Limits of applicability of the quasilinear approximation to the   electrostatic wave-plasma interaction
  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 heating 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. 
Georgios Zacharegkas, Heinz Isliker, Loukas Vlahos
physics.plasm-ph astro-ph.SR