Generalized brillouin flow

The 1945 paper by Brillouin1 presented an exact solution to the problem of space charge flow of electrons in a magnetic field. As is well known, this solution demonstrates the possibility of an electron beam of cylindrical or rectangular cross section in which the repelling forces due to the space charge are exactly balanced by the magnetic field forces so that the beam maintains its shape for an indefinite length. The many electron tubes which have been designed to make use of this type of flow as well as the large number of research papers published on problems associated with Brillouin flow constitutes substantial evidence of the impact on the electron tube industry of the Brillouin paper.