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Instability of the Ionospheric Plasma: Modeling and Analysis

This paper is concerned with the theory and modeling of plasma instabilities in the ionosphere. We first consider the so-called striation model, which consists of balance equations for the density and momenta of the plasma species, coupled with an elliptic equation for the potential. The linearized instability of this model is analyzed in the framework of Fourier theory, both for smooth and discontinuous steady states. Then, we show that the dissipation mechanisms at work in the more refined "dynamo model" allow us to stabilize high wave-number perturbations. We also analyze turbulence as a possible source of additional dissipation (in a similar way as in fluid mechanics). To this aim, we use the statistical approach to turbulence and derive a so-called turbulent striation model, of which we analyze the stability properties. Numerical experiments are used to support our investigations.