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194 Chapter 5 The maximum perveance that can be achieved by an accelerator is given by the coefficient in the Child–Langmuir equation: Pmax 4 o 2q[A/V3/2]. (5.1-2) 9M For an electron accelerator, this coefficient is the familiar value of 2.33 10–6 A/V3/2, and for singly charged xenon ions it is 4.8 10–9 A/V3/2. For round apertures, the Child–Langmuir equation can be written J = Ib = 4 o 2q V3/2 [A/m2], (5.1-3) D2 9 M d2 4 where d is the effective grid gap and D is the beamlet diameter. Inserting Eq. (5.1-3) into Eq. (5.1-1), the maximum perveance for round apertures is P o 2q D2 [A/V3/2]. (5.1-4) max 9 M d2 Therefore, to maximize the perveance of the accelerator, it is desirable to make the grid gap smaller than the aperture diameters, as illustrated in the example configuration shown in Fig. 5-4. The ion trajectories plotted in Fig. 5-4 that do not intercept either of the grids, and the minimal beamlet divergence, result from operating at or near the optimal ion current density and voltage for the grid geometry shown. Operating at significantly less than the optimal perveance, called “under-perveance” and Screen Accel Decel Grid Grid Grid Fig. 5-4. Ion trajectories from a plasma sheath (on the left) in a half-beamlet inside an example three-grid accelerator. Discharge PlasmaPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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