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266 Chapter 6 n = n(0,0) 2J1( 01) = n(0,0) (2)(0.5191) = 0.43n(0,0). 01 2.4048 Using Eq. (6.4-26) in Eq. (6.4-25) and solving for the value of gives i (6.4-26) (6.4-27) = I 0.43 R2 non(0,0)e ive . For example, the axial plasma density profile from the scanning probe inside the NSTAR hollow cathode [31] operating at 15 A and 3.7 sccm is shown in Fig.6-13. Taking the peak plasma density from the figure of n(0,0) = 1.6 1021 m–3 as the reference density at position (0,0) and using the neutral density, calculated inside the insert from Eq. (2.7-2), of 2.5 1022 m–3, Eq. (6.4-27) gives a value of = 6.0 if the ion current to the insert is 0.5 A. The fit to the exponential decrease in the plasma density upstream of the orifice shown in Fig. 6-13 gives = 6.1. The assumed value of 0.5 A for the ion current actually results from a two-dimensional model of the insert plasma [5], which will be discussed below. This simple diffusion model shows an exponential behavior in the axial plasma density profile, predicted from Eq. (6.4-23), which is consistent with the near-exponential profiles measured in the NSTAR cathode sufficiently far away from the orifice region. A closer examination of Eq. (6.4-27) shows that the terms on the right-hand side represent the ionization rate per unit volume. If the geometry of the Fig. 6-13. Plasma density measured on axis in the insert region for an NSTAR cathode operating at TH15.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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