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The beam-plasma instability can be addressed as a reduced model in severalcontexts of plasma physics, from space to fusion plasma. In this paper, wereview and refine some non-linear features of this model. Specifically, byanalyzing the dependence of the non-linear velocity spread as a function of thelinear growth rate, we discuss the effective size of the resonance in view ofits role in the spectral overlap at saturation. The relevance of thischaracterization relies on the necessity of a quantitative determination of theoverlap degree to discriminate among different transport regimes of the selfconsistent dynamics. The analysis is enriched with a study of the phase-spacedynamics by means of the Lagrangian Coherent Structure technique, in order todefine the transport barriers of the system describing the relevant features ofthe overlap process. Finally, we discuss relevant features related to the modesaturation levels.

Resonance overlap and non-linear features of the beam-plasma system