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Ion Thruster Plasma Generators 119 the tail of the Maxwellian electron distribution will also contain electrons with an energy that exceeds the second ionization potential, and significant numbers of double ions will be produced if the electron temperature in the discharge chamber is high. The generation rate of double ions is determined in the same manner as single ions, discussed above, with different ionization cross sections [30]. The density of the double ions is determined by the continuity equation for that species, dn++ + (n++v+ 2)= n ++ , (4.3-27) dt where it is assumed that due to the double ions’ charge, the velocity will be increased over the singly ionized species by a square root of two. Defining the rate of double-ion production compared to single-ion production as R++ = n++ , (4.3-28) n+ the beam current density of single ions from the discharge plasma boundary through the ion optics (again with a transparency Tg ) is J =n ev T=nev T 1 R , (4.3-29) i+ +B+ iB+g(++) where ni is the total ion density. The double-ion current density is likewise Ji++ =n++(2e)( 2vB+)Tg = 8nievB+TgR++. (4.3-30) The total ion beam current is then the sum of the singly and doubly ionized particle currents. As discussed in Chapter 2, the discharge propellant efficiency is the ratio of the propellant that becomes beam ions (of any charge) to the rate of propellant flow into the discharge chamber. Considering the effect of double ions, the propellant efficiency of the discharge chamber is then = J++JB++ Ag , (4.3-31) md B 2 em dPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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