Self-magnetic field effects on electron emission in planar diodes as the critical current is approached

The self-magnetic field associated with the current in a planar diode is shown to reduce electron emission below the Child-Langmuir (1911) current density. As the magnetic field increases, the diode current is limited to the critical current. Here, a 1-D analysis is carried out to calculate the suppressed current density in the presence of a transverse magnetic field. The emitted current density is found to decrease modestly until the magnetic field associated with the critical current is reached, at which point the emission shuts off abruptly. The 1-D analysis remains valid until orbit crossing occurs as the current approaches the critical current. The minimum diode length required to reach critical current is also derived.