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372 Chapter 7 The plasma is always assumed to be quasi-neutral ( ni ne ). At the sheath boundary at the wall, the ion current normally is assumed to be the Bohm current and the electron current is the one-sided random electron flux. Total current continuity requires the ion flux and net electron flux (incident electrons and emitted secondary electrons) to the insulating walls to be equal, which establishes the sheath potential to produce quasineutrality and charge conservation as described above. The hybrid-model equations described above for determining the ion currents are normally evaluated numerically in either 1-D or 2-D with greatly different time steps between the electron fluid evolution and the ion and neutral motion evaluations. 7.4.2 Steady-State Modeling Results The physics of the Hall thruster discharge related to the transverse electron mobility, electron-wall interactions, and the exact nature of the electron distribution function are not completely understood at this time. However, the 1-D and 2-D models described above are reasonably successful in predicting plasma parameters and thruster behavior provided enhanced electron conductivity is incorporated in the channel due to wall collisions and turbulence, and modifications to the wall heat fluxes are made associated with the secondary electron behavior. In addition, enhanced electron transport in the plume region near the thruster exit is required to match the models’ predictions with the experimental results [61], which is normally provided by assuming collective oscillations drive Bohm-like diffusion. In this region, other mechanisms may also be responsible for the cross-field electron transport, and research in this area to determine the responsible mechanism(s) is continuing. The hybrid codes can provide very reasonable predictions of the steady-state plasma parameters in the thrusters. For example, Fig. 7-14 shows the average profiles (along the channel axis) predicted by a 1-D model [53] for the potential, electric field, plasma density, mean electron energy, neutral density, and ionization rate for the SPT-100 Hall thruster, where 4 cm corresponds to the channel exit. The average plasma density peaks upstream of the exit, as is also predicted by the 2-D HPHall code [30] result shown in Fig. 7-15 for the SPT-100 Hall thruster channel. In both cases, there is a characteristic peak in the plasma density upstream of the channel exit in the ionization region, and a decreasing plasma density is seen moving out of the channel as the ions are accelerated in the electric field of the acceleration region. The plasma density prediction by the 1-D code is slightly lower than the 2-D HPHall result because of differences in the heat flux calculation to the wall and the resulting values ofPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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