# Erosion Rate Measurements for DART Spacecraft Ion Propulsion System +
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Contributor** & **Downstream Face (mA)** & **Barrels (mA)** & **Energy (eV)** \\ \hline Background gas neutrals & 5 * & & \(\leq\)175 \\ Downstream source gas neutrals & 1.5 * & & \(\leq\)175 \\ Intergrid source gas neutrals & & 0.7 & varies \\ Neutralizer, direct impingement & & \(\leq\)2 & low-high \\ \hline \hline \end{tabular}  
* Some impingement may occur on the accel barrels and upstream face, and therefore not contribute to density in the LIF probe region.  
\end{table} 
Table 4: Rough estimate of accelerator grid current contributions for DTL28-H-H.  
source neutral density at any given location is proportional to \(1-\eta\) if the beam current is fixed. If the current increase for the DTL30 MOD transition occurs over just 25% of the grid area (uniformly), whereas the increase is over the entire grid for the DTL28-O-O case (and uniform), the efficiency ratio is about 4--a more feasible ratio to explain but still challenging. Even more challenging to rationalize is the observed 430% increase of mJy density for a fractional accel current increase of just 6%. Providing further evidence for different efficiencies in producing detectable mJy efflux at grid center is the very high DETL2.7B-H-O erosion rate shown in Figure 6. DETL2.7B-H-O has higher mass utilization than DTL28-A-A, yet only density is also higher. It matches the DTL30 MOD utilization, yet only density is about 8\(\times\) higher for DETL2.7B-H-O (\(V_{b}=850\), \(V_{a}=-175\)) compared to DTL30 MOD (\(V_{b}=1396\), \(V_{a}=-175\)). We attempt to explain this result as follows. Ion trajectories expand radially outward in the intergrid region as the beam voltage is lowered, reducing the axial to radial acceleration ratio and making barrel impingement more probable for a subset of CEX, primary, and scattered ion trajectories. As total voltage decreases and impingement rate rises, the average impingement energy is also increasing, and the average AOI for these ions is near the peak of the angular sputter profile (the sputter yield is about twice as high for 45 to 60-degree AOI compared to normal or near-normal incidence)--leading to much higher sputter yield and mJy density production in the LIF probe region. Sputter yield gain up to 15\(\times\) can result from impingement at the full total voltage (\(\sim\)6\(\times\)) rather than \(|V_{a}|\), together with more favorable AOI (\(\leq\)2.5\(\times\)) [31]. The intergrid accel current is estimated to be about an order of magnitude lower than the sum of downstream background and source current (see Table 4), but this statement applies globally for the accel surface and not necessarily at grid center. Based on Figures 8d and 12, propellant utilization dominates the mJy signal at grid center for DTL28, although not at the edge. At the center, beamlet current approaches the perveance limit, increasing the collection of upstream ions on the barrels. If neutral density is raised via reduced propellant utilization or elevated background pressure, CEX ion production increases, but the plasma sheath becomes even flatter to further elevate upstream ion collection. However, raising the beam voltage increases sheath curvature and causes ion trajectories to be focused more strongly. This greatly reduces barrel collection of upstream ions and reduces the neutralization length as well, as the beamlet diverges more rapidly after passing through the accel aperture. Collection of CEX ions formed from downstream source neutrals and background neutrals decreases, especially at grid center where the collection distance is well below the global average. Average impingement energy decreases as well, as the average location and its potential where downstream ions are birthed is closer to the accel. The high current beamlets constitute just a fraction of the total number, and as downstream collection current drops with increased beam voltage at grid center, Ia is less affected.