Transient regime and superradiance in a short-pulse free-electron-laser oscillator

We investigate the transient evolution of radiation in a low-gain free-electron-laser oscillator, driven by synchronized electron bunches much shorter than the slippage. We calculate analytically the radiation intensity and the gain in the linear regime. We show that, in the nonlinear regime and in the ideal case without losses, the radiation field is described, as in the short-pulse, high-gain amplifier, by the self-similar superradiant solution.