Recent progress on phase-space turbulence and dynamical response in collisionless plasmas

In the presence of wave dissipation, phase-space structures emerge in nonlinear Vlasov dynamics. Their dynamics can lead to a nonlinear continuous shifting of the wave frequency (chirping). This report summarizes my personal contribution to these topics in the fiscal year 2012. The effects of collisions on chirping characteristics were investigated, with a one-dimensional beam-plasma kinetic model. The long-time nonlinear evolution was systematically categorized as damped, steady-state, periodic, chaotic and chirping. The chirping regime was sub-categorized as periodic, chaotic, bursty, and intermittent. Existing analytic theory was extended to account for Krook-like collisions. Relaxation oscillations, associated with chirping bursts, were investigated in the presence of dynamical friction and velocity-diffusion. The period increases with decreasing drag, and weakly increases with decreasing diffusion. A new theory gives a simple relation between the growth of phase-space structures and that of the wave energy. When dissipation is modeled by a linear term in the field equation, simple expressions of a single hole growth rate and of the initial perturbation threshold are in agreement with numerical simulations.
Comment: 8 pages, 11 figures