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230 Chapter 5 5.6.2 Barrel Erosion As was illustrated in Fig. 5-20, charge exchange ions generated between the screen grid and the upstream surface of the accel grid can impact the interior surface of the accel grid holes. These ions sputter away grid material, increasing the barrel radius. While computer codes, such as CEX-2D [4], are normally used to calculate the erosion rate, it is instructive to derive an analytical estimate. The following calculation is based upon published performance and erosion data for NASA’s NSTAR thruster operating at its highest power TH15 level [29,50]. Assume that any ions generated downstream of the discharge chamber are not focused through the hole in the accelerator grid. For barrel erosion, the path length is taken as the sum of the grid gap and the accelerator grid thickness, which for NSTAR is about a millimeter. The upstream gas density is estimated by dividing the downstream density by the grid open area fraction, fa , and the Clausing [51] factor, c , which reduces the gas transmission due to the finite thickness of the accel grid. The Clausing factor depends only on the aperture length-to-radius ratio. The neutral gas density is then no= o 1 . (5.6-5) v r2 fa c o grid The neutral gas density in the accelerator grid apertures is higher than the gas density downstream of the accelerator grid, which was calculated using Eq. (5.6-2), due to the effects of the open area fraction and the Clausing factor. For an open area fraction of 0.24 and a Clausing factor of 0.6, the neutral density in the grid gap is about 9 1018 m–3. The number of grid apertures is approximately the grid open area divided by the area per aperture: f r2 Naperture a grid . (5.6-6) The average aperture current is the total beam current divided by the number of apertures, Iaperture = Ib . (5.6-7) N aperture r2 aperturePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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