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26 Chapter 2 For thrusters with both singly and doubly charged ions, the corrected mass utilization efficiency for multiple species is = IbM, (2.4-6) m mem p where m is a term that accounts for the fact that a doubly charged ion in the beam current carries two charges but only one unit of mass. In a manner similar to the derivation of the thrust correction due to double ions, the mass utilization correction m is given by 1+ 1I++ m = 2 I+ . (2.4-7) For small ratios of double-to-single ion content, m is essentially equal to one. Substituting Eq. (2.3-16) for the thrust and Eq. (2.4-5) for the propellant utilization efficiency into Eq. (2.4-3) yields an expression for the Isp: Isp= m 2eVb , (2.4-8) gM where the propellant utilization efficiency for singly charged ions must be used because Eq. (2.3-16) defines the beam current that way, and again the effective beam voltage must be used for Hall thrusters. Using the values for g and e, the Isp for an arbitrary propellant is Isp = 1.417 103 Vb , (2.4-9) m Ma where Vb is the beam voltage in volts and Ma is the ion mass in atomic mass units [1 AMU = 1.6605 10–27 kg]. For xenon, the atomic mass M a = 131.29 , and the Isp is given by Isp = 123.6 m Vb . (2.4-10) 1+ I++ I+PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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