This article re-examines the Brillouin flow solutions in crossed-field diodes, with applications to magnetrons, magnetically insulated line oscillators (MILOs), and transmission lines (MITLs). The are constructed for various geometries, including planar MILOs, MITLs, cylindrical magnetrons electrons flowing azimuthal direction, MITLs MILOs axial radial direction. A common theme of this analysis...