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Ion Thruster Accelerator Grids 205 system running at too high a perveance. At low discharge chamber plasma densities, which produce low beamlet currents, the beam is over-focused and interception of the ions on the accel grid due to cross-over trajectories increases the accel grid current. The ion trajectories for this case are shown in Fig. 5-6(c). At the nominal beam voltage of 2 kV, this system can be run from about 0.4 to 1.2 mA of beamlet current between the cross-over and perveance limits without producing excessive accel grid current. If the ion thruster has a current profile greater than about 3:1 peak to edge over the grid diameter (due to a poor plasma density uniformity), then grid interception will occur either in the center or at the edge of the beam. Since the grids are normally designed to deal with the high perveance condition at the peak current density near the axis, poor plasma profiles usually result in significant erosion of the edge holes due to cross-over interception. This will impact the life of the thruster and must be compensated by either changing the grid gap or screen aperture sizes as a function of the radius or modifying the plasma generator to produce more uniform profiles. Increasing the beam voltage shifts the curves in Fig. 5-7 to higher beamlet currents. This is clear from the dependence in the Child–Langmuir equation (Eq. 5.3-2) where the current scales as V3/2 if the sheath thickness and grid dimensions are held constant. In Fig. 5-7, the perveance-limited beamlet current, where direct grid interception occurs, increases as V3/2 as the beam voltage is raised. Figure 5-7 also illustrates that, in situations where the thruster power must decrease, which is typical of deep space solar electric propulsion missions where the power available decreases as the spacecraft moves away from the Sun, the beam voltage and Isp of the thruster must eventually decrease as the current is reduced to avoid grid interception. The voltage range available from a given accelerator design at a fixed (or nearly constant) beam current has limitations similar to the current dependence just discussed. However, the minimum voltage at a given current is of special interest in an ion thruster because this is related to the minimum Isp of the engine for a given thrust. The perveance limit of a thruster is usually defined relative to the rate at which the accel current increases as the beam voltage is decreased: Perveance limit 0.02 I A [mA/ V] . (5.3-6) Vscreen This is related to the optics situation illustrated in Fig. 5-6(a), where the current at a given voltage is too high for the designed gap and aperture size and the under-focused beamlet starts to directly intercept accel grid. Figure 5-8 shows the behavior of the accel grid current for the NASA Solar Electric PropulsionPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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