No abstract

Analysis of temperature-limited flow, space-chargelimited flow, and the transition between them using a simple planar diode with a thermionic cathode, in which the cathode surface has spatially nonuniform emission properties, is presented. Our theoretical results, which are derived from a model based on solutions to the Vlasov and Poisson equations, compare well with the results of particle-in-cell simulations. We find that the location and the shape of the knee in the anode current versus temperature characteristic (Miram or "rollover" curve) are significantly affected by non-uniformities in the space-charge density in the A-K gap, but are relatively unaffected by the electron motion parallel to the electrode surfaces. In particular, emission from an actively emitting region is strongly affected by the forces (or lack thereof) exerted by the space-charge of the electrons emitted by their neighbors. Perhaps, most remarkably, we find that the limiting current reaching the anode is approximately given by the classical 1-D Child-Langmuir law, even if a significant fraction of the cathode surface is nonemitting.

No abstract

No abstract

A model of a thermionic cathode in a planar diode in which the Poisson and Vlasov equations are solved in 3-D assuming an infinite magnetic field is presented. We explore how 2-D work function variations across the cathode surface may affect the transition between temperature-limited and spacecharge-limited flow, commonly known as the "knee" of the Miram curve. We study a variety of work function distributions, both realistic and idealized, and demonstrate how emission from the lowest work function regions dominates the total anode current even when such regions make up a relatively small fraction of cathode area. Our model also illustrates the ability of cathodes to reach the full Child-Langmuir current despite the presence of a sizeable nonemitting region. We find that as the length scale of these work function variations decreases, the Miram knee grows sharper, indicating improved cathode performance.