The source-driven dissipative nonlinear Schrödinger model of resonance absorption

Abstract

A source-driven dissipative nonlinear Schrödinger (NLS) equation is numerically studied, characterized by a nonlinearity parameter and a dissipative length, governing the generation of finite-amplitude, localized electrostatic plasma waves by resonance absorption of light in an inhomogeneous plasma. It is shown that as the nonlinearity parameter is increased a transition to chaos occurs through a quasiperiodic scenario. In the chaotic regime, it is shown from statistical diagnostics that as the dissipation length is increased, the system shifts from a convective regime governed by the competition between pumping and convection of the waves due to the inhomogeneity to a dissipative regime governed by the competition between pumping and a scale-length-dependent absorption mechanism, which approximately models Landau damping. The scaling laws obtained show that the turbulent state can be described in both regimes as a set of NLS solitons, interacting through the pumping and damping mechanisms.For a vanishing density gradient, the system admits a homogeneous limit, which is found to be chaotic and dissipative.