For a conventional tungsten-filament "electron gun" used in electron microscopes they say the Wehnelt cap suppress electron emission from the filament at the sides and base, concentrating emission from the tip only.
Is this done by changing the work function of the tungsten surface in these areas or is it by deflecting electrons emitted from these regions away to earth potential such that they don't contribute to the beam?
Sources say the Wehnelt cap is kept at -200 to -300 V relative to the filament.