Self-consistent gain in the optical-klystron free-electron laser

The gain of the klystron free-electron laser is calculated with use of the coupled, self-consistent Lorentz-Maxwell equations. For high gain, the objective of the klystron configuration, the gain spectrum is found to be modified from the previously known low-gain result. This is caused by the shifting of the optical phase during the gain process. The klystron saturation in strong nonlinear optical fields is also discussed.