[en] A 2D, hybrid (particle-ion, fluid-electron) simulation code characterized by the solution of the non-linear modified Poisson equation, which results assuming the Boltzmann distribution for the electrons, is presented. The field solution is achieved through an iterative procedure. Anyhow a new scheme is considered. The potential is not obtained by directly solving the finite difference equation but via the Green's function method. The procedure begins with the first guess for the potential. This is found through the solution of the linearized modified Poisson equation. The Green's function for this equation, in the 2D case which is considered, can be found analytically in terms of the Newmann functions. Once the potential corresponding to the linearized modified Poisson equation is known, the first approximation of the electron (Boltzmann) distribution can be calculated. This distribution, plus the one given by the (particle) ions, is considered as the source term for the Poisson equation (which now is not modified since the fluid electron component is taken into account in the source term itself). The solution of this Poisson equation gives the second approximation of the electric potential and is still obtained via the Green's function method (as it comes from the Coulomb law, modified for the 2D case). Each time step this procedure can be iterated according to the desired accuracy. The last iteration cycle is different: in fact the direct solution for the electric field can be obtained, without numerical differencing from the potential. It is sufficient in this case to consider the electric field Green's functions (x- and y-component) for the Poisson equation (in place of the electric potential Green's function). The first results obtained with this new code are here presented and compared with previous simulation runs based on a linearized Boltzmann distribution model. 3 refs