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344 Chapter 7 a=1T2 = T , (7.3-16) 2 m a P d o c which describes the basic thruster performance without considering the effects of the cathode flow or power used to generate the magnetic field. This is usually done to separate out the cathode and magnet losses so that trends in the plasma production and acceleration mechanisms can be discerned. The anode efficiency should not be confused with the total efficiency of the thruster given by Eq. (7.3-3). It is useful to show an example of the relative magnitude of the efficiency terms derived above. Figure 7-9 (from [10]) shows the anode efficiency that was defined in Eq. (7.3-16) and the other efficiency terms discussed above for the laboratory-model NASA-173Mv2 Hall thruster operating at 10 mg/s versus the discharge voltage. In this figure, the charge utilization efficiency is the net efficiency decrease due to multiply charged ions [10], the voltage utilization efficiency ( v ) is the conversion of voltage into axially directed ion velocity, the current utilization efficiency ( b ) is the fraction of ion current contained in the discharge current, and mass utilization efficiency ( m ) is the conversion of neutral mass flux into ion mass flux. The anode efficiency increases with discharge voltage, largely because the voltage efficiency and current efficiency increase with voltage. The current utilization is always lower than the other efficiency terms, suggesting that the ultimate efficiency of Hall thrusters is dominated by the electron dynamics involved in producing the plasma and neutralizing the beam. This emphasizes the importance [9,10] of optimizing the magnetic field design to maximize the thruster efficiency. The value of in Eq. (7.3-15) that is typically found for Hall thrusters can be evaluated using Eq. (2.3-15) and the data in the literature. For example, a 10% double-ion content gives a thruster correction factor in Eq. (2.3-14) of = 0.973. The thrust loss due to the beam angular divergence of Hall thrusters isgivenbyEq.(2.3-10),(FT =cos ).ForbothSPT-100Hallthrusters[6]and TAL thrusters [29], a half-angle divergence of equal to about 20~deg is observed, producing FT = 0.94 . The total correction factor is then = FT = 0.915 for typical Hall thruster conditions. Values for of about 0.9 have been reported. The equivalent discharge loss for a Hall thruster can also be calculated [4,6] to provide information on how the thruster design impacts the cost of producing the beam ions. The average energy cost for producing a beam ion is thePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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