## 3 Experimental Investigations of Hall Thruster Erosion
### Surface Investigations  
The presence of unexplained erosion features prompted [PERSON] and [PERSON] [22] and [PERSON] et al. [23] to investigate the microstructure of eroded laboratory Hall thruster walls. These studies found the presence of striations on the order of the electron gyroradius and surface damage in the form of delamination and microcracking. Though they observed opposite trends in relative sputtering rates of BN and SiO\({}_{2}\) in BN-SiO\({}_{2}\), both studies found that original compound atomic ratios were not maintained in highly eroded regions; the ratio of B to N atoms was not 1:1, and the ratio of Si to O atoms was not 1:2. These results indicate that sputtering occurs on an atomic, rather than molecular, level in the Hall thruster wall. Figure 7 shows an SEM image of grade M26 BN-SiO\({}_{2}\) after exposure to plasma, taken without the application of a conductive surface coating. Microcracks and striations are observable in the image, and BN delamination prevents discernment of BN grain boundaries. Figure 6: Erosion ridges in the Aerojet Rocketdyne BPT-4000, Snecma PPS-1350, and Fakel SPT-100 walls. Images reprinted with permission from [18], Aerojet Rocketdyne, 2010; with permission from [66], Snecma, 2019; and with permission from [15], American Institute of Aeronautics and Astronautics, 1995. Recent work has used controlled experiments to investigate sputtering mechanisms and isolate the impact of specific factors on sputtering characteristics. [PERSON] et al. [75] found that sintering pressure can impact BN erosion characteristics and that BN sputtering results in the breaking of B-N bonds and delamination of BN layers. Surface composition analysis showed that boron sputters more quickly than nitrogen when BN is exposed to xenon plasma. [PERSON] et al. [76] exposed pristine and Hall thruster-eroded BN and BN-SiO\({}_{2}\) samples to xenon magnetron plasma and found that previously eroded samples sputtered up to 90% faster than pristine samples. Their work found conflicting results regarding the relative sputtering rates of BN and SiO\({}_{2}\) in BN-SiO\({}_{2}\) but confirmed that compound atomic ratios were not maintained. [PERSON] et al. [69] attempted to explain the formation of anomalous erosion ridges in BN-SiO\({}_{2}\) with surface instabilities driven by hoop stresses, but experimental results failed to support this hypothesis. Experimental evidence for the role of electrons in the Hall thruster erosion process was provided by [PERSON] et al. [77], who exposed BN-SiO\({}_{2}\) and BN to both electron and ion beams. [PERSON] et al. [42] demonstrated that microcracks observed in BN-SiO\({}_{2}\) thruster walls were caused by thermal shock induced by thruster on/off cycling but did not find that cracking influenced erosion characteristics. X-ray photoelectron spectroscopy data and SEM images from their work supported the notion that SiO\({}_{2}\) is sputtered more quickly than BN. An important subset of surface investigations has attempted to quantify the low-energy sputtering yields of Hall thruster wall materials. Sputtering rates of BN and BN-SiO\({}_{2}\) at ion energies relevant to Hall thruster erosion (<500 eV) are vital for erosion models, so the Hall thruster community has attempted to measure these values in controlled experiments. [PERSON] et al. [38; 39] determined angle-dependent sputtering rates of these materials by measuring sample mass loss after exposure to xenon plasma with mean ion energies of 350 eV, 500 eV, and 1000 eV. Their work found BN-SiO\({}_{2}\) sputtered at a greater rate than BN but that the relative sputtering rate of BN was larger than SiO\({}_{2}\) in BN-SiO\({}_{2}\). Curiously, their work also found that the atomic ratios of B to N and Si to O remained 1:1 and 1:2, respectively, in contrast to the results of later thruster and controlled sputtering tests performed by other authors [22; 23; 42; 75; 76]. [PERSON] et al.