The limitation of the Quasilinear Theory (QLT) to describe the diffusion of electrons and ions in velocity space when interacting with a spectrum of large amplitude electrostatic Langmuir, Upper and Lower hybrid waves, is analyzed. We analytically and numerically estimate the threshold for the amplitude of the waves above which the QLT breaks down, using a test particle code. The evolution of the velocity distribution, the velocity-space diffusion coefficients, the driven current, and the

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... g of the particles are investigated, for the interaction with small and large amplitude electrostatic waves, i.e. in both regimes, there where QLT is valid and there where it clearly breaks down.