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Ion Thruster Plasma Generators 97 to producing ions and excited neutrals, and the second term related to heating the electrons that are lost to the walls. To evaluate Eq. (4.2-14), the ratio of the excitation to ionization reaction rates as a function of the Maxwellian electron temperature must be known. This is shown in Fig. 4-4 for xenon gas from data in Appendix E. For electron temperatures below about 8 V, the excitation rate exceeds the ionization rate in xenon for Maxwellian electrons. Since the lowest excitation potential is near the ionization potential in xenon, this higher excitation rate results in more of the input power being radiated to the walls than producing ions. This effect explains at least part of the inefficiency inherent in xenon plasma generators. Excitation rates equal to or higher than the ionization rate at low electron temperatures are also generally found for other inert gas propellants. The discharge loss from Eq. (4.2-14) for this ideal thruster example is plotted as a function of the mass utilization efficiency for a generic 20-cm-diameter thruster in Fig. 4-5, where the ionization potential of xenon is 12.13 V, the average excitation potential is 10 V, and 80% of the ions incident on the grids become beam ions ( Tg = 0.8 ). It was also assumed for simplicity that the plasma electrons were lost to the floating screen grid and the chamber wall. The mass utilization efficiency is inversely proportional to the neutral density in the thruster, which will be derived in Section 4.3.6. In the figure, the discharge loss is shown in (eV/ion), which is equivalent to watts of discharge power per ampere of beam ions (W/A). In an ideal plasma-generator case with 80% of the ions that are generated assumed to become beam current, the amount of power 14 12 10 8 6 4 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Electron Temperature (eV) Fig. 4-4. Ratio of the excitation to ionization rate coefficients for xenon as a function of the electron temperature. Excitation-to-Ionization RatioPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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