Nonlinear Landau damping in nonextensive statistics

Abstract

The evolution of electrostatic waves, in unmagnetized collisionless plasmas, is numerically investigated by using a semi-Lagrangian Vlasov-Poisson code, in the fully nonlinear regime and in the context of the nonextensive statistics proposed by Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)]. The effect of the Landau damping saturation, due to the nonlinear wave-particle interaction, is analyzed as a function of different values of the nonextensive parameter q, which quantifies the degree of nonextensivity of the system. A preliminary linear study is performed in order to compare the analytical results for the frequency and the damping rate of the electric oscillations, with the quantities obtained from the numerical simulations. In the nonlinear regime, the time evolution of the electric field amplitude shows how the non-Maxwellian shape of the equilibrium distribution function drastically modifies the energy exchange between wave and resonant particles and determines the saturation level of the electric field amplitude, in the long-time oscillating regime. A broad spectrum for the electrostatic oscillations is obtained in the case of the initial distribution functions with q<1, while in the case q>1 just a monochromatic component is visible.