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18 Chapter 2 Modern ion and Hall thrusters operating on xenon propellant have exhaust velocities in the range of 20–40 km/s and 10–20 km/s, respectively. The dramatic benefits of the high exhaust velocities of electric thrusters are clearly seen from Eq. (2.1-11). For example, consider an asteroid rendezvous mission for which it is desired to deliver 500 kg of payload with a mission v of 5 km/s. A spacecraft propelled by a chemical engine with a 3-km/s exhaust velocity, corresponding to an Isp of 306 s, would require 2147 kg of propellant to accomplish the mission. In contrast, an ion thruster with a 30-km/s exhaust velocity, corresponding to an Isp of 3060 s, would accomplish the same mission using only 91 kg of propellant. High- v missions such as this are often enabled by electric propulsion, allowing either a significant reduction in the amount of required propellant that has to be launched or the ability to increase the spacecraft dry mass for a given wet mass associated with a launch vehicle or mission requirement. 2.2 Force Transfer in Ion and Hall Thrusters The propellant ionized in ion and Hall thrusters is accelerated by the application of electric fields. However, the mechanism for transferring the thrust from the ion motion to the thruster body, and thereby the spacecraft, is different for ion thrusters and Hall thrusters. In ion thrusters, ions are produced by a plasma source and accelerated electrostaticly by the field applied between two (or more) grids, as illustrated in Fig. 2-1. The voltage applied between the two grids creates a vacuum electric field between the grids of the voltage divided by the gap d. The ions represent additional charge in the gap between the grids that modifies the electric field. Assuming infinitely large grids, the electric field distribution between the grids can be found from the one-dimensional Poisson’s Equation: dE(x) = (x) = qni (x) , dx o o (2.2-1) Screen Grid Accel Grid E Qi Faccel Fscreen Fig. 2-1. Schematic of ion thruster acceleration region. where o is the permittivity of free space, is the ion charge density in the gap, q is the charge on an ion, and ni is the ion number density in the gap. Equation (2.2-1) can be integrated from the screen grid to the accel grid to givePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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