Electric propulsion, particularly electrostatic propulsion, is becoming increasingly important in space exploration due to its high specific impulse and low propellant consumption, which are critical factors for long lasting missions. However, testing such propulsion systems presents significant challenges, as they require specialized environmental conditions and dedicated testing facilities. This thesis, under the supervision of Thales Alenia Space, provides a comprehen- sive analysis of ion thruster physics, the key technical challenges associated with this technology and of all the modeling theory behind the various kinds of simulations that could be conducted on ion thrusters. A particular focus is given to the study and simulation of electromagnetic emissions and compatibility issues, which are crucial to ensure reliable operation in space.