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

Summary form only given, as follows. High power vacuum diodes are used to produce intense electron beams for many applications. When self-magnetic field effects are negligible and the cathode is a space-charge-limited, emitter, Child-Langmuir flow is obtained in planar diodes. However, when the self-magnetic field associated with the diode current becomes large enough to significantly deflect the electron path as it crosses the diode gap, the addition electron space charge density in the gap reduces the emission below the Child-Langmuir current density. At high magnetic field, the diode current is limited to the critical current, which is obtained when the electrons reach the anode at grazing incidence (or equivalently the "electron gyroradius" equals the gap size). A 1-D analysis is carried out to calculate the suppressed current density in the presence of a transverse magnetic field. The problem is shown to be similar to that of the limiting current (i.e., Hall current) calculated in a crossed field gap, in which a constant transverse magnetic field is applied across the gap to insulate the electron flow. In the case considered, the magnetic field is produced by the diode current itself and this self-magnetic field decreases with distance along the gap. It is shown that the emitted current density is only modestly reduced from the Child-Langmuir current density. The 1-D analysis remains valid until critical current is approached, at which time orbit crossing occurs and a 2-D kinetic analysis is required.