A generator of turbulent electron beams in an independent mode and in the mode of amplification of an external single-frequency signal is experimentally investigated. The formation of higher harmonic components in the spectrum of output radiation of the generator is shown experimentally. The phenomenological model of the turbulent electron flow is constructed on the basis of a chain of interacting “electron vortices” described by the modified nonlinear Van-der-Pol differential equations. The modes of independent dynamics and the mode of amplification of an external harmonic signal are considered. The results of numerical modeling and experimental investigations are compared. The qualitative correspondence of the behavior of the dependences obtained from the experimental investigation of the generator of turbulent electron beams and the results obtained from numerical modeling is shown.