EHD thrusters are highly-efficient, low-thrust, high-specific-impulse and electrically powered spacecraft propulsion systems and thus the capabilities of payload transport for near-earth and deep-space missions are significantly increased . In this type of propulsion system, a set of energized electrodes are strategically placed in order to ionize and accelerate a gas, creating thrust for the thruster. In this work, we present an axisymmetric two-dimensional model of a DC-discharge plasma apparatus using the simulation program COMSOL Multiphysics® to compute the solution of the non-linear set of differential equations. The discharge is due to ionization initiated from the applied electric field between the cathode and the anode and the loss rates in volume (detachment ions, recombination and others) and surface recombination of nitrogen atoms in a pure nitrogen at low pressure (0.5 Torr)[2-4]. The heavy species taken into account are the following: N2, N2+, N, N+ and N4+[5-7].