Lenses for High Energy Electron Beams

In this report the solution of the equations of motion of relativistic particles in axisymmetric lenses is discussed, using boundary value solutions to represent the lens fields. Among electron microscopists it is well-known that in an ideal lens the axial field intensity diminishes radially. This condition cannot be met for a static field except in the superconducting case. However, time varying fields possess this characteristic and a cavity supporting the TE-01 mode is proposed as a microwave lens, useful where beams have an RF microstructure.