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24 Chapter 2 where I+ is the singly charged ion current and I++ is the doubly charged ion current, the total thrust for the multiple species, Tm , is the sum of the thrust from each species: T =I+ 2MVb+I++ MVb=I+ 2MVb 1+1I++ . (2.3-13) m e e e 2I+ The thrust correction factor, , for thrust in the presence of doubly ionized atoms is defined by the ratio of Eqs. (2.3-13) and (2.3-8), where the beam current in Eq. (2.3-8) is given by Eq. (2.3-12): (2.3-14) the beam. A similar ions (see Problem 4), be relatively small in and multiply charged ( 2 . 3 - 1 5 ) ( 2 . 3 - 1 6 ) divergence and a 10% doubles-to-singles ratio results in = 0.958 . For a thruster producing 2 A of xenon ions at 1500 V, the thrust produced is 122.4 mN. I++1I++ 1+0.707I++ = 2 = I+ , I+ + I++ I++ 1+ I+ where I++ / I+ is the fraction of double ion current in correction factor can be easily derived for higher charged although the number of these species is typically found to most ion and Hall thrusters. The total thrust correction is the product of the divergence species terms: = Ft . The total corrected thrust is then given by T = m i v i = 2 M I b e The total thrust for xenon can be simply written as V b . T = 1.65 Ib Vb [mN]. (2.3-17) For example, assuming an ion thruster with a 10-deg half-angle beamPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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