A Quasi-Particle Approach to Modulational Instabilities in Wave-Plasma Interactions

Abstract

The interaction of broadband turbulence with monochromatic plasma waves has been studied. A kinetic equation for quasi-particles is used to describe the turbulence. Beam instabilities occur in this interaction when the group velocity of the shortwavelength wave packets, or quasi-particles, is nearly equal to the phase velocity of the long-wavelength monochromatic wave. Depending on the bandwidth of the turbulence, either a kinetic resonant instability, e.g. quasi-particle Landau damping, or a hydrodynamic instability, e.g. a modulational instability, will develop. This establishes a direct link between short- and long-wavelength perturbations of the medium. In this paper, the interaction between broadband drift mode turbulence and nearly monochromatic zonal flows has been studied numerically. Simulations have been conducted in which a particle-in-cell representation is used for the quasi-particles, while a fluid model is employed for the plasma. The interactions have been studied in both a tokamak-like configuration and a pseudo-shockwave configuration. Simulation results show the development of a zonal flow through the modulational instability of the drift wave distribution, as well as the existence of solitary zonal flow structures drifting towards steeper relative density gradients. The coupling between short- and long-wavelength modes found here is distinct from the usual picture of direct and inverse energy cascades, and it can be used as a new paradigm for the fluid and plasma turbulence theories.