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136 Chapter 4 1 8kTe 1/2 e /kT –e 1/2 –1 Ia=4 m eneAae e 1 erf kT , (4.3-64) e where the potential is now a negative number. If the potential goes sufficiently negative relative to the anode, the current density can reach a factor of two higher than the one-sided random electron flux normally collected in order to satisfy the discharge current requirement. However, once the potential goes sufficiently negative relative to the anode to repel the ions (about Ti ), then the anode area for the plasma electron is not the hybrid area, but is just twice the plasma electron Larmor radius times the cusp length, similar to Eq. (4.3-3) for the primary loss area. This results in a significant decrease in the cusp anode area Aa in Eq. (4.3-63) for negative plasma potentials, which further lowers the plasma potential relative to the anode. Examining the potential distribution in the plasma in Fig. 4-22, the transition from the normal negative-going sheath to a negative plasma potential (positive-going anode sheath) will subtract from the primary electron energy Vpe at a given discharge voltage. The ionization rate then decreases, and the discharge collapses into a high impedance mode or oscillates between this mode and a positive potential typically on power supply time constants as the supply tries to reestablish the discharge by increasing the anode voltage. The stability of the plasma discharge at a given operating point (discharge current, beam current, neutral density in the discharge chamber, etc.) is therefore determined by the magnetic field design. For example, in Fig. 4-23, plasma potential is plotted as a function of the strength of the cusp magnetic field for an arbitrary thruster design with two different numbers of ring cusps. The cusp field strength enters into the anode area Aa in Eq. (4.3-6), into the primary electron loss area Ap in Eq. (4.3-3), and into the plasma potential in Eq. (4.3-63). The model predicts that a four-ring design would be unstable (when the potential goes negative relative to the anode) for cusp magnetic fields greater than 2000 G. Since strong magnetic fields are desirable from a primary electron and ion confinement point of view, additional rings are required to maintain a positive plasma potential. A six-ring design increased the anode area sufficiently to raise the plasma potential at the 2000-G magnet design point. An analysis of the discharge loss from Eq. (4.3-60) indicates that the improved stability associated with the larger anode area of the six-ring design comes with a loss in efficiency. The trade-off between efficiency and stability is an important aspect of ion thruster design.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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