The mapping theorem of two-dimensional electron beam trajectories

Two-dimensional electron beams in certain electrostatic fields are dealt with, ignoring space-charge effects. The central trajectories of electron beams were previously given. The electron beam in a suitable electrostatic field fluctuates near the given trajectory just as a paraxial electron beam fluctuates near the axis. If both fluctuations agree completely, the electron beam considered can be regarded as a projection of the paraxial electron beam. This situation is called here the mapping of electron beams and is verified in the mapping theorem.