Authors: Garyfallia Strus (University of Colorado Boulder), Steven Cranmer (University of Colorado Boulder)

One of the main features of the solar wind is its nonlinear character which maintains this plasma in a collisionless turbulent state from MHD to kinetic scales. In this work we focus on electromagnetic kinetic turbulence where a broad spectrum of small amplitude waves exists. At these scales the plasma can be studied within the framework of weak turbulence theory under the random phase approximation. The first order theory in this regard gives the well-known quasilinear limit which accurately describes the self-consistent evolution of the zeroth order particle distribution and the field spectrum within a short time interval right after the onset of linear instability. Within the context of the Vlasov cumulant hierarchy this limit corresponds to retention of two-body correlations, i.e. wave-particle interactions. The description of the self-consistent evolution of the particles and the fields for even longer times requires the retention of three-body correlations, i.e. wave-wave and wave-particle-wave interactions. To investigate this evolution we carry out a multiple-scale perturbation expansion on the set of equations that comprise the electromagnetic Vlasov cumulant hierarchy with closure achieved by neglecting fourth and higher order cumulants. Such an analysis ensures the convergence of the expansion by correctly treating secular terms. The result is a coupled set of evolution equations for the zeroth order particle distribution on a number of different timescales, accompanied by equations for the evolution of the field. We intend to explore the nature of the additional terms that appear as compared to the quasilinear limit and avenues for the modeling of these coupled equations for plasma environments appropriate to the solar corona and solar wind.