During the Spacelab 1 space shuttle mission, electron beam injection in the ionosphere produced a variety of radio waves. The most unusual kind of spectrum consisted of packets of cyclotron waves occurring at successive harmonics of a frequency F0 close to the upper hybrid ƒuh. A linear treatment of the generation mechanism has been proposed in a companion paper [Mourenas and Béghin, this issue]. It was shown that the emissions consist of the well-known electronic Bernstein modes, which are excited by an interaction between the neutralization return current and the ambient ionospheric plasma. The observed amplitude modulation of the cyclotron emissions around the fundamental wave at F0 = nƒce closest to ƒuh has been explained in the frame of a model which shows that some of the generated waves packets can escort the space-borne receiver. However, the observation of successive harmonic packets around pF0 remained to be interpreted. To this end, a two-dimensional single-wave model of the nonlinear interaction between a finite size ring beam and an infinite homogeneous magnetized plasma is presented. A system of scaled equations is developed and solved analytically for the initial evolution and shows a good agreement with the linear theory. The system is then solved numerically. The solution shows that the single F0 wave considered grows exponentially at the linear growth rate; then the wave potential saturates due to beam electron trapping, producing a power law spectrum of the higher pF0 harmonics of the electric field very similar to what was observed experimentally.