In the last 30 years, numerical models have been developed to properly analyze Hall eect thrusters (HET),leading to a bridge between analytical prediction/empirical intuition and experiments. For companies in thespace sector, these codes serve to much more than simply simulating the thruster, but it provides a fast, cheapand reliable tool for processes such as validation and verication procedures, as well as for technical developmentof the thruster. During the testing of the thruster, mostly measurements upstream from the thruster exhaustare obtained since the high density plasma inside the channel disturbs any measurement inside the channel. Thisresults in the company knowing about the output of the thruster performance, but having little knowledge aboutthe processes and behavior of the thruster itself. The purpose of this study is to help reduce the uncertainty,using existing software to eectively analyze and understand HETs. Because of the physical nature of theproblem, HET simulations follow a multi-scale approach where the thruster is divided into two regions: insidechannel/near-plume region and far-plume region. To study each zone dierent softwares are typically used.This thesis aims to nd a common ground between both software, coupling them and creating a line of analysisto follow when studying HETs.The present thesis will focus on the analysis of the famous SPT-100. The design of this work can be divided intotwo: an hybrid-PIC simulation with a software focusing on the inside channel and near-plume region, Hallis; andanother hybrid-PIC simulation regarding the plasma plume expansion performed with SPIS-EP. During thisproject both software were mastered. Hallis is investigated, emphasizing the empirical modelling of the electronanomalous transport inside the thruster and its consequences on the output results. A sensitivity analysis isperformed to obtain a good set of the empirical parameters that drive the overall performance of the thrusterand the plasma behavior. Once a good match persist between Hallis and nominal operating conditions, theoutput is used to construct the input injection distributions needed by the plasma expansion software (SPIS).Finally, the plasma plume is simulated and results are compared to in-house experimental data. In this way,one is able to control and understand the nal output directly from the behavior of the thruster. It is importantto mention that due to condentiality reasons, the testing data cannot be fully shown and sometimes only thetrend can be analyzed.As a results of the analysis, it is found that establishing the coupling between softwares is feasible, but Halliscode needs to include some characteristics to fully take advantage of its potential. It is determined that theion denition followed by Hallis is enough to perfectly dene the ion energy distribution as well as generalperformance parameters of the SPT-100 (thrust, ionization eciency, power...), but the poor electron modelgenerates some deviation in the results. SPIS simulations and comparison with testing data suggest that Hallisoutput is not enough to properly match the experimental measurements, especially regarding the ion angledistribution function. According to Hallis, such distribution is too narrow compared to the observed plasmaplume. This problem is found to be caused by the small simulation domain of Hallis. Hence, although couplingof the software is easy, more functionalities of Hallis would allow for a better study and more accurate results.