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Ion and Hall Thruster Plumes 409 The charge-exchange ion density is calculated by tracking particle trajectories in density-gradient electric fields using a finite-current barometric law for the electron density (electron current equals ion current). Poisson’s equation is solved on a finite element grid and iterated until steady-state CEX densities and density-gradient potentials are self-consistent. Comparisons of the CEX plume model with flight data from the NSTAR’s ion engine exhibited good agreement [8]. Figure 8-11 shows plume maps at one meter, calculated using this method for the BPT-4000 under both laboratory and space conditions. The CEX density in the laboratory is found to be more than one order of magnitude greater than it is in space due to the dominance of the background neutral gas in the chamber. With the exception of the neutral gas density, all the terms in the expression for charge-exchange ion generation [Eq. (8.3-6) above] are identical for the laboratory and space. Figure 8-10 showed that at distances greater than about a tenth of a meter downstream of the thruster exit plane, the chamber gas density is much greater than the gas coming directly from the thruster, resulting in greater charge-exchange ion generation. The computed total ion current in the laboratory case (5.3 A) is in approximate agreement with measurements of the integrated ion current (5–6 A for collector potential of 20V) [9]. The calculations assumed a charge-exchange cross section for 300-V ions of 55 Å2 based on the calculations and measurements by Miller [15]. 2 × 1018 1 × 1018 5 × 1017 2 × 1017 1 × 1017 5 × 1016 2 × 1016 1×1016 0.6 5 × 1015 2 × 1015 1×1015 0.4 5 × 1014 2 × 1014 1 × 1014 5 × 1013 2 × 1013 1 × 1013 5 × 1012 CL 1.0 Total Ion Density CL 1.0 0.8 0.6 0.4 0.2 1.0 0.0 0.8 0.2 0.0 0.2 0.4 0.6 (m) 0.2 0.4 0.6 0.8 1.0 (m) 0.8 CEX Ion Current = 0.74 A (a) Space (b) Laboratory CEX Ion Current = 5.26 A Fig. 8-11. Hall thruster plume maps for (a) space and (b) laboratory and conditions showing dominance of background density in the charge-exchange plume production (from [10]). (m)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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