The nonlinear evolution of initially monoenergetic (v(t=0)=(0,0,u)) electron beam propagating in a nonmagnetized dielectric medium of permittivity in >1, with initial velocity u>or=c/ square root in (where c is the vacuum speed of light) is investigated. The specific instability of the beam under such conditions is the cause of the generation of a broad spectrum of transverse electromagnetic waves coupled to the simultaneous excitation of the second harmonic of the beam's oscillations, both at the expense of the beam's initial kinetic energy. The system of self-consistent nonlinear equations, describing the particle-field dynamics, is treated in the spirit of the weak-turbulence approach. The integrals of the resulting nonlinear system of equations for the amplitudes of the fields of the electron density are used to evaluate the spectral distribution of the amplitudes in the saturation phase, and hence the efficiency of the transformation of the beam's energy into electromagnetic radiation as a function of the width of the spectrum of the initially present electromagnetic fluctuations. A substantial increase in this efficiency is observed in comparison with the single-mode case.