Transmission of intense electron beams through apertures

Apertures are an effective and widely used means for altering the properties of charged particle beams. Despite their conceptual simplicity, they can lead to interesting and seemingly paradoxical behavior. For example, when an intense beam is incident on an aperture, space charge will cause the beam spot size to be a function of beam current. Increasing the beam current can cause the beam area to increase so rapidly that the current density incident on the aperture will decrease, thereby decreasing the current transmitted through the aperture. When the beam source is a gridded electron gun, this will result in a condition of negative transconductance. Here, the properties of such a system are considered. First, a simple approximation is introduced for the expansion of a uniform, intense beam from a waist. This expression is validated by comparison to the full theory and to particle-in-cell simulations. It is then used to consider current transmission through an aperture, including the calculation of key system properties and the effects of changes in several system parameters. Simulations are used to assess the validity of the theory for beams with peaked and hollow transverse distributions, leading to a discussion of nonlinear forces present in the emission plane resulting from space and image charges.