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Aberration correctors using hexapole fields have proven useful to
correct for the spherical aberration in electron microscopy. We
investigate the limits of the present design for the hexapole corrector
with respect to minimum probe size for the scanning transmission electron
microscope and discuss several ways in which the design could be improved
by rather small and incremental design changes for the next generation of
advanced probe-forming systems equipped with a gun monochromator.