Resonant Behavior of Electron Beams in Periodically Focused Tubes for Transverse Signal Fields

A ribbon beam which is focused by a series of bidimensional electrostatic lenses exhibits a well-defined transverse resonance within a certain range of focusing conditions. The frequency of the resonance is derived for the case of a simple space-periodic focusing field; it is also shown that the focusing field determines the current density in the beam (and thus, in practice, the maximum usable beam current). An experiment is described which demonstrates by means of a transverse signal field the existence of the transverse electron resonance.