  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.
