Statistical properties of cooperative radiation produced by nonisochronous electron-oscillators

We study the influence of shot noise and energy spread on statistical properties of cooperative radiation produced by the ensemble of nonisochronous electron-oscillators. We find how the root-mean-square deviations of radiated peak power and phasing time depend on the number of particles in the absence of energy spread. It has been shown that when the number of electrons N_e ≈ 10⁹-10¹² (characteristic number of electrons in single-pass free electron lasers), the relative root-mean-square deviation of the self-phasing time from its mean is δ_T≈1,1/lnN_e ~ 0,03-0,05. In this case, the fluctuations of the peak radiated power appear to be negligibly small δ_T<10^-4. Under phase pre-modulation of electron-oscillators the behavior of δ_T depending on the number of particles changes. The relative root-mean-square deviation of the self-phasing time δ_T become inversely proportional to √N_e. It is shown that even a low energy spread (~4%) leads to a sufficient suppression of the radiated power. (authors)