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Hall Thrusters 355 0 −10 −20 −30 −40 −50 −60 −70 −80 −90 −100 0 5 10 15 20 25 30 35 40 45 50 Electron Temperature (eV) Fig. 7-13. Sheath potential versus electron temperature for two materials. The sheath transitions to space-charge limited where the dashed lines intersect the potential curves. Space Charge Limited Emission No Emission Al2O3 BNSiO2 No Emission (γ = 0) emission has been neglected. Equation (7.3-45) can be rewritten in terms of the total ion current to the wall as M 1/2 e /kT kTe P w = I i w 2 m e s e 2 e + ( E s ) . ( 7 . 3 - 4 6 ) For the case of space charge–limited secondary electron emission, the sheath potential is s = o = 1.02TeV , and the ion energy is E = 0.58 TeV in order to satisfy the Bohm condition. Equation (7.3-45) predicts the maximum heat loading to the wall in the presence of a Maxwellian electron distribution and secondary electron emission from the wall, which is the dominant power loss mechanism in dielectric-wall Hall thrusters. If the electron distribution function is non-Maxwellian, the heat load to the wall can differ from that predicted by Eq. (7.3-45). In the case of TAL thrusters, the channel wall is metallic and biased to the cathode potential. This eliminates the zero-net current condition found on the insulating walls of dielectric-channel Hall thrusters and used to determine the local heat flux in Eq. (7.3-45). The electron flux to the cathode-biased TAL channel wall is negligible, and the secondary yield for metals is much lower than for insulators, so the secondary electron emission by the wall in TAL thrusters has little effect on the thruster operation. In addition, the plasma tends to be localized near the channel center by the anode design and gas feed geometry. The plasma then tends to be in poor contact with the guard rings at Sheath Potential (V)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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