Calculation of the current of matrix auto-emission cathodes

The potential and electric field intensity in matrix auto-emission cathodes (MAECs) are calculated by the finite element method. The density of the cu rrent and cathode current are determined using the Fowler-Nordheim formula. It is shown that, in order to calculate more accurately the held intensity and current, one should cut the calculation domain several times along one of equipotential and force lines approaching the emitting part of the cath ode edge. The calculation accuracy is estimated by means of comparison with the problems that can be solved explicitly and with experimental results. The method proposed in the paper enables one to perform reliable calculatio ns of devices with micro- and nanostructures. The work function of the carb on film is determined.