여 전자빔의 동적 특성을 살펴보았다. Stable한 발진 영역에서 광펄스의 위상이 전자빔의 폰데로모티브 위상 (ponderomotive phase)을 뒤쪽 끝에서 π/2로 되도록 급격히 변화하는 것을 확인하였다. 이것은 이들 시스템에서 보여지는 초복사 현상을 단진자 모형에서도 설명할 수 있음을 보여준다. 돌이 떨기(limit cycle oscillation) 영역에서는 전자가 퍼텐셜 우물에서 디트랩되는(detrapping) 현상에 의해 전자빔 번치가 찢어지고 다시 합쳐지는 현상이 관찰되었는데, 이 현상이 끝돌이 떨기 현상의 주요 원인으로 보인다. 전자빔 전류를 매우 작게 하면 공진기 디튜닝 값이 작은 영역에서 발진될 경우, 포화상태에 이르기 전에 일시적인 출력의 상승(bump)이 생긴다. 이 값은 포화상태의 출력보다도 더 강한데, 이는 전자빔과 광펄스의 매칭 조건이 발진중에 바뀌기 때문임을 확인하였다.
전자빔 펄스의 반복률에 시간적 난조(timing jitter)가 오실레이터 시스템에 미치는 영향에 대해서 조사하였다. 시간적 난조의 크기에 따라서 자유전자 레이저는 발진이 안 되거나, 난조의 모양에 따라 변조되기도 하는데, 이 효과는 보다 큰 공진기 디튜닝 값을 사용함으로써 억제할 수 있다는 사실이 확인되었다. 또한 FOM에서 구현한 동적 공진기 디튜닝 실험을 컴퓨터로 재현하고, 개선점을 찾았다. 마지막으로 되먹임을 사용한 공진기 디튜닝값의 조절을 제안하고, 이를 컴퓨터를 사용하여 수치적으로 구현하였다.
