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Ion Thruster Plasma Generators 141 during the recycle to the desired level without oscillating, which facilitates re- starting the high voltage. Of course, the larger anode area increased the loss in the discharge chamber and raised the discharge loss. This trade-off is often required to provide good performance and stable discharge operation. 4.3.11 Limitations of a 0-D Model While the 0-D models described in this chapter provide useful information on the design parameters of ion thrusters and give good insight into the plasma production and loss mechanisms, there are several limitations to their use. First, 0-D models assume that the electron and neutral densities are uniform and averages the ion production throughout the volume of the discharge chamber. For ion thrusters with significantly non-uniform plasmas, this leads to inaccuracies in the average plasma density and beam current calculated by the 0-D model that can be handled only by multi-dimensional discharge chamber models. Second, the source of the gas in actual discharge chambers is from the localized hollow cathode aperture and the gas manifold inside the discharge chamber. The neutral density, therefore, is never completely uniform, and variations in the neutral density can affect the transport, diffusion, and ionization rates in the discharge chamber. Third, ion thrusters with localized electron sources like hollow cathodes have strongly varying primary electron densities within the discharge chamber. As shown earlier, the primary electron density strongly affects the ionization rate, and so localized sources of primaries produce non-uniform plasmas that the 0-D models cannot address. In addition, these models utilize a monoenergetic primary energy. A distribution in the primary electron energy has been measured in some ion thrusters [43,44], which changes the ionization and primary electron thermalization rates compared to the monoenergetic calculations presented here. While primary electron energy distributions can be incorporated in 0-D models, this has not been attempted to date. Finally, the 0-D model assumed that the monoenergetic primary electrons have an energy of e(Vd Vc + ) . For typical discharge voltages of 25 V and cathode voltage drops of 5 to 10 V, this means that potentially none of the primaries has sufficient energy to doubly ionize xenon, which has an ionization potential of 21.2 V. Double ions can then only be produced by the tail of the plasma electron distribution. For electron temperatures of 3 to 5 eV, less than 1% of the electrons have sufficient energy to produce double ions. Since the double-ion content in NSTAR thrusters has been reported to exceed 20%, a monoenergetic primary electron energy results in a model that cannot accurately address double-ion production. While including primary electrons is necessary to obtain agreement between the 0-D models and experimental results, knowledge of thePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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