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380 Chapter 7 a significantly higher impact if deposited on most spacecraft components. Therefore, understanding the wall erosion rate and its dependence on thruster materials and operating parameters is of importance in predicting the thruster life and performance over time and its potential impact on the spacecraft. The erosion rate, given by the rate of change of the wall thickness, w, is = w = J i W Y ( i ) , ( 7 . 5 - 1 ) t eAv where Ji is the ion flux, W is the atomic weight, is the material density, e is the ion charge, Av is Avogadro’s number, and Y is the sputtering yield of the material, which is dependent on the ion type and energy i . Since the material properties are known, the issue becomes one of knowing the ion flux, ion energy, and sputtering yield of the wall. Several analytical models of the Hall thruster have been developed and applied to this problem [37,60,64]. The most accurate predictions have been achieved using a modified 2-D HPHall code [58] to obtain the ion fluxes and energies. The sputtering yield of boron nitride compounds used in dielectric-wall Hall thrusters has been measured by Garnier [65] versus incidence angle and ion energy, and is used in several of these models. However, the Garnier data are at only a few energies and in excess of 300 V. Gamero extrapolated these data to lower energies using the semi-emperical sputtering law scaling of Yamamura and Tawara [66], obtaining the following expression for the sputtering yield in units of mm3/coulomb: 2 6 3 8 58.6 2.5 Y =(0.0099+ 6.04 10 4.75 10 ) i 1 i , (7.5-2) where is the incident angle of the ion. In Eq. (7.5-2), the value 58.6 represents the estimated threshold energy for sputtering required by Yamamura’s model. Figure 7-21 shows an example of the yield predicted by Eq. (7.5-2) for two different incidence angles. Equation (7.5-2) was shown [58] to accurately fit the data of Garnier and provides projections of the sputtering yield down to low ion energies predicted by HPHall deeper in the channel. Figure 7-22 shows the predicted [58] and experimentally measured erosion profiles [67] for the SPT-100 thruster inner and outer channel walls. Good agreement with the observed channel erosion is seen near the thruster exit, and the profiles have the correct functional shape. It is likely that inaccuracies in the extrapolated sputtering yield at low energies caused the disagreement with thePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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