On the Theory of Axially Symmetric Electron Beams in an Axial Magnetic Field

One of the more perplexing problems in the design of klystrons and traveling-wave tubes has been the formation of well collimated electron beams. An axially symmetric form of an electron beam is proposed in which the space-charge repulsive forces are just balanced by magnetic focusing forces so that the beam may be made as long as desirable without any change in its cross section. The equations governing the existence of such beams are derived.