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464 Appendix B 1 sccm = 10–3[liters]*760[torr] = 0.01267 torr–1 6 0 [ s / m i n ] s 1 sccm = 4.47796 1017 atoms *1.660539 10–27 * M s =7.43583 10–4M mg , a s a *106 (B-3) (B-4) for its com- where Ma is the propellant mass in atomic mass units (AMU). For xenon, M a = 131.293 , and a correction must be made pressibility at standard temperature and pressure (STP), which changes the mass flow rate by 0.9931468. Therefore, for xenon, 1 sccm (Xe) = 7.17448 10–2 0.9931468 = 0.0722399 [equilvalent amperes] (B-5) = 0.0983009 [mg s]. It is possible to make an estimate of the neutral gas pressure inside of a hollow cathode insert region and in the orifice as a function of the propellant flow rate and cathode temperature, using analytic gas flow equations. While these equations may not be strictly valid in some locations, especially the relatively short orifices found in discharge cathodes, they can still provide an estimate that is usually within 10% to 20% of the actual measured pressures. In the viscous flow regime, where the transport is due to gas atoms or molecules primarily making collisions with each other rather than walls, the pressure through a cylindrical tube is governed by the Poiseuille law [1,2] modified for compressible gas [3]. The rate at which compressible gas flows through a tube of length l and radius a (in moles per second) is given [2] from this law by a4 Pa (P1–P2 ) a4 P12 –P2 Nm = 8 l RoT = 16 l RoT , (B-6) where a is the tube radius, l is the tube length, Pa is the average pressure in the tube given by (P1 + P2 ) / 2 , is the viscosity, P2 is the downstream pressure at the end of the tube, P1 is the upstream pressure of the tube, Ro is the universalPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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