Statistical fluctuations in cooperative cyclotron radiation

Abstract

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 Ne 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 δT changes from a logarithmic dependence on Ne (δT∼1∕lnNe) to square-root (δT∼1∕Ne).A slight energy spread (∼4%) results in a twofold drop of the maximum attainable power of cooperative cyclotron radiation.