Analysis of optical klystron wave guide free electron laser with betatron oscillation effects

In this paper, we analyze the effect of the betatron oscillation on spontaneous emission and gain spectrum of an optical klystron wave guide free electron laser. The analysis also includes the effects of length mismatch of the two undulator sections of the klystron configuration. We observe that intensity and gain can be change with length mismatch parameter without changing the central emission frequency.