Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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Ion Thruster Plasma Generators 123 Some care needs to be used in including the Spitzer slowing time because some ion thruster designs have a very non-monoenergetic primary energy distribution, which is not described well by Eq. (4.3-40). The current emitted from the hollow cathode is Ie =Id –Is –Ik, (4.3-43) where Is is the screen current and Ik is the ion current back to the cathode. Using Eqs. (4.3-4) and (4.3-38) in Eq. (4.3-37), the primary electron density is given by Ie t Ie 1 1 1 –1 np= eV =eV + + pcs (4.3-44) Ie vpAp 4vpQin(1–md) 1 1 =eVV+vAT +. osac s Assuming that the primary electron loss directly to the anode is negligible, the electron equilibration time is long, and the ion current flowing back to the cathode is small, then Eq. (4.3-44) can be written as np = IevoAsTac md = (Id – Is )voAsTac md . (4.3-45) 4VvpIb (1–md) 4VvpIb (1–md) This equation demonstrates the characteristic behavior of the primary electron density being proportional to the mass utilization efficiency divided by one minus the mass utilization efficiency originally described by Brophy [18,19]. This dependence is valid unless there are paths for the primary electrons to be lost other than just collisionally with the neutral gas, such as ballistically to the anode or by thermalization with the plasma electrons. The behavior of the primary electron density with changes in the mass utilization efficiency is shown in Fig. 4-17, where the primary electron density is normalized to the value at md = 0 . As the neutral density decreases in the discharge chamber at higher mass utilization efficiencies, the primary electron density increases rapidly. At 90% mass utilization efficiency, the primary electron density in the discharge chamber is nine times higher than at 50% mass utilization efficiency. This strongly affects the ionization rate and the discharge loss behavior with neutral gas pressure, which will be shown later.

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