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Hall Thrusters 391 6. A xenon Hall thruster has a channel outside diameter of 10 cm and a channel width of 3.5 cm with BNSiO2 walls. Assume a plasma density of 2 1017 m–3 and an electron temperature of 20 eV in the channel with the majority of the plasma in contact with 1 cm of the wall axially. a. What is the electron current to the wall? b. What is the net electron current to the wall? c. What is the power deposited on the wall associated with this electron current? d. What is the power deposited on the wall associated with ion current? 7. Assume that the thruster in Problem 5 has alumina walls and produces 3.5 A of beam current at 400 V with an electron temperature in the channel of 15 eV. The thruster also has a beam current utilization efficiency b = 0.5 . a. Whatisthepowerintothedischarge? b. What is the total power into the alumina walls? c. Assuming that the electron temperature at the anode is 5 eV, the mass utilization efficiency is 90%, and the thrust correction factor = 0.9 , and neglecting all other power loss channels, what is the thruster efficiency? d. For a beam voltage utilization efficiency of 0.9, how much thrust is produced? 8. The electron current to the anode in a Hall thruster can be estimated from the perpendicular electron flux diffusing through the plasma channel. a. Neglecting the pressure gradient terms, derive an expression for the current to the anode in terms of the collision frequency in the channel plasma. b. For the thruster in Problem 5 with a transverse magnetic field of 150 G and an axial electric field of 3 104 V/m, what is the anode current if only classic electron–ion collisions are considered? c. The effective wall collision frequency can be estimated as the electron current to the wall times the secondary electron yield and divided by the total number of particles in the plasma ( vw = Iew / N , where N is approximately the plasma density times the channel cross-sectional area times the plasma length L). Derive an expression for the anode current due to the electron-wall collisions in terms of the electron current to the wall. d. What is the total anode current for this thruster example, using L = 1 cm for the bulk of the plasma density?PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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