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Hall Thrusters 363 7.3.6 TAL Hall Thruster Efficiency (Metallic Walls) As with the 1.35-kW SPT-100 Hall thruster example above, an estimate will be made of the power loss terms in Eq. (7.3-27) to obtain an electrical efficiency for the 1.4-kW D-55 TAL thruster [29]. Equation (2.5-7) will then be used to obtain an estimate for the thruster efficiency. The beam power Pb is, again, just IbVb . As stated in the previous section, the wall losses ( Pw ) are essentially negligible in TAL thrusters, and the power to the anode is given by Eq. (7.3-49): P =2T Ib =0.29I V . (7.3-69) a eV b bb In Eq. (7.3-69), it is again assumed b = 0.7 and TeV = 0.1Vb , although these values may be somewhat different in TAL thrusters. The power to produce the ions is again approximately 0.09IbVb . The total discharge power, Eq. (7.3-27), then becomes Pd = IbVb + 0.29 IbVb + 0.09 IbVb = 1.4 IbVb . (7.3-70) Neglecting the power in the cathode keeper (if any) and the magnet as small compared to the beam power, the electrical utilization efficiency from Eq. (2.5-1) is then e= Pd =0.72. (7.3-71) 1.4 Pd The total thruster efficiency, assuming a 10% double-ion content, a 20-deg angular divergence [29,48], and a 90% mass utilization efficiency reported for TAL thrusters [29,49], is then, from Eq. (2.4-7), T =(0.915)2(0.72)(0.9)=54%. (7.3-72) This result is on the same order as that reported in the literature [29,49,50] for this power-level TAL and is essentially the same as the SPT-100 efficiency in this simple example if the wall losses had been included. However, the power loss to the anode is seen as the dominant mechanism in the TAL efficiency.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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