Electric propulsion optimizes propellant mass and meets new propulsion device demands. These devices adjust satellite orbits and enable long missions. Among various thrusters, electrostatic ones have well-defined physics, simplifying operational parameter optimization. This study developed a global model for an Inductively Coupled Plasma (ICP) cylindrical ion thruster with an output polarized grid system. Argon propellant is injected into the chamber, and ICP plasma is generated by a radiofrequency current. Neutral and excited species are accelerated out by diffusion, while ionized species are accelerated via the polarized grids' electric field. The polarized grid system was optimized for better plasma sheath use. The model considers single and multi-step ionization, the Electron Energy Distribution Function (EEDF), neutral gas, and electron power balance equations. Excited species influence ionization energy, but not ionic density. However, the ion substitution rate increases, essential for thrust and specific impulse. The model determines the neutral gas temperature by considering the power balance and interactions with other species.