The resonant interaction of a narrow electron beam spiraling in a cold homogeneous magnetized plasma with electromagnetic cylindrical waves is considered. The conclusions derived in recent papers about the formation, in the presence of effective electromagnetic energy dissipation out of the radially bounded beam, of dynamically stable and longtime living bunches of resonant electrons in the developed stage of their nonlinear interaction with the waves are discussed in this paper for more general physical cases and for wider ranges of characteristic parameters. General analytical formulas for the excited electromagnetic fields, the radiated electromagnetic power flux and the linear growth rate as well as relevant numerical simulations results are presented.