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Thruster Principles 29 known outright from measurements of electrical or gas flow parameters external to the vacuum system. In ion thrusters, the beam is nearly monoenergetic, the exhaust velocity can be found from the net acceleration voltage applied to the thruster [using Eq. (2.3-6)], and the beam current is measured by the high voltage power supply. This allows the total efficiency to be accurately calculated from the electrical and gas flow inputs to the thruster. Using Eq. (2.3-16) for the thrust, Eq. (2.3-6) for the exhaust velocity, and Eq. (2.4-5) for the propellant flow rate, the total efficiency in Eq. (2.5-4) can be written as = mTvi = 2 IbVb . T 2 m i P i n m P i n The input power into the thruster, from Eq. (2.5-1), is Pin = Pb = IbVb , e e Substituting Eq. (2.5-6) into Eq. (2.5-5) gives T = 2 e m. (2.5-5) (2.5-6) (2.5-7) Measurements of the input propellant flow rate and electrical parameters (currents and voltages), and knowledge of the thrust correction factors from thruster plume measurements or code predictions, permit the total efficiency of ion thrusters to be calculated with high accuracy using Eq. (2.5-7). Using our previous example of an ion thruster with 10-deg half-angle divergence, 10% double ion current, 90% mass utilization efficiency, and 250 eV/ion to produce a 2-A beam at 1500 V, the electrical efficiency is e = 2 1500 = 0.857, 2 1500+250 2 and the total efficiency is T=(0.958)2 (0.857)(0.9)=0.708, which says that the thruster converts 70.8% of the supplied electrical energy into useful kinetic energy imparted to the spacecraft.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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