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Ion Thruster Accelerator Grids 229 computational region is long enough to include all the charge exchange ions that can return to the grid. Using Eq. (5.6-1) and the current ratio from Fig. 5-24, an estimate can be made of the effective path length ( d ) for the NSTAR thruster. If the measured accel grid current is all due to charge exchange (i.e., no direct interception), then Eq. (5.6-1) can be rewritten as d = Iaccel . (5.6-2) IBeam CEX no Assuming the effective charge exchange path length is much longer than the gap between the screen and accelerator grids, the average neutral gas density can be estimated from the grid diameter, the flow of neutral gas out of the thruster, and the thruster beam current. The neutral gas density downstream of the grids close to the thruster is then no = o , (5.6-3) v r2 o grid where vo is the neutral velocity, and o is the flux of unutilized propellant escaping from the discharge chamber. Using the parameters for the NSTAR at TH15 from [29], the total neutral flow into the thruster is 28 sccm. The thruster discharge chamber has a mass utilization efficiency of about 88%, so the neutral gas flow escaping the thruster is about 3.4 sccm, which corresponds to 1.5 1018 particles per second. Assuming the gas exits the thruster at about an operating temperature of 250 ̊C, the neutral velocity c /2 is about 110 m/s. The average neutral density from Eq. (5.6-3) is then about 2.3 1017 m–3, and neutral density varies over the grid by more than a factor of two. Using the data in Fig. 5-24 extrapolated to the beam current of 1.76 A in TH15, and a charge exchange cross section of 5 10–19 m2, the average effective path length from Eq. (5.6-2) becomes = (0.003) = 0.03[m]. (5.6-4) d (5 10 19 )(2.3 1017 ) The path length is more than an order of magnitude larger than the grid gap, consistent with our assumption. The very long path length compared with grid hole spacing means that the computational space in ion optics codes is very long (several centimeters), and so the computer codes must allow for the axial zone sizes to increase downstream of the grids.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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