We use a Hamiltonian formalism to analyse the self-consistent wave–particle dynamical interaction involving magnetized electrons and ordinarily polarized electromagnetic waves. Considering first-harmonic cyclotron resonances, we show that there is a critical value of the electronic average density. For systems with lower than critical densities the saturation process is dictated by relativistic detuning effects, and wave dynamics may be disregarded. However, for systems with larger densities, saturation is governed by the available electromagnetic free energy, and the wave dynamics turns out to be essential.