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288 Chapter 6 Fig. 6-33. Potential and temperature profiles from the 1-D cathode plume model and the axial probe data for the NEXIS cathode at 25 A and 10 sccm [39]. the double layer, the ion and electron charge densities integrate to zero. The relationship between the ion and electron currents flowing across the layer is given by J e = k Mm J i , ( 6 . 7 - 7 ) where k is a constant that is about 0.5 for Te / Ti 10 . The double layer forms if the electron drift speed exceeds the electron thermal speed. This can occur if the ionization rate in the plume along the current path drops and there is insufficient plasma generated to support the discharge current. In this case, the double layer accelerates the electrons to higher energies, which increases the ionization rate. The axial location of a double layer can be found by finding the location along the cathode plume where Eq. (6.7-7) is satisfied. Assuming that the neutral gas expands at a fixed cone angle, the tangent of which is the half angle , the neutral density along the plume is no(z)= Qgas . (6.7-8) vo (r + z)2PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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