A theoretical analysis has been carried out to determine the trajectories of charged particles incident upon a pair of concentric spherical grids, where the inner grid is maintained at a large accelerating potential with respect to the outer grid. The results show that under certain conditions a beam of charged particles incident on the outer grid is sharply focused inside the inner grid. These results were confirmed experimentally using hemispherical grids and electron beams.
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Reynolds et al. (1967) studied this question.
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