Gain and startup conditions for the BNL visible FEL oscillator experiment

The Visible FEL oscillator experiment at BNL is designed to lase at 530 nm using the 50 MeV high-brightness ATF electron beam and a micro-undulator of 8.8 mm period. The relatively low energy and short wavelength of this FEL require a high-quality electron beam. In this paper, we study the necessary electron beam requirements via a one-dimensional first-order simulation method. This method takes into account the finite length of the micropulse and the bandwidth of the spontaneous emission. It assumes a long electron pulse, weak optical fields, and low gain. For our experiment, startup time is of particular concern because of the limited length of the macropulse. The simulation method is extended to include the effects of emittance and energy spread. The expected gain and startup conditions for different beam parameters are compared with measured parameters. Scaling of gain versus beam parameters is examined and an experiment is proposed to verify these results.