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200 Chapter 5 removed to extinguish the arc and then reapplied. It is common to also decrease the discharge plasma density during a recycle so that the reapplication of the acceleration voltages corresponds with ramping up the discharge current such that the accelerator approximately tracks the right perveance during start up. This minimizes ion bombardment of the accel grid during a recycle. To obtain reliable operation and avoid frequent recycles, the maximum field strength in the ion thruster typically is set to less than half the vacuum breakdown field. For example, if the grid spacing were a millimeter and the acceleration potential between the grids a thousand volts, the theoretical maximum xenon ion beam current density would be 15 mA/cm2. A 25-cm-diameter, uniform-profile beam with a 75% transparent grid system would then produce about 5.5 A of beam current. In practice, because of high voltage breakdown considerations, the maximum beam current obtainable from grid sets is typically about half the theoretical maximum. The ion thruster size is determined by the perveance limit on the beam current density and practical considerations on the grids, such as maximum grid transparency and electric field [1]. For this reason, ion thruster beam current densities are typically on the order of a tenth that found in Hall thrusters, resulting in a larger thruster footprint on the spacecraft. Alternatively, the maximum Isp that is achievable is limited by the voltage that can be applied to the grids to extract a given current density before electrical breakdown or electron backstreaming occurs [9]. Very high Isp thrusters (>10,000 s), with a size that depends on the thrust requirement, have been built and successfully tested. 5.3 Ion Optics While the simple formulas above provide estimates of the ion accelerator optics performance, a number of computer simulation codes have been developed [4,10–17] to more accurately evaluate the ion trajectories produced by thruster grids. Ion optics codes solve in two or three dimensions the combined ion charge density and Poisson’s equations for the given grid geometry and beamlet parameters [18]. These codes have been used for the design and analysis of two- and three-grid systems, and were extended to four-grid systems [19] to examine “two-stage” ion optics performance [20] for very high voltage, high Isp applications. 5.3.1 Ion Trajectories There are a number of codes that calculate ion trajectories and grid performance in ion thrusters, and an extensive analysis of ion optics behavior in thrusters was recently completed by Farnell [21]. An example of a multi-dimensional code CEX-2D, which is an ion optics code developed at JPL that calculates ionPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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