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204 Chapter 5 A fraction of the ions from the plasma at the largest radii run directly into the screen grid, as seen in Fig. 5-6, and do not enter into the thrust beam. These ions represent the effect of the finite screen grid transparency that was so important in the discharge loss calculations in Chapter 4. For the near-optimal and under-perveance conditions, the screen grid transparency is greater than its geometric open area fraction, as mentioned above, because the self-consistent electric fields actually extract some of the ions at large radii that would have hit the screen grid instead of going into the screen aperture. 5.3.2 Perveance Limits Figure 5-6 demonstrated that electrostatic accelerators produce focused ion trajectories when operated near a given design perveance and avoid grid interception or large beam divergence angles over a limited range of voltages and currents that are related by space charge considerations in the grid gap. In ion thrusters, operating sufficiently away from the perveance design of the grids results in beam interception on the downstream accel and (eventually) decel grids. Figure 5-7 shows an illustration of the accel grid current as a function of the current in a beamlet (a single aperture) for three different beam voltages. In this case, the optics were designed to run at about 2 kV and 0.8 mA of beamlet current, and the design demonstrates low grid interception over about ±50% of this current. As the beamlet current is increased, by raising the plasma density in the discharge chamber, the sheath thickness in the acceleration gap decreases, which flattens the sheath and causes the accel grid interception to increase. Eventually, the system becomes under-focused at the perveance limit where a large fraction of the beamlet is intercepted, as shown in Fig. 5-6(a). The accel grid current then increases rapidly with beamlet current due to the 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Vb = 2.0 kV Vb = 2.2 kV Vb = 2.4 kV 0.0 0.5 1.0 Beamlet Current (mA) Fig. 5-7. Accel grid current-to-beam current ratio as a function of the beamlet current for three values of the beam voltage. 1.5 2.0 2.5 Accel-to-Beam Current Ratio (%)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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