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

In this work we focus on electromagnetic kinetic turbulence where a broad spectrum of small amplitude waves exists, making weak turbulence theory (with the random phase approximation) an appropriate tool of analysis. Specifically we employ the Vlasov cumulant hierarchy which describes the plasma in terms of a background distribution and the products of its perturbations in different phase-space locations (correlators or cumulants), and apply a multiple-timescale perturbation expansion on its equations. To first order (retention of up to first-order accurate two-body correlators) this theory gives the well-known quasilinear limit which accurately describes the self-consistent evolution of the background distribution and the field spectrum within a short time interval right after the onset of linear instability. The description of the evolution of the particles and the fields for longer times requires retention of at least second-order accurate two-body correlations (wave-wave and nonlinear wave-particle interactions) and second-order accurate three-body correlators (wave-particle-wave interactions). We explore this longer-time evolution and find that, in addition to the classical diffusion of the quasilinear limit, KdV-type (third-order) diffusion appears when these additional processes are considered.