Relativistic planar diode in a magnetic field

The exact steady‐state solution for the planar relativistic diode in space‐charge‐limited conditions is given in the presence of magnetic fluxes below magnetic insulation. It is shown that, as in the classical case, at fixed diode voltage the value of the current density reaching the anode goes discontinuously from a finite value to zero as a function of the magnetic flux at the magnetic insulation cut‐off point. The limiting current density just below cutoff is given as a function of voltage and gap distance. This steady‐state one‐dimensional result below and very near the magnetic insulation threshold is in contradiction with experimental observations.