Effects of resonant wave-particle interactions in weakly turbulent plasmas

This paper gives a rewiew of new progress in the theory of weak turbulence in plasmas, in the case of a turbulence generated by resonant wave-particle interactions; that is on one hand the theories which make use of renormalized propagators and on the other hand the phase-space granulation theory. We work out a diagrammatic method which makes it possible to derive in a systematic way each one of these approaches and to make the connection between them. We show that the resonance broadening theories do not improve signicantly the results obtained from conventional expansions. On the contrary, we establish that phase-space granulation leads to question the weak turbulence assumptions: under definite conditions, clumps emit coherently an additional induced electric field which modifies the statistical properties of the field