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410 Chapter 8 The distinctive second peak in the energy spectra captured by the collimated retarding potential analyzer (RPA) data shown in Fig. 8-7 is from elastic scattering of xenon ions by neutral xenon atoms. Mikellides et al. [10] have calculated differential cross-section data for elastic Xe+ Xe scattering in a center-of-mass frame of reference. The calculations involve averaging over the pertinent Xe2+ potentials, without inclusion of charge exchange. The results are then subsequently corrected for charge exchange. The derived, center-of-mass differential cross sections were converted to values in a fixed frame of reference relative to the laboratory and implemented in the plume model. For comparisons with RPA measurements, the flux of scattered ions is, is = x Ibno d d 0 d2 d Ibno xc d , d2 d (8.3-36) was computed at a radius of 1 m (the RPA location). In Eq. (8.3-36), Ib and no are the main-beam ion current and neutral density, respectively. The dimension xc is the characteristic length of the beam column and d is the radial distance between the thruster and the RPA. The differential contribution due to the column element along the beam is denoted by d , and d / d is the differential cross section. The results from the complete calculation, compared with data, are shown in Fig.8-12. Plotted in the figure are the results of the calculations of the expanding beam ions, and the beam and scattered ions combined. Also plotted are the ion current probe data for four bias levels of 50 V and 100 V. The probe bias potential prevents lower energy ions from being collected. As expected, the beam-only values compare best with the ion probe biased to 100 V, since, at this value, most of the scattered and charge-exchanged ions are excluded. The calculation combining beam and elastic scattering compares well with 50 V-biased probe data since these data include most of the elastically scattered ions. 8.4 Spacecraft Interactions In order to design a spacecraft to accommodate electric thrusters, it is necessary to understand how the thruster plumes interact with the spacecraft and itsPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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