In this paper, we study transport features of a one-dimensional beam-plasmasystem in the presence of multiple resonances. As a model description of thegeneral problem of a warm energetic particle beam, we assume $n$ coldsupra-thermal beams and investigate the self-consistent evolution in thepresence of the complete spectrum of nearly degenerate Langmuir modes. Aqualitative transport estimation is obtained by computing the LagrangianCoherent Structures of the system on given temporal scales. This leads to thesplitting of the phase space into regions where the local transport processesare relatively faster. The general theoretical framework is applied to the caseof the nonlinear dynamics of two cold beams, for which numerical simulationresults are illustrated and analyzed.
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