The multi-wave interaction of a thin-walled tubular rectilinear electron beam with delayed electromagnetic waves of a cylindrical electrodynamic system with plasma filling is considered. General nonlinear equations of the multi-wave regime of Cherenkov beam instability are obtained. For the case of the collective forced Cherenkov effect, multi-wave equations with cubic nonlinearity are obtained. The nonlinear dynamics of the spectrum of waves excited by a beam in a plasma waveguide is investigated. It is shown that there is a broadening of the instability spectrum in the regime of the collective forced Cherenkov effect because of the mechanism of collective nonlinear deceleration of the electron beam during its interaction with many modes of delayed electromagnetic waves.
Ershov et al. (Wed,) studied this question.