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Multiscale Splitting method for Boltzmann-Poisson Equation: Application for Dynamic of Electrons

In this paper we present a model based on dynamics of the electrons in the plasma using a simplified Boltzmann equation coupled with a Poisson equation. The motivation arose to simulate active plasma resonance spectroscopy which is used for plasma diagnostic techniques, see [Braith2009]. We are interested on designing splitting methods to the model problem. First we reduce to a simplified transport equation and start to analyze the abstract Cauchy problem based on semi-groups. Second we extent to the coupled transport and kinetic model and apply the splitting ideas. The results are discussed with first numerical experiments to give discuss the numerical methods.