Simulation of thermionic cathodes

A technique is described of simulating thermionic cathodes in the Boundary Element Method by replacing the space charges in the cathode region by a set of thin sheets of charge. These sheets are subdivided into segments in the same way that the cathode itself is subdivided. This technique has been applied to cathodes that have zero and non-zero temperature T. It is shown that for T>0 the potential and position of the virtual cathode is well reproduced. Planar and non-planar cathodes are considered as well as unsaturated cathodes.