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Hollow Cathodes 277 f =1 exp n wall , (6.5-11) no CEX and wall is the average time between collisions with the wall for a neutral particle. This effective heating mechanism by charge exchange has been observed in experiments where the neutral temperatures are higher than the orifice wall temperatures. Combining the electron and ion momentum equations [Eqs. (6.4-30) and (6.4-31)] to eliminate the electric field term gives an expression for the particle motion in terms of the ambipolar diffusion coefficient and the ion and electron mobilities: n(v v )= D n+ μi Je . (6.5-12) io a zμee The ambipolar diffusion coefficient for this case is given by Eq. (6.4-4). In the orifice, the radial drift velocity will often exceed the ion thermal speed due to the radial potential gradient, so the ion scattering velocity must be approximated by v = v2+(v v)2+v, (6.5-13) scat th i o r where vr is the radial ion velocity found from Eq. (6.4-7). The continuity equations in the orifice [Eqs. (6.5-5) through (6.5-7)] are solved using the electron energy equation, Eq. (6.4-28), in the cylindrical orifice, which produces ion density and plasma potential profiles in the orifice region. The first result from this work is that a double sheath postulated in the orifice region [36] is not observed for xenon ion thruster cathodes. There is a potential change through the orifice, but this results from resistive effects in the orifice channel due to electron-ion and electron-neutral collisions. As an example, Fig. 6-20 shows a plot of the neutral and plasma densities along the axis of an NSTAR neutralizer cathode orifice operating at the TH15 power point, producing 3.76 A of current with a xenon gas flow rate of 3.5 sccm [37]. The peak plasma density occurs in the cylindrical section of the orifice, and the density falls though the chamfered region due to the neutral gas density decrease. It should be noted that the peak plasma density predicted by the 1-D model in the orifice is in reasonable agreement with the 0-D model results shown above that used the average neutral density and temperature along the length of the orifice. Reasonably accurate results can be obtained using simple 0-D models to illustrate the driving physics in this region.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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