Focusing of Charged Particles

In a number of devices a beam of charged particles traverses a region that is at a constant, uniform, electrostatic potential; in others, the region is one in which a uniform, axially directed electrostatic field exists. If the current density in the beam is high, the beam will spread significantly due to space-charge repulsion effects. A beam initially diverging, that is upon entering the region, will travel with continual increase of the divergence and a beam initially converging will reach a minimum diameter at a certain point along the optical axis and then diverge continually from there on. In addition to the space-charge repulsion effect, the space charge of the beam modifies the potential in the region that it traverses. This has the effect that the velocity of the charged particles is not determined by the potential of the region alone but requires a knowledge of t h e b e am shape and density distribution. This effect can often be neglected especially if the regions are free from confining magnetic fields, as is the case for the regions discussed in this section.