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Hollow Cathodes 321 [70] D. M. Goebel, K. Jameson, I. Katz, and I. Mikellides, “Plasma Potential Behavior and Plume Mode Transitions in Hollow Cathode Discharge,” IEPC-2007-027, 30th International Electric Propulsion Conference, Florence, Italy, September 17–20, 2007. [71] J. R. Brophy, D. E. Brinza, J. E. Polk, M. D. Henry, and A. Sengupta, “The DSI Hyper-Extended Mission,” AIAA-2002-3673, 38th Joint Propulsion Conference, Indianapolis, Indiana, July 7–10, 2002. [72] I. D. Boyd and M. W. Crofton, “Modeling the Plasma Plume of a Hollow Cathode,” Journal of Applied Physics, vol. 95, pp. 3285–3296, 2004. [73] I. Mikellides, I. Katz, and D. M. Goebel, “Numerical Simulation of the Hollow Cathode Discharge Plasma Dynamics,” IEPC-2005-200, 29th International Electric Propulsion Conference, Princeton University, Princeton, New Jersey, October 31–November 4, 2005. Homework Problems 1. The power radiated from a surface is given by P = T 4 A , where is the Stephan–Boltzmann constant, is the emissivity of the surface, T is the surface temperature in K, and A is the radiating area. a. Design a 0.5-mm-diameter tungsten filament electron emitter that emits 10 A and radiates only 200 W of power. Specifically, what is the filament length and emission current density? You can neglect axial conduction of power to the electrical connections and assume that the emissivity of tungsten is 0.3 at emission temperatures. b. You decide to use a 0.25-mm-diameter and 4-cm-long filament to limit the radiated power. What is the temperature of the emitter, and how much power is actually radiated? 2. The insert in a BaO hollow cathode has a 3-mm inside diameter, is 2.5-cm long, and is at a temperature of 1100 ̊C. a. Using Cronin’s expression for the work function, how much current is emitted by the insert? b. If the insert has a uniform plasma with ne = 1020 m–3 density and Te = 2 eV inside of it, how much is the electron emission enhanced by the Schottky effect if the sheath is 10 V and 3 Debye lengths thick? What is the total emission current? c. Istheemissioncurrentspacechargelimited?PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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