Cathodes consisting of arrays of high aspect ratio field emitters are of great interest as sources of electron beams for vacuum electronic devices. The desire for high currents and current densities drives the cathode designer towards a denser array, but for ungated emitters, denser arrays also lead to increased shielding, in which the field enhancement factor β of each emitter is reduced due to the presence of the other emitters in the array. To facilitate the study of these arrays, we have developed a method for modeling high aspect ratio emitters using tapered dipole line charges. This method can be used to investigate proximity effects from similar emitters an arbitrary distance away and is much less computationally demanding than competing simulation approaches. Here, we introduce this method and use it to study shielding as a function of array geometry. Emitters with aspect ratios of 102–104 are modeled, and the shielding-induced reduction in β is considered as a function of tip-to-tip spacing for emitter pairs and for large arrays with triangular and square unit cells. Shielding is found to be negligible when the emitter spacing is greater than the emitter height for the two-emitter array, or about 2.5 times the emitter height in the large arrays, in agreement with previously published results. Because the onset of shielding occurs at virtually the same emitter spacing in the square and triangular arrays, the triangular array is preferred for its higher emitter density at a given emitter spacing. The primary contribution to shielding in large arrays is found to come from emitters within a distance of three times the unit cell spacing for both square and triangular arrays.
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.
The emittance of high brightness electron sources, particularly field emitters and photocathodes but also thermionic sources, is increased by surface roughness on the emitter. Such structure causes local field enhancement and complicates both the prediction of emittance and the underlying emission models on which such predictions depend. In the present work, a method to find the emission trajectories near regions of high field enhancement is given and applied to emittance predictions for field, photo, and thermal emission for an analytically tractable hemispherical model. The dependence of the emittance on current density, spatial variation, and acceleration close to the emission site is identified and the impact of space charge discussed. The methodology is extensible to field emission from close-spaced wirelike structures, in particular, and extensions to that configuration are discussed. The models have application to electron sources for high frequency vacuum electronics, high power microwave devices, and free-electron lasers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.