## 1 Introduction:  
The space industry has now fully opened its doors to electric propulsion (EP) devices [1, 2, 3, 4]. To provide space operators with an accurate map of electric thruster performance and behavior, EP manufacturers must study plasma and beam properties of the sold product. Electrostatic EP devices such as Hall thrusters (HT), gridded ion engines (GIE) and Field Emission Electric Propulsion (FEEP) thrusters, provide thrust by accelerating and ejecting ions at very high speed. To avoid any charge up effect of the device and the satellite during operation the ion beam must be neutralized with the help of an electron gun, also termed cathode [5, 6]. Consequently, the beam of an EP device is composed of ions and electrons during operation. Many techniques exist to analyze EP ion beams [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Beam diagnostics by means of electrostatic probes is of interest in terms of implementation, use, data collection and cost. Probes can provide information about temperature, density, velocity, energy as well as flux and current. This data can lead to the assessment of the thruster performance, its beam divergence angle and current use. The electrostatic probe family is wide. It includes Langmuir probes [19], simple planar and guarded probes [16; 17], retarding potential analyzers (RPA) [7; 20; 21], magnetically filtered Faraday probes [22], E \(\times\) B probes [12; 23] and Faraday cups [15; 24]. A FC is certainly one of the most accurate tools to access ion current in the beam. The functioning principles of a FC are similar to that of planar probes. A negative potential is applied to the diagnostic collector to attract and collect ions and repel electrons. Although planar probes are heavily impacted by sheath expansion and secondary electron emission (SEE), the geometry of a FC is thought to reduce and suppress these disturbances. Faraday cups architecture differs from planar probes as they use a hollow cylinder closed at one end as a collector and an additional electrode, called collimator, placed at the front of the probe. This electrode defines the collection solid angle, which confines the flux going through the collector. Due to the cylindrical shape of the collection surface, plasma sheath effects are negligible which greatly improve the accuracy of ion current measurement. The collimator along with the cavity shape, material properties and dimensions provide extra degrees of freedom enabling recollection of secondary electrons, a phenomenon which tends to artificially increase the ion current. Please note that many studies were conducted to prove the advantages of using a Faraday cup instead of a planar probe design [16; 25; 26] to study the plasma produced by an EP device. However, published work dealing with Faraday cup optimization can only be found for fields [15; 24; 27; 28] where ion energies are three to six orders of magnitude larger (MeV) than expected energies in the electric propulsion filed (eV to keV). More precisely, previous research on an optimum collimator design for a Faraday cup was mostly performed in the field of nuclear physics where the ion energy is in the keV--MeV range [15; 28; 29]. In those cases, the collimator is mainly used to suppress secondary electrons produced by the collector. A negative potential, with a magnitude higher than the collector voltage, is applied to the collimator to repel all secondary electrons back into the cavity therefore avoiding large overestimate of the ion current. Considering the high energy of the ion in nuclear physics, thermal simulations as well as material sputtering yield determination are of great relevance [15; 24]. In the field of EP, collimated Faraday cups are of interest as they give the possibility to shield the collection electrode against SEE and charge-exchange collisions (CEX). CEX collision events correspond to collision between slow neutrals and fast ions. They therefore produce fast neutrals and slow ions. This collision type is very often encountered in the beam of EP devices [30].