Thermal Electron Flow in a Planar Crossed-Field Diode

A self-consistent model of steady-state electron flow in a planar crossed-field diode with a thermionic cathode is presented. Our formulation is a generalization of the classic work of Fry and Langmuir, to include a constant magnetic field B of arbitrary strength parallel to the electrode surfaces. Some effects of the magnetic field on the electron flow are illustrated in an example.