Saturation behaviour of a waveguide optical klystron in the presence of electron energy spread

A waveguide optical klystron configuration has recently been suggested to enhance the small signal gain of compact waveguide free electron lasers (FELs) driven by low current electron beams. Based on an analytical formulation, it has been demonstrated that the small signal gain of waveguide free electron lasers can be increased significantly when incorporated into the waveguide optical klystron configuration. However, this enhanced small signal gain may be realised at the expense of achievable saturation power when the device is operated as an oscillator. In this study, a computer package was developed to investigate numerically saturation behaviours of waveguide optical klystrons taking into account the energy spread effects. It is shown that when the small signal gain of a waveguide FEL is only marginally greater than the round-trip loss of the radiation power, the waveguide optical klystron arrangement can provide not only a much larger small signal gain but also a greater saturation power.