# Future Directions for Electric Propulsion Research
## 5 Strategies for Addressing Technical Challenges for Electric Propulsion Development
### Facility Effects  
From an operational perspective, there is a pressing need to try to account for the influence of the facility on a thruster's operation. As reviewed in Section 4.2.1, due to limitations in facility pumping speeds, it is not possible to recreate pressures consistent with a flight environment. Instead, it is becoming an increasingly common practice to try to account for this facility effect by performing parametric studies: the facility pressure is varied above the minimum operating pressure while key aspects of thruster behavior (performance and power) are monitored. A function is then fit to these data and used to extrapolate to a space-like environment (i.e., zero pressure). Studies like this have also yielded certain practical solutions to facility pressure effects, such as using a centrally-mounted cathode [134] or operating at an elevated cathode flow fraction to \"drown out\" background gas [110] in Hall thrusters. A major difficulty in performing these types of studies is that only a few orders of magnitude of pressure can be spanned in ground testing. That is, work by [PERSON] et al. suggested 50 uTorr as an upper limit of pressure for Hall thruster testing based on the onset of background pressure-induced oscillations [60], which means most ground studies of pressure effects are limited to only two orders of magnitude, \(\sim\)1 to \(\sim\)10 uTorr. In contrast, there are at least four orders of magnitude of pressure difference (\(\sim\)1 nTorr to \(\sim\)10 uTorr) between ground testing and in-space operation, so there is no guarantee that ground pressure studies are extensible to flight operation. An equally important limitation of the parametric approach is that it is not clear what type of model should be used to fit the resulting data. Different models ranging from simple linear extrapolations to transcendental functions have been applied in the past [134; 135; 136; 137; 138; 139; 140]. In each case, however, these models are not rooted in the underlying physical processes, but are simply empirical fits. For example, the decrease in thrust with pressure may be linear over the experimental range that can be tested, but there is no theoretical basis to expect this trend should hold as pressures approach zero. Faced with this limitation, there is a pressing need to identify physics-based, experimentally-validated models for the response of the thruster to facility pressure. This remains a critical area of research, as evinced by [141; 142; 143; 144]. In an effort to overcome these challenges, one promising strategy to understanding the pressure effect on thrusters is to adopt a probabilistic approach. This builds on the current methods for determining facility effects that are based on extrapolating parametric studies of pressure to space-like conditions. In this case, however, simplified physics-based scaling laws are combined with rigorous model inference to make predictions within well-defined uncertainty for on-orbit behavior. For example, Bayesian analysis of thruster performance metrics as a function of pressure can yield rigorous quantifications of performance uncertainty when extrapolating to lower pressures [143]. Alternatively, high-fidelity models can be tuned to experimental data at non-zero pressure and then used to estimate performance at zero pressure without explicitly assuming any functional forms for pressure dependence [144]. Further, these sophisticated statistical and numerical analysis techniques can be used synergistically to understand the underlying physics of facility interaction. As an example, given a set of thrust data taken in a ground facility and an assumed functional form for thrust, a Bayesian analysis can provide physical insight into estimates of thrust and its uncertainty at space-like pressures. This sort of approach can be used to identify the important thruster parameters that are affected by pressure and thereby assist the theoretical and numerical modeling of pressure effects.