Enhanced space charge limited current for curved electron emitters
Gaurav Singh, Raghwendra Kumar, Debabrata Biswas
Abstract
The maximum current that can be transported across a vacuum diode is limited by forces arising due to space charge. In a planar thermionic or explosive emission diode, the space charge limited current density from an emitting patch is given by the Child–Langmuir law JCL∼Vg3/2/D2, where Vg is the potential difference across the diode and D is the separation between the anode and the cathode. We show here, analytically using the nonlinear line charge model, that for a curved emitter in a planar diode configuration, the limiting current obeys the scaling relationship JSCL∼γaVg3/2/D2, where γa is the apex field enhancement factor of the curved emitter. For an emitter with a large height (h) to the apex radius of curvature (Ra) ratio, the limiting current far exceeds the planar value. The result is verified using the particle-in-cell code PASUPAT for two curved emitter shapes.