Statistical fluctuations in cooperative cyclotron radiation

Shot noise is the cause of statistical fluctuations in cooperative cyclotron radiation generated by an ensemble of electrons oscillating in magnetic field. Autophasing time – the time required for the cooperative cyclotron radiation power to peak – is the critical parameter characterizing the dynamics of electron-oscillators interacting via the radiation field. It is shown that premodulation of charged particles leads to a considerable narrowing of the autophasing time distribution function for which the analytic expression is obtained. 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 ${\delta }_T$ changes from a logarithmic dependence on $N_e$ (${\delta }_T\sim 1∕ln{N}_e$) to square-root (${\delta }_T\sim 1∕\sqrt{N_e}$). A slight energy spread ($\sim$4%) results in a twofold drop of the maximum attainable power of cooperative cyclotron radiation.