Reduced nonlinear description of Farley-Buneman instability
  In the study on nonlinear wave-wave processes in an ionosphere and a magnetosphere usually the main attention is paid to investigation of plasma turbulence at well developed stage, when the wide spectrum of plasma wave is present. On the other side, it is well known that even if the number of cooperating waves remains small due to a competition of processes of their instability and attenuation, the turbulence appears in the result of their stochastic behavior. The regimes of nonlinear dynamics of low frequency waves excited due to Farley-Buneman instability in weakly ionized and inhomogeneous ionospheric plasma in the presence of electric current perpendicular to ambient magnetic field are considered. The problem is essentially three dimensional and difficult for full numerical simulation, but the strong collisional damping of waves allow to assume that in this case a perturbed state of plasma can be described as finite set of interacting waves, some of which are unstable and other strongly damping. The proposed nonlinear model allow to make full study of nonlinear stabilization, conditions of stochasticity and to consider the different regimes and properties of few mode plasma turbulence. 
A. S. Volokitin, B. Atamaniuk