## 3 Faraday Cup
### Perturbations  
Introducing an object inside the main beam of an EP device disturbs the plasma. Therefore, one must minimize the exposed surface and reduce the size of the probe as much as possible. Figure 6 shows the three physical mechanisms which depend on material properties during ion or electron bombardment: reflection, sputtering and secondary electron emission (SEE). In this study, ion reflection events are considered minimal due to the length of the cup and the properties of the collector foam at the cup rear side. Indeed, the pores of the foam material should increase the probability to trap ions. If not, the reflected ion would not be able to reach the top of the cup entrance due to its length. In contrast to ion reflection, SEE has a great impact on the measured ion current. The rate of electron emitted by a material depends on its properties, the projectile energy and angle of incidence [57; 58; 59; 60; 61; 62; 63]. In our study, we consider two possibilities:  
* First, we consider an electron emitted by either the FC housing front or collimator. If the electron manages to reach the collector, the measured ion current will artificially be lowered and would read: \(I_{measured}=I_{i}-I_{SEE_{1}}\) with \(I_{SEE_{1}}>0\). Figure 6: Schematic of three physical mechanism occurring on different FC parts which can lead to measurement perturbation. The arrows have arbitrary length and direction. Secondly, we consider now an electron emitted by the collector but not recollected by the latter. Therefore, the measured ion current will be higher than reality and would read: \(I_{measured}=I_{i}+I_{SEE_{2}}\) with \(I_{SEE_{2}}>0\). In both cases the real ion current is not properly measured. Therefore, one must minimize and control the rate of SEE. Lastly, sputtering is characterized by its yield (\(\gamma\)) which defines the ratio of emitted atoms per incident ions. This parameter depends on the projectile and the target inner properties as well as the energy of impacting ions. Table 4 shows the yield for graphite, molybdenum and aluminum for ion energy corresponding to different thruster discharge voltages. These figures were obtained with the software SRIM [64], see Section 6.1. The primary danger with material sputtering is the collector deterioration which leads to a decrease of ion collection efficiency and prevent long operation. Another issue concerns particle deposition caused by sputtered material. It can lead to short-circuit between electrodes and create a current leak. Neutral sputtered atoms cannot directly contribute to the measured ion current. However, a collision between a neutral and the collector or collimator can create a secondary electron, which can lead to change the measured ion current as previously mentioned. A Hall thruster beam is composed of high kinetic energy ions and low temperature electrons [26; 65]. A negative potential is therefore applied to the cup preventing any primary and secondary electrons to be captured. Section 5.4 shows the trade-off which must be considered between ion collection and electron repulsion. A Hall thruster plume is subject to charge-exchange collisions (CEX). These events occur when a fast ion and a slow atom collide inelastically, resulting in a change of velocity distribution for both particles. The collision results in a slow ion with a random velocity distribution and a fast atom. The latter moved towards the edge of the plume which increase the so-called \"wings\" of the thruster, see Section 5.3. The probe becomes a potential sink which trap these ions with low energy and random velocity distribution. This effect occurs at large angle where the ion density is low, and the Debye length is large. CEX can occur in the HT channels or in the plume core due to high level of ion and neutrals density. Therefore, it increases when the propellant flow rate or the ionization efficiency increases. Consequently, higher ion current at the thruster \"wings\" increases the whole ion current measured.