Coherent structures in the plasma wave–particle interaction

A study of phase space coherent structures in the plasma wave–particle interaction is presented. The study is based on a reduced single wave model (SWM) of the Vlasov–Poisson system. The reduced model describes the weakly nonlinear dynamics of generic electrostatic instabilities and incorporates the self-consistent wave–particle interaction through a mean field that couples the resonant particles to the amplitude of a single wave potential. Following a brief review of the SWM, we show numerical evidence of trapped and untrapped hole–clump dipole states for both symmetric and weakly asymmetric initial conditions. The rotation (in the trapped case) and translation (in the untrapped case) of the dipole manifest as periodic (in the case of symmetric states) and quasi-periodic (in the case of asymmetric states) time dependences of the potential that gives rise to self-consistent chaos. The role of chaotic mixing and hyperbolic–elliptic bifurcations in the relaxation of initial conditions far from equilibrium is also discussed.