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Statistical fluctuations of cooperative radiation produced by nonisochronous electrons-oscillators

Shot noise, intrinsic to the ensemble of nonisochronous electrons-oscillators, is the cause of statistical fluctuations in cooperative radiation generated by single-pass cyclotron-resonance masers (CRMs). Autophasing time --- the time required for the cooperative radiation power to peak --- is the critical parameter characterizing the dynamics of electrons-oscillators interacting via the radiation field. Shot-noise related fluctuations of the autophasing time imposes appreciable limitations on the possibility of coherent summation of electromagnetic oscillations from several single-pass CRMs. Premodulation of charged particles leads to a considerable narrowing of the autophasing time distribution function. When the number of particles $N_e$ exceeds a certain value that depends on the degree to which the particles have been premodulated, the relative root-mean-square deviation (RMSD) of the autophasing time $δ_T$ changes from a logarithmic dependence on $N_e$ ($δ_T\sim1/\ln N_e$) to square-root ($δ_T\sim1/\sqrt{N_e}$). As a result, there is an increased probability of coherent summation of electromagnetic oscillations from several single-pass generators. A slight energy spread ~($\sim$4\%) results in a twofold drop of the maximum attainable power of cooperative radiation.