Statistical fluctuations of cooperative radiation produced by nonisochronous electrons-oscillators

TL;DR

This paper investigates the statistical fluctuations in cooperative radiation from nonisochronous electrons-oscillators, highlighting how shot noise affects autophasing time and how premodulation can improve coherence in single-pass cyclotron-resonance masers.

Contribution

It introduces a detailed analysis of shot noise effects on autophasing time fluctuations and demonstrates how premodulation reduces these fluctuations, enhancing coherent summation in CRMs.

Findings

Premodulation narrows autophasing time distribution.

Relative RMSD of autophasing time scales as 1/ln N_e or 1/√N_e depending on premodulation.

Energy spread reduces maximum power of cooperative radiation.

Abstract

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 $\delta_T$ changes from a logarithmic dependence on $N_e$ ($\delta_T\sim1/\ln N_e$) to square-root ($\delta_T\sim1/\sqrt{N_e}$). 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.