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Hall Thrusters 347 m IM f m=b=bd i. (7.3-24) m p m peiZi If the current utilization efficiency is the same for each species, then the mass utilization efficiency for arbitrary species can be written as m = m+ f i , ( 7 . 3 - 2 5 ) i Zi where m+ is the usual mass utilization for a singly charged species. This is an easily implemented correction in most models if the species fractions are known. Likewise, the thrust obtained for multiple species can be generalized from Eq. (2.3-16) for Hall thrusters to 2M V f Tm = Ti = bId b d i cos . (7.3-26) i eiZi 7.3.3 Dominant Power Loss Mechanisms In preparation for examining the terms that drive the efficiency of Hall thrusters, it is useful to examine the dominant power-loss mechanisms in the thruster. Globally, the power into the thruster comes from the discharge power supply. The power out of the thruster, which is equal to the input power, is given to first order by Pd =Pb +Pw +Pa +PR +Pion, (7.3-27) where Pb is the beam power given by IbVb , Pw is the power to the channel walls due to ion and electron loss, Pa is the power to the anode due to electron collection, PR is the radiative power loss from the plasma, and Pion is the power to produce the ions that hit the walls and become the beam. Additional loss terms, such as the power that electrons take into the beam, the ion power to the anode, etc., are relatively small and can usually be neglected. In Hall thrusters with dielectric walls, the power loss due to electron and ion currents flowing along the radial magnetic field through the sheath to the channel walls (Pw) represents the most significant power loss. The current deposition and power lost to the walls can be estimated from the sheath potentials and electric fields in the plasma edge. Since the wall is insulating, the net ion and electron currents to the surface must be equal. However, ion and electron bombardment of common insulator materials, such as boron nitride, atPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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