# Erosion Rate Measurements for DART Spacecraft Ion Propulsion System +
## 3 Results  
### Relative Erosion Rates at Grid Center  
The dependence of LIF signal on the throttle condition was studied at grid center, with the laser frequency tuned to the center of the Doppler profile. For each setpoint, the beam current was 2.70 Amperes. Beam (\(V_{b}\)) and accelerator grid voltages (\(-V_{a}\)) are indicated in Figure 5, which plots the relative LIF signal amplitude at the peak of the Doppler profile, with additional engine parameters listed in Table 1. At grid center, this profile is highly symmetric, and its peak position coincides with the molybdenum rest frequency. To generate the plot, we have assumed the width of the Doppler profile to be constant, and the off-resonance signal due to laser scatter has been subtracted. The variation of molybdenum peak density indicates significant dependence on propellant mass utilization. This is to be expected if the erosion rate at the LIF probe location is strongly affected by ion-neutral charge exchange (CEX) interactions [5; 12]. Figure 4: Flow rates and uncorrected mass utilization settings for evaluating NEXT over the range of potential DART operating conditions. The most “flooded” condition is at the upper left and corresponds to DTL28-A-A. The “nominal” condition is DTL28-H-H (0.900, 41.812), and most “lean” is DTL28-O-O (0.931, 40.434). Note that DTL28-H-H is equivalent to TL28 with respect to flow through the discharge chamber. Ion-neutral CEX interactions convert fast ions into relatively slow ions, for which accel grid impingement probability is greatly enhanced. Their volumetric production rate is proportional to the product of neutral density and ion flux. Because total flow rate variation is small over the range of throttle conditions in Figure 5, neutral fraction in the source flow is clearly an influential factor. However, comparison of DETL2.7B-H-O and DTL30 MOD, which have the same propellant utilization and accel voltage, reveals the critical importance of beam (or total) voltage. This is a general trend, apparent from the rapid falloff of only density with total (\(V_{b}+|V_{a}|\)) voltage, shown in Figure 6. The data were fitted to an exponential function, chosen on a phenomenological rather than theoretical basis. Most of the scatter in the plot is likely attributable to variations in \(V_{a}\) and \(\eta\). A similar trend was observed previously, for data obtained over a range of the beam current, flow rate, and other variables [7]. For the present dataset, the beam current was not varied. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Throttle Condition**} & **Ia** & **(\(\mathbf{1-\eta}\))/\(\mathbf{\eta}\)** & **Facility Pressure (Torr;** **Corrected)** & **Flow Rates (sccm)** \\ \hline DTLNEW-H-O-1021-xxx & 9.51 & 0.119 & \(2.58\times 10^{-6}\) & \(37.54/4.26/4.71\) \\ \hline DTL28-H-H & 9.40 & 0.119 & \(2.61\times 10^{-6}\) & \(37.54/4.26/5.00\) \\ \hline DTL28-O-O & 8.70 & 0.0788 & \(2.50\times 10^{-6}\) & \(36.40/4.01/4.71\) \\ \hline DTL28-A-A & 10.0 & 0.155 & \(2.73\times 10^{-6}\) & \(38.68/4.52/5.30\) \\ \hline DTL29-A-A & 9.90 & 0.155 & \(2.76\times 10^{-6}\) & \(38.68/4.52/5.30\) \\ \hline DETL2.7B-H-O & 9.55 & 0.118 & \(2.58\times 10^{-6}\) & \(37.54/4.26/4.71\) \\ \hline DTL30 MOD & 8.85 & 0.118 & \(2.67\times 10^{-6}\) & \(37.54/4.26/4.71\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Engine parameters for Figure 5 throttle conditions. Figure 5: Relative peak molybdenum density at grid center as a function of throttle condition. Nominal ion beam (\(V_{b}\)) and absolute value accelerator grid voltages (\(|V_{a}|\)) are as shown, with throttle condition labels underneath. Table 1 provides additional information. Comparison of moly density for the two \"DTLNEW-H-O\" cases indicates that accel voltage is also influential. A plot showing the \"DTLNEW-H-O\" cases with \(-125\) and \(-200\) accel voltages is given in Figure 7, together with DTL-H-H, which has the same discharge flow conditions.