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Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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Thruster Principles 33 n = PT [torr] * 133.32 [pascal/ torr] 1.381023 [J/K]*T[K] = 9.661024*PT particles, T m3 (2.7-2) where PT is the pressure in the vacuum system in torrs and T is the gas temperature in kelvins. It should be noted that the pressure must be corrected for the gas type in whatever measurement system is used to obtain the actual pressure data. As an example, for a pressure of 10–6 torr and a temperature of 290 K, the density of gas atoms is 3.3 1016 per cubic meter. The pressure in a vacuum system [3] in which a thruster is being tested is determined by the gas flow rate and the pumping speed P = QS , (2.7-3) where Q is the total propellant throughput and S is the pumping speed. The most common units for pumping speed are liters per second, so utilizing a throughput in torr-l/s directly provides the pressure in the vacuum system in torr. The conversions of different flow units to torr-l/s can be obtained from Appendix B. The finite pressure in the test vacuum system causes a backflow of neutral gas into the thruster that may artificially improve the performance. This ingestion of facility gas by the thruster can be calculated if the pressure in the chamber is known by evaluating the flux of neutral gas from the chamber into the thruster ionization region. The equivalent flow into the thruster is then the injected flow Q plus the equivalent ingested flow. The ingested flow (in particles per second) is given by Qingested = nc A*c , (2.7-4) 4 where n is the neutral density in the chamber, c is the gas thermal velocity, A is the total open area fraction of the thruster to the vacuum system, and c is a correction factor related to the conductance into the thruster from the vacuum system. The neutral gas density is given by Eq. (2.7-2), and the gas thermal velocity is given by c = 8kT , (2.7-5) M

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