Limiting current in a relativistic diode under the condition of magnetic insulation

The maximum emission current density is calculated for a time-independent, relativistic, cycloidal electron flow in a diode that is under the condition of magnetic insulation. Contrary to conventional thinking, this maximum current is not determined by the space charge limited condition on the cathode, even when the emission velocity of the electrons is assumed to be zero. The self electric and magnetic fields associated with the cycloidal flow are completely accounted for. This maximum current density is confirmed by a two-dimensional, fully electromagnetic and fully relativistic particle-in-cell code.