# Erosion Rate Measurements for DART Spacecraft Ion Propulsion System +
## 3 Results
### Relative Doppler and Density Profiles across the Grid Face
Accounting for the square root relationship between energy and velocity, we estimate the velocity component aligned with laser direction equals \(V_{0}/\sqrt{2}\), and the most probable direction therefore crosses the laser beam at approximately 45 degrees. For low energy Xe\({}^{+}\)-Mo sputtering with 45 degrees the most probable angle of efflux, the Xe\({}^{+}\) angle of incidence (AOI) is approximately 45 degrees off-normal and in the plane defined by surface normal and Xe\({}^{+}\) incoming trajectory [15]. The sum of these angles is roughly 90 degrees for the AOI range 30-70 degrees, although it increases slightly for higher AOI and decreases for lower AOI. Figure 11 depicts example impingement and efflux directions, with laser beam crossings that generate blue Doppler shifts consistent with results near the grid edge. We have CEX ion impacts on accel barrels by ions traveling in the downstream direction and similar impacts by ions traveling in the upstream direction, but the upstreaming ions will little affect molybdenum density in the region probed by LIF. Barrel impacts over a range of AOI values by downstreaming ions and accel downstream face impacts by upstreaming ions can both produce blue-shift laser crossings of the required magnitude. Figure 11: Diagram of a single screen and accel grid aperture pair (not to scale), illustrating hypothetical scenarios for Xe\({}^{+}\) impingement trajectories and associated directionality for peak molybdenum density distributions. The diagram applies to grid locations away from the center. Preferential carbon deposition sites and radial velocity of backstreaming CEX ions are potential causes of only directional bias. Cusps are an artifact of the grid formation process and gradually wear away; they are not shown. The grid fabrication process leaves a cusp in the middle of the accel barrel, which reduces its effective diameter and raises the barrel erosion rate. Residual cusps would have been present for the grid set used in the present study. Their existence changes the AOI distribution for both upstream and downstream ion barrel impingement and modifies the neutral densities. Upstreaming ions could produce significant Doppler shift at the laser crossing, even if well-aligned with the beamlet axis, due to cusp impingement. More details about cusp geometry are available in the literature [16]. Moly density decreases substantially across the grid face, especially near the perimeter, as shown by Figure 12, where the profiles were scaled according to the relative magnitudes measured at grid center (see Figure 5 results). The profiles depend on propellant utilization. With other factors remaining constant, only density will vary with the local product of beam current density and neutral density. Beam current density has been measured near the grid face using a miniature planar probe, with less than 15% variation from 0 to 12-degree grid angle [11]. Whereas the source neutral density may change more than this, the anticipated only density reduction at 12 degrees--even if background density made no contribution, although it certainly does--is less than observed. The reduced width of the Doppler profile at 12 degrees compared to 0 degrees and its peak shift are consistent with carbon deposition on the large-radius side of the barrel, or with radial velocity bias for CEX ion impingement on the downstream accel face at 12 degrees. Post-test grid inspection did suggest preferential carbon deposition on the large-radius side of barrels displaced from grid center, supporting the former explanation. The densities of source flow and background xenon neutrals will affect overall grid erosion rate as well as local rates, only density profile across the grid, accel current collection, and so on.