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174 Chapter 4 of gas out the ion optic apertures, and the internal “loss” of neutral particles by ionization. Wirz and Katz [58] developed a technique that accurately predicts the neutral gas density profiles in ion thrusters. Their model utilizes a three-dimensional generalization of the view factor formulation used in thermal models [59]. The view factor approach assumes that neutral particles travel in straight lines between surfaces, and that, after hitting a surface, they are emitted isotropically. In this technique [60], a 3-D boundary mesh and a 2-D internal mesh in the thruster discharge chamber are created for an axisymmetric discharge. The steady-state neutral fluxes are determined by balancing the injection sources, re-emission from the walls, loss through the ion optics, and loss due to ionization. The local neutral density at each of the internal mesh points is calculated by integrating its view factor from the source points (all the other mesh points in the thruster), which includes the “loss” of neutrals between the source and the mesh point due to ionization by the plasma. The ionization losses affect the neutral gas analogous to absorption diminishing the intensity of a light ray. The neutral gas code and the rest of the model components, discussed below, are iterated until a stable solution for the neutral density at each mesh point is found. One advantage of this model is that the neutral gas temperature can be tracked after the gas interacts with the wall temperatures specified at the boundary mesh points. Also, this technique is much faster than a Monte Carlo code since it requires a single matrix solution, allowing the coupling of the neutral and plasma codes to quickly determine both neutral and plasma density profiles. An example of the axisymmetric boundary (“wall”) and internal meshes for the NSTAR ion thruster from Wirz and Katz [58] is shown in Fig. 4-41. Gas enters from the hollow cathode at the center rear and the propellant injection manifold at the front corner of the discharge chamber. The neutral gas density calculated from this code for the NSTAR thruster in its high-power TH15 mode is shown in Fig. 4-42. The neutral density is highest near the injection sources at the hollow cathode and the propellant injection manifold. The neutral gas is the lowest on axis near the grids due to the NSTAR feed arrangement; however, as discussed below, the high primary electron density found in this region of the thruster produces significant ionization and “burns-out” the neutral gas. This result is critically important because the production of doubly ionized atoms increases dramatically in regions where the neutral gas is burned out and most of the electron energy goes into secondary ionization of the ions in the discharge chamber [58].PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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