The processes governing the resonant interaction of lower hybrid waves with a radially bounded electron beam spiraling in a magnetized plasma are investigated for various physical parameters and beam-waves resonance conditions. It is shown that the nonlinear behavior of the beam-waves system strongly depends on three main parameters, that is, the growth rates of the waves' instabilities in the presence of the spiraling beam, the waves' amplitude maxima achieved at the stage of the first trapping process as well as the frequency and the intensity of the initial beam current modulation. The dependence of these factors on the system's nonlinear evolution is examined in detail with the help of numerical simulations. Results obtained when studying the interaction of the spiral beam with two waves indicate that the control of the initial stage of the system's evolution should be of great importance when one considers the interaction of the beam with several waves. Moreover, it is found that the waves' instability growth rates as well as the radial flux of beam energy nonmonotonically depend on the beam injection pitch angle. In actual space experiments involving electron beam injection by a gun located on a rotating satellite, one should expect that the beam emission, even for a fixed pitch angle, will reveal a nonmonotonic behavior with fields' amplitude maxima and minima depending on the time of registration.