Geodesic
Modeling of Farley-Buneman instability using four-dimensional kinetic equation
Matematičeskoe modelirovanie, Tome 20 (2008) no. 12, pp. 89-104.

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Numerical modeling of the Farley-Buneman instability in the E-region of the Earth's ionosphere is performed with the help of numerical methods. The mathematical model of instability consists of two-dimensional fluid electron equation, two-dimensional Poisson equation and four-dimensional kinetic ion equation. This model takes into account all major features crucial for development and nonlinear saturation of the instability. The developed algorithm allows to perform modeling with a wide range of physical parameters corresponding to the Earth's ionosphere conditions. Previous studies of Farley-Buneman instability were based on particle-in-cell methods, which produce substantial numerical noise comparable to ion and electron density fluctuations. The use of numerical methods allows to avoid numerical noises and so to perform simulations with the driving electric field which is close to its linear threshold. Results of numerical computations show qualitative agreement with previous simulations. The following major effects of instability which are also presented in experimental data were observed: nonlinear saturation, increase of wavelength in the quasi-steady saturation state, and deviation of dominating wave vector from the direction of the electron drift velocity. The developed simulator is optimized for runs on multiprocessor computers. It can be used for explanations of some Earth's ionosphere phenomena. 
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     title = {Modeling of {Farley-Buneman} instability using four-dimensional kinetic equation},
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D. V. Kovalev. Modeling of Farley-Buneman instability using four-dimensional kinetic equation. Matematičeskoe modelirovanie, Tome 20 (2008) no. 12, pp. 89-104. http://geodesic.mathdoc.fr/item/MM_2008_20_12_a6/

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