The transverse magnetic field effect on steady-state solutions of the Bursian diode

A study of steady-states of a planar vacuum diode driven by a cold electron beam (the Bursian diode) under an external transverse magnetic field is presented. The regime of no electrons turned around by a magnetic field only is under the consideration. The emitter electric field is evaluated as a characteristic function for the existence of solutions depending on the diode length, the applied voltage, and the magnetic field strength. At certain conditions, it is shown that a region of non-unique solutions exists in the Bursian diode when the magnetic field is absent. An expression for the maximum current transmitted through the diode is derived. The external magnetic field is put forth to control fast electronic switches based on the Bursian diode