We revisit the applications of quasi-linear theory as a paradigmatic model
for weak plasma turbulence and the associated bump-on-tail problem. The work,
presented here, is built around the idea that large-amplitude or strongly
shaped beams do not relax through diffusion only and that there exists an
intermediate time scale where the relaxations are convective (ballistic-like).
We cast this novel idea in the rigorous form of a self-consistent nonlinear
dynamical model, which generalizes the classic equations of the quasi-linear
theory to "broad" beams with internal structure. Read More