  A three species one-dimensional kinetic model is presented for a spatially
homogeneous weakly ionized plasma subjected to the action of a time varying
electric field. Planar geometry is assumed, which means that the plasma
dynamics evolves in the privileged direction of the field. The energy
transmitted to the charges is be channelized to the neutrals thanks to
collisions and impacting the plasma dynamics. Charge-charge interactions have
been designed as a one dimensional collision term equivalent to the Landau
operator used for fully ionized plasmas. Charge-neutral collisions are modelled
by a conservative drift diffusion operator in the Doughertys form. The
resulting set of coupled drift diffusion equations is solved with the stable
and robust Propagator Integral Method. This method feasibility accounts for
non-linear effects without appealing to linearisation or simplifications,
providing conservative physically meaningful solutions. It is found that charge
neutral collisions exert a significant effect since a quite different plasma
dynamics arises if compared to the collisionless limit. In addition,
substantial differences in the system evolution are found for constant and
temperature dependent collision frequencies cases.
