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Hall Thrusters 361 Pa = 2TeVId . (7.3-61) The electron temperature near the anode is very low, typically less than 5 eV [34–36]. Using the thruster current utilization efficiency and assuming b = 0.7 and TeV = 0.01Vb near the anode, this can be written as Pa =2 bIb(0.01Vb)=0.014IbVb. (7.3-62) The power required to produce the ions is given by Eq. (7.3-56). This can be written as Pion =(Ib +Iiw)U+ =(1+ b)IdU+. (7.3-63) Taking the beam utilization efficiency as 0.7 and estimating that the ionization potential is roughly 5% of the beam voltage, the power required to produce the ions is approximately Pi = 0.09 IdVb . The radiation power and other power loss mechanisms are small and will be neglected in this simple example. The total discharge power into the thruster is then Pd = IbVb + 0.49 IbVb + 0.014 IbVb + 0.09 IbVb = 1.59 IbVb . (7.3-64) The electrical efficiency of the dielectric-wall thruster is then e = IbVb / (1.59 IbVb ) = 0.63 . (7.3-65) The total thruster efficiency, assuming the same beam divergence and double- ion content as evaluated above and a mass utilization efficiency of 95% reported for SPT thrusters [4], is T =(0.915)2(0.63)(0.95)=50%. (7.3-66) The SPT-100 thruster is reported to run at about 50% efficiency. Since the power loss is dominated by the electron wall losses, this analysis illustrates how critical the wall material selection is to minimizing the secondary electron yield and maintaining a sufficient wall sheath potential for good efficiency. For example, if the wall had been made of alumina and the electron temperature was about 20 V, the sheath potential would be –1.02TeV in the space charge– limited regime. The wall power from Eq. (7.3-57) would then be about three times higher than in the BNSiO2 case: Pw =142IiwTeV =1.4IbVb. (7.3-67)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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