Electron gun systems with a particular inner width dimension, sweep electrodes, or a combination of a particular inner width dimension and sweep electrodes are disclosed. The inner width dimension may be less than twice a value of a Larmor radius of secondary electrons in a channel downstream of a beam limiting aperture, and a Larmor time for the secondary electrons may be greater than 1 ns. The sweep electrode can generates an electric field in a drift region, which can increase kinetic energy of secondary electrons in the channel.