Edge imaging in intense beams

The appearance of rings of charge observed near the edge of beams from high-perveance guns is described with a simple ray tracing technique inspired by the particle-core model. We illustrate the technique, which has no analog in light optics, with examples from experiments employing solenoid focusing of an electron beam. The rings of charge result from the combined effects of external focusing and space-charge forces acting on paraxial fringe particles with relatively large initial transverse velocities. The model is independent of the physical mechanisms responsible for the fringe particles. Furthermore, the focal length for edge imaging in a uniform focusing channel is derived using a linearized trajectory equation for the motion of fringe particles. Counterintuitively, the focal length decreases as the beam current increases.