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

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