Theoretical study on wavelength stabilization feedback in a free-electron laser

One-dimensional, time-dependent code for free-electron laser oscillator has been improved to include wavelength stabilization feedback, and the change of interval between the electron pulses caused by the variation of the electron beam energy has been considered. The modulation phenomenon of the FEL power caused by the wavelength stabilization feedback loop, which has been observed in FEL experiments, has been confirmed. The modulation frequencies and depths are in good agreement with experiments. This type of limit-cycle-like oscillation is analyzed and found to be caused by the frequency creep which stems mainly from the superradiance. The synchrotron oscillations of the electrons in potential are also found to play important roles. The stability and the requirement for bandwidth of the wavelength stabilization feedback loop are investigated. Although the stochastic fluctuation of the FEL wavelength could be removed by a wavelength stabilization feedback loop with a bandwidth enough high, the variation of the wavelength produced by the nonlinear FEL interactions is very difficult to be reduced because the required bandwidth is too high. The feasibility of stabilizing the wavelength with a feedback loop in a high power FEL needs further investigations. (author)