Electric propulsion has proven to be the best solution to reduce propellant mass, meeting new demands for new propulsion devices for corrections and adjustments in the orbits of space systems composed of satellite constellations in specific arrangements, in addition to allowing long mission times. Among the different types of thrusters, electrostatic thrusters have a well-defined physics, enabling computational models for the study and optimization of their operating parameters. This work developed a global model for an inductively coupled cylindrical ion thruster (ICP) with an output polarized grid system. Argon propellant is injected into the impeller chamber at a fixed gas flow, and an ICP plasma is generated by circulating a radiofrequency current in an inductive coil around the thruster. The neutral and excited species are accelerated out of the propellant by diffusion, while ionized species are accelerated due to the electric field generated by the pair of direct current polarized grids. The polarized grid system was optimized for better use of the plasma sheath governed by Child-Langmuir Law in the acceleration of ionized species. The global model is based on particle balance equations, considering the effect of single and multi-step ionization, as well as the effect of the electron energy distribution function (EEDF), neutral gas and electrons power balance equations. Finding that excited species directly influences ionization energy, however, it does not interfere much in ionic density, there is a relevant increase in the ion substitution rate, which is extremely important to gain thrust and specific impulse. By considering the neutral gas potency balance and its interactions with other species, the model determines the neutral gas temperature in the evaluation.