## 2 Materials and Methods  
The AtOx ground-test facility is based on an OS-PREY Plasma Source manufactured by Oxford Scientific Instruments (Abingdon, UK): the system works through the dissociation of molecular oxygen flowing inside a vacuum chamber (allowable pressure \(\sim\)10\({}^{-3}\) Pa), controlled by high-precision flowmeters, by means of the energy from a radio frequency source (13.56 MHz). This procedure gives rise to an oxygen-based beam comprised of 99% neutral species (about 60% of monoatomic O and 40% of molecular O\({}_{2}\)) with energy in the range of 5-25 eV. A mercury-xenom lamp (Hamamatsu--model LC8 Lightning Cure (Hamamatsu Photonics, Shizuoka, Japan)) was adopted to simulate UV irradiation: this device was mounted on the AtOx chamber, providing high-intensity UV line spectra with an elliptical reflector (UV cold mirror (Abrisa Technologies, Santa Paula, CA, USA)) with reflectivity higher than 90% in the UV range and a quartz light guide with UV transmittance. The spectral emittance field was in the 200-600 nm range, with a maximum emission value of 365 nm, and the radiation intensity of the lamp system was 410 mW/cm\({}^{2}\) (around 10 Suns) at a distance of 30 mm with an aperture size of 20 mm. The experimental facilities and setup conditions are shown in Figure 1. During the tests, the mean environmental temperature was recorded by means of a sensor placed on the sample holder, as reported in the plot of Figure 2. The temperature rise was a consequence of the combined use of AtOx and UV rays. The environment reached 100 \({}^{\circ}\)C in around two hours with a non-linear gradient that was very steep during the first hour; in the remaining exposure time (test duration \(\sim\)11 h), the temperature asymptotically approached the maximum value of about 105 \({}^{\circ}\)C.  
The C/C material samples tested were obtained from a Mitsubishi carbon/carbon slab obtained through the waterjet cutting method, providing several pieces measuring 3 \(\times\) 6 cm and about 4 mm in thickness. The tests were performed considering a fixed time of exposure, with a AtOx base fluence of 7.6 \(\times\) 10\({}^{19}\) n.at./cm\({}^{2}\) as measured by the normal irradiation of the reference samples (Kapton HN, [16]). The simulation of the different attitudes was made possible by the axial rotation of the sample holder at four tilted positions (15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\)) with respect to the AtOx beam direction. The analysis of the surface damage was carried out by measuring the mass loss and consequent evaluation of the erosion yield parameter. The basic background lies within the operative expression of the erosion rate \(E_{Y}\), which is given in [cm\({}^{3}\)/n.at.]--i.e., as the eroded volume for an impinging atom--by the relationship:  
\[E_{Y}=\frac{\Delta M}{\rho\cdot F\cdot A}\quad,\quad\quad F=f\cdot\Delta t \tag{1}\]  
where \(\Delta M\) is the mass loss [g], \(\rho\) is the material density [g/cm\({}^{3}\)], \(A\) is the exposed surface [cm\({}^{2}\)], and \(F\) is the fluence, which is given as the total number of impacts per surface unit [n.at./cm\({}^{2}\)]; the latter quantity takes into account the whole time of exposure \(\Delta t\) [s] and is typically related to a supposed constant AtOx flux \(f\), which is expressed in [n.at./(s\(\cdot\)cm\({}^{2}\))], as indicated by the second expression in Equation (1). On this basis, a physical modeling was introduced in order to study how the mechanism (and in turn, the measurement) of AtOx erosion may be dependent on the orientation of the exposed surface with respect to the direction of the AtOx flux (i.e., the direction of the spacecraft motion) as well as on the concomitant vacuum UV radiation.  
Figure 1: AtOx/UV experimental facilities at the Aerospace Systems Laboratory (LSA—Sapienza University of Rome) (**a**) and setup conditions showing the control of sample attitude variation (**b**).