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228 Chapter 5 0.2% to 0.3% of the total beam current, which is shown in Fig. 5-24. Accel grid currents on the order of 1% or less of the beam current are standard in most ion thrusters. Calculating the ion generation rate in the grid region due to charge exchange is relatively straightforward. The charge exchange currents generated by a single aperture’s beamlet are given by ICEX = IBeamlet no CEX d , (5.6-1) where d is the effective collection length downstream of the accel grid from which ions flow back to the grid and no is the average neutral density along this length. The charge exchange cross section, CEX, is well known and varies slowly with beam energy [48]. The average neutral density along the path length d is estimated from the thruster propellant flow rate utilization fraction, which is the difference between the neutral atom flow rate and the beam ion current over the open area fraction of the accel grid. The neutral density is usually assumed to remain constant in the accel grid hole and decreases as the gas expands downstream of the grid surface. The neutral gas density is normally highest in holes near the edge of the grid and lower at the center where nearly all the gas has been “burned up” through ionization in the discharge chamber. The effective path length, d , is a basic result of the ion optics calculations, and is essentially the distance downstream at which the beamlets have completely merged to form a beam plasma with a uniform potential across the beam diameter. An estimate of the effective path length is needed when setting up a grid erosion calculation to make certain that the 0.35 0.30 0.25 0.20 0.15 0.10 0.4 0.6 0.8 1.0 1.2 Beam Current (A) 1.4 1.6 Fig. 5-24. Ratio of the accel grid current to the beam current as a function of the beam current in NSTAR, showing that the accel current is typically less than 1% of the beam current (from [30]). Ja/Jb (%)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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