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408 Chapter 8 neutralizer. The cylindrically averaged neutral density for any point at a distance z downstream is estimated as if the point were along the thruster centerline. The vacuum chamber background neutral density is usually assumed to be constant. Based on values of the ambient temperature and pressure, the background density can be determined assuming an ideal gas law. No background density is assumed for calculations in space conditions. Figure 8-10 shows each of the three components and the total calculated neutral density [10] for the BPT-4000 Hall thruster. 8.3.3 Secondary-Ion Generation Low energy ions are created near a thruster exit plane by charge exchange collisions between the main ion beam and the neutral gas. The mechanism is the same for both gridded ion and Hall thrusters. Charge-exchange ion density can be computed using a two-dimensional, R,Z-geometry PIC code, while using the main-beam ion densities computed by the Lagrangian calculations and the neutral gas profile as inputs. The charge-exchange ion production rate, n CEX , is calculated assuming that the beam ions have a velocity, vb , much greater than the neutral gas velocity: n CEX =nin0vb CEX. (8.3-35) Resonant charge-exchange cross sections between singly charged xenon ions and neutral xenon atoms range from 30 Å2 to 100 Å2 for typical ion and Hall thruster energies [15]. 4 × 1018 2 × 1018 0 0.00 0.10 0.20 0.30 0.40 Distance Downstream of Thruster Exit (m) Fig. 8-10. Neutral gas density downstream of the BPT 4000 exit plane (from [10]). Total Chamber Hall Thruster Hallow Cathode Neutral Particle Density (m−3)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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