Mode-locked super-radiant free-electron laser oscillator

Evolution of the time domain fields and the spectral power of super-radiant radiation in a free-electron laser oscillator (e-beam pulses shorter than a wavelength) are investigated. We consider a finite train of N short bunches of electrons propagating through the undulator. The coherence of the synchrotron radiation emitted from the bunched beam grows with the number N of the e-beam pulses entering the interaction region. When N grows to infinity, the radiation becomes perfectly coherent at all harmonic frequencies of the pulse injection (bunching) frequency. he super-radiant emission takes place inside a resonator, the coherence of the emitted radiation is enhanced. Under the condition of mode-locking, the fields add in phase and the spectral energy distribution becomes narrow. When the finesse F of the resonator is small F < N, the spectral width of the out-coupled radiation emitted from the resonator is limited by N, and in the opposite case F >N, it will be limited by F. If the number of pulses N grows to infinity, the out-coupled radiation reaches a steady state of perfect coherence with reduced harmonic contents (determined by the Finesse of the resonator). There is no threshold for emission of this kind of coherent radiation.